TSTP Solution File: DAT038_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT038_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 : n022.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 9.45s 3.43s
% Output : CNFRefutation 9.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 58 ( 16 unt; 10 typ; 0 def)
% Number of atoms : 95 ( 59 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 30 ~; 36 |; 3 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 112 ( 0 atm; 12 fun; 58 num; 42 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 : 16 ( 8 usr; 10 con; 0-2 aty)
% Number of variables : 67 (; 67 !; 0 ?; 67 :)
% 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_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_147,negated_conjecture,
~ ! [U: collection] :
( ( in(2,U)
& in(3,U)
& ( count(U) = 2 ) )
=> ~ in(5,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_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_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_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_60,axiom,
! [Ua: $int] : ~ in(Ua,empty),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax1) ).
tff(f_113,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax2) ).
tff(c_56,plain,
count('#skF_1') = 2,
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_55,plain,
in(3,'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_203,plain,
! [X14_42a: $int,X15_43: collection] :
( ~ in(X14_42a,X15_43)
| ( count(remove(X14_42a,X15_43)) != count(X15_43) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_218,plain,
count(remove(3,'#skF_1')) != count('#skF_1'),
inference(resolution,[status(thm)],[c_55,c_203]) ).
tff(c_233,plain,
count(remove(3,'#skF_1')) != 2,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_218]) ).
tff(c_258,plain,
count(remove(3,'#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_233]) ).
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_941,plain,
! [X12_79a: $int,X13_80: collection] :
( ( count(remove(X12_79a,X13_80)) = $sum($uminus(1),count(X13_80)) )
| ~ in(X12_79a,X13_80) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_965,plain,
count(remove(3,'#skF_1')) = $sum($uminus(1),count('#skF_1')),
inference(resolution,[status(thm)],[c_55,c_941]) ).
tff(c_986,plain,
'#skE_2' = $sum($uminus(1),2),
inference(demodulation,[status(thm),theory(equality)],[c_258,c_56,c_965]) ).
tff(c_988,plain,
'#skE_2' = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_986]) ).
tff(c_1070,plain,
count(remove(3,'#skF_1')) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_988,c_258]) ).
tff(c_57,plain,
in(5,'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_482,plain,
! [X3_53a: $int,X5_54a: $int,X4_55: collection] :
( in(X3_53a,remove(X5_54a,X4_55))
| ~ in(X3_53a,X4_55)
| ( X5_54a = X3_53a ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_58,plain,
! [X16_22a: $int,X17_23: collection] :
( ( add(X16_22a,remove(X16_22a,X17_23)) = X17_23 )
| ~ in(X16_22a,X17_23) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_9242,plain,
! [X3_277a: $int,X5_278a: $int,X4_279: collection] :
( ( add(X3_277a,remove(X3_277a,remove(X5_278a,X4_279))) = remove(X5_278a,X4_279) )
| ~ in(X3_277a,X4_279)
| ( X5_278a = X3_277a ) ),
inference(resolution,[status(thm)],[c_482,c_58]) ).
tff(c_9406,plain,
! [X5_287a: $int] :
( ( add(5,remove(5,remove(X5_287a,'#skF_1'))) = remove(X5_287a,'#skF_1') )
| ( X5_287a = 5 ) ),
inference(resolution,[status(thm)],[c_57,c_9242]) ).
tff(c_74,plain,
! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_9776,plain,
! [X5_289a: $int] :
( in(5,remove(X5_289a,'#skF_1'))
| ( X5_289a = 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_9406,c_74]) ).
tff(c_64,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_11379,plain,
! [X5_313a: $int] :
( ( count(add(5,remove(X5_313a,'#skF_1'))) = count(remove(X5_313a,'#skF_1')) )
| ( X5_313a = 5 ) ),
inference(resolution,[status(thm)],[c_9776,c_64]) ).
tff(c_54,plain,
in(2,'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_10470,plain,
! [X5_302a: $int] :
( ( add(2,remove(2,remove(X5_302a,'#skF_1'))) = remove(X5_302a,'#skF_1') )
| ( X5_302a = 2 ) ),
inference(resolution,[status(thm)],[c_54,c_9242]) ).
tff(c_10655,plain,
! [X5_303a: $int] :
( in(2,remove(X5_303a,'#skF_1'))
| ( X5_303a = 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_10470,c_74]) ).
tff(c_73,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_78,plain,
! [U_1a: $int] : ~ in(U_1a,empty),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3905,plain,
! [X2_174a: $int,X1_175: collection] : ( count(remove(X2_174a,add(X2_174a,X1_175))) = $sum($uminus(1),count(add(X2_174a,X1_175))) ),
inference(resolution,[status(thm)],[c_74,c_941]) ).
tff(c_67,plain,
! [X7_13: collection] :
( ( empty = X7_13 )
| ( count(X7_13) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_3972,plain,
! [X2_174a: $int,X1_175: collection] :
( ( remove(X2_174a,add(X2_174a,X1_175)) = empty )
| ( $sum($uminus(1),count(add(X2_174a,X1_175))) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_3905,c_67]) ).
tff(c_6464,plain,
! [X2_225a: $int,X1_226: collection] :
( ( remove(X2_225a,add(X2_225a,X1_226)) = empty )
| ( count(add(X2_225a,X1_226)) != 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3972]) ).
tff(c_72,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_6577,plain,
! [X3_9a: $int,X2_225a: $int,X1_226: collection] :
( in(X3_9a,empty)
| ~ in(X3_9a,add(X2_225a,X1_226))
| ( X3_9a = X2_225a )
| ( count(add(X2_225a,X1_226)) != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_6464,c_72]) ).
tff(c_8834,plain,
! [X3_259a: $int,X2_260a: $int,X1_261: collection] :
( ~ in(X3_259a,add(X2_260a,X1_261))
| ( X3_259a = X2_260a )
| ( count(add(X2_260a,X1_261)) != 1 ) ),
inference(negUnitSimplification,[status(thm)],[c_78,c_6577]) ).
tff(c_8949,plain,
! [Z_6a: $int,X2_8a: $int,X1_7: collection] :
( ( Z_6a = X2_8a )
| ( count(add(X2_8a,X1_7)) != 1 )
| ~ in(Z_6a,X1_7) ),
inference(resolution,[status(thm)],[c_73,c_8834]) ).
tff(c_10727,plain,
! [X2_8a: $int,X5_303a: $int] :
( ( X2_8a = 2 )
| ( count(add(X2_8a,remove(X5_303a,'#skF_1'))) != 1 )
| ( X5_303a = 2 ) ),
inference(resolution,[status(thm)],[c_10655,c_8949]) ).
tff(c_11385,plain,
! [X5_313a: $int] :
( ( 5 = 2 )
| ( count(remove(X5_313a,'#skF_1')) != 1 )
| ( X5_313a = 2 )
| ( X5_313a = 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_11379,c_10727]) ).
tff(c_11666,plain,
! [X5_317a: $int] :
( ( count(remove(X5_317a,'#skF_1')) != 1 )
| ( X5_317a = 2 )
| ( X5_317a = 5 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_11385]) ).
tff(c_11732,plain,
( ( 3 = 2 )
| ( 5 = 3 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1070,c_11666]) ).
tff(c_11735,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_11732]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT038_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
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 13:11:49 EDT 2023
% 0.15/0.35 % CPUTime :
% 9.45/3.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.45/3.44
% 9.45/3.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.85/3.47
% 9.85/3.47 Inference rules
% 9.85/3.47 ----------------------
% 9.85/3.47 #Ref : 0
% 9.85/3.47 #Sup : 2338
% 9.85/3.47 #Fact : 2
% 9.85/3.47 #Define : 3
% 9.85/3.47 #Split : 22
% 9.85/3.47 #Chain : 0
% 9.85/3.47 #Close : 0
% 9.85/3.47
% 9.85/3.47 Ordering : LPO
% 9.85/3.47
% 9.85/3.47 Simplification rules
% 9.85/3.47 ----------------------
% 9.85/3.47 #Subsume : 585
% 9.85/3.47 #Demod : 1616
% 9.85/3.47 #Tautology : 1043
% 9.85/3.47 #SimpNegUnit : 38
% 9.85/3.47 #BackRed : 5
% 9.85/3.47
% 9.85/3.47 #Partial instantiations: 0
% 9.85/3.47 #Strategies tried : 1
% 9.85/3.47
% 9.85/3.47 Timing (in seconds)
% 9.85/3.47 ----------------------
% 9.85/3.47 Preprocessing : 0.60
% 9.85/3.47 Parsing : 0.31
% 9.85/3.47 CNF conversion : 0.04
% 9.85/3.47 Main loop : 1.68
% 9.85/3.47 Inferencing : 0.48
% 9.85/3.47 Reduction : 0.51
% 9.85/3.47 Demodulation : 0.37
% 9.85/3.47 BG Simplification : 0.17
% 9.85/3.47 Subsumption : 0.38
% 9.85/3.47 Abstraction : 0.07
% 9.85/3.47 MUC search : 0.00
% 9.85/3.47 Cooper : 0.02
% 9.85/3.47 Total : 2.33
% 9.85/3.47 Index Insertion : 0.00
% 9.85/3.47 Index Deletion : 0.00
% 9.85/3.47 Index Matching : 0.00
% 9.85/3.47 BG Taut test : 0.00
%------------------------------------------------------------------------------