TSTP Solution File: SET009-1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET009-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n024.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 15.50s 5.89s
% Output : CNFRefutation 15.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 59 ( 13 unt; 11 typ; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 105 ( 48 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 6 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 78 (; 78 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ difference > subset > member > equal_sets > k > member_of_1_not_of_2 > #nlpp > d > bDd > bDa > b > 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(bDd,type,
bDd: $i ).
tff(k,type,
k: ( $i * $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(difference,type,
difference: ( $i * $i * $i ) > $o ).
tff(equal_sets,type,
equal_sets: ( $i * $i ) > $o ).
tff(d,type,
d: $i ).
tff(bDa,type,
bDa: $i ).
tff(f_158,axiom,
~ subset(bDa,bDd),
file(unknown,unknown) ).
tff(f_56,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [Subset,Superset] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [Set1,Set2] :
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ),
file(unknown,unknown) ).
tff(f_155,axiom,
difference(b,a,bDa),
file(unknown,unknown) ).
tff(f_109,axiom,
! [Set1,Set2,Difference,Element] :
( ~ difference(Set1,Set2,Difference)
| ~ member(Element,Difference)
| member(Element,Set1) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [Subset,Superset] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [Element,Subset,Superset] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) ),
file(unknown,unknown) ).
tff(f_156,axiom,
difference(b,d,bDd),
file(unknown,unknown) ).
tff(f_128,axiom,
! [Element,Set1,Set2,Difference] :
( ~ member(Element,Set1)
| ~ difference(Set1,Set2,Difference)
| member(Element,Difference)
| member(Element,Set2) ),
file(unknown,unknown) ).
tff(f_154,axiom,
subset(d,a),
file(unknown,unknown) ).
tff(f_71,axiom,
! [Superset,Subset] :
( ~ equal_sets(Superset,Subset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_118,axiom,
! [Element,Set1,Set2,A_set] :
( ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ difference(A_set,Set1,Set2) ),
file(unknown,unknown) ).
tff(c_32,plain,
~ subset(bDa,bDd),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_44,plain,
! [Subset_41,Superset_42] :
( member(member_of_1_not_of_2(Subset_41,Superset_42),Subset_41)
| subset(Subset_41,Superset_42) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_6,plain,
! [Subset_6,Superset_7] :
( subset(Subset_6,Superset_7)
| ~ member(member_of_1_not_of_2(Subset_6,Superset_7),Superset_7) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_49,plain,
! [Subset_41] : subset(Subset_41,Subset_41),
inference(resolution,[status(thm)],[c_44,c_6]) ).
tff(c_77,plain,
! [Set2_49,Set1_50] :
( equal_sets(Set2_49,Set1_50)
| ~ subset(Set2_49,Set1_50)
| ~ subset(Set1_50,Set2_49) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_79,plain,
! [Subset_41] :
( equal_sets(Subset_41,Subset_41)
| ~ subset(Subset_41,Subset_41) ),
inference(resolution,[status(thm)],[c_49,c_77]) ).
tff(c_88,plain,
! [Subset_41] : equal_sets(Subset_41,Subset_41),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_79]) ).
tff(c_28,plain,
difference(b,a,bDa),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_4,plain,
! [Subset_4,Superset_5] :
( member(member_of_1_not_of_2(Subset_4,Superset_5),Subset_4)
| subset(Subset_4,Superset_5) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_92,plain,
! [Element_51,Set1_52,Difference_53,Set2_54] :
( member(Element_51,Set1_52)
| ~ member(Element_51,Difference_53)
| ~ difference(Set1_52,Set2_54,Difference_53) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_446,plain,
! [Subset_99,Superset_100,Set1_101,Set2_102] :
( member(member_of_1_not_of_2(Subset_99,Superset_100),Set1_101)
| ~ difference(Set1_101,Set2_102,Subset_99)
| subset(Subset_99,Superset_100) ),
inference(resolution,[status(thm)],[c_4,c_92]) ).
tff(c_453,plain,
! [Superset_103] :
( member(member_of_1_not_of_2(bDa,Superset_103),b)
| subset(bDa,Superset_103) ),
inference(resolution,[status(thm)],[c_28,c_446]) ).
tff(c_8,plain,
! [Subset_8,Superset_9] :
( subset(Subset_8,Superset_9)
| ~ equal_sets(Subset_8,Superset_9) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_51,plain,
! [Element_44,Superset_45,Subset_46] :
( member(Element_44,Superset_45)
| ~ subset(Subset_46,Superset_45)
| ~ member(Element_44,Subset_46) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_61,plain,
! [Element_44,Superset_9,Subset_8] :
( member(Element_44,Superset_9)
| ~ member(Element_44,Subset_8)
| ~ equal_sets(Subset_8,Superset_9) ),
inference(resolution,[status(thm)],[c_8,c_51]) ).
tff(c_464,plain,
! [Superset_103,Superset_9] :
( member(member_of_1_not_of_2(bDa,Superset_103),Superset_9)
| ~ equal_sets(b,Superset_9)
| subset(bDa,Superset_103) ),
inference(resolution,[status(thm)],[c_453,c_61]) ).
tff(c_30,plain,
difference(b,d,bDd),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_129,plain,
! [Element_63,Set2_64,Difference_65,Set1_66] :
( member(Element_63,Set2_64)
| member(Element_63,Difference_65)
| ~ difference(Set1_66,Set2_64,Difference_65)
| ~ member(Element_63,Set1_66) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_137,plain,
! [Element_68] :
( member(Element_68,d)
| member(Element_68,bDd)
| ~ member(Element_68,b) ),
inference(resolution,[status(thm)],[c_30,c_129]) ).
tff(c_26,plain,
subset(d,a),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_63,plain,
! [Element_44] :
( member(Element_44,a)
| ~ member(Element_44,d) ),
inference(resolution,[status(thm)],[c_26,c_51]) ).
tff(c_281,plain,
! [Element_83] :
( member(Element_83,a)
| member(Element_83,bDd)
| ~ member(Element_83,b) ),
inference(resolution,[status(thm)],[c_137,c_63]) ).
tff(c_39529,plain,
! [Subset_682] :
( subset(Subset_682,bDd)
| member(member_of_1_not_of_2(Subset_682,bDd),a)
| ~ member(member_of_1_not_of_2(Subset_682,bDd),b) ),
inference(resolution,[status(thm)],[c_281,c_6]) ).
tff(c_39565,plain,
( member(member_of_1_not_of_2(bDa,bDd),a)
| ~ equal_sets(b,b)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[c_464,c_39529]) ).
tff(c_39614,plain,
( member(member_of_1_not_of_2(bDa,bDd),a)
| subset(bDa,bDd) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_39565]) ).
tff(c_39615,plain,
member(member_of_1_not_of_2(bDa,bDd),a),
inference(negUnitSimplification,[status(thm)],[c_32,c_39614]) ).
tff(c_10,plain,
! [Subset_11,Superset_10] :
( subset(Subset_11,Superset_10)
| ~ equal_sets(Superset_10,Subset_11) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_230,plain,
! [Element_76,Superset_77,Subset_78] :
( member(Element_76,Superset_77)
| ~ member(Element_76,Subset_78)
| ~ equal_sets(Superset_77,Subset_78) ),
inference(resolution,[status(thm)],[c_10,c_51]) ).
tff(c_656,plain,
! [Subset_122,Superset_123,Superset_124] :
( member(member_of_1_not_of_2(Subset_122,Superset_123),Superset_124)
| ~ equal_sets(Superset_124,Subset_122)
| subset(Subset_122,Superset_123) ),
inference(resolution,[status(thm)],[c_4,c_230]) ).
tff(c_109,plain,
! [A_set_56,Set1_57,Set2_58,Element_59] :
( ~ difference(A_set_56,Set1_57,Set2_58)
| ~ member(Element_59,Set2_58)
| ~ member(Element_59,Set1_57) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_114,plain,
! [Element_59] :
( ~ member(Element_59,bDa)
| ~ member(Element_59,a) ),
inference(resolution,[status(thm)],[c_28,c_109]) ).
tff(c_701,plain,
! [Subset_122,Superset_123] :
( ~ member(member_of_1_not_of_2(Subset_122,Superset_123),a)
| ~ equal_sets(bDa,Subset_122)
| subset(Subset_122,Superset_123) ),
inference(resolution,[status(thm)],[c_656,c_114]) ).
tff(c_39680,plain,
( ~ equal_sets(bDa,bDa)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[c_39615,c_701]) ).
tff(c_39734,plain,
subset(bDa,bDd),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_39680]) ).
tff(c_39736,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_39734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.14 % 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
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 16:27:30 EDT 2023
% 0.14/0.36 % CPUTime :
% 15.50/5.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.54/5.90
% 15.54/5.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.61/5.94
% 15.61/5.94 Inference rules
% 15.61/5.94 ----------------------
% 15.61/5.94 #Ref : 0
% 15.61/5.94 #Sup : 9266
% 15.61/5.94 #Fact : 30
% 15.61/5.94 #Define : 0
% 15.61/5.94 #Split : 27
% 15.61/5.94 #Chain : 0
% 15.61/5.94 #Close : 0
% 15.61/5.94
% 15.61/5.94 Ordering : KBO
% 15.61/5.94
% 15.61/5.94 Simplification rules
% 15.61/5.94 ----------------------
% 15.61/5.94 #Subsume : 5653
% 15.61/5.94 #Demod : 2235
% 15.61/5.94 #Tautology : 627
% 15.61/5.94 #SimpNegUnit : 672
% 15.61/5.94 #BackRed : 8
% 15.61/5.94
% 15.61/5.94 #Partial instantiations: 0
% 15.61/5.94 #Strategies tried : 1
% 15.61/5.94
% 15.61/5.94 Timing (in seconds)
% 15.61/5.94 ----------------------
% 15.61/5.94 Preprocessing : 0.48
% 15.61/5.94 Parsing : 0.27
% 15.61/5.94 CNF conversion : 0.02
% 15.61/5.94 Main loop : 4.27
% 15.61/5.94 Inferencing : 1.08
% 15.61/5.94 Reduction : 1.16
% 15.61/5.94 Demodulation : 0.71
% 15.61/5.94 BG Simplification : 0.06
% 15.61/5.94 Subsumption : 1.68
% 15.61/5.94 Abstraction : 0.09
% 15.61/5.94 MUC search : 0.00
% 15.61/5.94 Cooper : 0.00
% 15.61/5.94 Total : 4.81
% 15.61/5.94 Index Insertion : 0.00
% 15.61/5.94 Index Deletion : 0.00
% 15.61/5.94 Index Matching : 0.00
% 15.61/5.94 BG Taut test : 0.00
%------------------------------------------------------------------------------