TSTP Solution File: SET014+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n025.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 10:55:31 EDT 2023
% Result : Theorem 130.52s 100.91s
% Output : CNFRefutation 130.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 130 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 122 ( 47 ~; 68 |; 1 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 125 (; 125 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > #nlpp > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_64,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(D,C) )
=> subset(union(B,D),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_subset) ).
tff(f_42,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_34,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
tff(f_56,axiom,
! [B,C] :
( ( B = C )
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
tff(f_45,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(c_30,plain,
~ subset(union('#skF_4','#skF_6'),'#skF_5'),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_34,plain,
subset('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_12,plain,
! [B_4,C_5] :
( member('#skF_1'(B_4,C_5),B_4)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_6,plain,
! [D_3,B_1,C_2] :
( ~ member(D_3,B_1)
| member(D_3,union(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_77,plain,
! [B_25,C_26] :
( ~ member('#skF_1'(B_25,C_26),C_26)
| subset(B_25,C_26) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_262,plain,
! [B_58,B_59,C_60] :
( subset(B_58,union(B_59,C_60))
| ~ member('#skF_1'(B_58,union(B_59,C_60)),B_59) ),
inference(resolution,[status(thm)],[c_6,c_77]) ).
tff(c_288,plain,
! [B_4,C_60] : subset(B_4,union(B_4,C_60)),
inference(resolution,[status(thm)],[c_12,c_262]) ).
tff(c_111,plain,
! [D_33,C_34,B_35] :
( member(D_33,C_34)
| member(D_33,B_35)
| ~ member(D_33,union(B_35,C_34)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_1909,plain,
! [B_181,C_182,C_183] :
( member('#skF_1'(union(B_181,C_182),C_183),C_182)
| member('#skF_1'(union(B_181,C_182),C_183),B_181)
| subset(union(B_181,C_182),C_183) ),
inference(resolution,[status(thm)],[c_12,c_111]) ).
tff(c_8,plain,
! [D_8,C_5,B_4] :
( member(D_8,C_5)
| ~ member(D_8,B_4)
| ~ subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_20908,plain,
! [B_868,C_869,C_870,C_871] :
( member('#skF_1'(union(B_868,C_869),C_870),C_871)
| ~ subset(C_869,C_871)
| member('#skF_1'(union(B_868,C_869),C_870),B_868)
| subset(union(B_868,C_869),C_870) ),
inference(resolution,[status(thm)],[c_1909,c_8]) ).
tff(c_10,plain,
! [B_4,C_5] :
( ~ member('#skF_1'(B_4,C_5),C_5)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_75348,plain,
! [B_1777,C_1778,C_1779] :
( member('#skF_1'(union(B_1777,C_1778),B_1777),C_1779)
| ~ subset(C_1778,C_1779)
| subset(union(B_1777,C_1778),B_1777) ),
inference(resolution,[status(thm)],[c_20908,c_10]) ).
tff(c_75507,plain,
! [C_1778,C_1779] :
( ~ subset(C_1778,C_1779)
| subset(union(C_1779,C_1778),C_1779) ),
inference(resolution,[status(thm)],[c_75348,c_10]) ).
tff(c_208,plain,
! [B_54,C_55] :
( member('#skF_2'(B_54,C_55),C_55)
| member('#skF_3'(B_54,C_55),B_54)
| ( C_55 = B_54 ) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_606,plain,
! [B_93,C_94,C_95] :
( member('#skF_3'(B_93,C_94),C_95)
| ~ subset(B_93,C_95)
| member('#skF_2'(B_93,C_94),C_94)
| ( C_94 = B_93 ) ),
inference(resolution,[status(thm)],[c_208,c_8]) ).
tff(c_6015,plain,
! [B_378,C_379,C_380,C_381] :
( member('#skF_2'(B_378,C_379),C_380)
| ~ subset(C_379,C_380)
| member('#skF_3'(B_378,C_379),C_381)
| ~ subset(B_378,C_381)
| ( C_379 = B_378 ) ),
inference(resolution,[status(thm)],[c_606,c_8]) ).
tff(c_242,plain,
! [B_56,C_57] :
( ~ member('#skF_2'(B_56,C_57),B_56)
| member('#skF_3'(B_56,C_57),B_56)
| ( C_57 = B_56 ) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_261,plain,
! [B_56,C_57,C_5] :
( member('#skF_3'(B_56,C_57),C_5)
| ~ subset(B_56,C_5)
| ~ member('#skF_2'(B_56,C_57),B_56)
| ( C_57 = B_56 ) ),
inference(resolution,[status(thm)],[c_242,c_8]) ).
tff(c_6088,plain,
! [C_380,C_379,C_5,C_381] :
( member('#skF_3'(C_380,C_379),C_5)
| ~ subset(C_380,C_5)
| ~ subset(C_379,C_380)
| member('#skF_3'(C_380,C_379),C_381)
| ~ subset(C_380,C_381)
| ( C_380 = C_379 ) ),
inference(resolution,[status(thm)],[c_6015,c_261]) ).
tff(c_308089,plain,
! [C_3807,C_3808,C_3809] :
( ~ subset(C_3807,C_3808)
| ~ subset(C_3808,C_3809)
| ( C_3808 = C_3807 )
| member('#skF_3'(C_3808,C_3807),C_3809) ),
inference(factorization,[status(thm),theory(equality)],[c_6088]) ).
tff(c_24,plain,
! [B_12,C_13] :
( member('#skF_2'(B_12,C_13),C_13)
| ~ member('#skF_3'(B_12,C_13),C_13)
| ( C_13 = B_12 ) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_647,plain,
! [B_96,C_97] :
( ~ subset(B_96,C_97)
| member('#skF_2'(B_96,C_97),C_97)
| ( C_97 = B_96 ) ),
inference(resolution,[status(thm)],[c_606,c_24]) ).
tff(c_953,plain,
! [B_122,C_123,C_124] :
( member('#skF_2'(B_122,C_123),C_124)
| ~ subset(C_123,C_124)
| ~ subset(B_122,C_123)
| ( C_123 = B_122 ) ),
inference(resolution,[status(thm)],[c_647,c_8]) ).
tff(c_22,plain,
! [B_12,C_13] :
( ~ member('#skF_2'(B_12,C_13),B_12)
| ~ member('#skF_3'(B_12,C_13),C_13)
| ( C_13 = B_12 ) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_980,plain,
! [C_124,C_123] :
( ~ member('#skF_3'(C_124,C_123),C_123)
| ~ subset(C_123,C_124)
| ~ subset(C_124,C_123)
| ( C_124 = C_123 ) ),
inference(resolution,[status(thm)],[c_953,c_22]) ).
tff(c_308352,plain,
! [C_3810,C_3811] :
( ~ subset(C_3810,C_3811)
| ~ subset(C_3811,C_3810)
| ( C_3811 = C_3810 ) ),
inference(resolution,[status(thm)],[c_308089,c_980]) ).
tff(c_308948,plain,
! [C_1779,C_1778] :
( ~ subset(C_1779,union(C_1779,C_1778))
| ( union(C_1779,C_1778) = C_1779 )
| ~ subset(C_1778,C_1779) ),
inference(resolution,[status(thm)],[c_75507,c_308352]) ).
tff(c_320637,plain,
! [C_3819,C_3820] :
( ( union(C_3819,C_3820) = C_3819 )
| ~ subset(C_3820,C_3819) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_308948]) ).
tff(c_322511,plain,
union('#skF_5','#skF_4') = '#skF_5',
inference(resolution,[status(thm)],[c_34,c_320637]) ).
tff(c_32,plain,
subset('#skF_6','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_89,plain,
! [D_27,C_28,B_29] :
( ~ member(D_27,C_28)
| member(D_27,union(B_29,C_28)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_289,plain,
! [B_61,B_62,C_63] :
( subset(B_61,union(B_62,C_63))
| ~ member('#skF_1'(B_61,union(B_62,C_63)),C_63) ),
inference(resolution,[status(thm)],[c_89,c_10]) ).
tff(c_315,plain,
! [B_4,B_62] : subset(B_4,union(B_62,B_4)),
inference(resolution,[status(thm)],[c_12,c_289]) ).
tff(c_14,plain,
! [C_10,B_9] : ( union(C_10,B_9) = union(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_75509,plain,
! [C_1780,C_1781] :
( ~ subset(C_1780,C_1781)
| subset(union(C_1781,C_1780),C_1781) ),
inference(resolution,[status(thm)],[c_75348,c_10]) ).
tff(c_75771,plain,
! [C_10,B_9] :
( ~ subset(C_10,B_9)
| subset(union(C_10,B_9),B_9) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_75509]) ).
tff(c_308946,plain,
! [B_9,C_10] :
( ~ subset(B_9,union(C_10,B_9))
| ( union(C_10,B_9) = B_9 )
| ~ subset(C_10,B_9) ),
inference(resolution,[status(thm)],[c_75771,c_308352]) ).
tff(c_309752,plain,
! [C_3812,B_3813] :
( ( union(C_3812,B_3813) = B_3813 )
| ~ subset(C_3812,B_3813) ),
inference(demodulation,[status(thm),theory(equality)],[c_315,c_308946]) ).
tff(c_311565,plain,
union('#skF_6','#skF_5') = '#skF_5',
inference(resolution,[status(thm)],[c_32,c_309752]) ).
tff(c_100,plain,
! [B_4,B_29,C_28] :
( subset(B_4,union(B_29,C_28))
| ~ member('#skF_1'(B_4,union(B_29,C_28)),C_28) ),
inference(resolution,[status(thm)],[c_89,c_10]) ).
tff(c_4460,plain,
! [B_298,C_299,B_300] :
( member('#skF_1'(union(B_298,C_299),union(B_300,C_299)),B_298)
| subset(union(B_298,C_299),union(B_300,C_299)) ),
inference(resolution,[status(thm)],[c_1909,c_100]) ).
tff(c_4,plain,
! [D_3,C_2,B_1] :
( ~ member(D_3,C_2)
| member(D_3,union(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_286,plain,
! [B_58,B_1,C_2,C_60] :
( subset(B_58,union(union(B_1,C_2),C_60))
| ~ member('#skF_1'(B_58,union(union(B_1,C_2),C_60)),C_2) ),
inference(resolution,[status(thm)],[c_4,c_262]) ).
tff(c_4542,plain,
! [B_301,C_302,B_303] : subset(union(B_301,C_302),union(union(B_303,B_301),C_302)),
inference(resolution,[status(thm)],[c_4460,c_286]) ).
tff(c_4731,plain,
! [B_313,C_314,B_315] : subset(union(B_313,C_314),union(union(B_315,C_314),B_313)),
inference(superposition,[status(thm),theory(equality)],[c_14,c_4542]) ).
tff(c_4765,plain,
! [B_313,B_9,C_10] : subset(union(B_313,B_9),union(union(B_9,C_10),B_313)),
inference(superposition,[status(thm),theory(equality)],[c_14,c_4731]) ).
tff(c_330875,plain,
! [B_3828] : subset(union(B_3828,'#skF_6'),union('#skF_5',B_3828)),
inference(superposition,[status(thm),theory(equality)],[c_311565,c_4765]) ).
tff(c_331040,plain,
subset(union('#skF_4','#skF_6'),'#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_322511,c_330875]) ).
tff(c_331183,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_331040]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % 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
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 16:46:34 EDT 2023
% 0.14/0.36 % CPUTime :
% 130.52/100.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 130.52/100.92
% 130.52/100.92 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 130.52/100.96
% 130.52/100.96 Inference rules
% 130.52/100.96 ----------------------
% 130.52/100.96 #Ref : 0
% 130.52/100.96 #Sup : 87141
% 130.52/100.96 #Fact : 92
% 130.52/100.96 #Define : 0
% 130.52/100.96 #Split : 4
% 130.52/100.96 #Chain : 0
% 130.52/100.96 #Close : 0
% 130.52/100.96
% 130.52/100.96 Ordering : KBO
% 130.52/100.96
% 130.52/100.96 Simplification rules
% 130.52/100.96 ----------------------
% 130.52/100.96 #Subsume : 18614
% 130.52/100.96 #Demod : 38064
% 130.52/100.96 #Tautology : 17624
% 130.52/100.96 #SimpNegUnit : 21
% 130.52/100.96 #BackRed : 27
% 130.52/100.96
% 130.52/100.96 #Partial instantiations: 0
% 130.52/100.96 #Strategies tried : 1
% 130.52/100.96
% 130.52/100.96 Timing (in seconds)
% 130.52/100.96 ----------------------
% 130.52/100.96 Preprocessing : 0.47
% 130.52/100.96 Parsing : 0.24
% 130.52/100.96 CNF conversion : 0.03
% 130.52/100.96 Main loop : 99.34
% 130.52/100.96 Inferencing : 5.84
% 130.52/100.96 Reduction : 39.01
% 130.52/100.96 Demodulation : 35.02
% 130.52/100.96 BG Simplification : 0.46
% 130.52/100.96 Subsumption : 48.36
% 130.52/100.96 Abstraction : 0.72
% 130.52/100.96 MUC search : 0.00
% 130.52/100.96 Cooper : 0.00
% 130.52/100.96 Total : 99.86
% 130.52/100.96 Index Insertion : 0.00
% 130.52/100.96 Index Deletion : 0.00
% 130.52/100.96 Index Matching : 0.00
% 130.52/100.96 BG Taut test : 0.00
%------------------------------------------------------------------------------