TSTP Solution File: DAT046_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT046_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 : n007.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 10:37:02 EDT 2023
% Result : Theorem 6.54s 2.63s
% Output : CNFRefutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 54 ( 19 unt; 7 typ; 0 def)
% Number of atoms : 83 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 29 ~; 28 |; 1 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 112 ( 0 atm; 17 fun; 50 num; 45 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 : 12 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 74 (; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
%Foreground operators:
tff(empty,type,
empty: collection ).
tff(count,type,
count: collection > $int ).
tff(in,type,
in: ( $int * collection ) > $o ).
tff(remove,type,
remove: ( $int * collection ) > collection ).
tff(add,type,
add: ( $int * collection ) > collection ).
tff(f_139,negated_conjecture,
count(add(1,add(3,empty))) != 2,
file('/export/starexec/sandbox2/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/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_78,axiom,
! [X3a: $int,X4: collection,X5a: $int] :
( ( in(X3a,X4)
& ( X3a != X5a ) )
<=> in(X3a,remove(X5a,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax5) ).
tff(f_60,axiom,
! [Ua: $int] : ~ in(Ua,empty),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax1) ).
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_113,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax2) ).
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(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(c_48,plain,
count(add(1,add(3,empty))) != 2,
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_92,plain,
count(add(1,add(3,empty))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_48]) ).
tff(c_96,plain,
'#skE_1' != 2,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_48]) ).
tff(c_95,plain,
count(add(1,add(3,empty))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_48]) ).
tff(c_65,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_668,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_2345,plain,
! [X2_160a: $int,X1_161: collection] : ( count(remove(X2_160a,add(X2_160a,X1_161))) = $sum($uminus(1),count(add(X2_160a,X1_161))) ),
inference(resolution,[status(thm)],[c_65,c_668]) ).
tff(c_64,plain,
! [Z_6a: $int,X1_7: collection,X2_8a: $int] :
( ~ in(Z_6a,X1_7)
| in(Z_6a,add(X2_8a,X1_7)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_63,plain,
! [X3_9a: $int,X5_11a: $int,X4_10: collection] :
( in(X3_9a,remove(X5_11a,X4_10))
| ~ in(X3_9a,X4_10)
| ( X5_11a = X3_9a ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_69,plain,
! [U_1a: $int] : ~ in(U_1a,empty),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_167,plain,
! [X14_44a: $int,X15_45: collection] :
( ( count(remove(X14_44a,X15_45)) = count(X15_45) )
| in(X14_44a,X15_45) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_62,plain,
! [X3_9a: $int,X4_10: collection] : ~ in(X3_9a,remove(X3_9a,X4_10)),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_341,plain,
! [X14_62a: $int,X4_63: collection] : ( count(remove(X14_62a,remove(X14_62a,X4_63))) = count(remove(X14_62a,X4_63)) ),
inference(resolution,[status(thm)],[c_167,c_62]) ).
tff(c_58,plain,
! [X7_13: collection] :
( ( empty = X7_13 )
| ( count(X7_13) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_483,plain,
! [X14_71a: $int,X4_72: collection] :
( ( remove(X14_71a,remove(X14_71a,X4_72)) = empty )
| ( count(remove(X14_71a,X4_72)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_341,c_58]) ).
tff(c_501,plain,
! [X3_9a: $int,X14_71a: $int,X4_72: collection] :
( in(X3_9a,empty)
| ~ in(X3_9a,remove(X14_71a,X4_72))
| ( X3_9a = X14_71a )
| ( count(remove(X14_71a,X4_72)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_483,c_63]) ).
tff(c_1389,plain,
! [X3_111a: $int,X14_112a: $int,X4_113: collection] :
( ~ in(X3_111a,remove(X14_112a,X4_113))
| ( X3_111a = X14_112a )
| ( count(remove(X14_112a,X4_113)) != 0 ) ),
inference(negUnitSimplification,[status(thm)],[c_69,c_501]) ).
tff(c_1429,plain,
! [X5_114a: $int,X4_115: collection,X3_116a: $int] :
( ( count(remove(X5_114a,X4_115)) != 0 )
| ~ in(X3_116a,X4_115)
| ( X5_114a = X3_116a ) ),
inference(resolution,[status(thm)],[c_63,c_1389]) ).
tff(c_1732,plain,
! [X5_133a: $int,X2_134a: $int,X1_135: collection,Z_136a: $int] :
( ( count(remove(X5_133a,add(X2_134a,X1_135))) != 0 )
| ( Z_136a = X5_133a )
| ~ in(Z_136a,X1_135) ),
inference(resolution,[status(thm)],[c_64,c_1429]) ).
tff(c_1767,plain,
! [X5_133a: $int,X2_134a: $int,X2_8a: $int,X1_7: collection] :
( ( count(remove(X5_133a,add(X2_134a,add(X2_8a,X1_7)))) != 0 )
| ( X5_133a = X2_8a ) ),
inference(resolution,[status(thm)],[c_65,c_1732]) ).
tff(c_2355,plain,
! [X2_160a: $int,X2_8a: $int,X1_7: collection] :
( ( $sum($uminus(1),count(add(X2_160a,add(X2_8a,X1_7)))) != 0 )
| ( X2_8a = X2_160a ) ),
inference(superposition,[status(thm),theory(equality)],[c_2345,c_1767]) ).
tff(c_2713,plain,
! [X2_173a: $int,X2_174a: $int,X1_175: collection] :
( ( count(add(X2_173a,add(X2_174a,X1_175))) != 1 )
| ( X2_174a = X2_173a ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2355]) ).
tff(c_2735,plain,
( ( '#skE_1' != 1 )
| ( 3 = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_95,c_2713]) ).
tff(c_2744,plain,
'#skE_1' != 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2735]) ).
tff(c_59,plain,
count(empty) = 0,
inference(cnfTransformation,[status(thm)],[f_113]) ).
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_417,plain,
! [X8_68a: $int,X9_69: collection] :
( ( count(add(X8_68a,X9_69)) = $sum(1,count(X9_69)) )
| in(X8_68a,X9_69) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_445,plain,
! [X8_68a: $int] : ( count(add(X8_68a,empty)) = $sum(1,count(empty)) ),
inference(resolution,[status(thm)],[c_417,c_69]) ).
tff(c_461,plain,
! [X8_68a: $int] : ( count(add(X8_68a,empty)) = $sum(1,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_59,c_445]) ).
tff(c_463,plain,
! [X8_68a: $int] : ( count(add(X8_68a,empty)) = 1 ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_461]) ).
tff(c_55,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_4495,plain,
! [X8_224a: $int,X9_225: collection] :
( ( count(add(X8_224a,X9_225)) = count(X9_225) )
| ( count(add(X8_224a,X9_225)) = $sum(1,count(X9_225)) ) ),
inference(resolution,[status(thm)],[c_417,c_55]) ).
tff(c_4567,plain,
( ( $sum(1,count(add(3,empty))) = '#skE_1' )
| ( count(add(1,add(3,empty))) = count(add(3,empty)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4495,c_95]) ).
tff(c_4655,plain,
( ( '#skE_1' = $sum(1,1) )
| ( '#skE_1' = 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_95,c_463,c_4567]) ).
tff(c_4656,plain,
'#skE_1' = $sum(1,1),
inference(negUnitSimplification,[status(thm)],[c_2744,c_4655]) ).
tff(c_4658,plain,
'#skE_1' = 2,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4656]) ).
tff(c_4697,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_96,c_4658]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT046_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
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 13:01:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 6.54/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.54/2.64
% 6.54/2.64 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.54/2.67
% 6.54/2.67 Inference rules
% 6.54/2.67 ----------------------
% 6.54/2.67 #Ref : 0
% 6.54/2.67 #Sup : 956
% 6.54/2.67 #Fact : 1
% 6.54/2.67 #Define : 1
% 6.54/2.67 #Split : 7
% 6.54/2.67 #Chain : 0
% 6.54/2.67 #Close : 0
% 6.54/2.67
% 6.54/2.67 Ordering : LPO
% 6.54/2.67
% 6.54/2.67 Simplification rules
% 6.54/2.67 ----------------------
% 6.54/2.67 #Subsume : 269
% 6.54/2.67 #Demod : 451
% 6.54/2.67 #Tautology : 341
% 6.54/2.67 #SimpNegUnit : 18
% 6.54/2.67 #BackRed : 2
% 6.54/2.67
% 6.54/2.67 #Partial instantiations: 0
% 6.54/2.67 #Strategies tried : 1
% 6.54/2.67
% 6.54/2.67 Timing (in seconds)
% 6.54/2.67 ----------------------
% 6.54/2.68 Preprocessing : 0.57
% 6.54/2.68 Parsing : 0.31
% 6.54/2.68 CNF conversion : 0.03
% 6.54/2.68 Main loop : 1.01
% 6.54/2.68 Inferencing : 0.32
% 6.54/2.68 Reduction : 0.27
% 6.54/2.68 Demodulation : 0.20
% 6.54/2.68 BG Simplification : 0.12
% 6.54/2.68 Subsumption : 0.21
% 6.54/2.68 Abstraction : 0.05
% 6.54/2.68 MUC search : 0.00
% 6.54/2.68 Cooper : 0.02
% 6.54/2.68 Total : 1.63
% 6.54/2.68 Index Insertion : 0.00
% 6.54/2.68 Index Deletion : 0.00
% 6.54/2.68 Index Matching : 0.00
% 6.54/2.68 BG Taut test : 0.00
%------------------------------------------------------------------------------