TSTP Solution File: SET015-4 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET015-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n006.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 10:55:32 EDT 2023
% Result : Unsatisfiable 53.47s 39.21s
% Output : CNFRefutation 53.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 70 ( 15 unt; 12 typ; 0 def)
% Number of atoms : 138 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 149 ( 69 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 74 (; 74 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > little_set > union > intersection > f1 > #nlpp > complement > universal_set > empty_set > ds > cs > bs > as
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(ds,type,
ds: $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(bs,type,
bs: $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(little_set,type,
little_set: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(universal_set,type,
universal_set: $i ).
tff(as,type,
as: $i ).
tff(f1,type,
f1: ( $i * $i ) > $i ).
tff(cs,type,
cs: $i ).
tff(f_97,axiom,
cs != ds,
file(unknown,unknown) ).
tff(f_33,axiom,
! [X,Y] :
( little_set(f1(X,Y))
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_94,axiom,
union(as,bs) = cs,
file(unknown,unknown) ).
tff(f_83,axiom,
! [X,Y] : ( union(X,Y) = complement(intersection(complement(X),complement(Y))) ),
file(unknown,unknown) ).
tff(f_80,axiom,
! [Z,X] :
( member(Z,complement(X))
| ~ little_set(Z)
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(f_95,axiom,
union(bs,as) = ds,
file(unknown,unknown) ).
tff(f_53,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [X,Y] :
( ~ member(f1(X,Y),X)
| ~ member(f1(X,Y),Y)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_39,axiom,
! [X,Y] :
( member(f1(X,Y),X)
| member(f1(X,Y),Y)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,X)
| ~ member(Z,Y) ),
file(unknown,unknown) ).
tff(c_30,plain,
ds != cs,
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_4,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| little_set(f1(X_3,Y_4)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_26,plain,
union(as,bs) = cs,
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_59,plain,
! [X_42,Y_43] : ( complement(intersection(complement(X_42),complement(Y_43))) = union(X_42,Y_43) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_18,plain,
! [Z_20,X_21] :
( member(Z_20,X_21)
| ~ little_set(Z_20)
| member(Z_20,complement(X_21)) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_1499,plain,
! [Z_92,X_93,Y_94] :
( member(Z_92,intersection(complement(X_93),complement(Y_94)))
| ~ little_set(Z_92)
| member(Z_92,union(X_93,Y_94)) ),
inference(superposition,[status(thm),theory(equality)],[c_59,c_18]) ).
tff(c_12,plain,
! [Z_12,Y_14,X_13] :
( member(Z_12,Y_14)
| ~ member(Z_12,intersection(X_13,Y_14)) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_1591,plain,
! [Z_95,Y_96,X_97] :
( member(Z_95,complement(Y_96))
| ~ little_set(Z_95)
| member(Z_95,union(X_97,Y_96)) ),
inference(resolution,[status(thm)],[c_1499,c_12]) ).
tff(c_1647,plain,
! [Z_98] :
( member(Z_98,complement(bs))
| ~ little_set(Z_98)
| member(Z_98,cs) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1591]) ).
tff(c_16,plain,
! [Z_18,X_19] :
( ~ member(Z_18,X_19)
| ~ member(Z_18,complement(X_19)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1673,plain,
! [Z_98] :
( ~ member(Z_98,bs)
| ~ little_set(Z_98)
| member(Z_98,cs) ),
inference(resolution,[status(thm)],[c_1647,c_16]) ).
tff(c_28,plain,
union(bs,as) = ds,
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_10,plain,
! [Z_9,X_10,Y_11] :
( member(Z_9,X_10)
| ~ member(Z_9,intersection(X_10,Y_11)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_1751,plain,
! [Z_102,X_103,Y_104] :
( member(Z_102,complement(X_103))
| ~ little_set(Z_102)
| member(Z_102,union(X_103,Y_104)) ),
inference(resolution,[status(thm)],[c_1499,c_10]) ).
tff(c_1860,plain,
! [Z_107] :
( member(Z_107,complement(bs))
| ~ little_set(Z_107)
| member(Z_107,ds) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_1751]) ).
tff(c_1889,plain,
! [Z_108] :
( ~ member(Z_108,bs)
| ~ little_set(Z_108)
| member(Z_108,ds) ),
inference(resolution,[status(thm)],[c_1860,c_16]) ).
tff(c_8,plain,
! [Y_8,X_7] :
( ( Y_8 = X_7 )
| ~ member(f1(X_7,Y_8),Y_8)
| ~ member(f1(X_7,Y_8),X_7) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_221854,plain,
! [X_1531] :
( ( ds = X_1531 )
| ~ member(f1(X_1531,ds),X_1531)
| ~ member(f1(X_1531,ds),bs)
| ~ little_set(f1(X_1531,ds)) ),
inference(resolution,[status(thm)],[c_1889,c_8]) ).
tff(c_222019,plain,
( ( ds = cs )
| ~ member(f1(cs,ds),bs)
| ~ little_set(f1(cs,ds)) ),
inference(resolution,[status(thm)],[c_1673,c_221854]) ).
tff(c_222103,plain,
( ~ member(f1(cs,ds),bs)
| ~ little_set(f1(cs,ds)) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_222019]) ).
tff(c_222113,plain,
~ little_set(f1(cs,ds)),
inference(splitLeft,[status(thm)],[c_222103]) ).
tff(c_222116,plain,
ds = cs,
inference(resolution,[status(thm)],[c_4,c_222113]) ).
tff(c_222120,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_222116]) ).
tff(c_222122,plain,
little_set(f1(cs,ds)),
inference(splitRight,[status(thm)],[c_222103]) ).
tff(c_6,plain,
! [Y_6,X_5] :
( ( Y_6 = X_5 )
| member(f1(X_5,Y_6),Y_6)
| member(f1(X_5,Y_6),X_5) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_1792,plain,
! [Z_102] :
( member(Z_102,complement(as))
| ~ little_set(Z_102)
| member(Z_102,cs) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1751]) ).
tff(c_1632,plain,
! [Z_95] :
( member(Z_95,complement(bs))
| ~ little_set(Z_95)
| member(Z_95,cs) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1591]) ).
tff(c_14,plain,
! [Z_15,Y_17,X_16] :
( ~ member(Z_15,Y_17)
| ~ member(Z_15,X_16)
| member(Z_15,intersection(X_16,Y_17)) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_613,plain,
! [Z_67,X_68,Y_69] :
( ~ member(Z_67,intersection(complement(X_68),complement(Y_69)))
| ~ member(Z_67,union(X_68,Y_69)) ),
inference(superposition,[status(thm),theory(equality)],[c_59,c_16]) ).
tff(c_9380,plain,
! [Z_246,X_247,Y_248] :
( ~ member(Z_246,union(X_247,Y_248))
| ~ member(Z_246,complement(Y_248))
| ~ member(Z_246,complement(X_247)) ),
inference(resolution,[status(thm)],[c_14,c_613]) ).
tff(c_9600,plain,
! [Z_251] :
( ~ member(Z_251,ds)
| ~ member(Z_251,complement(as))
| ~ member(Z_251,complement(bs)) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_9380]) ).
tff(c_10095,plain,
! [Z_260] :
( ~ member(Z_260,ds)
| ~ member(Z_260,complement(as))
| ~ little_set(Z_260)
| member(Z_260,cs) ),
inference(resolution,[status(thm)],[c_1632,c_9600]) ).
tff(c_10179,plain,
! [Z_261] :
( ~ member(Z_261,ds)
| ~ little_set(Z_261)
| member(Z_261,cs) ),
inference(resolution,[status(thm)],[c_1792,c_10095]) ).
tff(c_10260,plain,
! [X_5] :
( ~ little_set(f1(X_5,ds))
| member(f1(X_5,ds),cs)
| ( ds = X_5 )
| member(f1(X_5,ds),X_5) ),
inference(resolution,[status(thm)],[c_6,c_10179]) ).
tff(c_224815,plain,
( ~ little_set(f1(cs,ds))
| ( ds = cs )
| member(f1(cs,ds),cs) ),
inference(factorization,[status(thm),theory(equality)],[c_10260]) ).
tff(c_224818,plain,
( ( ds = cs )
| member(f1(cs,ds),cs) ),
inference(demodulation,[status(thm),theory(equality)],[c_222122,c_224815]) ).
tff(c_224819,plain,
member(f1(cs,ds),cs),
inference(negUnitSimplification,[status(thm)],[c_30,c_224818]) ).
tff(c_1635,plain,
! [Z_95] :
( member(Z_95,complement(as))
| ~ little_set(Z_95)
| member(Z_95,ds) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_1591]) ).
tff(c_1795,plain,
! [Z_102] :
( member(Z_102,complement(bs))
| ~ little_set(Z_102)
| member(Z_102,ds) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_1751]) ).
tff(c_9531,plain,
! [Z_250] :
( ~ member(Z_250,cs)
| ~ member(Z_250,complement(bs))
| ~ member(Z_250,complement(as)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_9380]) ).
tff(c_9929,plain,
! [Z_257] :
( ~ member(Z_257,cs)
| ~ member(Z_257,complement(as))
| ~ little_set(Z_257)
| member(Z_257,ds) ),
inference(resolution,[status(thm)],[c_1795,c_9531]) ).
tff(c_10061,plain,
! [Z_259] :
( ~ member(Z_259,cs)
| ~ little_set(Z_259)
| member(Z_259,ds) ),
inference(resolution,[status(thm)],[c_1635,c_9929]) ).
tff(c_10093,plain,
! [X_7] :
( ( ds = X_7 )
| ~ member(f1(X_7,ds),X_7)
| ~ member(f1(X_7,ds),cs)
| ~ little_set(f1(X_7,ds)) ),
inference(resolution,[status(thm)],[c_10061,c_8]) ).
tff(c_225133,plain,
( ( ds = cs )
| ~ member(f1(cs,ds),cs)
| ~ little_set(f1(cs,ds)) ),
inference(resolution,[status(thm)],[c_224819,c_10093]) ).
tff(c_225146,plain,
ds = cs,
inference(demodulation,[status(thm),theory(equality)],[c_222122,c_224819,c_225133]) ).
tff(c_225148,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_225146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET015-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n006.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 16:42:58 EDT 2023
% 0.15/0.35 % CPUTime :
% 53.47/39.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.54/39.22
% 53.54/39.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.68/39.26
% 53.68/39.26 Inference rules
% 53.68/39.26 ----------------------
% 53.68/39.26 #Ref : 0
% 53.68/39.26 #Sup : 54841
% 53.68/39.26 #Fact : 72
% 53.68/39.26 #Define : 0
% 53.68/39.26 #Split : 129
% 53.68/39.26 #Chain : 0
% 53.68/39.26 #Close : 0
% 53.68/39.26
% 53.68/39.26 Ordering : KBO
% 53.68/39.26
% 53.68/39.26 Simplification rules
% 53.68/39.26 ----------------------
% 53.68/39.26 #Subsume : 22188
% 53.68/39.26 #Demod : 87972
% 53.68/39.26 #Tautology : 11512
% 53.68/39.26 #SimpNegUnit : 1081
% 53.68/39.26 #BackRed : 1418
% 53.68/39.26
% 53.68/39.26 #Partial instantiations: 0
% 53.68/39.26 #Strategies tried : 1
% 53.68/39.26
% 53.68/39.26 Timing (in seconds)
% 53.68/39.26 ----------------------
% 53.68/39.26 Preprocessing : 0.46
% 53.68/39.26 Parsing : 0.24
% 53.68/39.26 CNF conversion : 0.02
% 53.68/39.26 Main loop : 37.69
% 53.68/39.26 Inferencing : 3.90
% 53.68/39.26 Reduction : 21.55
% 53.68/39.26 Demodulation : 19.31
% 53.68/39.26 BG Simplification : 0.31
% 53.68/39.26 Subsumption : 8.89
% 53.68/39.26 Abstraction : 0.68
% 53.68/39.26 MUC search : 0.00
% 53.68/39.26 Cooper : 0.00
% 53.68/39.26 Total : 38.20
% 53.68/39.26 Index Insertion : 0.00
% 53.68/39.26 Index Deletion : 0.00
% 53.68/39.26 Index Matching : 0.00
% 53.68/39.26 BG Taut test : 0.00
%------------------------------------------------------------------------------