TSTP Solution File: SET012-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET012-2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n031.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 10:55:30 EDT 2023
% Result : Unsatisfiable 44.11s 32.95s
% Output : CNFRefutation 44.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 28
% Syntax : Number of formulae : 97 ( 23 unt; 12 typ; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 145 ( 65 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 129 (; 129 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_sets > equal_elements > union > member_of_1_not_of_2 > intersection > #nlpp > complement > empty_set > c > 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(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(b,type,
b: $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(c,type,
c: $i ).
tff(f_170,axiom,
~ equal_sets(a,c),
file(unknown,unknown) ).
tff(f_61,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Xs] :
( member(X,Xs)
| member(X,complement(Xs)) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [X,Xs] :
( ~ member(X,Xs)
| ~ member(X,complement(Xs)) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [Subset,Superset] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_133,axiom,
! [Set1,Set2] :
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ),
file(unknown,unknown) ).
tff(f_141,axiom,
! [Xs,Ys] :
( ~ equal_sets(Xs,Ys)
| equal_sets(Ys,Xs) ),
file(unknown,unknown) ).
tff(f_167,axiom,
equal_sets(complement(a),b),
file(unknown,unknown) ).
tff(f_149,axiom,
! [Xs,Ys,Zs] :
( ~ equal_sets(Xs,Ys)
| ~ equal_sets(Ys,Zs)
| equal_sets(Xs,Zs) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [Subset,Superset] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [Element,Subset,Superset] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) ),
file(unknown,unknown) ).
tff(f_168,axiom,
equal_sets(complement(b),c),
file(unknown,unknown) ).
tff(f_125,axiom,
! [Superset,Subset] :
( ~ equal_sets(Superset,Subset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_136,axiom,
! [Xs] : equal_sets(Xs,Xs),
file(unknown,unknown) ).
tff(f_88,axiom,
! [X,Ys,Xs] :
( ~ member(X,Ys)
| member(X,union(Xs,Ys)) ),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Xs,Ys] :
( ~ member(X,union(Xs,Ys))
| member(X,Xs)
| member(X,Ys) ),
file(unknown,unknown) ).
tff(c_48,plain,
~ equal_sets(a,c),
inference(cnfTransformation,[status(thm)],[f_170]) ).
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_61]) ).
tff(c_10,plain,
! [X_9,Xs_10] :
( member(X_9,complement(Xs_10))
| member(X_9,Xs_10) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_96,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_61]) ).
tff(c_12,plain,
! [X_11,Xs_12] :
( ~ member(X_11,complement(Xs_12))
| ~ member(X_11,Xs_12) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_557,plain,
! [Xs_125,Superset_126] :
( ~ member(member_of_1_not_of_2(complement(Xs_125),Superset_126),Xs_125)
| subset(complement(Xs_125),Superset_126) ),
inference(resolution,[status(thm)],[c_96,c_12]) ).
tff(c_4899,plain,
! [Xs_364,Superset_365] :
( subset(complement(complement(Xs_364)),Superset_365)
| member(member_of_1_not_of_2(complement(complement(Xs_364)),Superset_365),Xs_364) ),
inference(resolution,[status(thm)],[c_10,c_557]) ).
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_66]) ).
tff(c_4983,plain,
! [Xs_364] : subset(complement(complement(Xs_364)),Xs_364),
inference(resolution,[status(thm)],[c_4899,c_8]) ).
tff(c_85,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_66]) ).
tff(c_337,plain,
! [Subset_109,Xs_110] :
( subset(Subset_109,complement(Xs_110))
| member(member_of_1_not_of_2(Subset_109,complement(Xs_110)),Xs_110) ),
inference(resolution,[status(thm)],[c_10,c_85]) ).
tff(c_6278,plain,
! [Subset_411,Xs_412] :
( ~ member(member_of_1_not_of_2(Subset_411,complement(complement(Xs_412))),Xs_412)
| subset(Subset_411,complement(complement(Xs_412))) ),
inference(resolution,[status(thm)],[c_337,c_12]) ).
tff(c_6435,plain,
! [Subset_413] : subset(Subset_413,complement(complement(Subset_413))),
inference(resolution,[status(thm)],[c_6,c_6278]) ).
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_133]) ).
tff(c_6449,plain,
! [Subset_413] :
( equal_sets(Subset_413,complement(complement(Subset_413)))
| ~ subset(complement(complement(Subset_413)),Subset_413) ),
inference(resolution,[status(thm)],[c_6435,c_30]) ).
tff(c_6458,plain,
! [Subset_414] : equal_sets(Subset_414,complement(complement(Subset_414))),
inference(demodulation,[status(thm),theory(equality)],[c_4983,c_6449]) ).
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_141]) ).
tff(c_6492,plain,
! [Subset_414] : equal_sets(complement(complement(Subset_414)),Subset_414),
inference(resolution,[status(thm)],[c_6458,c_34]) ).
tff(c_44,plain,
equal_sets(complement(a),b),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_57,plain,
! [Ys_54,Xs_55] :
( equal_sets(Ys_54,Xs_55)
| ~ equal_sets(Xs_55,Ys_54) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_64,plain,
equal_sets(b,complement(a)),
inference(resolution,[status(thm)],[c_44,c_57]) ).
tff(c_132,plain,
! [Xs_82,Zs_83,Ys_84] :
( equal_sets(Xs_82,Zs_83)
| ~ equal_sets(Ys_84,Zs_83)
| ~ equal_sets(Xs_82,Ys_84) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_144,plain,
! [Xs_82] :
( equal_sets(Xs_82,complement(a))
| ~ equal_sets(Xs_82,b) ),
inference(resolution,[status(thm)],[c_64,c_132]) ).
tff(c_26,plain,
! [Subset_31,Superset_32] :
( subset(Subset_31,Superset_32)
| ~ equal_sets(Subset_31,Superset_32) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_279,plain,
! [Element_97,Superset_98,Subset_99] :
( member(Element_97,Superset_98)
| ~ subset(Subset_99,Superset_98)
| ~ member(Element_97,Subset_99) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_324,plain,
! [Element_106,Superset_107,Subset_108] :
( member(Element_106,Superset_107)
| ~ member(Element_106,Subset_108)
| ~ equal_sets(Subset_108,Superset_107) ),
inference(resolution,[status(thm)],[c_26,c_279]) ).
tff(c_1862,plain,
! [X_238,Superset_239,Xs_240] :
( member(X_238,Superset_239)
| ~ equal_sets(complement(Xs_240),Superset_239)
| member(X_238,Xs_240) ),
inference(resolution,[status(thm)],[c_10,c_324]) ).
tff(c_87574,plain,
! [X_2433,Xs_2434] :
( member(X_2433,complement(a))
| member(X_2433,Xs_2434)
| ~ equal_sets(complement(Xs_2434),b) ),
inference(resolution,[status(thm)],[c_144,c_1862]) ).
tff(c_87638,plain,
! [X_2435] :
( member(X_2435,complement(a))
| member(X_2435,complement(b)) ),
inference(resolution,[status(thm)],[c_6492,c_87574]) ).
tff(c_46,plain,
equal_sets(complement(b),c),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_65,plain,
equal_sets(c,complement(b)),
inference(resolution,[status(thm)],[c_46,c_57]) ).
tff(c_28,plain,
! [Subset_34,Superset_33] :
( subset(Subset_34,Superset_33)
| ~ equal_sets(Superset_33,Subset_34) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_297,plain,
! [Element_100,Superset_101,Subset_102] :
( member(Element_100,Superset_101)
| ~ member(Element_100,Subset_102)
| ~ equal_sets(Superset_101,Subset_102) ),
inference(resolution,[status(thm)],[c_28,c_279]) ).
tff(c_1667,plain,
! [X_230,Superset_231,Xs_232] :
( member(X_230,Superset_231)
| ~ equal_sets(Superset_231,complement(Xs_232))
| member(X_230,Xs_232) ),
inference(resolution,[status(thm)],[c_10,c_297]) ).
tff(c_1745,plain,
! [X_234] :
( member(X_234,c)
| member(X_234,b) ),
inference(resolution,[status(thm)],[c_65,c_1667]) ).
tff(c_1807,plain,
! [Subset_236] :
( subset(Subset_236,c)
| member(member_of_1_not_of_2(Subset_236,c),b) ),
inference(resolution,[status(thm)],[c_1745,c_8]) ).
tff(c_110,plain,
! [Xs_12,Superset_70] :
( ~ member(member_of_1_not_of_2(complement(Xs_12),Superset_70),Xs_12)
| subset(complement(Xs_12),Superset_70) ),
inference(resolution,[status(thm)],[c_96,c_12]) ).
tff(c_1816,plain,
subset(complement(b),c),
inference(resolution,[status(thm)],[c_1807,c_110]) ).
tff(c_4,plain,
! [Element_2,Superset_4,Subset_3] :
( member(Element_2,Superset_4)
| ~ subset(Subset_3,Superset_4)
| ~ member(Element_2,Subset_3) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1823,plain,
! [Element_2] :
( member(Element_2,c)
| ~ member(Element_2,complement(b)) ),
inference(resolution,[status(thm)],[c_1816,c_4]) ).
tff(c_87807,plain,
! [X_2436] :
( member(X_2436,c)
| member(X_2436,complement(a)) ),
inference(resolution,[status(thm)],[c_87638,c_1823]) ).
tff(c_87976,plain,
! [X_2437] :
( ~ member(X_2437,a)
| member(X_2437,c) ),
inference(resolution,[status(thm)],[c_87807,c_12]) ).
tff(c_88734,plain,
! [Subset_2446] :
( subset(Subset_2446,c)
| ~ member(member_of_1_not_of_2(Subset_2446,c),a) ),
inference(resolution,[status(thm)],[c_87976,c_8]) ).
tff(c_88981,plain,
subset(a,c),
inference(resolution,[status(thm)],[c_6,c_88734]) ).
tff(c_88991,plain,
( equal_sets(a,c)
| ~ subset(c,a) ),
inference(resolution,[status(thm)],[c_88981,c_30]) ).
tff(c_88997,plain,
~ subset(c,a),
inference(negUnitSimplification,[status(thm)],[c_48,c_88991]) ).
tff(c_1731,plain,
! [X_230] :
( member(X_230,b)
| member(X_230,a) ),
inference(resolution,[status(thm)],[c_64,c_1667]) ).
tff(c_32,plain,
! [Xs_37] : equal_sets(Xs_37,Xs_37),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_16,plain,
! [X_16,Xs_18,Ys_17] :
( member(X_16,union(Xs_18,Ys_17))
| ~ member(X_16,Ys_17) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_872,plain,
! [Subset_151,Xs_152,Ys_153] :
( subset(Subset_151,union(Xs_152,Ys_153))
| ~ member(member_of_1_not_of_2(Subset_151,union(Xs_152,Ys_153)),Ys_153) ),
inference(resolution,[status(thm)],[c_16,c_85]) ).
tff(c_905,plain,
! [Subset_5,Xs_152] : subset(Subset_5,union(Xs_152,Subset_5)),
inference(resolution,[status(thm)],[c_6,c_872]) ).
tff(c_310,plain,
! [X_103,Ys_104,Xs_105] :
( member(X_103,Ys_104)
| member(X_103,Xs_105)
| ~ member(X_103,union(Xs_105,Ys_104)) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_1313,plain,
! [Xs_203,Ys_204,Superset_205] :
( member(member_of_1_not_of_2(union(Xs_203,Ys_204),Superset_205),Ys_204)
| member(member_of_1_not_of_2(union(Xs_203,Ys_204),Superset_205),Xs_203)
| subset(union(Xs_203,Ys_204),Superset_205) ),
inference(resolution,[status(thm)],[c_6,c_310]) ).
tff(c_1414,plain,
! [Xs_203,Ys_204] :
( member(member_of_1_not_of_2(union(Xs_203,Ys_204),Ys_204),Xs_203)
| subset(union(Xs_203,Ys_204),Ys_204) ),
inference(resolution,[status(thm)],[c_1313,c_8]) ).
tff(c_88972,plain,
subset(union(a,c),c),
inference(resolution,[status(thm)],[c_1414,c_88734]) ).
tff(c_89464,plain,
( equal_sets(union(a,c),c)
| ~ subset(c,union(a,c)) ),
inference(resolution,[status(thm)],[c_88972,c_30]) ).
tff(c_89471,plain,
equal_sets(union(a,c),c),
inference(demodulation,[status(thm),theory(equality)],[c_905,c_89464]) ).
tff(c_221,plain,
! [Xs_91] :
( equal_sets(Xs_91,complement(b))
| ~ equal_sets(Xs_91,c) ),
inference(resolution,[status(thm)],[c_65,c_132]) ).
tff(c_36,plain,
! [Xs_40,Zs_42,Ys_41] :
( equal_sets(Xs_40,Zs_42)
| ~ equal_sets(Ys_41,Zs_42)
| ~ equal_sets(Xs_40,Ys_41) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_230,plain,
! [Xs_40,Xs_91] :
( equal_sets(Xs_40,complement(b))
| ~ equal_sets(Xs_40,Xs_91)
| ~ equal_sets(Xs_91,c) ),
inference(resolution,[status(thm)],[c_221,c_36]) ).
tff(c_89622,plain,
( equal_sets(union(a,c),complement(b))
| ~ equal_sets(c,c) ),
inference(resolution,[status(thm)],[c_89471,c_230]) ).
tff(c_89635,plain,
equal_sets(union(a,c),complement(b)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_89622]) ).
tff(c_335,plain,
! [X_16,Superset_107,Xs_18,Ys_17] :
( member(X_16,Superset_107)
| ~ equal_sets(union(Xs_18,Ys_17),Superset_107)
| ~ member(X_16,Ys_17) ),
inference(resolution,[status(thm)],[c_16,c_324]) ).
tff(c_90864,plain,
! [X_2484] :
( member(X_2484,complement(b))
| ~ member(X_2484,c) ),
inference(resolution,[status(thm)],[c_89635,c_335]) ).
tff(c_91048,plain,
! [X_2488] :
( ~ member(X_2488,b)
| ~ member(X_2488,c) ),
inference(resolution,[status(thm)],[c_90864,c_12]) ).
tff(c_96940,plain,
! [Superset_2559] :
( ~ member(member_of_1_not_of_2(c,Superset_2559),b)
| subset(c,Superset_2559) ),
inference(resolution,[status(thm)],[c_6,c_91048]) ).
tff(c_97373,plain,
! [Superset_2576] :
( subset(c,Superset_2576)
| member(member_of_1_not_of_2(c,Superset_2576),a) ),
inference(resolution,[status(thm)],[c_1731,c_96940]) ).
tff(c_97454,plain,
subset(c,a),
inference(resolution,[status(thm)],[c_97373,c_8]) ).
tff(c_97484,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_88997,c_88997,c_97454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SET012-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.09/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.36 % Computer : n031.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu Aug 3 17:23:14 EDT 2023
% 0.16/0.36 % CPUTime :
% 44.11/32.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.11/32.96
% 44.11/32.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 44.17/33.01
% 44.17/33.01 Inference rules
% 44.17/33.01 ----------------------
% 44.17/33.01 #Ref : 0
% 44.17/33.01 #Sup : 21636
% 44.17/33.01 #Fact : 46
% 44.17/33.01 #Define : 0
% 44.17/33.01 #Split : 42
% 44.17/33.01 #Chain : 0
% 44.17/33.01 #Close : 0
% 44.17/33.01
% 44.17/33.01 Ordering : KBO
% 44.17/33.01
% 44.17/33.01 Simplification rules
% 44.17/33.01 ----------------------
% 44.17/33.01 #Subsume : 5645
% 44.17/33.01 #Demod : 3438
% 44.17/33.01 #Tautology : 2590
% 44.17/33.01 #SimpNegUnit : 682
% 44.17/33.01 #BackRed : 0
% 44.17/33.01
% 44.17/33.01 #Partial instantiations: 0
% 44.17/33.01 #Strategies tried : 1
% 44.17/33.01
% 44.17/33.01 Timing (in seconds)
% 44.17/33.01 ----------------------
% 44.17/33.01 Preprocessing : 0.46
% 44.17/33.01 Parsing : 0.25
% 44.17/33.01 CNF conversion : 0.03
% 44.17/33.01 Main loop : 31.46
% 44.17/33.01 Inferencing : 4.40
% 44.17/33.01 Reduction : 15.07
% 44.17/33.02 Demodulation : 11.47
% 44.17/33.02 BG Simplification : 0.11
% 44.17/33.02 Subsumption : 9.76
% 44.17/33.02 Abstraction : 0.18
% 44.17/33.02 MUC search : 0.00
% 44.17/33.02 Cooper : 0.00
% 44.17/33.02 Total : 31.99
% 44.17/33.02 Index Insertion : 0.00
% 44.17/33.02 Index Deletion : 0.00
% 44.17/33.02 Index Matching : 0.00
% 44.17/33.02 BG Taut test : 0.00
%------------------------------------------------------------------------------