%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWW600_2 : TPTP v9.0.0. 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 : n010.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 : Wed Apr 9 09:53:03 PM UTC 2025
% Result : Theorem 7.45s 2.61s
% Output : CNFRefutation 7.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 23 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 0 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 97 ( 5 atm; 61 fun; 5 num; 26 var)
% Number of types : 6 ( 4 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 38 ( 34 usr; 24 con; 0-4 aty)
% Number of variables : 26 ( 24 !; 2 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
%$ sort > divides > odd > even > match_bool > mod > mk_ref > gcd > div > contents > #nlpp > witness > ref > abs > tuple02 > tuple01 > true > real > qtmark > int > false > bool1 > #skF_1 > #skF_2
%Foreground sorts:
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('#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('#skF_8',type,
'#skF_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_5',type,
'#skF_5': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_10',type,
'#skF_10': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
tff('#skF_9',type,
'#skF_9': $int ).
%Foreground operators:
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(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_1',type,
'#skF_1': ( $int * $int ) > $int ).
tff(mod,type,
mod: ( $int * $int ) > $int ).
tff(gcd,type,
gcd: ( $int * $int ) > $int ).
tff(qtmark,type,
qtmark: ty ).
tff(bool1,type,
bool1: ty ).
tff(odd,type,
odd: $int > $o ).
tff('#skF_2',type,
'#skF_2': ( $int * $int * $int ) > $int ).
tff(even,type,
even: $int > $o ).
tff(sort,type,
sort: ( ty * uni ) > $o ).
tff(true,type,
true: bool ).
tff(ref,type,
ref: ty > ty ).
tff(witness,type,
witness: ty > uni ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(f_4507,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_420,negated_conjecture,
~ ! [Xa: $int,Ya: $int] :
( ( $lesseq(0,Xa)
& $lesseq(0,Ya) )
=> ! [Da: $int,Ca: $int,Ba: $int,Aa: $int,Y1a: $int,X1a: $int] :
( ( $lesseq(0,X1a)
& $lesseq(0,Y1a)
& ( gcd(X1a,Y1a) = gcd(Xa,Ya) )
& ( $sum($product(Aa,Xa),$product(Ba,Ya)) = X1a )
& ( $sum($product(Ca,Xa),$product(Da,Ya)) = Y1a ) )
=> ( ~ $less(0,Y1a)
=> ? [A1a: $int,B1a: $int] : ( $sum($product(A1a,Xa),$product(B1a,Ya)) = X1a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_gcd) ).
tff(c_378,plain,
! [B_186: $int,A_187: $int] : ( $product(B_186,A_187) = $product(A_187,B_186) ),
inference(cnfTransformation,[status(thm)],[f_4507]) ).
tff(c_190,plain,
$sum($product('#skF_8','#skF_3'),$product('#skF_7','#skF_4')) = '#skF_10',
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_236,plain,
$product('#skF_8','#skF_3') = $sum('#skF_10',$uminus($product('#skF_7','#skF_4'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_190]) ).
tff(c_991,plain,
$product('#skF_8','#skF_3') = $sum('#skF_10',$uminus($product('#skF_4','#skF_7'))),
inference(demodulation,[status(thm),theory(equality)],[c_378,c_236]) ).
tff(c_1001,plain,
$product('#skF_8','#skF_3') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_991]) ).
tff(c_1004,plain,
$product('#skF_4','#skF_7') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_991]) ).
tff(c_994,plain,
$product('#skF_4','#skF_7') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_991]) ).
tff(c_993,plain,
$product('#skF_8','#skF_3') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_991]) ).
tff(c_992,plain,
$product('#skF_8','#skF_3') = $sum('#skF_10',$uminus($product('#skF_4','#skF_7'))),
inference(demodulation,[status(thm),theory(equality)],[c_378,c_236]) ).
tff(c_996,plain,
$sum('#skF_10',$uminus('#skE_4')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_994,c_993,c_992]) ).
tff(c_1006,plain,
'#skF_10' = $sum('#skE_4','#skE_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_996]) ).
tff(c_183,plain,
! [A1_178a: $int,B1_179a: $int] : ( $sum($product(A1_178a,'#skF_3'),$product(B1_179a,'#skF_4')) != '#skF_10' ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_707,plain,
! [B1_381a: $int,A1_380a: $int] : ( $sum('#skF_10',$uminus($product(B1_381a,'#skF_4'))) != $product(A1_380a,'#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_183]) ).
tff(c_771,plain,
! [B1_381a: $int,A1_380a: $int] : ( $sum('#skF_10',$uminus($product('#skF_4',B1_381a))) != $product(A1_380a,'#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_378,c_707]) ).
tff(c_2290,plain,
! [A1_380a: $int,B1_381a: $int] : ( $product(A1_380a,'#skF_3') != $sum($sum('#skE_4','#skE_3'),$uminus($product('#skF_4',B1_381a))) ),
inference(demodulation,[status(thm),theory(equality)],[c_1006,c_771]) ).
tff(c_2295,plain,
! [B1_778a: $int,A1_779a: $int] : ( $sum('#skE_3',$sum('#skE_4',$uminus($product('#skF_4',B1_778a)))) != $product(A1_779a,'#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2290]) ).
tff(c_2356,plain,
! [A1_779a: $int] : ( $product(A1_779a,'#skF_3') != $sum('#skE_3',$sum('#skE_4',$uminus('#skE_4'))) ),
inference(superposition,[status(thm),theory(equality)],[c_1004,c_2295]) ).
tff(c_2432,plain,
! [A1_837a: $int] : ( $product(A1_837a,'#skF_3') != '#skE_3' ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2356]) ).
tff(c_2463,plain,
$false,
inference(superposition,[status(thm),theory(equality)],[c_1001,c_2432]) ).
tff(c_2466,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW600_2 : TPTP v9.0.0. Released v6.1.0.
% 0.04/0.13 % 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
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Apr 9 06:17:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.45/2.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.45/2.61
% 7.45/2.61 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------