TSTP Solution File: SWW613_2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW613_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 11:07:48 EDT 2023
% Result : Theorem 40.70s 16.41s
% Output : CNFRefutation 40.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 88
% Syntax : Number of formulae : 189 ( 71 unt; 82 typ; 0 def)
% Number of atoms : 234 ( 34 equ)
% Maximal formula atoms : 65 ( 2 avg)
% Number of connectives : 207 ( 80 ~; 55 |; 39 &)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 248 ( 98 atm; 14 fun; 96 num; 40 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 52 ( 30 >; 22 *; 0 +; 0 <<)
% Number of predicates : 10 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 75 ( 71 usr; 50 con; 0-5 aty)
% Number of variables : 43 (; 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
%$ sort > divides > coprime > prime > odd > even > match_list > match_bool > cons > mod > mk_ref > gcd > div > contents > cons_proj_2 > cons_proj_1 > #nlpp > witness > tb2t1 > tb2t > t2tb1 > t2tb > ref > nil > list > abs > tuple02 > tuple01 > true > real > qtmark > int > false > bool1 > #skF_14 > #skF_8 > #skF_4 > #skF_1 > #skF_3 > #skF_2 > #skF_11 > #skF_5
%Foreground sorts:
tff(list_int,type,
list_int: $tType ).
tff(bool,type,
bool: $tType ).
tff(tuple0,type,
tuple0: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_21',type,
'#skE_21': $int ).
tff('#skE_11',type,
'#skE_11': $int ).
tff('#skE_25',type,
'#skE_25': $int ).
tff('#skE_28',type,
'#skE_28': $int ).
tff('#skE_23',type,
'#skE_23': $int ).
tff('#skE_12',type,
'#skE_12': $int ).
tff('#skF_13',type,
'#skF_13': $int ).
tff('#skF_6',type,
'#skF_6': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_16',type,
'#skF_16': $int ).
tff('#skE_20',type,
'#skE_20': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skF_15',type,
'#skF_15': $int ).
tff('#skE_13',type,
'#skE_13': $int ).
tff('#skE_26',type,
'#skE_26': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_24',type,
'#skE_24': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_15',type,
'#skE_15': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_10',type,
'#skF_10': $int ).
tff('#skF_12',type,
'#skF_12': $int ).
tff('#skE_22',type,
'#skE_22': $int ).
tff('#skE_16',type,
'#skE_16': $int ).
tff('#skE_17',type,
'#skE_17': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skE_27',type,
'#skE_27': $int ).
tff('#skF_9',type,
'#skF_9': $int ).
tff('#skE_18',type,
'#skE_18': $int ).
tff('#skE_19',type,
'#skE_19': $int ).
tff('#skE_14',type,
'#skE_14': $int ).
%Foreground operators:
tff(list,type,
list: ty > ty ).
tff(prime,type,
prime: $int > $o ).
tff(coprime,type,
coprime: ( $int * $int ) > $o ).
tff(cons_proj_1,type,
cons_proj_1: ( ty * uni ) > uni ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff(t2tb1,type,
t2tb1: $int > uni ).
tff(nil,type,
nil: ty > uni ).
tff(tuple02,type,
tuple02: tuple0 ).
tff(div,type,
div: ( $int * $int ) > $int ).
tff(tuple01,type,
tuple01: ty ).
tff(int,type,
int: ty ).
tff(abs,type,
abs: $int > $int ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(tb2t1,type,
tb2t1: uni > $int ).
tff('#skF_14',type,
'#skF_14': list_int ).
tff('#skF_8',type,
'#skF_8': list_int ).
tff(t2tb,type,
t2tb: list_int > uni ).
tff(real,type,
real: ty ).
tff(divides,type,
divides: ( $int * $int ) > $o ).
tff(match_bool,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(false,type,
false: bool ).
tff('#skF_4',type,
'#skF_4': ( $int * $int * $int ) > $int ).
tff('#skF_1',type,
'#skF_1': ( $int * $int ) > $int ).
tff('#skF_3',type,
'#skF_3': $int > $int ).
tff(mod,type,
mod: ( $int * $int ) > $int ).
tff(gcd,type,
gcd: ( $int * $int ) > $int ).
tff('#skF_2',type,
'#skF_2': $int > $int ).
tff(qtmark,type,
qtmark: ty ).
tff('#skF_11',type,
'#skF_11': list_int ).
tff(bool1,type,
bool1: ty ).
tff(odd,type,
odd: $int > $o ).
tff(match_list,type,
match_list: ( ty * ty * uni * uni * uni ) > uni ).
tff(even,type,
even: $int > $o ).
tff(tb2t,type,
tb2t: uni > list_int ).
tff(sort,type,
sort: ( ty * uni ) > $o ).
tff(true,type,
true: bool ).
tff(ref,type,
ref: ty > ty ).
tff(cons_proj_2,type,
cons_proj_2: ( ty * uni ) > uni ).
tff(witness,type,
witness: ty > uni ).
tff('#skF_5',type,
'#skF_5': $int > $int ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(f_681,negated_conjecture,
~ ! [Na: $int] :
( $lesseq(2,Na)
=> ( ( $lesseq(2,Na)
& $lesseq(2,2)
& $lesseq(2,Na)
& ! [Ia: $int] :
( ( $lesseq(2,Ia)
& $less(Ia,2) )
=> ~ divides(Ia,Na) ) )
=> ! [Da: $int] :
( ( $lesseq(2,Da)
& $lesseq(Da,Na)
& divides(Da,Na)
& ! [Ia: $int] :
( ( $lesseq(2,Ia)
& $less(Ia,Da) )
=> ~ divides(Ia,Na) ) )
=> ! [Factors: list_int] :
( ( Factors = tb2t(cons(int,t2tb1(Da),nil(int))) )
=> ( ( ( $product(div(Na,Da),Da) = Na )
& divides(div(Na,Da),Na) )
=> ( ! [Ia: $int] :
( ( prime(Ia)
& divides(Ia,Na)
& $less(Da,Ia) )
=> ( coprime(Da,Ia)
& divides(Ia,div(Na,Da)) ) )
=> ! [Targeta: $int,Factora: $int,Factors1: list_int] :
( ( $lesseq(1,Targeta)
& $lesseq(Targeta,Na)
& $lesseq(2,Factora)
& $lesseq(Factora,Na)
& divides(Factora,Na)
& prime(Factora)
& ! [Ia: $int] :
( ( divides(Ia,Targeta)
& $lesseq(2,Ia) )
=> ( $lesseq(Factora,Ia)
& divides(Ia,Na) ) )
& ! [Ia: $int] :
( ( prime(Ia)
& divides(Ia,Na)
& $less(Factora,Ia) )
=> divides(Ia,Targeta) ) )
=> ( $lesseq(2,Targeta)
=> ( ( divides(Targeta,Targeta)
& $lesseq(2,Targeta)
& $lesseq(Factora,Targeta) )
=> ( ( $lesseq(2,Targeta)
& $lesseq(2,Factora)
& $lesseq(Factora,Targeta)
& ! [Ia: $int] :
( ( $lesseq(2,Ia)
& $less(Ia,Factora) )
=> ~ divides(Ia,Targeta) ) )
=> ! [D1a: $int] :
( ( $lesseq(Factora,D1a)
& $lesseq(D1a,Targeta)
& divides(D1a,Targeta)
& ! [Ia: $int] :
( ( $lesseq(2,Ia)
& $less(Ia,D1a) )
=> ~ divides(Ia,Targeta) ) )
=> ( prime(D1a)
=> ! [Factor1a: $int] :
( ( Factor1a = D1a )
=> ! [Factors2: list_int] :
( ( Factors2 = tb2t(cons(int,t2tb1(D1a),t2tb(Factors1))) )
=> ! [Target1a: $int] :
( ( Target1a = div(Targeta,D1a) )
=> ( ( ( $product(Target1a,D1a) = Targeta )
& divides(Target1a,Targeta) )
=> ! [Ia: $int] :
( ( prime(Ia)
& divides(Ia,Na)
& $less(D1a,Ia) )
=> ( $less(Factora,Ia)
=> ( divides(Ia,Targeta)
=> ( ( $lesseq(1,D1a)
& $less(D1a,Ia) )
=> coprime(D1a,Ia) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_largest_prime_factor) ).
tff(f_458,axiom,
! [Pa: $int] :
( prime(Pa)
<=> ( $lesseq(2,Pa)
& ! [Na: $int] :
( ( $lesseq(1,Na)
& $less(Na,Pa) )
=> coprime(Na,Pa) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_coprime) ).
tff(f_386,axiom,
! [Pa: $int] :
( prime(Pa)
=> ( $lesseq(3,Pa)
=> odd(Pa) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odd_prime) ).
tff(f_324,axiom,
! [Aa: $int] :
( even(Aa)
<=> divides(2,Aa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_divides) ).
tff(f_161,axiom,
! [Na: $int] : divides(Na,Na),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divides_refl) ).
tff(f_329,axiom,
! [Aa: $int] :
( odd(Aa)
<=> ~ divides(2,Aa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odd_divides) ).
tff(c_467,plain,
prime('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_210,plain,
! [P_171a: $int] :
( ~ prime(P_171a)
| $lesseq(2,P_171a) ),
inference(cnfTransformation,[status(thm)],[f_458]) ).
tff(c_871,plain,
! [P_1056a: $int] :
( ~ prime(P_1056a)
| ~ $less(P_1056a,2) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_210]) ).
tff(c_892,plain,
~ $less('#skF_12',2),
inference(resolution,[status(thm)],[c_467,c_871]) ).
tff(c_493,plain,
$less('#skF_12','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_690,plain,
prime('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_208,plain,
! [N_174a: $int,P_171a: $int] :
( coprime(N_174a,P_171a)
| ~ prime(P_171a)
| ~ $lesseq(1,N_174a)
| ~ $less(N_174a,P_171a) ),
inference(cnfTransformation,[status(thm)],[f_458]) ).
tff(c_27416,plain,
! [N_5739a: $int,P_5740a: $int] :
( coprime(N_5739a,P_5740a)
| ~ prime(P_5740a)
| $less(N_5739a,1)
| ~ $less(N_5739a,P_5740a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_208]) ).
tff(c_504,plain,
~ coprime('#skF_12','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_27428,plain,
( ~ prime('#skF_16')
| $less('#skF_12',1)
| ~ $less('#skF_12','#skF_16') ),
inference(resolution,[status(thm)],[c_27416,c_504]) ).
tff(c_27441,plain,
$less('#skF_12',1),
inference(demodulation,[status(thm),theory(equality)],[c_493,c_690,c_27428]) ).
tff(c_172,plain,
! [P_136a: $int] :
( odd(P_136a)
| ~ prime(P_136a)
| ~ $lesseq(3,P_136a) ),
inference(cnfTransformation,[status(thm)],[f_386]) ).
tff(c_13310,plain,
! [P_3285a: $int] :
( odd(P_3285a)
| ~ prime(P_3285a)
| $less(P_3285a,3) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_172]) ).
tff(c_13328,plain,
( odd('#skF_12')
| $less('#skF_12',3) ),
inference(resolution,[status(thm)],[c_467,c_13310]) ).
tff(c_13689,plain,
$less('#skF_12',3),
inference(splitLeft,[status(thm)],[c_13328]) ).
tff(c_1236,plain,
divides('#skF_12','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_555,plain,
! [A_124a: $int] :
( even(A_124a)
| ~ divides(2,A_124a) ),
inference(cnfTransformation,[status(thm)],[f_324]) ).
tff(c_1250,plain,
( even('#skF_9')
| ( '#skF_12' != 2 ) ),
inference(resolution,[status(thm)],[c_1236,c_555]) ).
tff(c_13045,plain,
'#skF_12' != 2,
inference(splitLeft,[status(thm)],[c_1250]) ).
tff(c_13691,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_13689,c_13045,c_892]) ).
tff(c_13697,plain,
~ $less('#skF_12',3),
inference(splitRight,[status(thm)],[c_13328]) ).
tff(c_27442,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_27441,c_13697]) ).
tff(c_27448,plain,
'#skF_12' = 2,
inference(splitRight,[status(thm)],[c_1250]) ).
tff(c_480,plain,
$product('#skF_15','#skF_12') = '#skF_9',
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_27493,plain,
'#skF_9' = $product('#skF_15',2),
inference(demodulation,[status(thm),theory(equality)],[c_27448,c_480]) ).
tff(c_27495,plain,
'#skF_9' = $product(2,'#skF_15'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_27493]) ).
tff(c_484,plain,
divides('#skF_15','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_28763,plain,
divides('#skF_15',$product(2,'#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_27495,c_484]) ).
tff(c_383,plain,
! [I_774a: $int] :
( coprime('#skF_7',I_774a)
| ~ divides(I_774a,'#skF_6')
| ~ prime(I_774a)
| ~ $less('#skF_7',I_774a) ),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_28779,plain,
( coprime('#skF_7','#skF_15')
| ~ prime('#skF_15')
| ~ $less('#skF_7','#skF_15')
| ( '#skF_6' != $product(2,'#skF_15') ) ),
inference(resolution,[status(thm)],[c_28763,c_383]) ).
tff(c_30291,plain,
'#skF_6' != $product(2,'#skF_15'),
inference(splitLeft,[status(thm)],[c_28779]) ).
tff(c_630,plain,
! [N_54a: $int] : divides(N_54a,N_54a),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_28332,plain,
! [I_5946a: $int] :
( coprime('#skF_7',I_5946a)
| ~ divides(I_5946a,'#skF_6')
| ~ prime(I_5946a)
| ~ $less('#skF_7',I_5946a) ),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_28395,plain,
( coprime('#skF_7','#skF_6')
| ~ prime('#skF_6')
| ~ $less('#skF_7','#skF_6') ),
inference(resolution,[status(thm)],[c_630,c_28332]) ).
tff(c_30005,plain,
~ $less('#skF_7','#skF_6'),
inference(splitLeft,[status(thm)],[c_28395]) ).
tff(c_12866,plain,
! [N_3197a: $int,P_3198a: $int] :
( coprime(N_3197a,P_3198a)
| ~ prime(P_3198a)
| $less(N_3197a,1)
| ~ $less(N_3197a,P_3198a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_208]) ).
tff(c_12875,plain,
( ~ prime('#skF_16')
| $less('#skF_12',1)
| ~ $less('#skF_12','#skF_16') ),
inference(resolution,[status(thm)],[c_12866,c_504]) ).
tff(c_12883,plain,
$less('#skF_12',1),
inference(demodulation,[status(thm),theory(equality)],[c_493,c_690,c_12875]) ).
tff(c_1449,plain,
! [P_1164a: $int] :
( odd(P_1164a)
| ~ prime(P_1164a)
| $less(P_1164a,3) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_172]) ).
tff(c_1473,plain,
( odd('#skF_12')
| $less('#skF_12',3) ),
inference(resolution,[status(thm)],[c_467,c_1449]) ).
tff(c_1860,plain,
$less('#skF_12',3),
inference(splitLeft,[status(thm)],[c_1473]) ).
tff(c_431,plain,
divides('#skF_10','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_1038,plain,
! [A_1084a: $int] :
( ~ divides(2,A_1084a)
| ~ odd(A_1084a) ),
inference(cnfTransformation,[status(thm)],[f_329]) ).
tff(c_1073,plain,
( ~ odd('#skF_6')
| ( '#skF_10' != 2 ) ),
inference(resolution,[status(thm)],[c_431,c_1038]) ).
tff(c_1260,plain,
'#skF_10' != 2,
inference(splitLeft,[status(thm)],[c_1073]) ).
tff(c_296,plain,
$lesseq('#skF_10','#skF_12'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_454,plain,
~ $less('#skF_12','#skF_10'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_296]) ).
tff(c_321,plain,
$lesseq(2,'#skF_10'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_426,plain,
~ $less('#skF_10',2),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_321]) ).
tff(c_1873,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1860,c_1260,c_454,c_426]) ).
tff(c_1879,plain,
~ $less('#skF_12',3),
inference(splitRight,[status(thm)],[c_1473]) ).
tff(c_12884,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_12883,c_1879]) ).
tff(c_12890,plain,
'#skF_10' = 2,
inference(splitRight,[status(thm)],[c_1073]) ).
tff(c_12911,plain,
divides(2,'#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_12890,c_431]) ).
tff(c_333,plain,
! [I_697a: $int] :
( ~ divides(I_697a,'#skF_6')
| ~ $lesseq(2,I_697a)
| ~ $less(I_697a,'#skF_7') ),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_29319,plain,
! [I_6026a: $int] :
( ~ divides(I_6026a,'#skF_6')
| $less(I_6026a,2)
| ~ $less(I_6026a,'#skF_7') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_333]) ).
tff(c_29366,plain,
( $less(2,2)
| ~ $less(2,'#skF_7') ),
inference(resolution,[status(thm)],[c_12911,c_29319]) ).
tff(c_29368,plain,
~ $less(2,'#skF_7'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_29366]) ).
tff(c_323,plain,
$lesseq('#skF_9','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_425,plain,
~ $less('#skF_6','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_323]) ).
tff(c_27518,plain,
~ $less('#skF_6',$product(2,'#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_27495,c_425]) ).
tff(c_312,plain,
$lesseq(2,'#skF_9'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_440,plain,
~ $less('#skF_9',2),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_312]) ).
tff(c_27506,plain,
~ $less($product(2,'#skF_15'),2),
inference(demodulation,[status(thm),theory(equality)],[c_27495,c_440]) ).
tff(c_27517,plain,
~ $less('#skF_15',1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_27506]) ).
tff(c_31451,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_30291,c_30005,c_29368,c_27518,c_27517]) ).
tff(c_31457,plain,
'#skF_6' = $product(2,'#skF_15'),
inference(splitRight,[status(thm)],[c_28779]) ).
tff(c_419,plain,
$product(div('#skF_6','#skF_7'),'#skF_7') = '#skF_6',
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_28533,plain,
div('#skF_6','#skF_7') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_419]) ).
tff(c_476,plain,
div('#skF_9','#skF_12') = '#skF_15',
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_27483,plain,
div('#skF_9',2) = '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_27448,c_476]) ).
tff(c_27560,plain,
div($product(2,'#skF_15'),2) = '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_27495,c_27483]) ).
tff(c_28558,plain,
( ( '#skF_15' = '#skE_1' )
| ( '#skF_7' != 2 )
| ( '#skF_6' != $product(2,'#skF_15') ) ),
inference(superposition,[status(thm),theory(equality)],[c_28533,c_27560]) ).
tff(c_35063,plain,
( ( '#skF_15' = '#skE_1' )
| ( '#skF_7' != 2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_31457,c_28558]) ).
tff(c_35065,plain,
'#skF_7' != 2,
inference(splitLeft,[status(thm)],[c_35063]) ).
tff(c_339,plain,
$lesseq(2,'#skF_7'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_402,plain,
~ $less('#skF_7',2),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_339]) ).
tff(c_35066,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_35065,c_29368,c_402]) ).
tff(c_35070,plain,
'#skF_7' = 2,
inference(splitRight,[status(thm)],[c_35063]) ).
tff(c_492,plain,
divides('#skF_16','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_28353,plain,
( coprime('#skF_7','#skF_16')
| ~ prime('#skF_16')
| ~ $less('#skF_7','#skF_16')
| ( '#skF_6' != '#skF_6' ) ),
inference(resolution,[status(thm)],[c_492,c_28332]) ).
tff(c_28392,plain,
( coprime('#skF_7','#skF_16')
| ~ $less('#skF_7','#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_690,c_28353]) ).
tff(c_36349,plain,
( coprime(2,'#skF_16')
| ~ $less(2,'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_35070,c_35070,c_28392]) ).
tff(c_36352,plain,
~ $less(2,'#skF_16'),
inference(splitLeft,[status(thm)],[c_36349]) ).
tff(c_488,plain,
prime('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_27725,plain,
! [P_5838a: $int] :
( odd(P_5838a)
| ~ prime(P_5838a)
| $less(P_5838a,3) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_172]) ).
tff(c_27737,plain,
( odd('#skF_16')
| $less('#skF_16',3) ),
inference(resolution,[status(thm)],[c_488,c_27725]) ).
tff(c_27787,plain,
$less('#skF_16',3),
inference(splitLeft,[status(thm)],[c_27737]) ).
tff(c_1093,plain,
divides('#skF_16','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_681]) ).
tff(c_1107,plain,
( even('#skF_9')
| ( '#skF_16' != 2 ) ),
inference(resolution,[status(thm)],[c_1093,c_555]) ).
tff(c_1256,plain,
'#skF_16' != 2,
inference(splitLeft,[status(thm)],[c_1107]) ).
tff(c_890,plain,
~ $less('#skF_16',2),
inference(resolution,[status(thm)],[c_488,c_871]) ).
tff(c_27788,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_27787,c_1256,c_890]) ).
tff(c_27794,plain,
~ $less('#skF_16',3),
inference(splitRight,[status(thm)],[c_27737]) ).
tff(c_36353,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_36352,c_27794]) ).
tff(c_36360,plain,
coprime(2,'#skF_16'),
inference(splitRight,[status(thm)],[c_36349]) ).
tff(c_27489,plain,
~ coprime(2,'#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_27448,c_504]) ).
tff(c_36363,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36360,c_27489]) ).
tff(c_36369,plain,
'#skF_16' = 2,
inference(splitRight,[status(thm)],[c_1107]) ).
tff(c_36391,plain,
$less('#skF_12',2),
inference(demodulation,[status(thm),theory(equality)],[c_36369,c_493]) ).
tff(c_36411,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_892,c_36391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW613_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 19:53:16 EDT 2023
% 0.15/0.36 % CPUTime :
% 40.70/16.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.78/16.43
% 40.78/16.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 40.84/16.49
% 40.84/16.49 Inference rules
% 40.84/16.49 ----------------------
% 40.84/16.49 #Ref : 0
% 40.84/16.49 #Sup : 5697
% 40.84/16.49 #Fact : 1
% 40.84/16.49 #Define : 55
% 40.84/16.49 #Split : 130
% 40.84/16.49 #Chain : 0
% 40.84/16.49 #Close : 16
% 40.84/16.49
% 40.84/16.49 Ordering : LPO
% 40.84/16.49
% 40.84/16.49 Simplification rules
% 40.84/16.49 ----------------------
% 40.84/16.49 #Subsume : 660
% 40.84/16.49 #Demod : 1876
% 40.84/16.49 #Tautology : 2094
% 40.84/16.49 #SimpNegUnit : 44
% 40.84/16.49 #BackRed : 387
% 40.84/16.49
% 40.84/16.49 #Partial instantiations: 946
% 40.84/16.49 #Strategies tried : 1
% 40.84/16.49
% 40.84/16.50 Timing (in seconds)
% 40.84/16.50 ----------------------
% 40.84/16.50 Preprocessing : 1.03
% 40.84/16.50 Parsing : 0.50
% 40.84/16.50 CNF conversion : 0.09
% 40.84/16.50 Main loop : 14.33
% 40.84/16.50 Inferencing : 1.23
% 40.84/16.50 Reduction : 2.64
% 40.84/16.50 Demodulation : 1.72
% 40.84/16.50 BG Simplification : 0.30
% 40.84/16.50 Subsumption : 1.83
% 40.84/16.50 Abstraction : 0.12
% 40.84/16.50 MUC search : 4.46
% 40.84/16.50 Cooper : 7.64
% 40.84/16.50 Total : 15.46
% 40.84/16.50 Index Insertion : 0.00
% 40.84/16.50 Index Deletion : 0.00
% 40.84/16.50 Index Matching : 0.00
% 40.84/16.50 BG Taut test : 0.00
%------------------------------------------------------------------------------