TSTP Solution File: SET645+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET645+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/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 : n027.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 10:56:47 EDT 2023
% Result : Theorem 5.29s 2.33s
% Output : CNFRefutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 35
% Syntax : Number of formulae : 75 ( 11 unt; 27 typ; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 145 ( 58 ~; 55 |; 5 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 21 >; 11 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-2 aty)
% Number of variables : 93 (; 93 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > ilf_type > relation_like > empty > unordered_pair > relation_type > ordered_pair > cross_product > #nlpp > subset_type > singleton > power_set > member_type > set_type > #skF_9 > #skF_5 > #skF_2 > #skF_11 > #skF_3 > #skF_10 > #skF_14 > #skF_13 > #skF_8 > #skF_7 > #skF_1 > #skF_6 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $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(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $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(subset_type,type,
subset_type: $i > $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_273,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(D,B)
& member(E,C) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_7) ).
tff(f_251,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
tff(f_87,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/sandbox/benchmark/theBenchmark.p',p4) ).
tff(f_179,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
tff(f_135,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/sandbox/benchmark/theBenchmark.p',p10) ).
tff(f_192,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/sandbox/benchmark/theBenchmark.p',p15) ).
tff(f_171,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/sandbox/benchmark/theBenchmark.p',p13) ).
tff(f_44,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)
=> ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(B,D)
& member(C,E) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(c_90,plain,
( ~ member('#skF_13','#skF_11')
| ~ member('#skF_12','#skF_10') ),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_227,plain,
~ member('#skF_12','#skF_10'),
inference(splitLeft,[status(thm)],[c_90]) ).
tff(c_94,plain,
ilf_type('#skF_14',relation_type('#skF_10','#skF_11')),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_88,plain,
! [B_146] : ilf_type(B_146,set_type),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_14,plain,
! [E_60,B_50,C_56] :
( ilf_type(E_60,subset_type(cross_product(B_50,C_56)))
| ~ ilf_type(E_60,relation_type(B_50,C_56))
| ~ ilf_type(C_56,set_type)
| ~ ilf_type(B_50,set_type) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_735,plain,
! [E_277,B_278,C_279] :
( ilf_type(E_277,subset_type(cross_product(B_278,C_279)))
| ~ ilf_type(E_277,relation_type(B_278,C_279)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_14]) ).
tff(c_58,plain,
! [B_102] :
( ~ empty(power_set(B_102))
| ~ ilf_type(B_102,set_type) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_136,plain,
! [B_102] : ~ empty(power_set(B_102)),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_58]) ).
tff(c_30,plain,
! [C_79,B_77] :
( ilf_type(C_79,member_type(power_set(B_77)))
| ~ ilf_type(C_79,subset_type(B_77))
| ~ ilf_type(C_79,set_type)
| ~ ilf_type(B_77,set_type) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_156,plain,
! [C_79,B_77] :
( ilf_type(C_79,member_type(power_set(B_77)))
| ~ ilf_type(C_79,subset_type(B_77)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_30]) ).
tff(c_62,plain,
! [B_103,C_105] :
( member(B_103,C_105)
| ~ ilf_type(B_103,member_type(C_105))
| ~ ilf_type(C_105,set_type)
| empty(C_105)
| ~ ilf_type(B_103,set_type) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_315,plain,
! [B_210,C_211] :
( member(B_210,C_211)
| ~ ilf_type(B_210,member_type(C_211))
| empty(C_211) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_62]) ).
tff(c_318,plain,
! [C_79,B_77] :
( member(C_79,power_set(B_77))
| empty(power_set(B_77))
| ~ ilf_type(C_79,subset_type(B_77)) ),
inference(resolution,[status(thm)],[c_156,c_315]) ).
tff(c_324,plain,
! [C_79,B_77] :
( member(C_79,power_set(B_77))
| ~ ilf_type(C_79,subset_type(B_77)) ),
inference(negUnitSimplification,[status(thm)],[c_136,c_318]) ).
tff(c_92,plain,
member(ordered_pair('#skF_12','#skF_13'),'#skF_14'),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_48,plain,
! [D_101,C_98,B_92] :
( member(D_101,C_98)
| ~ member(D_101,B_92)
| ~ ilf_type(D_101,set_type)
| ~ member(B_92,power_set(C_98))
| ~ ilf_type(C_98,set_type)
| ~ ilf_type(B_92,set_type) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_403,plain,
! [D_224,C_225,B_226] :
( member(D_224,C_225)
| ~ member(D_224,B_226)
| ~ member(B_226,power_set(C_225)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_88,c_48]) ).
tff(c_427,plain,
! [C_225] :
( member(ordered_pair('#skF_12','#skF_13'),C_225)
| ~ member('#skF_14',power_set(C_225)) ),
inference(resolution,[status(thm)],[c_92,c_403]) ).
tff(c_6,plain,
! [B_1,D_13,C_9,E_15] :
( member(B_1,D_13)
| ~ member(ordered_pair(B_1,C_9),cross_product(D_13,E_15))
| ~ ilf_type(E_15,set_type)
| ~ ilf_type(D_13,set_type)
| ~ ilf_type(C_9,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_579,plain,
! [B_249,D_250,C_251,E_252] :
( member(B_249,D_250)
| ~ member(ordered_pair(B_249,C_251),cross_product(D_250,E_252)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_88,c_88,c_6]) ).
tff(c_585,plain,
! [D_253,E_254] :
( member('#skF_12',D_253)
| ~ member('#skF_14',power_set(cross_product(D_253,E_254))) ),
inference(resolution,[status(thm)],[c_427,c_579]) ).
tff(c_592,plain,
! [D_253,E_254] :
( member('#skF_12',D_253)
| ~ ilf_type('#skF_14',subset_type(cross_product(D_253,E_254))) ),
inference(resolution,[status(thm)],[c_324,c_585]) ).
tff(c_941,plain,
! [B_294,C_295] :
( member('#skF_12',B_294)
| ~ ilf_type('#skF_14',relation_type(B_294,C_295)) ),
inference(resolution,[status(thm)],[c_735,c_592]) ).
tff(c_948,plain,
member('#skF_12','#skF_10'),
inference(resolution,[status(thm)],[c_94,c_941]) ).
tff(c_953,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_227,c_948]) ).
tff(c_954,plain,
~ member('#skF_13','#skF_11'),
inference(splitRight,[status(thm)],[c_90]) ).
tff(c_1485,plain,
! [E_393,B_394,C_395] :
( ilf_type(E_393,subset_type(cross_product(B_394,C_395)))
| ~ ilf_type(E_393,relation_type(B_394,C_395)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_14]) ).
tff(c_1026,plain,
! [C_320,B_321] :
( ilf_type(C_320,member_type(power_set(B_321)))
| ~ ilf_type(C_320,subset_type(B_321)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_30]) ).
tff(c_132,plain,
! [B_103,C_105] :
( member(B_103,C_105)
| ~ ilf_type(B_103,member_type(C_105))
| empty(C_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_62]) ).
tff(c_1029,plain,
! [C_320,B_321] :
( member(C_320,power_set(B_321))
| empty(power_set(B_321))
| ~ ilf_type(C_320,subset_type(B_321)) ),
inference(resolution,[status(thm)],[c_1026,c_132]) ).
tff(c_1032,plain,
! [C_320,B_321] :
( member(C_320,power_set(B_321))
| ~ ilf_type(C_320,subset_type(B_321)) ),
inference(negUnitSimplification,[status(thm)],[c_136,c_1029]) ).
tff(c_1182,plain,
! [D_348,C_349,B_350] :
( member(D_348,C_349)
| ~ member(D_348,B_350)
| ~ member(B_350,power_set(C_349)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_88,c_48]) ).
tff(c_1270,plain,
! [C_361] :
( member(ordered_pair('#skF_12','#skF_13'),C_361)
| ~ member('#skF_14',power_set(C_361)) ),
inference(resolution,[status(thm)],[c_92,c_1182]) ).
tff(c_4,plain,
! [C_9,E_15,B_1,D_13] :
( member(C_9,E_15)
| ~ member(ordered_pair(B_1,C_9),cross_product(D_13,E_15))
| ~ ilf_type(E_15,set_type)
| ~ ilf_type(D_13,set_type)
| ~ ilf_type(C_9,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_182,plain,
! [C_9,E_15,B_1,D_13] :
( member(C_9,E_15)
| ~ member(ordered_pair(B_1,C_9),cross_product(D_13,E_15)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_88,c_88,c_4]) ).
tff(c_1320,plain,
! [E_364,D_365] :
( member('#skF_13',E_364)
| ~ member('#skF_14',power_set(cross_product(D_365,E_364))) ),
inference(resolution,[status(thm)],[c_1270,c_182]) ).
tff(c_1327,plain,
! [E_364,D_365] :
( member('#skF_13',E_364)
| ~ ilf_type('#skF_14',subset_type(cross_product(D_365,E_364))) ),
inference(resolution,[status(thm)],[c_1032,c_1320]) ).
tff(c_1562,plain,
! [C_403,B_404] :
( member('#skF_13',C_403)
| ~ ilf_type('#skF_14',relation_type(B_404,C_403)) ),
inference(resolution,[status(thm)],[c_1485,c_1327]) ).
tff(c_1569,plain,
member('#skF_13','#skF_11'),
inference(resolution,[status(thm)],[c_94,c_1562]) ).
tff(c_1574,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_954,c_1569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % 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
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 16:34:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.29/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.29/2.33
% 5.29/2.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.29/2.37
% 5.29/2.37 Inference rules
% 5.29/2.37 ----------------------
% 5.29/2.37 #Ref : 0
% 5.29/2.37 #Sup : 280
% 5.29/2.37 #Fact : 2
% 5.29/2.37 #Define : 0
% 5.29/2.37 #Split : 3
% 5.29/2.37 #Chain : 0
% 5.29/2.37 #Close : 0
% 5.29/2.37
% 5.29/2.37 Ordering : KBO
% 5.29/2.37
% 5.29/2.37 Simplification rules
% 5.29/2.37 ----------------------
% 5.29/2.37 #Subsume : 51
% 5.29/2.37 #Demod : 120
% 5.29/2.37 #Tautology : 82
% 5.29/2.37 #SimpNegUnit : 18
% 5.29/2.37 #BackRed : 0
% 5.29/2.37
% 5.29/2.37 #Partial instantiations: 0
% 5.29/2.37 #Strategies tried : 1
% 5.29/2.37
% 5.29/2.37 Timing (in seconds)
% 5.29/2.37 ----------------------
% 5.29/2.37 Preprocessing : 0.63
% 5.29/2.37 Parsing : 0.33
% 5.29/2.37 CNF conversion : 0.06
% 5.29/2.37 Main loop : 0.59
% 5.29/2.37 Inferencing : 0.22
% 5.29/2.37 Reduction : 0.19
% 5.29/2.37 Demodulation : 0.13
% 5.29/2.37 BG Simplification : 0.04
% 5.29/2.37 Subsumption : 0.11
% 5.29/2.37 Abstraction : 0.02
% 5.29/2.37 MUC search : 0.00
% 5.29/2.37 Cooper : 0.00
% 5.29/2.37 Total : 1.28
% 5.29/2.37 Index Insertion : 0.00
% 5.29/2.37 Index Deletion : 0.00
% 5.29/2.37 Index Matching : 0.00
% 5.29/2.37 BG Taut test : 0.00
%------------------------------------------------------------------------------