TSTP Solution File: DAT034_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT034_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/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 : n029.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 10:37:00 EDT 2023
% Result : Theorem 6.48s 2.71s
% Output : CNFRefutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 53 ( 24 unt; 10 typ; 0 def)
% Number of atoms : 63 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 19 ~; 15 |; 0 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 87 ( 15 atm; 23 fun; 28 num; 21 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 44 (; 44 !; 0 ?; 44 :)
% 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 ).
%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_140,negated_conjecture,
~ ! [U: collection,Va: $int] : $greatereq($sum(count(U),1),count(add(Va,U))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_122,axiom,
! [X10a: $int,X11: collection] :
( in(X10a,X11)
<=> ( count(add(X10a,X11)) = count(X11) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/DAT002=1.ax',ax7) ).
tff(f_71,axiom,
! [Za: $int,X1: collection,X2a: $int] :
( ( in(Za,X1)
| ( Za = X2a ) )
<=> in(Za,add(X2a,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax4) ).
tff(f_126,axiom,
! [X12a: $int,X13: collection] :
( in(X12a,X13)
<=> ( count(remove(X12a,X13)) = $difference(count(X13),1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax5) ).
tff(f_109,axiom,
! [X6: collection] : $greatereq(count(X6),0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/DAT002=1.ax',ax3) ).
tff(c_47,plain,
~ $greatereq($sum(count('#skF_1'),1),count(add('#skF_2','#skF_1'))),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_52,plain,
$less($sum(1,count('#skF_1')),count(add('#skF_2','#skF_1'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_125,plain,
count('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_52]) ).
tff(c_128,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_52]) ).
tff(c_58,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_54a: $int,X17_55: collection] :
( ( add(X16_54a,remove(X16_54a,X17_55)) = X17_55 )
| ~ in(X16_54a,X17_55) ),
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_58,c_272]) ).
tff(c_69,plain,
! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
inference(cnfTransformation,[status(thm)],[f_71]) ).
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_506,plain,
! [X12_76a: $int,X13_77: collection] :
( ( count(remove(X12_76a,X13_77)) = $sum($uminus(1),count(X13_77)) )
| ~ in(X12_76a,X13_77) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_1206,plain,
! [X2_105a: $int,X1_106: collection] : ( count(remove(X2_105a,add(X2_105a,X1_106))) = $sum($uminus(1),count(add(X2_105a,X1_106))) ),
inference(resolution,[status(thm)],[c_69,c_506]) ).
tff(c_18,plain,
! [X6_12: collection] : $greatereq(count(X6_12),0),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_64,plain,
! [X6_12: collection] : ~ $less(count(X6_12),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_18]) ).
tff(c_1226,plain,
! [X2_105a: $int,X1_106: collection] : ~ $less($sum($uminus(1),count(add(X2_105a,X1_106))),0),
inference(superposition,[status(thm),theory(equality)],[c_1206,c_64]) ).
tff(c_1280,plain,
! [X2_107a: $int,X1_108: collection] : ~ $less(count(add(X2_107a,X1_108)),1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1226]) ).
tff(c_1519,plain,
! [X11_123: collection,X10_124a: $int] :
( ~ $less(count(X11_123),1)
| ( count(add(X10_124a,X11_123)) != count(X11_123) ) ),
inference(superposition,[status(thm),theory(equality)],[c_288,c_1280]) ).
tff(c_1540,plain,
( ~ $less(count('#skF_1'),1)
| ( count('#skF_1') != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_1519]) ).
tff(c_1553,plain,
( ~ $less('#skE_1',1)
| ( '#skE_2' != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_125,c_1540]) ).
tff(c_1555,plain,
'#skE_2' != '#skE_1',
inference(splitLeft,[status(thm)],[c_1553]) ).
tff(c_146,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_52]) ).
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_459,plain,
! [X8_74a: $int,X9_75: collection] :
( ( count(add(X8_74a,X9_75)) = $sum(1,count(X9_75)) )
| in(X8_74a,X9_75) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_59,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_4589,plain,
! [X8_230a: $int,X9_231: collection] :
( ( count(add(X8_230a,X9_231)) = count(X9_231) )
| ( count(add(X8_230a,X9_231)) = $sum(1,count(X9_231)) ) ),
inference(resolution,[status(thm)],[c_459,c_59]) ).
tff(c_4654,plain,
( ( $sum(1,count('#skF_1')) = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_4589,c_128]) ).
tff(c_4738,plain,
( ( '#skE_2' = $sum(1,'#skE_1') )
| ( '#skE_2' = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_125,c_125,c_4654]) ).
tff(c_4740,plain,
'#skE_2' = $sum(1,'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_1555,c_4738]) ).
tff(c_121,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_52]) ).
tff(c_120,plain,
count('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_52]) ).
tff(c_74,plain,
$less($sum(1,count('#skF_1')),count(add('#skF_2','#skF_1'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_129,plain,
$less($sum(1,'#skE_1'),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_120,c_74]) ).
tff(c_4793,plain,
$less($sum(1,'#skE_1'),$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_4740,c_129]) ).
tff(c_4799,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4793]) ).
tff(c_4803,plain,
'#skE_2' = '#skE_1',
inference(splitRight,[status(thm)],[c_1553]) ).
tff(c_4811,plain,
$less($sum(1,'#skE_1'),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_4803,c_129]) ).
tff(c_4818,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT034_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 13:30:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.48/2.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.48/2.72
% 6.48/2.72 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.48/2.76
% 6.48/2.76 Inference rules
% 6.48/2.76 ----------------------
% 6.48/2.76 #Ref : 0
% 6.48/2.76 #Sup : 951
% 6.48/2.76 #Fact : 1
% 6.48/2.76 #Define : 2
% 6.48/2.76 #Split : 13
% 6.48/2.76 #Chain : 0
% 6.48/2.76 #Close : 0
% 6.48/2.76
% 6.48/2.76 Ordering : LPO
% 6.48/2.76
% 6.48/2.76 Simplification rules
% 6.48/2.76 ----------------------
% 6.48/2.76 #Subsume : 243
% 6.48/2.76 #Demod : 471
% 6.48/2.76 #Tautology : 357
% 6.48/2.76 #SimpNegUnit : 18
% 6.48/2.76 #BackRed : 8
% 6.48/2.76
% 6.48/2.76 #Partial instantiations: 0
% 6.48/2.76 #Strategies tried : 1
% 6.48/2.76
% 6.48/2.76 Timing (in seconds)
% 6.48/2.76 ----------------------
% 6.48/2.76 Preprocessing : 0.60
% 6.48/2.76 Parsing : 0.33
% 6.48/2.76 CNF conversion : 0.03
% 6.48/2.76 Main loop : 1.06
% 6.48/2.76 Inferencing : 0.31
% 6.48/2.76 Reduction : 0.31
% 6.48/2.76 Demodulation : 0.23
% 6.48/2.76 BG Simplification : 0.11
% 6.48/2.76 Subsumption : 0.23
% 6.48/2.76 Abstraction : 0.05
% 6.48/2.76 MUC search : 0.00
% 6.48/2.76 Cooper : 0.02
% 6.48/2.76 Total : 1.72
% 6.48/2.76 Index Insertion : 0.00
% 6.48/2.76 Index Deletion : 0.00
% 6.48/2.76 Index Matching : 0.00
% 6.48/2.77 BG Taut test : 0.00
%------------------------------------------------------------------------------