TSTP Solution File: DAT036_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT036_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n021.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 10:37:01 EDT 2023
% Result : Theorem 6.33s 2.55s
% Output : CNFRefutation 6.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 31 unt; 11 typ; 0 def)
% Number of atoms : 74 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 20 ~; 16 |; 0 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 95 ( 21 atm; 24 fun; 26 num; 24 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 6 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 49 (; 49 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty > #skF_1
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
%Foreground operators:
tff(empty,type,
empty: collection ).
tff(count,type,
count: collection > $int ).
tff('#skF_1',type,
'#skF_1': collection ).
tff(in,type,
in: ( $int * collection ) > $o ).
tff(remove,type,
remove: ( $int * collection ) > collection ).
tff(add,type,
add: ( $int * collection ) > collection ).
tff(f_142,negated_conjecture,
~ ! [U: collection,Va: $int,Wa: $int] :
( $greater(Wa,0)
=> $greatereq($sum(count(U),Wa),count(add(Va,add(Va,U)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_71,axiom,
! [Za: $int,X1: collection,X2a: $int] :
( ( in(Za,X1)
| ( Za = X2a ) )
<=> in(Za,add(X2a,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4) ).
tff(f_122,axiom,
! [X10a: $int,X11: collection] :
( in(X10a,X11)
<=> ( count(add(X10a,X11)) = count(X11) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4) ).
tff(f_135,axiom,
! [X16a: $int,X17: collection] :
( in(X16a,X17)
=> ( X17 = add(X16a,remove(X16a,X17)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax7) ).
tff(f_126,axiom,
! [X12a: $int,X13: collection] :
( in(X12a,X13)
<=> ( count(remove(X12a,X13)) = $difference(count(X13),1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5) ).
tff(f_109,axiom,
! [X6: collection] : $greatereq(count(X6),0),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax1) ).
tff(f_118,axiom,
! [X8a: $int,X9: collection] :
( ~ in(X8a,X9)
<=> ( count(add(X8a,X9)) = $sum(count(X9),1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3) ).
tff(c_47,plain,
~ $greatereq($sum(count('#skF_1'),'#skF_3'),count(add('#skF_2',add('#skF_2','#skF_1')))),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_55,plain,
$less($sum('#skF_3',count('#skF_1')),count(add('#skF_2',add('#skF_2','#skF_1')))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_108,plain,
count('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_72,plain,
! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_251,plain,
! [X10_60a: $int,X11_61: collection] :
( ( count(add(X10_60a,X11_61)) = count(X11_61) )
| ~ in(X10_60a,X11_61) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_414,plain,
! [X2_78a: $int,X1_79: collection] : ( count(add(X2_78a,add(X2_78a,X1_79))) = count(add(X2_78a,X1_79)) ),
inference(resolution,[status(thm)],[c_72,c_251]) ).
tff(c_111,plain,
count(add('#skF_2',add('#skF_2','#skF_1'))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_439,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_414,c_111]) ).
tff(c_442,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_439]) ).
tff(c_61,plain,
! [X10_16a: $int,X11_17: collection] :
( in(X10_16a,X11_17)
| ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_272,plain,
! [X16_62a: $int,X17_63: collection] :
( ( add(X16_62a,remove(X16_62a,X17_63)) = X17_63 )
| ~ in(X16_62a,X17_63) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_288,plain,
! [X10_16a: $int,X11_17: collection] :
( ( add(X10_16a,remove(X10_16a,X11_17)) = X11_17 )
| ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
inference(resolution,[status(thm)],[c_61,c_272]) ).
tff(c_35,plain,
! [X12_18a: $int,X13_19: collection] :
( ( count(remove(X12_18a,X13_19)) = $difference(count(X13_19),1) )
| ~ in(X12_18a,X13_19) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_702,plain,
! [X12_94a: $int,X13_95: collection] :
( ( count(remove(X12_94a,X13_95)) = $sum($uminus(1),count(X13_95)) )
| ~ in(X12_94a,X13_95) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_1828,plain,
! [X2_147a: $int,X1_148: collection] : ( count(remove(X2_147a,add(X2_147a,X1_148))) = $sum($uminus(1),count(add(X2_147a,X1_148))) ),
inference(resolution,[status(thm)],[c_72,c_702]) ).
tff(c_18,plain,
! [X6_12: collection] : $greatereq(count(X6_12),0),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_67,plain,
! [X6_12: collection] : ~ $less(count(X6_12),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_18]) ).
tff(c_1860,plain,
! [X2_147a: $int,X1_148: collection] : ~ $less($sum($uminus(1),count(add(X2_147a,X1_148))),0),
inference(superposition,[status(thm),theory(equality)],[c_1828,c_67]) ).
tff(c_1932,plain,
! [X2_149a: $int,X1_150: collection] : ~ $less(count(add(X2_149a,X1_150)),1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1860]) ).
tff(c_2209,plain,
! [X11_175: collection,X10_176a: $int] :
( ~ $less(count(X11_175),1)
| ( count(add(X10_176a,X11_175)) != count(X11_175) ) ),
inference(superposition,[status(thm),theory(equality)],[c_288,c_1932]) ).
tff(c_2227,plain,
( ~ $less(count('#skF_1'),1)
| ( count('#skF_1') != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_442,c_2209]) ).
tff(c_2246,plain,
( ~ $less('#skE_1',1)
| ( '#skE_2' != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_2227]) ).
tff(c_2291,plain,
'#skE_2' != '#skE_1',
inference(splitLeft,[status(thm)],[c_2246]) ).
tff(c_452,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_439]) ).
tff(c_25,plain,
! [X8_14a: $int,X9_15: collection] :
( ( count(add(X8_14a,X9_15)) = $sum(count(X9_15),1) )
| in(X8_14a,X9_15) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_503,plain,
! [X8_85a: $int,X9_86: collection] :
( ( count(add(X8_85a,X9_86)) = $sum(1,count(X9_86)) )
| in(X8_85a,X9_86) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_62,plain,
! [X10_16a: $int,X11_17: collection] :
( ( count(add(X10_16a,X11_17)) = count(X11_17) )
| ~ in(X10_16a,X11_17) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_3500,plain,
! [X8_211a: $int,X9_212: collection] :
( ( count(add(X8_211a,X9_212)) = count(X9_212) )
| ( count(add(X8_211a,X9_212)) = $sum(1,count(X9_212)) ) ),
inference(resolution,[status(thm)],[c_503,c_62]) ).
tff(c_3545,plain,
( ( $sum(1,count('#skF_1')) = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_3500,c_442]) ).
tff(c_3618,plain,
( ( '#skE_2' = $sum(1,'#skE_1') )
| ( '#skE_2' = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_452,c_108,c_108,c_3545]) ).
tff(c_3620,plain,
'#skE_2' = $sum(1,'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_2291,c_3618]) ).
tff(c_104,plain,
count(add('#skF_2',add('#skF_2','#skF_1'))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_103,plain,
count('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_77,plain,
$less($sum('#skF_3',count('#skF_1')),count(add('#skF_2',add('#skF_2','#skF_1')))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_106,plain,
$less($sum('#skF_3','#skE_1'),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_103,c_77]) ).
tff(c_113,plain,
$less($sum('#skE_1','#skF_3'),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_106]) ).
tff(c_3682,plain,
$less($sum('#skE_1','#skF_3'),$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_3620,c_113]) ).
tff(c_3691,plain,
$less('#skF_3',1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3682]) ).
tff(c_49,plain,
$greater('#skF_3',0),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_51,plain,
$less(0,'#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_49]) ).
tff(c_3692,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3691,c_51]) ).
tff(c_3696,plain,
'#skE_2' = '#skE_1',
inference(splitRight,[status(thm)],[c_2246]) ).
tff(c_3709,plain,
$less($sum('#skE_1','#skF_3'),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_3696,c_113]) ).
tff(c_3719,plain,
$less('#skF_3',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3709]) ).
tff(c_3793,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3719,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT036_1 : TPTP v8.1.2. Released v5.0.0.
% 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
% 0.17/0.35 % Computer : n021.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 13:12:36 EDT 2023
% 0.17/0.35 % CPUTime :
% 6.33/2.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.33/2.56
% 6.33/2.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.58/2.64
% 6.58/2.64 Inference rules
% 6.58/2.64 ----------------------
% 6.58/2.64 #Ref : 0
% 6.58/2.64 #Sup : 734
% 6.58/2.64 #Fact : 1
% 6.58/2.64 #Define : 2
% 6.58/2.64 #Split : 11
% 6.58/2.64 #Chain : 0
% 6.58/2.64 #Close : 2
% 6.58/2.64
% 6.58/2.64 Ordering : LPO
% 6.58/2.64
% 6.58/2.64 Simplification rules
% 6.58/2.64 ----------------------
% 6.58/2.64 #Subsume : 192
% 6.58/2.64 #Demod : 370
% 6.58/2.64 #Tautology : 265
% 6.58/2.64 #SimpNegUnit : 16
% 6.58/2.64 #BackRed : 11
% 6.58/2.64
% 6.58/2.64 #Partial instantiations: 0
% 6.58/2.64 #Strategies tried : 1
% 6.58/2.64
% 6.58/2.64 Timing (in seconds)
% 6.58/2.64 ----------------------
% 6.58/2.64 Preprocessing : 0.58
% 6.58/2.64 Parsing : 0.31
% 6.58/2.64 CNF conversion : 0.03
% 6.58/2.65 Main loop : 0.93
% 6.58/2.65 Inferencing : 0.28
% 6.58/2.65 Reduction : 0.25
% 6.58/2.65 Demodulation : 0.18
% 6.58/2.65 BG Simplification : 0.12
% 6.58/2.65 Subsumption : 0.18
% 6.58/2.65 Abstraction : 0.04
% 6.58/2.65 MUC search : 0.00
% 6.58/2.65 Cooper : 0.03
% 6.58/2.65 Total : 1.62
% 6.58/2.65 Index Insertion : 0.00
% 6.58/2.65 Index Deletion : 0.00
% 6.58/2.65 Index Matching : 0.00
% 6.58/2.65 BG Taut test : 0.00
%------------------------------------------------------------------------------