TSTP Solution File: DAT049_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT049_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 : n011.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 10:37:03 EDT 2023
% Result : Theorem 7.24s 2.97s
% Output : CNFRefutation 7.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 81 ( 41 unt; 12 typ; 0 def)
% Number of atoms : 98 ( 80 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 26 ~; 24 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 103 ( 0 atm; 45 fun; 34 num; 24 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 47 (; 47 !; 0 ?; 47 :)
% 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('#skE_4',type,
'#skE_4': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skE_3',type,
'#skE_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_140,negated_conjecture,
~ ! [U: collection,Va: $int] : ( count(remove(Va,add(Va,U))) = count(remove(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_131,axiom,
! [X14a: $int,X15: collection] :
( ~ in(X14a,X15)
<=> ( count(remove(X14a,X15)) = count(X15) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax6) ).
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_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_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_51,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) != count(remove('#skF_2','#skF_1')),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_120,plain,
count(remove('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_119,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_73,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) != count(remove('#skF_2','#skF_1')),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_131,plain,
'#skE_2' != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_120,c_119,c_73]) ).
tff(c_127,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_68,plain,
! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_284,plain,
! [X14_66a: $int,X15_67: collection] :
( ~ in(X14_66a,X15_67)
| ( count(remove(X14_66a,X15_67)) != count(X15_67) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_408,plain,
! [X2_80a: $int,X1_81: collection] : ( count(remove(X2_80a,add(X2_80a,X1_81))) != count(add(X2_80a,X1_81)) ),
inference(resolution,[status(thm)],[c_68,c_284]) ).
tff(c_413,plain,
count(add('#skF_2','#skF_1')) != '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_127,c_408]) ).
tff(c_416,plain,
count(add('#skF_2','#skF_1')) != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_413]) ).
tff(c_428,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_416]) ).
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_658,plain,
! [X12_98a: $int,X13_99: collection] :
( ( count(remove(X12_98a,X13_99)) = $sum($uminus(1),count(X13_99)) )
| ~ in(X12_98a,X13_99) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_8312,plain,
! [X2_346a: $int,X1_347: collection] : ( count(remove(X2_346a,add(X2_346a,X1_347))) = $sum($uminus(1),count(add(X2_346a,X1_347))) ),
inference(resolution,[status(thm)],[c_68,c_658]) ).
tff(c_8390,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_8312]) ).
tff(c_8442,plain,
$sum($uminus(1),'#skE_3') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_428,c_8390]) ).
tff(c_8444,plain,
'#skE_3' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8442]) ).
tff(c_2638,plain,
! [X2_176a: $int,X1_177: collection] : ( count(remove(X2_176a,add(X2_176a,X1_177))) = $sum($uminus(1),count(add(X2_176a,X1_177))) ),
inference(resolution,[status(thm)],[c_68,c_658]) ).
tff(c_2676,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_2638,c_127]) ).
tff(c_2743,plain,
$sum($uminus(1),'#skE_3') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_428,c_2676]) ).
tff(c_2745,plain,
'#skE_3' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2743]) ).
tff(c_194,plain,
! [X14_58a: $int,X15_59: collection] :
( ( count(remove(X14_58a,X15_59)) = count(X15_59) )
| in(X14_58a,X15_59) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_58,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_820,plain,
! [X14_106a: $int,X15_107: collection] :
( ( count(add(X14_106a,X15_107)) = count(X15_107) )
| ( count(remove(X14_106a,X15_107)) = count(X15_107) ) ),
inference(resolution,[status(thm)],[c_194,c_58]) ).
tff(c_130,plain,
count(remove('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_842,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_820,c_130]) ).
tff(c_879,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count('#skF_1') = '#skE_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_428,c_842]) ).
tff(c_898,plain,
count('#skF_1') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_879]) ).
tff(c_902,plain,
( ( '#skE_4' = '#skE_2' )
| ( '#skE_4' = '#skE_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_898,c_898,c_879]) ).
tff(c_919,plain,
'#skE_4' = '#skE_3',
inference(splitLeft,[status(thm)],[c_902]) ).
tff(c_901,plain,
count('#skF_1') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_879]) ).
tff(c_926,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_919,c_901]) ).
tff(c_57,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_1570,plain,
! [X10_128a: $int,X11_129: collection] :
( ( count(remove(X10_128a,X11_129)) != count(X11_129) )
| ( count(add(X10_128a,X11_129)) != count(X11_129) ) ),
inference(resolution,[status(thm)],[c_57,c_284]) ).
tff(c_1597,plain,
( ( count('#skF_1') != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_1570]) ).
tff(c_1617,plain,
'#skE_3' != '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_428,c_926,c_926,c_1597]) ).
tff(c_2791,plain,
'#skE_2' != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_2745,c_1617]) ).
tff(c_134,plain,
count(remove('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_2792,plain,
count('#skF_1') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_2745,c_926]) ).
tff(c_54,plain,
! [X14_20a: $int,X15_21: collection] :
( ( count(remove(X14_20a,X15_21)) = count(X15_21) )
| in(X14_20a,X15_21) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_6136,plain,
! [X14_264a: $int,X15_265: collection] :
( ( count(remove(X14_264a,X15_265)) = $sum($uminus(1),count(X15_265)) )
| ( count(remove(X14_264a,X15_265)) = count(X15_265) ) ),
inference(resolution,[status(thm)],[c_54,c_658]) ).
tff(c_6202,plain,
( ( $sum($uminus(1),count('#skF_1')) = '#skE_2' )
| ( count(remove('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_6136,c_130]) ).
tff(c_6287,plain,
( ( '#skE_2' = $sum($uminus(1),$sum(1,'#skE_1')) )
| ( '#skE_2' = $sum(1,'#skE_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_2792,c_2792,c_6202]) ).
tff(c_6288,plain,
'#skE_2' = $sum($uminus(1),$sum(1,'#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_2791,c_6287]) ).
tff(c_6290,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6288]) ).
tff(c_6323,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_6290]) ).
tff(c_6326,plain,
'#skE_4' = '#skE_2',
inference(splitRight,[status(thm)],[c_902]) ).
tff(c_6327,plain,
'#skE_4' != '#skE_3',
inference(splitRight,[status(thm)],[c_902]) ).
tff(c_6336,plain,
'#skE_3' != '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_6326,c_6327]) ).
tff(c_8610,plain,
'#skE_2' != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8444,c_6336]) ).
tff(c_425,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_416]) ).
tff(c_8616,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8444,c_425]) ).
tff(c_6334,plain,
count('#skF_1') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_6326,c_901]) ).
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_452,plain,
! [X8_87a: $int,X9_88: collection] :
( ( count(add(X8_87a,X9_88)) = $sum(1,count(X9_88)) )
| in(X8_87a,X9_88) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_9278,plain,
! [X8_375a: $int,X9_376: collection] :
( ( count(add(X8_375a,X9_376)) = count(X9_376) )
| ( count(add(X8_375a,X9_376)) = $sum(1,count(X9_376)) ) ),
inference(resolution,[status(thm)],[c_452,c_58]) ).
tff(c_8613,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8444,c_425]) ).
tff(c_9306,plain,
( ( $sum(1,count('#skF_1')) = $sum(1,'#skE_1') )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_9278,c_8613]) ).
tff(c_9386,plain,
( ( $sum(1,'#skE_2') = $sum(1,'#skE_1') )
| ( '#skE_2' = $sum(1,'#skE_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8616,c_6334,c_6334,c_9306]) ).
tff(c_9387,plain,
$sum(1,'#skE_2') = $sum(1,'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_8610,c_9386]) ).
tff(c_9389,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9387]) ).
tff(c_9438,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_9389]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT049_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/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
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 13:15:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.24/2.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.24/2.97
% 7.24/2.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.24/3.01
% 7.24/3.01 Inference rules
% 7.24/3.01 ----------------------
% 7.24/3.01 #Ref : 0
% 7.24/3.01 #Sup : 1850
% 7.24/3.01 #Fact : 3
% 7.24/3.01 #Define : 6
% 7.24/3.01 #Split : 29
% 7.24/3.01 #Chain : 0
% 7.24/3.01 #Close : 0
% 7.24/3.01
% 7.24/3.01 Ordering : LPO
% 7.24/3.01
% 7.24/3.01 Simplification rules
% 7.24/3.01 ----------------------
% 7.24/3.01 #Subsume : 535
% 7.24/3.01 #Demod : 1033
% 7.24/3.01 #Tautology : 646
% 7.24/3.01 #SimpNegUnit : 85
% 7.24/3.01 #BackRed : 19
% 7.24/3.01
% 7.24/3.01 #Partial instantiations: 0
% 7.24/3.01 #Strategies tried : 1
% 7.24/3.01
% 7.24/3.01 Timing (in seconds)
% 7.24/3.01 ----------------------
% 7.24/3.01 Preprocessing : 0.60
% 7.24/3.01 Parsing : 0.31
% 7.24/3.01 CNF conversion : 0.03
% 7.24/3.01 Main loop : 1.33
% 7.24/3.01 Inferencing : 0.40
% 7.24/3.01 Reduction : 0.37
% 7.24/3.01 Demodulation : 0.26
% 7.24/3.01 BG Simplification : 0.14
% 7.24/3.01 Subsumption : 0.28
% 7.24/3.01 Abstraction : 0.06
% 7.24/3.01 MUC search : 0.00
% 7.24/3.01 Cooper : 0.03
% 7.24/3.01 Total : 1.99
% 7.24/3.01 Index Insertion : 0.00
% 7.24/3.01 Index Deletion : 0.00
% 7.24/3.01 Index Matching : 0.00
% 7.24/3.01 BG Taut test : 0.00
%------------------------------------------------------------------------------