TSTP Solution File: SET578+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET578+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 : n015.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 10:56:36 EDT 2023
% Result : Theorem 23.29s 12.62s
% Output : CNFRefutation 23.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 20 unt; 9 typ; 0 def)
% Number of atoms : 148 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 128 ( 50 ~; 67 |; 3 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 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 : 113 (; 113 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > intersection > #nlpp > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(intersection,type,
intersection: ( $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_43,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_73,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
& member(E,D) ) )
=> ( B = intersection(C,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th19) ).
tff(f_51,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_33,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
tff(f_40,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(f_62,axiom,
! [B,C] :
( ( B = C )
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
tff(c_14,plain,
! [C_7,B_6] : ( intersection(C_7,B_6) = intersection(B_6,C_7) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_36,plain,
intersection('#skF_5','#skF_6') != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_43,plain,
intersection('#skF_6','#skF_5') != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_14,c_36]) ).
tff(c_20,plain,
! [B_8,C_9] :
( member('#skF_1'(B_8,C_9),B_8)
| subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_40,plain,
! [E_20] :
( member(E_20,'#skF_6')
| ~ member(E_20,'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_181,plain,
! [D_48,B_49,C_50] :
( member(D_48,intersection(B_49,C_50))
| ~ member(D_48,C_50)
| ~ member(D_48,B_49) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_18,plain,
! [B_8,C_9] :
( ~ member('#skF_1'(B_8,C_9),C_9)
| subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_2366,plain,
! [B_209,B_210,C_211] :
( subset(B_209,intersection(B_210,C_211))
| ~ member('#skF_1'(B_209,intersection(B_210,C_211)),C_211)
| ~ member('#skF_1'(B_209,intersection(B_210,C_211)),B_210) ),
inference(resolution,[status(thm)],[c_181,c_18]) ).
tff(c_2415,plain,
! [B_212,B_213] :
( ~ member('#skF_1'(B_212,intersection(B_213,B_212)),B_213)
| subset(B_212,intersection(B_213,B_212)) ),
inference(resolution,[status(thm)],[c_20,c_2366]) ).
tff(c_2558,plain,
! [B_215] :
( subset(B_215,intersection('#skF_6',B_215))
| ~ member('#skF_1'(B_215,intersection('#skF_6',B_215)),'#skF_4') ),
inference(resolution,[status(thm)],[c_40,c_2415]) ).
tff(c_2582,plain,
subset('#skF_4',intersection('#skF_6','#skF_4')),
inference(resolution,[status(thm)],[c_20,c_2558]) ).
tff(c_2597,plain,
subset('#skF_4',intersection('#skF_4','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_2582]) ).
tff(c_102,plain,
! [D_33,B_34,C_35] :
( member(D_33,B_34)
| ~ member(D_33,intersection(B_34,C_35)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_584,plain,
! [B_74,C_75,C_76] :
( member('#skF_1'(intersection(B_74,C_75),C_76),B_74)
| subset(intersection(B_74,C_75),C_76) ),
inference(resolution,[status(thm)],[c_20,c_102]) ).
tff(c_648,plain,
! [B_79,C_80] : subset(intersection(B_79,C_80),B_79),
inference(resolution,[status(thm)],[c_584,c_18]) ).
tff(c_8,plain,
! [C_5,B_4] :
( ( C_5 = B_4 )
| ~ subset(C_5,B_4)
| ~ subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_657,plain,
! [B_79,C_80] :
( ( intersection(B_79,C_80) = B_79 )
| ~ subset(B_79,intersection(B_79,C_80)) ),
inference(resolution,[status(thm)],[c_648,c_8]) ).
tff(c_2939,plain,
intersection('#skF_4','#skF_6') = '#skF_4',
inference(resolution,[status(thm)],[c_2597,c_657]) ).
tff(c_113,plain,
! [B_34,C_35,C_9] :
( member('#skF_1'(intersection(B_34,C_35),C_9),B_34)
| subset(intersection(B_34,C_35),C_9) ),
inference(resolution,[status(thm)],[c_20,c_102]) ).
tff(c_42,plain,
! [E_20] :
( member(E_20,'#skF_5')
| ~ member(E_20,'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_90,plain,
! [D_30,C_31,B_32] :
( member(D_30,C_31)
| ~ member(D_30,intersection(B_32,C_31)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_101,plain,
! [B_32,C_31,C_9] :
( member('#skF_1'(intersection(B_32,C_31),C_9),C_31)
| subset(intersection(B_32,C_31),C_9) ),
inference(resolution,[status(thm)],[c_20,c_90]) ).
tff(c_8879,plain,
! [B_315,C_316,B_317] :
( ~ member('#skF_1'(intersection(B_315,C_316),intersection(B_317,C_316)),B_317)
| subset(intersection(B_315,C_316),intersection(B_317,C_316)) ),
inference(resolution,[status(thm)],[c_101,c_2366]) ).
tff(c_9221,plain,
! [B_322,C_323] :
( subset(intersection(B_322,C_323),intersection('#skF_5',C_323))
| ~ member('#skF_1'(intersection(B_322,C_323),intersection('#skF_5',C_323)),'#skF_4') ),
inference(resolution,[status(thm)],[c_42,c_8879]) ).
tff(c_9492,plain,
! [C_327] : subset(intersection('#skF_4',C_327),intersection('#skF_5',C_327)),
inference(resolution,[status(thm)],[c_113,c_9221]) ).
tff(c_9543,plain,
subset('#skF_4',intersection('#skF_5','#skF_6')),
inference(superposition,[status(thm),theory(equality)],[c_2939,c_9492]) ).
tff(c_9585,plain,
subset('#skF_4',intersection('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_9543]) ).
tff(c_656,plain,
! [B_6,C_7] : subset(intersection(B_6,C_7),C_7),
inference(superposition,[status(thm),theory(equality)],[c_14,c_648]) ).
tff(c_150,plain,
! [D_40,C_41,B_42] :
( member(D_40,C_41)
| ~ member(D_40,B_42)
| ~ subset(B_42,C_41) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_157,plain,
! [B_8,C_9,C_41] :
( member('#skF_1'(B_8,C_9),C_41)
| ~ subset(B_8,C_41)
| subset(B_8,C_9) ),
inference(resolution,[status(thm)],[c_20,c_150]) ).
tff(c_3903,plain,
! [B_225,C_226] :
( ~ subset(B_225,C_226)
| subset(B_225,intersection(C_226,B_225)) ),
inference(resolution,[status(thm)],[c_157,c_2415]) ).
tff(c_773,plain,
! [B_91,C_92] :
( ( intersection(B_91,C_92) = B_91 )
| ~ subset(B_91,intersection(B_91,C_92)) ),
inference(resolution,[status(thm)],[c_648,c_8]) ).
tff(c_779,plain,
! [C_7,B_6] :
( ( intersection(C_7,B_6) = C_7 )
| ~ subset(C_7,intersection(B_6,C_7)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_773]) ).
tff(c_4009,plain,
! [B_225,C_226] :
( ( intersection(B_225,C_226) = B_225 )
| ~ subset(B_225,C_226) ),
inference(resolution,[status(thm)],[c_3903,c_779]) ).
tff(c_9606,plain,
intersection('#skF_4',intersection('#skF_6','#skF_5')) = '#skF_4',
inference(resolution,[status(thm)],[c_9585,c_4009]) ).
tff(c_348,plain,
! [B_65,C_66] :
( member('#skF_2'(B_65,C_66),C_66)
| member('#skF_3'(B_65,C_66),B_65)
| ( C_66 = B_65 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_6,plain,
! [D_3,B_1,C_2] :
( member(D_3,B_1)
| ~ member(D_3,intersection(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_1719,plain,
! [B_168,C_169,C_170] :
( member('#skF_3'(intersection(B_168,C_169),C_170),B_168)
| member('#skF_2'(intersection(B_168,C_169),C_170),C_170)
| ( intersection(B_168,C_169) = C_170 ) ),
inference(resolution,[status(thm)],[c_348,c_6]) ).
tff(c_30,plain,
! [B_14,C_15] :
( member('#skF_2'(B_14,C_15),C_15)
| ~ member('#skF_3'(B_14,C_15),C_15)
| ( C_15 = B_14 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_1817,plain,
! [B_173,C_174] :
( member('#skF_2'(intersection(B_173,C_174),B_173),B_173)
| ( intersection(B_173,C_174) = B_173 ) ),
inference(resolution,[status(thm)],[c_1719,c_30]) ).
tff(c_1837,plain,
! [B_6,C_7] :
( member('#skF_2'(intersection(B_6,C_7),C_7),C_7)
| ( intersection(C_7,B_6) = C_7 ) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1817]) ).
tff(c_10220,plain,
( member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5'))
| ( intersection(intersection('#skF_6','#skF_5'),'#skF_4') = intersection('#skF_6','#skF_5') ) ),
inference(superposition,[status(thm),theory(equality)],[c_9606,c_1837]) ).
tff(c_10359,plain,
( member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5'))
| ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9606,c_14,c_10220]) ).
tff(c_10360,plain,
member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5')),
inference(negUnitSimplification,[status(thm)],[c_43,c_10359]) ).
tff(c_56601,plain,
member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_6'),
inference(resolution,[status(thm)],[c_10360,c_6]) ).
tff(c_16,plain,
! [D_12,C_9,B_8] :
( member(D_12,C_9)
| ~ member(D_12,B_8)
| ~ subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_1249,plain,
! [B_137,C_138,C_139] :
( member('#skF_3'(B_137,C_138),C_139)
| ~ subset(B_137,C_139)
| member('#skF_2'(B_137,C_138),C_138)
| ( C_138 = B_137 ) ),
inference(resolution,[status(thm)],[c_348,c_16]) ).
tff(c_1381,plain,
! [B_144,C_145] :
( ~ subset(B_144,C_145)
| member('#skF_2'(B_144,C_145),C_145)
| ( C_145 = B_144 ) ),
inference(resolution,[status(thm)],[c_1249,c_30]) ).
tff(c_1973,plain,
! [B_183,C_184,C_185] :
( member('#skF_2'(B_183,C_184),C_185)
| ~ subset(C_184,C_185)
| ~ subset(B_183,C_184)
| ( C_184 = B_183 ) ),
inference(resolution,[status(thm)],[c_1381,c_16]) ).
tff(c_38,plain,
! [E_20] :
( member(E_20,'#skF_4')
| ~ member(E_20,'#skF_6')
| ~ member(E_20,'#skF_5') ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_2031,plain,
! [B_183,C_184] :
( member('#skF_2'(B_183,C_184),'#skF_4')
| ~ member('#skF_2'(B_183,C_184),'#skF_6')
| ~ subset(C_184,'#skF_5')
| ~ subset(B_183,C_184)
| ( C_184 = B_183 ) ),
inference(resolution,[status(thm)],[c_1973,c_38]) ).
tff(c_56605,plain,
( member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4')
| ~ subset(intersection('#skF_6','#skF_5'),'#skF_5')
| ~ subset('#skF_4',intersection('#skF_6','#skF_5'))
| ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_56601,c_2031]) ).
tff(c_56610,plain,
( member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4')
| ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9585,c_656,c_56605]) ).
tff(c_56611,plain,
member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_43,c_56610]) ).
tff(c_32,plain,
! [B_14,C_15] :
( ~ member('#skF_2'(B_14,C_15),B_14)
| member('#skF_3'(B_14,C_15),B_14)
| ( C_15 = B_14 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_4,plain,
! [D_3,C_2,B_1] :
( member(D_3,C_2)
| ~ member(D_3,intersection(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_10306,plain,
! [D_3] :
( member(D_3,intersection('#skF_6','#skF_5'))
| ~ member(D_3,'#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_9606,c_4]) ).
tff(c_28,plain,
! [B_14,C_15] :
( ~ member('#skF_2'(B_14,C_15),B_14)
| ~ member('#skF_3'(B_14,C_15),C_15)
| ( C_15 = B_14 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_57335,plain,
( ~ member('#skF_3'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5'))
| ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_56611,c_28]) ).
tff(c_57343,plain,
~ member('#skF_3'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5')),
inference(negUnitSimplification,[status(thm)],[c_43,c_57335]) ).
tff(c_66963,plain,
~ member('#skF_3'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4'),
inference(resolution,[status(thm)],[c_10306,c_57343]) ).
tff(c_67013,plain,
( ~ member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4')
| ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_32,c_66963]) ).
tff(c_67055,plain,
intersection('#skF_6','#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_56611,c_67013]) ).
tff(c_67057,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_43,c_67055]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET578+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
% 0.15/0.35 % Computer : n015.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 16:39:14 EDT 2023
% 0.15/0.35 % CPUTime :
% 23.29/12.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.29/12.62
% 23.29/12.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.50/12.66
% 23.50/12.66 Inference rules
% 23.50/12.66 ----------------------
% 23.50/12.66 #Ref : 0
% 23.50/12.66 #Sup : 16553
% 23.50/12.66 #Fact : 0
% 23.50/12.66 #Define : 0
% 23.50/12.66 #Split : 12
% 23.50/12.66 #Chain : 0
% 23.50/12.66 #Close : 0
% 23.50/12.66
% 23.50/12.66 Ordering : KBO
% 23.50/12.66
% 23.50/12.66 Simplification rules
% 23.50/12.66 ----------------------
% 23.50/12.66 #Subsume : 4956
% 23.50/12.66 #Demod : 23288
% 23.50/12.66 #Tautology : 4496
% 23.50/12.66 #SimpNegUnit : 271
% 23.50/12.66 #BackRed : 17
% 23.50/12.66
% 23.50/12.66 #Partial instantiations: 0
% 23.50/12.66 #Strategies tried : 1
% 23.50/12.66
% 23.50/12.66 Timing (in seconds)
% 23.50/12.66 ----------------------
% 23.50/12.66 Preprocessing : 0.51
% 23.50/12.66 Parsing : 0.27
% 23.50/12.66 CNF conversion : 0.04
% 23.50/12.66 Main loop : 11.00
% 23.50/12.66 Inferencing : 1.48
% 23.50/12.66 Reduction : 5.19
% 23.50/12.66 Demodulation : 4.40
% 23.50/12.66 BG Simplification : 0.12
% 23.50/12.66 Subsumption : 3.71
% 23.50/12.66 Abstraction : 0.16
% 23.50/12.66 MUC search : 0.00
% 23.50/12.67 Cooper : 0.00
% 23.50/12.67 Total : 11.57
% 23.50/12.67 Index Insertion : 0.00
% 23.50/12.67 Index Deletion : 0.00
% 23.50/12.67 Index Matching : 0.00
% 23.50/12.67 BG Taut test : 0.00
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