TSTP Solution File: SET649+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET649+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 : n019.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 10:56:48 EDT 2023
% Result : Theorem 44.14s 32.13s
% Output : CNFRefutation 44.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 41
% Syntax : Number of formulae : 78 ( 10 unt; 30 typ; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 167 ( 63 ~; 63 |; 6 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 24 >; 13 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-2 aty)
% Number of variables : 97 (; 97 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > domain_of > set_type > binary_relation_type > #skF_9 > #skF_15 > #skF_3 > #skF_14 > #skF_13 > #skF_10 > #skF_8 > #skF_4 > #skF_11 > #skF_2 > #skF_12 > #skF_7 > #skF_1 > #skF_5 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(set_type,type,
set_type: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $i > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(subset_type,type,
subset_type: $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(binary_relation_type,type,
binary_relation_type: $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $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(f_300,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( ( subset(domain_of(D),B)
& subset(range_of(D),C) )
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_11) ).
tff(f_46,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,cross_product(domain_of(B),range_of(B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
tff(f_284,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
tff(f_64,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( ( subset(B,C)
& subset(D,E) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
tff(f_41,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(B,C)
& subset(C,D) )
=> subset(B,D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(f_233,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
tff(f_152,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
tff(f_241,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
tff(f_254,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
tff(f_178,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
tff(f_80,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
tff(c_100,plain,
~ ilf_type('#skF_15',relation_type('#skF_13','#skF_14')),
inference(cnfTransformation,[status(thm)],[f_300]) ).
tff(c_104,plain,
subset(domain_of('#skF_15'),'#skF_13'),
inference(cnfTransformation,[status(thm)],[f_300]) ).
tff(c_106,plain,
ilf_type('#skF_15',binary_relation_type),
inference(cnfTransformation,[status(thm)],[f_300]) ).
tff(c_102,plain,
subset(range_of('#skF_15'),'#skF_14'),
inference(cnfTransformation,[status(thm)],[f_300]) ).
tff(c_4,plain,
! [B_8] :
( subset(B_8,cross_product(domain_of(B_8),range_of(B_8)))
| ~ ilf_type(B_8,binary_relation_type) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_98,plain,
! [B_140] : ilf_type(B_140,set_type),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_6,plain,
! [B_9,D_21,C_17,E_23] :
( subset(cross_product(B_9,D_21),cross_product(C_17,E_23))
| ~ subset(D_21,E_23)
| ~ subset(B_9,C_17)
| ~ ilf_type(E_23,set_type)
| ~ ilf_type(D_21,set_type)
| ~ ilf_type(C_17,set_type)
| ~ ilf_type(B_9,set_type) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_941,plain,
! [B_286,D_287,C_288,E_289] :
( subset(cross_product(B_286,D_287),cross_product(C_288,E_289))
| ~ subset(D_287,E_289)
| ~ subset(B_286,C_288) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_98,c_98,c_98,c_6]) ).
tff(c_2,plain,
! [B_1,D_7,C_5] :
( subset(B_1,D_7)
| ~ subset(C_5,D_7)
| ~ subset(B_1,C_5)
| ~ ilf_type(D_7,set_type)
| ~ ilf_type(C_5,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_200,plain,
! [B_1,D_7,C_5] :
( subset(B_1,D_7)
| ~ subset(C_5,D_7)
| ~ subset(B_1,C_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_98,c_98,c_2]) ).
tff(c_2990,plain,
! [C_401,E_402,B_403,B_400,D_399] :
( subset(B_403,cross_product(C_401,E_402))
| ~ subset(B_403,cross_product(B_400,D_399))
| ~ subset(D_399,E_402)
| ~ subset(B_400,C_401) ),
inference(resolution,[status(thm)],[c_941,c_200]) ).
tff(c_95708,plain,
! [B_1482,C_1483,E_1484] :
( subset(B_1482,cross_product(C_1483,E_1484))
| ~ subset(range_of(B_1482),E_1484)
| ~ subset(domain_of(B_1482),C_1483)
| ~ ilf_type(B_1482,binary_relation_type) ),
inference(resolution,[status(thm)],[c_4,c_2990]) ).
tff(c_95721,plain,
! [C_1483] :
( subset('#skF_15',cross_product(C_1483,'#skF_14'))
| ~ subset(domain_of('#skF_15'),C_1483)
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_102,c_95708]) ).
tff(c_95733,plain,
! [C_1485] :
( subset('#skF_15',cross_product(C_1485,'#skF_14'))
| ~ subset(domain_of('#skF_15'),C_1485) ),
inference(demodulation,[status(thm),theory(equality)],[c_106,c_95721]) ).
tff(c_95763,plain,
subset('#skF_15',cross_product('#skF_13','#skF_14')),
inference(resolution,[status(thm)],[c_104,c_95733]) ).
tff(c_76,plain,
! [B_119,C_125] :
( member('#skF_10'(B_119,C_125),B_119)
| member(B_119,power_set(C_125))
| ~ ilf_type(C_125,set_type)
| ~ ilf_type(B_119,set_type) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_134,plain,
! [B_119,C_125] :
( member('#skF_10'(B_119,C_125),B_119)
| member(B_119,power_set(C_125)) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_98,c_76]) ).
tff(c_38,plain,
! [D_73,C_70,B_64] :
( member(D_73,C_70)
| ~ member(D_73,B_64)
| ~ ilf_type(D_73,set_type)
| ~ subset(B_64,C_70)
| ~ ilf_type(C_70,set_type)
| ~ ilf_type(B_64,set_type) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_406,plain,
! [D_201,C_202,B_203] :
( member(D_201,C_202)
| ~ member(D_201,B_203)
| ~ subset(B_203,C_202) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_98,c_98,c_38]) ).
tff(c_1649,plain,
! [B_343,C_344,C_345] :
( member('#skF_10'(B_343,C_344),C_345)
| ~ subset(B_343,C_345)
| member(B_343,power_set(C_344)) ),
inference(resolution,[status(thm)],[c_134,c_406]) ).
tff(c_74,plain,
! [B_119,C_125] :
( ~ member('#skF_10'(B_119,C_125),C_125)
| member(B_119,power_set(C_125))
| ~ ilf_type(C_125,set_type)
| ~ ilf_type(B_119,set_type) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_136,plain,
! [B_119,C_125] :
( ~ member('#skF_10'(B_119,C_125),C_125)
| member(B_119,power_set(C_125)) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_98,c_74]) ).
tff(c_1695,plain,
! [B_346,C_347] :
( ~ subset(B_346,C_347)
| member(B_346,power_set(C_347)) ),
inference(resolution,[status(thm)],[c_1649,c_136]) ).
tff(c_82,plain,
! [B_129] :
( ~ empty(power_set(B_129))
| ~ ilf_type(B_129,set_type) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_128,plain,
! [B_129] : ~ empty(power_set(B_129)),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_82]) ).
tff(c_84,plain,
! [B_130,C_132] :
( ilf_type(B_130,member_type(C_132))
| ~ member(B_130,C_132)
| ~ ilf_type(C_132,set_type)
| empty(C_132)
| ~ ilf_type(B_130,set_type) ),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_126,plain,
! [B_130,C_132] :
( ilf_type(B_130,member_type(C_132))
| ~ member(B_130,C_132)
| empty(C_132) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_98,c_84]) ).
tff(c_50,plain,
! [C_82,B_80] :
( ilf_type(C_82,subset_type(B_80))
| ~ ilf_type(C_82,member_type(power_set(B_80)))
| ~ ilf_type(C_82,set_type)
| ~ ilf_type(B_80,set_type) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_381,plain,
! [C_198,B_199] :
( ilf_type(C_198,subset_type(B_199))
| ~ ilf_type(C_198,member_type(power_set(B_199))) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_98,c_50]) ).
tff(c_385,plain,
! [B_130,B_199] :
( ilf_type(B_130,subset_type(B_199))
| ~ member(B_130,power_set(B_199))
| empty(power_set(B_199)) ),
inference(resolution,[status(thm)],[c_126,c_381]) ).
tff(c_395,plain,
! [B_130,B_199] :
( ilf_type(B_130,subset_type(B_199))
| ~ member(B_130,power_set(B_199)) ),
inference(negUnitSimplification,[status(thm)],[c_128,c_385]) ).
tff(c_1752,plain,
! [B_348,C_349] :
( ilf_type(B_348,subset_type(C_349))
| ~ subset(B_348,C_349) ),
inference(resolution,[status(thm)],[c_1695,c_395]) ).
tff(c_10,plain,
! [D_33,B_24,C_30] :
( ilf_type(D_33,relation_type(B_24,C_30))
| ~ ilf_type(D_33,subset_type(cross_product(B_24,C_30)))
| ~ ilf_type(C_30,set_type)
| ~ ilf_type(B_24,set_type) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_194,plain,
! [D_33,B_24,C_30] :
( ilf_type(D_33,relation_type(B_24,C_30))
| ~ ilf_type(D_33,subset_type(cross_product(B_24,C_30))) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_98,c_10]) ).
tff(c_120306,plain,
! [B_1783,B_1784,C_1785] :
( ilf_type(B_1783,relation_type(B_1784,C_1785))
| ~ subset(B_1783,cross_product(B_1784,C_1785)) ),
inference(resolution,[status(thm)],[c_1752,c_194]) ).
tff(c_120399,plain,
ilf_type('#skF_15',relation_type('#skF_13','#skF_14')),
inference(resolution,[status(thm)],[c_95763,c_120306]) ).
tff(c_121221,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_100,c_120399]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET649+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 : n019.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 16:45:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 44.14/32.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.14/32.14
% 44.14/32.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.14/32.17
% 44.14/32.17 Inference rules
% 44.14/32.17 ----------------------
% 44.14/32.17 #Ref : 1
% 44.14/32.17 #Sup : 29592
% 44.14/32.17 #Fact : 0
% 44.14/32.17 #Define : 0
% 44.14/32.17 #Split : 17
% 44.14/32.17 #Chain : 0
% 44.14/32.17 #Close : 0
% 44.14/32.17
% 44.14/32.17 Ordering : KBO
% 44.14/32.17
% 44.14/32.17 Simplification rules
% 44.14/32.17 ----------------------
% 44.14/32.17 #Subsume : 5572
% 44.14/32.17 #Demod : 561
% 44.14/32.17 #Tautology : 486
% 44.14/32.17 #SimpNegUnit : 201
% 44.14/32.17 #BackRed : 3
% 44.14/32.17
% 44.14/32.17 #Partial instantiations: 0
% 44.14/32.17 #Strategies tried : 1
% 44.14/32.17
% 44.14/32.17 Timing (in seconds)
% 44.14/32.17 ----------------------
% 44.14/32.17 Preprocessing : 0.59
% 44.14/32.17 Parsing : 0.32
% 44.14/32.17 CNF conversion : 0.05
% 44.14/32.17 Main loop : 30.38
% 44.14/32.17 Inferencing : 3.84
% 44.14/32.17 Reduction : 15.19
% 44.14/32.17 Demodulation : 13.17
% 44.14/32.17 BG Simplification : 0.16
% 44.14/32.17 Subsumption : 9.53
% 44.14/32.17 Abstraction : 0.21
% 44.14/32.17 MUC search : 0.00
% 44.14/32.17 Cooper : 0.00
% 44.14/32.17 Total : 31.03
% 44.14/32.17 Index Insertion : 0.00
% 44.14/32.17 Index Deletion : 0.00
% 44.14/32.17 Index Matching : 0.00
% 44.14/32.17 BG Taut test : 0.00
%------------------------------------------------------------------------------