TSTP Solution File: SWW588_2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW588_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 : 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 : Tue Aug 22 11:07:45 EDT 2023
% Result : Theorem 4.58s 2.22s
% Output : CNFRefutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 78 ( 23 unt; 24 typ; 0 def)
% Number of atoms : 145 ( 58 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 155 ( 64 ~; 74 |; 10 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 331 ( 86 atm; 151 fun; 66 num; 28 var)
% Number of types : 6 ( 4 usr; 1 ari)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 19 usr; 16 con; 0-4 aty)
% Number of variables : 28 (; 27 !; 1 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
%$ sort1 > match_bool1 > mk_ref > contents > #nlpp > witness1 > ref > tuple03 > tuple0 > true1 > real > qtmark > int > false1 > bool
%Foreground sorts:
tff(tuple02,type,
tuple02: $tType ).
tff(bool1,type,
bool1: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff('#skF_6',type,
'#skF_6': $int ).
tff('#skF_5',type,
'#skF_5': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
tff('#skF_1',type,
'#skF_1': $int ).
%Foreground operators:
tff(true1,type,
true1: bool1 ).
tff(int,type,
int: ty ).
tff(false1,type,
false1: bool1 ).
tff(sort1,type,
sort1: ( ty * uni ) > $o ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(witness1,type,
witness1: ty > uni ).
tff(real,type,
real: ty ).
tff(match_bool1,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(tuple0,type,
tuple0: ty ).
tff(qtmark,type,
qtmark: ty ).
tff(bool,type,
bool: ty ).
tff(tuple03,type,
tuple03: tuple02 ).
tff(ref,type,
ref: ty > ty ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(f_106,negated_conjecture,
~ ! [Aa: $int,Ba: $int] :
( ( $lesseq(0,Aa)
& $less(0,Ba) )
=> ( ( $sum($product(0,Ba),Aa) = Aa )
& $lesseq(0,Aa)
& ! [Ra: $int,Qa: $int] :
( ( ( $sum($product(Qa,Ba),Ra) = Aa )
& $lesseq(0,Ra) )
=> ( ( $lesseq(Ba,Ra)
=> ! [Q1a: $int] :
( ( Q1a = $sum(Qa,1) )
=> ! [R1a: $int] :
( ( R1a = $difference(Ra,Ba) )
=> ( ( $sum($product(Q1a,Ba),R1a) = Aa )
& $lesseq(0,R1a)
& $lesseq(0,Ra)
& $less(R1a,Ra) ) ) ) )
& ( ~ $lesseq(Ba,Ra)
=> ? [R1a: $int] :
( ( $sum($product(Qa,Ba),R1a) = Aa )
& $lesseq(0,R1a)
& $less(R1a,Ba) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_division) ).
tff(f_1640,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_1656,axiom,
! [C: $int,B: $int] :
( ( $product(C,B) = C )
<=> ( ( C = 0 )
| ( B = 1 ) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_cancel_right1) ).
tff(f_1642,axiom,
! [A: $int,B: $int,C: $int] : ( $product(A,$sum(B,C)) = $sum($product(A,B),$product(A,C)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_dist) ).
tff(c_26,plain,
$lesseq(0,'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_99,plain,
~ $less('#skF_1',0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_26]) ).
tff(c_30,plain,
( ( $sum($product('#skF_4','#skF_2'),'#skF_3') = '#skF_1' )
| ( $sum(0,'#skF_1') != '#skF_1' )
| ~ $lesseq(0,'#skF_1') ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_97,plain,
( ( $product('#skF_4','#skF_2') = $sum('#skF_1',$uminus('#skF_3')) )
| $less('#skF_1',0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_30]) ).
tff(c_159,plain,
$product('#skF_4','#skF_2') = $sum('#skF_1',$uminus('#skF_3')),
inference(negUnitSimplification,[status(thm)],[c_99,c_97]) ).
tff(c_269,plain,
$product('#skF_4','#skF_2') = $sum($uminus('#skF_3'),'#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_159]) ).
tff(c_111,plain,
! [B_47: $int,A_48: $int] : ( $product(B_47,A_48) = $product(A_48,B_47) ),
inference(cnfTransformation,[status(thm)],[f_1640]) ).
tff(c_355,plain,
$product('#skF_2','#skF_4') = $sum($uminus('#skF_3'),'#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_269,c_111]) ).
tff(c_539,plain,
$product('#skF_2','#skF_4') = $sum('#skF_1',$uminus('#skF_3')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_355]) ).
tff(c_104,plain,
! [C_63: $int] : ( $product(C_63,1) = C_63 ),
inference(cnfTransformation,[status(thm)],[f_1656]) ).
tff(c_55,plain,
! [A_49: $int,C_51: $int,B_50: $int] : ( $product(A_49,$sum(C_51,B_50)) = $sum($product(A_49,B_50),$product(A_49,C_51)) ),
inference(cnfTransformation,[status(thm)],[f_1642]) ).
tff(c_249,plain,
! [A_52: $int,B_53: $int,C_54: $int] : ( $product(A_52,$sum(B_53,C_54)) = $sum($product(A_52,B_53),$product(A_52,C_54)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_55]) ).
tff(c_28,plain,
( ( $sum(0,'#skF_1') != '#skF_1' )
| ~ $lesseq(0,'#skF_1')
| $lesseq(0,'#skF_3') ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_98,plain,
( $less('#skF_1',0)
| ~ $less('#skF_3',0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_127,plain,
~ $less('#skF_3',0),
inference(negUnitSimplification,[status(thm)],[c_99,c_98]) ).
tff(c_186,plain,
$product('#skF_4','#skF_2') = $sum($uminus('#skF_3'),'#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_159]) ).
tff(c_38,plain,
! [R1_40a: $int] :
( ( $sum($product('#skF_4','#skF_2'),R1_40a) != '#skF_1' )
| ( $sum(0,'#skF_1') != '#skF_1' )
| ~ $lesseq(0,'#skF_1')
| ~ $lesseq(0,R1_40a)
| ~ $less(R1_40a,'#skF_2')
| $lesseq('#skF_2','#skF_3') ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_81,plain,
! [R1_40a: $int] :
( ( $product('#skF_4','#skF_2') != $sum('#skF_1',$uminus(R1_40a)) )
| $less('#skF_1',0)
| $less(R1_40a,0)
| ~ $less(R1_40a,'#skF_2')
| ~ $less('#skF_3','#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_38]) ).
tff(c_154,plain,
! [R1_40a: $int] :
( ( $product('#skF_4','#skF_2') != $sum('#skF_1',$uminus(R1_40a)) )
| $less(R1_40a,0)
| ~ $less(R1_40a,'#skF_2')
| ~ $less('#skF_3','#skF_2') ),
inference(negUnitSimplification,[status(thm)],[c_99,c_81]) ).
tff(c_157,plain,
! [R1_40a: $int] :
( ( $product('#skF_4','#skF_2') != $sum($uminus(R1_40a),'#skF_1') )
| $less(R1_40a,0)
| ~ $less(R1_40a,'#skF_2')
| ~ $less('#skF_3','#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_154]) ).
tff(c_187,plain,
! [R1_40a: $int] :
( ( $sum($uminus(R1_40a),'#skF_1') != $sum($uminus('#skF_3'),'#skF_1') )
| $less(R1_40a,0)
| ~ $less(R1_40a,'#skF_2')
| ~ $less('#skF_3','#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_186,c_157]) ).
tff(c_190,plain,
( $less('#skF_3',0)
| ~ $less('#skF_3','#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_187]) ).
tff(c_209,plain,
~ $less('#skF_3','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_127,c_190]) ).
tff(c_100,plain,
$less(0,'#skF_2'),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_42,plain,
( ( $sum(0,'#skF_1') != '#skF_1' )
| ~ $lesseq(0,'#skF_1')
| ~ $lesseq('#skF_2','#skF_3')
| ( '#skF_6' = $difference('#skF_3','#skF_2') ) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_73,plain,
( $less('#skF_1',0)
| $less('#skF_3','#skF_2')
| ( '#skF_6' = $sum('#skF_3',$uminus('#skF_2')) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_42]) ).
tff(c_135,plain,
( $less('#skF_3','#skF_2')
| ( '#skF_6' = $sum('#skF_3',$uminus('#skF_2')) ) ),
inference(negUnitSimplification,[status(thm)],[c_99,c_73]) ).
tff(c_137,plain,
( $less('#skF_3','#skF_2')
| ( '#skF_6' = $sum($uminus('#skF_2'),'#skF_3') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_135]) ).
tff(c_212,plain,
'#skF_6' = $sum($uminus('#skF_2'),'#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_209,c_137]) ).
tff(c_214,plain,
'#skF_6' = $sum('#skF_3',$uminus('#skF_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_212]) ).
tff(c_44,plain,
( ( $sum(0,'#skF_1') != '#skF_1' )
| ~ $lesseq(0,'#skF_1')
| ~ $lesseq('#skF_2','#skF_3')
| ( '#skF_5' = $sum('#skF_4',1) ) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_72,plain,
( $less('#skF_1',0)
| $less('#skF_3','#skF_2')
| ( '#skF_5' = $sum(1,'#skF_4') ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_44]) ).
tff(c_129,plain,
( $less('#skF_3','#skF_2')
| ( '#skF_5' = $sum(1,'#skF_4') ) ),
inference(negUnitSimplification,[status(thm)],[c_99,c_72]) ).
tff(c_211,plain,
'#skF_5' = $sum(1,'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_209,c_129]) ).
tff(c_40,plain,
( ( $sum($product('#skF_5','#skF_2'),'#skF_6') != '#skF_1' )
| ( $sum(0,'#skF_1') != '#skF_1' )
| ~ $lesseq(0,'#skF_1')
| ~ $lesseq('#skF_2','#skF_3')
| ~ $lesseq(0,'#skF_6')
| ~ $lesseq(0,'#skF_3')
| ~ $less('#skF_6','#skF_3') ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_77,plain,
( ( $product('#skF_5','#skF_2') != $sum('#skF_1',$uminus('#skF_6')) )
| $less('#skF_1',0)
| $less('#skF_3','#skF_2')
| $less('#skF_6',0)
| $less('#skF_3',0)
| ~ $less('#skF_6','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_40]) ).
tff(c_144,plain,
( ( $product('#skF_5','#skF_2') != $sum('#skF_1',$uminus('#skF_6')) )
| $less('#skF_3','#skF_2')
| $less('#skF_6',0)
| $less('#skF_3',0)
| ~ $less('#skF_6','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_99,c_77]) ).
tff(c_147,plain,
( ( $product('#skF_5','#skF_2') != $sum($uminus('#skF_6'),'#skF_1') )
| $less('#skF_3','#skF_2')
| $less('#skF_6',0)
| $less('#skF_3',0)
| ~ $less('#skF_6','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_144]) ).
tff(c_169,plain,
( ( $product('#skF_5','#skF_2') != $sum($uminus('#skF_6'),'#skF_1') )
| $less('#skF_3','#skF_2')
| $less('#skF_6',0)
| ~ $less('#skF_6','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_127,c_147]) ).
tff(c_172,plain,
( ( $product('#skF_5','#skF_2') != $sum('#skF_1',$uminus('#skF_6')) )
| $less('#skF_3','#skF_2')
| $less('#skF_6',0)
| ~ $less('#skF_6','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_169]) ).
tff(c_216,plain,
( ( $product('#skF_5','#skF_2') != $sum('#skF_1',$uminus('#skF_6')) )
| $less('#skF_6',0)
| ~ $less('#skF_6','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_209,c_172]) ).
tff(c_219,plain,
( ( $product('#skF_5','#skF_2') != $sum($uminus('#skF_6'),'#skF_1') )
| $less('#skF_6',0)
| ~ $less('#skF_6','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_216]) ).
tff(c_227,plain,
( ( $product($sum(1,'#skF_4'),'#skF_2') != $sum($uminus($sum('#skF_3',$uminus('#skF_2'))),'#skF_1') )
| $less($sum('#skF_3',$uminus('#skF_2')),0)
| ~ $less($sum('#skF_3',$uminus('#skF_2')),'#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_214,c_214,c_211,c_214,c_219]) ).
tff(c_230,plain,
( ( $product($sum(1,'#skF_4'),'#skF_2') != $sum('#skF_1',$sum('#skF_2',$uminus('#skF_3'))) )
| $less('#skF_3','#skF_2')
| ~ $less(0,'#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_227]) ).
tff(c_236,plain,
( ( $product($sum(1,'#skF_4'),'#skF_2') != $sum('#skF_1',$sum('#skF_2',$uminus('#skF_3'))) )
| $less('#skF_3','#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_230]) ).
tff(c_239,plain,
( ( $product($sum(1,'#skF_4'),'#skF_2') != $sum('#skF_2',$sum($uminus('#skF_3'),'#skF_1')) )
| $less('#skF_3','#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_236]) ).
tff(c_242,plain,
$product($sum(1,'#skF_4'),'#skF_2') != $sum('#skF_2',$sum($uminus('#skF_3'),'#skF_1')),
inference(negUnitSimplification,[status(thm)],[c_209,c_239]) ).
tff(c_245,plain,
$product($sum(1,'#skF_4'),'#skF_2') != $sum($uminus('#skF_3'),$sum('#skF_1','#skF_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_242]) ).
tff(c_1116,plain,
$sum($uminus('#skF_3'),$sum('#skF_1','#skF_2')) != $sum('#skF_2',$sum('#skF_1',$uminus('#skF_3'))),
inference(demodulation,[status(thm),theory(equality)],[c_539,c_104,c_249,c_111,c_245]) ).
tff(c_1118,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW588_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
% 0.14/0.35 % Computer : n010.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 19:06:58 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.58/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.58/2.23
% 4.58/2.23 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.58/2.26
% 4.58/2.26 Inference rules
% 4.58/2.26 ----------------------
% 4.58/2.26 #Ref : 0
% 4.58/2.26 #Sup : 153
% 4.58/2.26 #Fact : 1
% 4.58/2.26 #Define : 0
% 4.58/2.26 #Split : 9
% 4.58/2.26 #Chain : 0
% 4.58/2.26 #Close : 0
% 4.58/2.26
% 4.58/2.26 Ordering : LPO
% 4.58/2.26
% 4.58/2.26 Simplification rules
% 4.58/2.26 ----------------------
% 4.58/2.26 #Subsume : 15
% 4.58/2.26 #Demod : 65
% 4.58/2.26 #Tautology : 72
% 4.58/2.26 #SimpNegUnit : 20
% 4.58/2.26 #BackRed : 0
% 4.58/2.26
% 4.58/2.26 #Partial instantiations: 39
% 4.58/2.26 #Strategies tried : 1
% 4.58/2.26
% 4.58/2.26 Timing (in seconds)
% 4.58/2.26 ----------------------
% 4.58/2.32 Preprocessing : 0.66
% 4.58/2.32 Parsing : 0.34
% 4.58/2.32 CNF conversion : 0.04
% 4.58/2.32 Main loop : 0.52
% 4.58/2.32 Inferencing : 0.13
% 4.58/2.32 Reduction : 0.15
% 4.58/2.32 Demodulation : 0.11
% 4.58/2.32 BG Simplification : 0.09
% 4.58/2.32 Subsumption : 0.10
% 4.58/2.32 Abstraction : 0.03
% 4.58/2.32 MUC search : 0.00
% 4.58/2.32 Cooper : 0.04
% 4.58/2.32 Total : 1.24
% 4.58/2.32 Index Insertion : 0.00
% 4.58/2.32 Index Deletion : 0.00
% 4.58/2.32 Index Matching : 0.00
% 4.58/2.32 BG Taut test : 0.00
%------------------------------------------------------------------------------