TSTP Solution File: SET090+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET090+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 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 : n009.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 10:55:55 EDT 2023
% Result : Theorem 5.49s 2.31s
% Output : CNFRefutation 5.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 46
% Syntax : Number of formulae : 65 ( 10 unt; 41 typ; 0 def)
% Number of atoms : 44 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 12 ~; 14 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 32 >; 16 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 9 con; 0-3 aty)
% Number of variables : 20 (; 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subclass > member > disjoint > inductive > function > restrict > unordered_pair > union > ordered_pair > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > range_of > power_class > member_of > inverse > flip > first > domain_of > complement > universal_class > successor_relation > null_class > identity_relation > element_relation > #skF_4 > #skF_7 > #skF_3 > #skF_2 > #skF_9 > #skF_8 > #skF_1 > #skF_5 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(null_class,type,
null_class: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(subclass,type,
subclass: ( $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(sum_class,type,
sum_class: $i > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(element_relation,type,
element_relation: $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(second,type,
second: $i > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(flip,type,
flip: $i > $i ).
tff(power_class,type,
power_class: $i > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff(member_of,type,
member_of: $i > $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(first,type,
first: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(inductive,type,
inductive: $i > $o ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(successor,type,
successor: $i > $i ).
tff(successor_relation,type,
successor_relation: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(universal_class,type,
universal_class: $i ).
tff(f_400,negated_conjecture,
~ ! [X,U] :
( ( member(U,universal_class)
& ( X = singleton(U) ) )
=> ( member_of(X) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_singleton) ).
tff(f_380,axiom,
! [Y] :
( member(Y,universal_class)
=> member(member_of(singleton(Y)),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_singleton_universal) ).
tff(f_384,axiom,
! [Y] :
( member(Y,universal_class)
=> ( singleton(member_of(singleton(Y))) = singleton(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_singleton_singleton) ).
tff(f_101,axiom,
! [X] : ( singleton(X) = unordered_pair(X,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
tff(f_88,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
tff(c_188,plain,
member_of('#skF_8') != '#skF_9',
inference(cnfTransformation,[status(thm)],[f_400]) ).
tff(c_192,plain,
member('#skF_9',universal_class),
inference(cnfTransformation,[status(thm)],[f_400]) ).
tff(c_190,plain,
singleton('#skF_9') = '#skF_8',
inference(cnfTransformation,[status(thm)],[f_400]) ).
tff(c_657,plain,
! [Y_199] :
( member(member_of(singleton(Y_199)),universal_class)
| ~ member(Y_199,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_663,plain,
( member(member_of('#skF_8'),universal_class)
| ~ member('#skF_9',universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_657]) ).
tff(c_665,plain,
member(member_of('#skF_8'),universal_class),
inference(demodulation,[status(thm),theory(equality)],[c_192,c_663]) ).
tff(c_925,plain,
! [Y_220] :
( ( singleton(member_of(singleton(Y_220))) = singleton(Y_220) )
| ~ member(Y_220,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_967,plain,
( ( singleton(member_of('#skF_8')) = singleton('#skF_9') )
| ~ member('#skF_9',universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_925]) ).
tff(c_978,plain,
singleton(member_of('#skF_8')) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_192,c_190,c_967]) ).
tff(c_26,plain,
! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_371,plain,
! [X_142,Y_143] :
( member(X_142,unordered_pair(X_142,Y_143))
| ~ member(X_142,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_374,plain,
! [X_14] :
( member(X_14,singleton(X_14))
| ~ member(X_14,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_371]) ).
tff(c_995,plain,
( member(member_of('#skF_8'),'#skF_8')
| ~ member(member_of('#skF_8'),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_978,c_374]) ).
tff(c_1015,plain,
member(member_of('#skF_8'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_665,c_995]) ).
tff(c_1196,plain,
! [Y_237,U_238,X_239] :
( ( Y_237 = U_238 )
| ( X_239 = U_238 )
| ~ member(U_238,unordered_pair(X_239,Y_237)) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_1235,plain,
! [X_240,U_241] :
( ( X_240 = U_241 )
| ( X_240 = U_241 )
| ~ member(U_241,singleton(X_240)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1196]) ).
tff(c_1312,plain,
! [U_243] :
( ( U_243 = '#skF_9' )
| ( U_243 = '#skF_9' )
| ~ member(U_243,'#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_1235]) ).
tff(c_1315,plain,
member_of('#skF_8') = '#skF_9',
inference(resolution,[status(thm)],[c_1015,c_1312]) ).
tff(c_1342,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_188,c_188,c_1315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET090+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.00/0.13 % 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
% 0.13/0.35 % Computer : n009.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 16:09:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.49/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.49/2.32
% 5.49/2.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.72/2.34
% 5.72/2.34 Inference rules
% 5.72/2.34 ----------------------
% 5.72/2.34 #Ref : 0
% 5.72/2.34 #Sup : 258
% 5.72/2.34 #Fact : 0
% 5.72/2.34 #Define : 0
% 5.72/2.34 #Split : 9
% 5.72/2.34 #Chain : 0
% 5.72/2.34 #Close : 0
% 5.72/2.34
% 5.72/2.34 Ordering : KBO
% 5.72/2.34
% 5.72/2.34 Simplification rules
% 5.72/2.34 ----------------------
% 5.72/2.34 #Subsume : 35
% 5.72/2.34 #Demod : 31
% 5.72/2.34 #Tautology : 73
% 5.72/2.34 #SimpNegUnit : 1
% 5.72/2.34 #BackRed : 0
% 5.72/2.35
% 5.72/2.35 #Partial instantiations: 0
% 5.72/2.35 #Strategies tried : 1
% 5.72/2.35
% 5.72/2.35 Timing (in seconds)
% 5.72/2.35 ----------------------
% 5.72/2.35 Preprocessing : 0.65
% 5.72/2.35 Parsing : 0.33
% 5.72/2.35 CNF conversion : 0.05
% 5.72/2.35 Main loop : 0.60
% 5.72/2.35 Inferencing : 0.22
% 5.72/2.35 Reduction : 0.17
% 5.72/2.35 Demodulation : 0.12
% 5.72/2.35 BG Simplification : 0.04
% 5.72/2.35 Subsumption : 0.13
% 5.72/2.35 Abstraction : 0.03
% 5.72/2.35 MUC search : 0.00
% 5.72/2.35 Cooper : 0.00
% 5.72/2.35 Total : 1.30
% 5.72/2.35 Index Insertion : 0.00
% 5.72/2.35 Index Deletion : 0.00
% 5.72/2.35 Index Matching : 0.00
% 5.72/2.35 BG Taut test : 0.00
%------------------------------------------------------------------------------