TSTP Solution File: SET611+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET611+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 10:56:42 EDT 2023
% Result : Theorem 22.33s 10.55s
% Output : CNFRefutation 22.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 94 ( 28 unt; 16 typ; 0 def)
% Number of atoms : 137 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 110 ( 51 ~; 49 |; 3 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 11 >; 9 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 93 (; 93 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > intersection > difference > #nlpp > empty_set > #skF_7 > #skF_3 > #skF_10 > #skF_9 > #skF_8 > #skF_2 > #skF_1 > #skF_5 > #skF_6 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_96,negated_conjecture,
~ ! [B,C] :
( ( intersection(B,C) = empty_set )
<=> ( difference(B,C) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th84) ).
tff(f_80,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_50,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
tff(f_54,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_42,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_61,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(f_64,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_90,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
tff(c_58,plain,
( ( difference('#skF_7','#skF_8') = '#skF_7' )
| ( difference('#skF_9','#skF_10') != '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_138,plain,
difference('#skF_9','#skF_10') != '#skF_9',
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_48,plain,
! [B_20,C_21] :
( member('#skF_5'(B_20,C_21),B_20)
| subset(B_20,C_21) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_296,plain,
! [D_69,B_70,C_71] :
( member(D_69,difference(B_70,C_71))
| member(D_69,C_71)
| ~ member(D_69,B_70) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_46,plain,
! [B_20,C_21] :
( ~ member('#skF_5'(B_20,C_21),C_21)
| subset(B_20,C_21) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_22733,plain,
! [B_643,B_644,C_645] :
( subset(B_643,difference(B_644,C_645))
| member('#skF_5'(B_643,difference(B_644,C_645)),C_645)
| ~ member('#skF_5'(B_643,difference(B_644,C_645)),B_644) ),
inference(resolution,[status(thm)],[c_296,c_46]) ).
tff(c_90239,plain,
! [B_1124,C_1125] :
( member('#skF_5'(B_1124,difference(B_1124,C_1125)),C_1125)
| subset(B_1124,difference(B_1124,C_1125)) ),
inference(resolution,[status(thm)],[c_48,c_22733]) ).
tff(c_22,plain,
! [B_10] : ~ member(B_10,empty_set),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_62,plain,
( ( difference('#skF_7','#skF_8') = '#skF_7' )
| ( intersection('#skF_9','#skF_10') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_137,plain,
intersection('#skF_9','#skF_10') = empty_set,
inference(splitLeft,[status(thm)],[c_62]) ).
tff(c_426,plain,
! [D_79,B_80,C_81] :
( member(D_79,intersection(B_80,C_81))
| ~ member(D_79,C_81)
| ~ member(D_79,B_80) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_444,plain,
! [D_79] :
( member(D_79,empty_set)
| ~ member(D_79,'#skF_10')
| ~ member(D_79,'#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_137,c_426]) ).
tff(c_456,plain,
! [D_79] :
( ~ member(D_79,'#skF_10')
| ~ member(D_79,'#skF_9') ),
inference(negUnitSimplification,[status(thm)],[c_22,c_444]) ).
tff(c_91232,plain,
! [B_1128] :
( ~ member('#skF_5'(B_1128,difference(B_1128,'#skF_10')),'#skF_9')
| subset(B_1128,difference(B_1128,'#skF_10')) ),
inference(resolution,[status(thm)],[c_90239,c_456]) ).
tff(c_91345,plain,
subset('#skF_9',difference('#skF_9','#skF_10')),
inference(resolution,[status(thm)],[c_48,c_91232]) ).
tff(c_155,plain,
! [B_46,C_47] :
( member('#skF_5'(B_46,C_47),B_46)
| subset(B_46,C_47) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_20,plain,
! [D_9,B_7,C_8] :
( member(D_9,B_7)
| ~ member(D_9,difference(B_7,C_8)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_4405,plain,
! [B_250,C_251,C_252] :
( member('#skF_5'(difference(B_250,C_251),C_252),B_250)
| subset(difference(B_250,C_251),C_252) ),
inference(resolution,[status(thm)],[c_155,c_20]) ).
tff(c_4478,plain,
! [B_253,C_254] : subset(difference(B_253,C_254),B_253),
inference(resolution,[status(thm)],[c_4405,c_46]) ).
tff(c_24,plain,
! [C_12,B_11] :
( ( C_12 = B_11 )
| ~ subset(C_12,B_11)
| ~ subset(B_11,C_12) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_4533,plain,
! [B_253,C_254] :
( ( difference(B_253,C_254) = B_253 )
| ~ subset(B_253,difference(B_253,C_254)) ),
inference(resolution,[status(thm)],[c_4478,c_24]) ).
tff(c_91966,plain,
difference('#skF_9','#skF_10') = '#skF_9',
inference(resolution,[status(thm)],[c_91345,c_4533]) ).
tff(c_91991,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_138,c_91966]) ).
tff(c_91993,plain,
difference('#skF_9','#skF_10') = '#skF_9',
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_30,plain,
! [C_14,B_13] : ( intersection(C_14,B_13) = intersection(B_13,C_14) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_56,plain,
( ( intersection('#skF_7','#skF_8') != empty_set )
| ( difference('#skF_9','#skF_10') != '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_63,plain,
( ( intersection('#skF_8','#skF_7') != empty_set )
| ( difference('#skF_9','#skF_10') != '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_56]) ).
tff(c_92059,plain,
intersection('#skF_8','#skF_7') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_91993,c_63]) ).
tff(c_54,plain,
! [B_26] :
( empty(B_26)
| member('#skF_6'(B_26),B_26) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_113,plain,
! [D_37,C_38,B_39] :
( member(D_37,C_38)
| ~ member(D_37,intersection(B_39,C_38)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_124,plain,
! [B_39,C_38] :
( member('#skF_6'(intersection(B_39,C_38)),C_38)
| empty(intersection(B_39,C_38)) ),
inference(resolution,[status(thm)],[c_54,c_113]) ).
tff(c_125,plain,
! [D_40,B_41,C_42] :
( member(D_40,B_41)
| ~ member(D_40,intersection(B_41,C_42)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_93931,plain,
! [B_1257,C_1258] :
( member('#skF_6'(intersection(B_1257,C_1258)),B_1257)
| empty(intersection(B_1257,C_1258)) ),
inference(resolution,[status(thm)],[c_54,c_125]) ).
tff(c_91992,plain,
difference('#skF_7','#skF_8') = '#skF_7',
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_92019,plain,
! [D_1134,C_1135,B_1136] :
( ~ member(D_1134,C_1135)
| ~ member(D_1134,difference(B_1136,C_1135)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_92025,plain,
! [D_1134] :
( ~ member(D_1134,'#skF_8')
| ~ member(D_1134,'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_91992,c_92019]) ).
tff(c_94083,plain,
! [C_1263] :
( ~ member('#skF_6'(intersection('#skF_7',C_1263)),'#skF_8')
| empty(intersection('#skF_7',C_1263)) ),
inference(resolution,[status(thm)],[c_93931,c_92025]) ).
tff(c_94091,plain,
empty(intersection('#skF_7','#skF_8')),
inference(resolution,[status(thm)],[c_124,c_94083]) ).
tff(c_94105,plain,
empty(intersection('#skF_8','#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_94091]) ).
tff(c_92061,plain,
! [B_1144,C_1145] :
( member('#skF_5'(B_1144,C_1145),B_1144)
| subset(B_1144,C_1145) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_52,plain,
! [C_29,B_26] :
( ~ member(C_29,B_26)
| ~ empty(B_26) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_92105,plain,
! [B_1144,C_1145] :
( ~ empty(B_1144)
| subset(B_1144,C_1145) ),
inference(resolution,[status(thm)],[c_92061,c_52]) ).
tff(c_92107,plain,
! [C_1146] : subset(empty_set,C_1146),
inference(resolution,[status(thm)],[c_92061,c_22]) ).
tff(c_92122,plain,
! [C_1152] :
( ( empty_set = C_1152 )
| ~ subset(C_1152,empty_set) ),
inference(resolution,[status(thm)],[c_92107,c_24]) ).
tff(c_92135,plain,
! [B_1144] :
( ( empty_set = B_1144 )
| ~ empty(B_1144) ),
inference(resolution,[status(thm)],[c_92105,c_92122]) ).
tff(c_94117,plain,
intersection('#skF_8','#skF_7') = empty_set,
inference(resolution,[status(thm)],[c_94105,c_92135]) ).
tff(c_94125,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_92059,c_94117]) ).
tff(c_94127,plain,
intersection('#skF_9','#skF_10') != empty_set,
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_60,plain,
( ( intersection('#skF_7','#skF_8') != empty_set )
| ( intersection('#skF_9','#skF_10') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_64,plain,
( ( intersection('#skF_8','#skF_7') != empty_set )
| ( intersection('#skF_9','#skF_10') = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_60]) ).
tff(c_94225,plain,
intersection('#skF_8','#skF_7') != empty_set,
inference(negUnitSimplification,[status(thm)],[c_94127,c_64]) ).
tff(c_94666,plain,
! [B_1321,C_1322] :
( member('#skF_6'(intersection(B_1321,C_1322)),C_1322)
| empty(intersection(B_1321,C_1322)) ),
inference(resolution,[status(thm)],[c_54,c_113]) ).
tff(c_94126,plain,
difference('#skF_7','#skF_8') = '#skF_7',
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_94226,plain,
! [D_1280,C_1281,B_1282] :
( ~ member(D_1280,C_1281)
| ~ member(D_1280,difference(B_1282,C_1281)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_94233,plain,
! [D_1280] :
( ~ member(D_1280,'#skF_8')
| ~ member(D_1280,'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_94126,c_94226]) ).
tff(c_94877,plain,
! [B_1329] :
( ~ member('#skF_6'(intersection(B_1329,'#skF_7')),'#skF_8')
| empty(intersection(B_1329,'#skF_7')) ),
inference(resolution,[status(thm)],[c_94666,c_94233]) ).
tff(c_95704,plain,
! [C_1372] :
( ~ member('#skF_6'(intersection('#skF_7',C_1372)),'#skF_8')
| empty(intersection(C_1372,'#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_94877]) ).
tff(c_95720,plain,
( empty(intersection('#skF_8','#skF_7'))
| empty(intersection('#skF_7','#skF_8')) ),
inference(resolution,[status(thm)],[c_124,c_95704]) ).
tff(c_95736,plain,
( empty(intersection('#skF_8','#skF_7'))
| empty(intersection('#skF_8','#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_95720]) ).
tff(c_95738,plain,
empty(intersection('#skF_8','#skF_7')),
inference(splitLeft,[status(thm)],[c_95736]) ).
tff(c_94149,plain,
! [B_1269,C_1270] :
( member('#skF_5'(B_1269,C_1270),B_1269)
| subset(B_1269,C_1270) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_94172,plain,
! [B_1269,C_1270] :
( ~ empty(B_1269)
| subset(B_1269,C_1270) ),
inference(resolution,[status(thm)],[c_94149,c_52]) ).
tff(c_94174,plain,
! [C_1271] : subset(empty_set,C_1271),
inference(resolution,[status(thm)],[c_94149,c_22]) ).
tff(c_94183,plain,
! [C_1274] :
( ( empty_set = C_1274 )
| ~ subset(C_1274,empty_set) ),
inference(resolution,[status(thm)],[c_94174,c_24]) ).
tff(c_94196,plain,
! [B_1269] :
( ( empty_set = B_1269 )
| ~ empty(B_1269) ),
inference(resolution,[status(thm)],[c_94172,c_94183]) ).
tff(c_95753,plain,
intersection('#skF_8','#skF_7') = empty_set,
inference(resolution,[status(thm)],[c_95738,c_94196]) ).
tff(c_95763,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_94225,c_95753]) ).
tff(c_95764,plain,
empty(intersection('#skF_8','#skF_7')),
inference(splitRight,[status(thm)],[c_95736]) ).
tff(c_95780,plain,
intersection('#skF_8','#skF_7') = empty_set,
inference(resolution,[status(thm)],[c_95764,c_94196]) ).
tff(c_95790,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_94225,c_95780]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET611+3 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.14/0.35 % Computer : n025.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 16:48:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 22.33/10.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.33/10.56
% 22.33/10.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.69/10.59
% 22.69/10.59 Inference rules
% 22.69/10.59 ----------------------
% 22.69/10.59 #Ref : 0
% 22.69/10.59 #Sup : 25185
% 22.69/10.59 #Fact : 0
% 22.69/10.59 #Define : 0
% 22.69/10.59 #Split : 29
% 22.69/10.59 #Chain : 0
% 22.69/10.59 #Close : 0
% 22.69/10.59
% 22.69/10.59 Ordering : KBO
% 22.69/10.59
% 22.69/10.59 Simplification rules
% 22.69/10.59 ----------------------
% 22.69/10.59 #Subsume : 10680
% 22.69/10.59 #Demod : 16674
% 22.69/10.59 #Tautology : 6974
% 22.69/10.59 #SimpNegUnit : 382
% 22.69/10.59 #BackRed : 19
% 22.69/10.59
% 22.69/10.59 #Partial instantiations: 0
% 22.69/10.59 #Strategies tried : 1
% 22.69/10.59
% 22.69/10.59 Timing (in seconds)
% 22.69/10.59 ----------------------
% 22.69/10.60 Preprocessing : 0.50
% 22.69/10.60 Parsing : 0.26
% 22.69/10.60 CNF conversion : 0.04
% 22.69/10.60 Main loop : 8.89
% 22.69/10.60 Inferencing : 1.73
% 22.69/10.60 Reduction : 2.69
% 22.69/10.60 Demodulation : 2.00
% 22.69/10.60 BG Simplification : 0.13
% 22.69/10.60 Subsumption : 3.79
% 22.69/10.60 Abstraction : 0.20
% 22.69/10.60 MUC search : 0.00
% 22.69/10.60 Cooper : 0.00
% 22.69/10.60 Total : 9.45
% 22.69/10.60 Index Insertion : 0.00
% 22.69/10.60 Index Deletion : 0.00
% 22.69/10.60 Index Matching : 0.00
% 22.69/10.60 BG Taut test : 0.00
%------------------------------------------------------------------------------