TSTP Solution File: DAT033_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT033_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 : n028.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 7.57s 2.75s
% Output : CNFRefutation 7.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 72 ( 32 unt; 12 typ; 0 def)
% Number of atoms : 89 ( 71 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 22 ~; 22 |; 0 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 81 ( 0 atm; 18 fun; 40 num; 23 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 : 17 ( 10 usr; 11 con; 0-2 aty)
% Number of variables : 46 (; 46 !; 0 ?; 46 :)
% 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_5',type,
'#skE_5': $int ).
tff('#skE_4',type,
'#skE_4': $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_142,negated_conjecture,
~ ! [U: collection] :
( ( count(add(5,U)) = count(add(3,U)) )
=> ( count(remove(5,U)) = count(remove(3,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_131,axiom,
! [X14a: $int,X15: collection] :
( ~ in(X14a,X15)
<=> ( count(remove(X14a,X15)) = count(X15) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax6) ).
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_60,axiom,
! [Ua: $int] : ~ in(Ua,empty),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax1) ).
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_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_113,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax2) ).
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(c_51,plain,
count(remove(5,'#skF_1')) != count(remove(3,'#skF_1')),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_97,plain,
count(remove(3,'#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_96,plain,
count(remove(5,'#skF_1')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_102,plain,
'#skE_2' != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_97,c_96,c_51]) ).
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_267,plain,
! [X16_46a: $int,X17_47: collection] :
( ( add(X16_46a,remove(X16_46a,X17_47)) = X17_47 )
| ~ in(X16_46a,X17_47) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_773,plain,
! [X14_83a: $int,X15_84: collection] :
( ( add(X14_83a,remove(X14_83a,X15_84)) = X15_84 )
| ( count(remove(X14_83a,X15_84)) = count(X15_84) ) ),
inference(resolution,[status(thm)],[c_54,c_267]) ).
tff(c_72,plain,
! [U_1a: $int] : ~ in(U_1a,empty),
inference(cnfTransformation,[status(thm)],[f_60]) ).
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_288,plain,
! [X10_48a: $int,X11_49: collection] :
( ( count(add(X10_48a,X11_49)) = count(X11_49) )
| ~ in(X10_48a,X11_49) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_386,plain,
! [X2_58a: $int,X1_59: collection] : ( count(add(X2_58a,add(X2_58a,X1_59))) = count(add(X2_58a,X1_59)) ),
inference(resolution,[status(thm)],[c_68,c_288]) ).
tff(c_61,plain,
! [X7_13: collection] :
( ( empty = X7_13 )
| ( count(X7_13) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_591,plain,
! [X2_73a: $int,X1_74: collection] :
( ( add(X2_73a,add(X2_73a,X1_74)) = empty )
| ( count(add(X2_73a,X1_74)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_386,c_61]) ).
tff(c_618,plain,
! [X2_73a: $int,X1_74: collection] :
( in(X2_73a,empty)
| ( count(add(X2_73a,X1_74)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_68]) ).
tff(c_643,plain,
! [X2_73a: $int,X1_74: collection] : ( count(add(X2_73a,X1_74)) != 0 ),
inference(negUnitSimplification,[status(thm)],[c_72,c_618]) ).
tff(c_901,plain,
! [X15_87: collection,X14_88a: $int] :
( ( count(X15_87) != 0 )
| ( count(remove(X14_88a,X15_87)) = count(X15_87) ) ),
inference(superposition,[status(thm),theory(equality)],[c_773,c_643]) ).
tff(c_101,plain,
count(remove(3,'#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_951,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count('#skF_1') != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_901,c_101]) ).
tff(c_967,plain,
count('#skF_1') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_951]) ).
tff(c_50,plain,
count(add(5,'#skF_1')) = count(add(3,'#skF_1')),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_104,plain,
count(add(3,'#skF_1')) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_50]) ).
tff(c_103,plain,
count(add(5,'#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_50]) ).
tff(c_109,plain,
'#skE_4' = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_104,c_103,c_50]) ).
tff(c_108,plain,
count(add(3,'#skF_1')) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_50]) ).
tff(c_124,plain,
count(add(3,'#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_109,c_108]) ).
tff(c_987,plain,
! [X14_89a: $int,X15_90: collection] :
( ( count(add(X14_89a,X15_90)) = count(X15_90) )
| ( count(remove(X14_89a,X15_90)) = count(X15_90) ) ),
inference(resolution,[status(thm)],[c_54,c_288]) ).
tff(c_1007,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count(add(3,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_987,c_101]) ).
tff(c_1048,plain,
( ( '#skE_5' = '#skE_2' )
| ( '#skE_5' = '#skE_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_967,c_124,c_967,c_1007]) ).
tff(c_1070,plain,
'#skE_5' = '#skE_3',
inference(splitLeft,[status(thm)],[c_1048]) ).
tff(c_1077,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_1070,c_967]) ).
tff(c_107,plain,
count(add(5,'#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_50]) ).
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_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_737,plain,
! [X12_81a: $int,X13_82: collection] :
( ( count(remove(X12_81a,X13_82)) = $sum($uminus(1),count(X13_82)) )
| ~ in(X12_81a,X13_82) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_7708,plain,
! [X10_269a: $int,X11_270: collection] :
( ( count(remove(X10_269a,X11_270)) = $sum($uminus(1),count(X11_270)) )
| ( count(add(X10_269a,X11_270)) != count(X11_270) ) ),
inference(resolution,[status(thm)],[c_57,c_737]) ).
tff(c_100,plain,
count(remove(5,'#skF_1')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_7784,plain,
( ( $sum($uminus(1),count('#skF_1')) = '#skE_1' )
| ( count(add(5,'#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_7708,c_100]) ).
tff(c_7884,plain,
$sum($uminus(1),'#skE_3') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_1077,c_107,c_1077,c_7784]) ).
tff(c_7886,plain,
'#skE_3' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7884]) ).
tff(c_7781,plain,
( ( $sum($uminus(1),count('#skF_1')) = '#skE_2' )
| ( count(add(3,'#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_7708,c_101]) ).
tff(c_7880,plain,
$sum($uminus(1),'#skE_3') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_1077,c_124,c_1077,c_7781]) ).
tff(c_7882,plain,
'#skE_3' = $sum(1,'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7880]) ).
tff(c_7955,plain,
$sum(1,'#skE_2') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_7886,c_7882]) ).
tff(c_7957,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7955]) ).
tff(c_7959,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_102,c_7957]) ).
tff(c_7962,plain,
'#skE_5' = '#skE_2',
inference(splitRight,[status(thm)],[c_1048]) ).
tff(c_7963,plain,
'#skE_5' != '#skE_3',
inference(splitRight,[status(thm)],[c_1048]) ).
tff(c_7979,plain,
'#skE_3' != '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_7962,c_7963]) ).
tff(c_1010,plain,
( ( count('#skF_1') = '#skE_1' )
| ( count(add(5,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_987,c_100]) ).
tff(c_1050,plain,
( ( '#skE_5' = '#skE_1' )
| ( '#skE_5' = '#skE_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_967,c_107,c_967,c_1010]) ).
tff(c_7992,plain,
( ( '#skE_2' = '#skE_1' )
| ( '#skE_3' = '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_7962,c_7962,c_1050]) ).
tff(c_7993,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7979,c_102,c_7992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT033_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/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
% 0.17/0.35 % Computer : n028.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 13:28:39 EDT 2023
% 0.17/0.35 % CPUTime :
% 7.57/2.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.57/2.76
% 7.57/2.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.57/2.78
% 7.57/2.78 Inference rules
% 7.57/2.78 ----------------------
% 7.57/2.78 #Ref : 0
% 7.57/2.78 #Sup : 1633
% 7.57/2.78 #Fact : 1
% 7.57/2.78 #Define : 6
% 7.57/2.78 #Split : 28
% 7.57/2.78 #Chain : 0
% 7.57/2.78 #Close : 0
% 7.57/2.78
% 7.57/2.78 Ordering : LPO
% 7.57/2.78
% 7.57/2.78 Simplification rules
% 7.57/2.78 ----------------------
% 7.57/2.78 #Subsume : 483
% 7.57/2.78 #Demod : 984
% 7.57/2.78 #Tautology : 564
% 7.57/2.78 #SimpNegUnit : 61
% 7.57/2.78 #BackRed : 17
% 7.57/2.78
% 7.57/2.78 #Partial instantiations: 0
% 7.57/2.78 #Strategies tried : 1
% 7.57/2.79
% 7.57/2.79 Timing (in seconds)
% 7.57/2.79 ----------------------
% 7.57/2.79 Preprocessing : 0.54
% 7.57/2.79 Parsing : 0.28
% 7.57/2.79 CNF conversion : 0.03
% 7.57/2.79 Main loop : 1.21
% 7.57/2.79 Inferencing : 0.36
% 7.57/2.79 Reduction : 0.34
% 7.57/2.79 Demodulation : 0.24
% 7.57/2.79 BG Simplification : 0.13
% 7.57/2.79 Subsumption : 0.26
% 7.57/2.79 Abstraction : 0.05
% 7.57/2.79 MUC search : 0.00
% 7.57/2.79 Cooper : 0.03
% 7.57/2.79 Total : 1.81
% 7.57/2.79 Index Insertion : 0.00
% 7.57/2.79 Index Deletion : 0.00
% 7.57/2.79 Index Matching : 0.00
% 7.57/2.79 BG Taut test : 0.00
%------------------------------------------------------------------------------