TSTP Solution File: SET012-1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET012-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n019.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 10:55:29 EDT 2023
% Result : Unsatisfiable 7.18s 2.65s
% Output : CNFRefutation 7.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 7 unt; 10 typ; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 41 (; 41 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_sets > equal_elements > union > member_of_1_not_of_2 > intersection > #nlpp > complement > empty_set > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(member_of_1_not_of_2,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(a,type,
a: $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(equal_elements,type,
equal_elements: ( $i * $i ) > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(equal_sets,type,
equal_sets: ( $i * $i ) > $o ).
tff(f_72,axiom,
! [X,Xs] :
( member(X,Xs)
| member(X,complement(Xs)) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X,Xs] :
( ~ member(X,Xs)
| ~ member(X,complement(Xs)) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [Subset,Superset] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_134,axiom,
! [Set1,Set2] :
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ),
file(unknown,unknown) ).
tff(f_142,axiom,
! [Xs,Ys] :
( ~ equal_sets(Xs,Ys)
| equal_sets(Ys,Xs) ),
file(unknown,unknown) ).
tff(f_169,axiom,
~ equal_sets(complement(complement(a)),a),
file(unknown,unknown) ).
tff(c_10,plain,
! [X_9,Xs_10] :
( member(X_9,complement(Xs_10))
| member(X_9,Xs_10) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_78,plain,
! [Subset_69,Superset_70] :
( member(member_of_1_not_of_2(Subset_69,Superset_70),Subset_69)
| subset(Subset_69,Superset_70) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_12,plain,
! [X_11,Xs_12] :
( ~ member(X_11,complement(Xs_12))
| ~ member(X_11,Xs_12) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_219,plain,
! [Xs_103,Superset_104] :
( ~ member(member_of_1_not_of_2(complement(Xs_103),Superset_104),Xs_103)
| subset(complement(Xs_103),Superset_104) ),
inference(resolution,[status(thm)],[c_78,c_12]) ).
tff(c_4812,plain,
! [Xs_402,Superset_403] :
( subset(complement(complement(Xs_402)),Superset_403)
| member(member_of_1_not_of_2(complement(complement(Xs_402)),Superset_403),Xs_402) ),
inference(resolution,[status(thm)],[c_10,c_219]) ).
tff(c_8,plain,
! [Subset_7,Superset_8] :
( subset(Subset_7,Superset_8)
| ~ member(member_of_1_not_of_2(Subset_7,Superset_8),Superset_8) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4889,plain,
! [Xs_402] : subset(complement(complement(Xs_402)),Xs_402),
inference(resolution,[status(thm)],[c_4812,c_8]) ).
tff(c_6,plain,
! [Subset_5,Superset_6] :
( member(member_of_1_not_of_2(Subset_5,Superset_6),Subset_5)
| subset(Subset_5,Superset_6) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_67,plain,
! [Subset_67,Superset_68] :
( subset(Subset_67,Superset_68)
| ~ member(member_of_1_not_of_2(Subset_67,Superset_68),Superset_68) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_240,plain,
! [Subset_105,Xs_106] :
( subset(Subset_105,complement(Xs_106))
| member(member_of_1_not_of_2(Subset_105,complement(Xs_106)),Xs_106) ),
inference(resolution,[status(thm)],[c_10,c_67]) ).
tff(c_5071,plain,
! [Subset_422,Xs_423] :
( ~ member(member_of_1_not_of_2(Subset_422,complement(complement(Xs_423))),Xs_423)
| subset(Subset_422,complement(complement(Xs_423))) ),
inference(resolution,[status(thm)],[c_240,c_12]) ).
tff(c_5173,plain,
! [Subset_424] : subset(Subset_424,complement(complement(Subset_424))),
inference(resolution,[status(thm)],[c_6,c_5071]) ).
tff(c_30,plain,
! [Set2_36,Set1_35] :
( equal_sets(Set2_36,Set1_35)
| ~ subset(Set2_36,Set1_35)
| ~ subset(Set1_35,Set2_36) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_5185,plain,
! [Subset_424] :
( equal_sets(Subset_424,complement(complement(Subset_424)))
| ~ subset(complement(complement(Subset_424)),Subset_424) ),
inference(resolution,[status(thm)],[c_5173,c_30]) ).
tff(c_5196,plain,
! [Subset_425] : equal_sets(Subset_425,complement(complement(Subset_425))),
inference(demodulation,[status(thm),theory(equality)],[c_4889,c_5185]) ).
tff(c_34,plain,
! [Ys_39,Xs_38] :
( equal_sets(Ys_39,Xs_38)
| ~ equal_sets(Xs_38,Ys_39) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_5243,plain,
! [Subset_425] : equal_sets(complement(complement(Subset_425)),Subset_425),
inference(resolution,[status(thm)],[c_5196,c_34]) ).
tff(c_44,plain,
~ equal_sets(complement(complement(a)),a),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_5247,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5243,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET012-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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
% 0.13/0.35 % Computer : n019.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 16:44:46 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.18/2.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.18/2.65
% 7.18/2.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.18/2.68
% 7.18/2.68 Inference rules
% 7.18/2.68 ----------------------
% 7.18/2.68 #Ref : 0
% 7.18/2.68 #Sup : 1191
% 7.18/2.68 #Fact : 4
% 7.18/2.68 #Define : 0
% 7.18/2.68 #Split : 6
% 7.18/2.68 #Chain : 0
% 7.18/2.68 #Close : 0
% 7.18/2.68
% 7.18/2.68 Ordering : KBO
% 7.18/2.68
% 7.18/2.68 Simplification rules
% 7.18/2.68 ----------------------
% 7.18/2.68 #Subsume : 168
% 7.18/2.68 #Demod : 274
% 7.18/2.68 #Tautology : 225
% 7.18/2.68 #SimpNegUnit : 33
% 7.18/2.68 #BackRed : 1
% 7.18/2.68
% 7.18/2.68 #Partial instantiations: 0
% 7.18/2.68 #Strategies tried : 1
% 7.18/2.68
% 7.18/2.68 Timing (in seconds)
% 7.18/2.68 ----------------------
% 7.18/2.69 Preprocessing : 0.43
% 7.18/2.69 Parsing : 0.23
% 7.18/2.69 CNF conversion : 0.03
% 7.18/2.69 Main loop : 1.22
% 7.18/2.69 Inferencing : 0.45
% 7.18/2.69 Reduction : 0.35
% 7.18/2.69 Demodulation : 0.25
% 7.18/2.69 BG Simplification : 0.03
% 7.18/2.69 Subsumption : 0.30
% 7.18/2.69 Abstraction : 0.04
% 7.18/2.69 MUC search : 0.00
% 7.18/2.69 Cooper : 0.00
% 7.18/2.69 Total : 1.70
% 7.18/2.69 Index Insertion : 0.00
% 7.18/2.69 Index Deletion : 0.00
% 7.18/2.69 Index Matching : 0.00
% 7.18/2.69 BG Taut test : 0.00
%------------------------------------------------------------------------------