TSTP Solution File: SET454-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET454-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n018.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 10:56:28 EDT 2023
% Result : Unsatisfiable 102.13s 84.58s
% Output : CNFRefutation 102.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 65
% Syntax : Number of formulae : 85 ( 16 unt; 56 typ; 0 def)
% Number of atoms : 45 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 12 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 44 >; 28 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 46 ( 46 usr; 12 con; 0-3 aty)
% Number of variables : 45 (; 45 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ maps > homomorphism > compatible > subclass > member > single_valued_class > operation > one_to_one > inductive > function > restrict > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordered_pair > not_subclass_element > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > single_valued3 > single_valued2 > single_valued1 > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > compose_class > complement > cantor > universal_class > successor_relation > subset_relation > singleton_relation > omega > null_class > identity_relation > element_relation > domain_relation > composition_function > choice > application_function
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(omega,type,
omega: $i ).
tff(null_class,type,
null_class: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff(subclass,type,
subclass: ( $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(single_valued_class,type,
single_valued_class: $i > $o ).
tff(operation,type,
operation: $i > $o ).
tff(sum_class,type,
sum_class: $i > $i ).
tff(single_valued3,type,
single_valued3: $i > $i ).
tff(maps,type,
maps: ( $i * $i * $i ) > $o ).
tff(compose_class,type,
compose_class: $i > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(compatible,type,
compatible: ( $i * $i * $i ) > $o ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(regular,type,
regular: $i > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(singleton_relation,type,
singleton_relation: $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
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(symmetric_difference,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(application_function,type,
application_function: $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(choice,type,
choice: $i ).
tff(subset_relation,type,
subset_relation: $i ).
tff(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(first,type,
first: $i > $i ).
tff(diagonalise,type,
diagonalise: $i > $i ).
tff(homomorphism,type,
homomorphism: ( $i * $i * $i ) > $o ).
tff(single_valued2,type,
single_valued2: $i > $i ).
tff(cantor,type,
cantor: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff(inductive,type,
inductive: $i > $o ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(composition_function,type,
composition_function: $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(domain_relation,type,
domain_relation: $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(single_valued1,type,
single_valued1: $i > $i ).
tff(successor,type,
successor: $i > $i ).
tff(successor_relation,type,
successor_relation: $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff(not_homomorphism1,type,
not_homomorphism1: ( $i * $i * $i ) > $i ).
tff(universal_class,type,
universal_class: $i ).
tff(f_779,axiom,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
file(unknown,unknown) ).
tff(f_239,axiom,
! [X,Y,Xr] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_521,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file(unknown,unknown) ).
tff(f_237,axiom,
! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_200,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_75,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_523,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(c_226,plain,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_58,plain,
! [X_66,Y_67,Xr_68] : ( intersection(cross_product(X_66,Y_67),Xr_68) = restrict(Xr_68,X_66,Y_67) ),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_148,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(cnfTransformation,[status(thm)],[f_521]) ).
tff(c_227,plain,
restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) = subset_relation,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_58,c_148]) ).
tff(c_56,plain,
! [Xr_63,X_64,Y_65] : ( intersection(Xr_63,cross_product(X_64,Y_65)) = restrict(Xr_63,X_64,Y_65) ),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_641,plain,
! [X_308,Y_309] :
( subclass(X_308,Y_309)
| member(not_subclass_element(X_308,Y_309),X_308) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_44,plain,
! [Z_49,Y_51,X_50] :
( member(Z_49,Y_51)
| ~ member(Z_49,intersection(X_50,Y_51)) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_118980,plain,
! [X_3895,Y_3896,Y_3897] :
( member(not_subclass_element(intersection(X_3895,Y_3896),Y_3897),Y_3896)
| subclass(intersection(X_3895,Y_3896),Y_3897) ),
inference(resolution,[status(thm)],[c_641,c_44]) ).
tff(c_6,plain,
! [X_6,Y_7] :
( subclass(X_6,Y_7)
| ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_119166,plain,
! [X_3898,Y_3899] : subclass(intersection(X_3898,Y_3899),Y_3899),
inference(resolution,[status(thm)],[c_118980,c_6]) ).
tff(c_119906,plain,
! [Xr_3928,X_3929,Y_3930] : subclass(restrict(Xr_3928,X_3929,Y_3930),cross_product(X_3929,Y_3930)),
inference(superposition,[status(thm),theory(equality)],[c_56,c_119166]) ).
tff(c_119924,plain,
subclass(subset_relation,cross_product(universal_class,universal_class)),
inference(superposition,[status(thm),theory(equality)],[c_227,c_119906]) ).
tff(c_150,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(cnfTransformation,[status(thm)],[f_523]) ).
tff(c_119123,plain,
! [Y_3897] :
( member(not_subclass_element(identity_relation,Y_3897),subset_relation)
| subclass(intersection(inverse(subset_relation),subset_relation),Y_3897) ),
inference(superposition,[status(thm),theory(equality)],[c_150,c_118980]) ).
tff(c_119896,plain,
! [Y_3927] :
( member(not_subclass_element(identity_relation,Y_3927),subset_relation)
| subclass(identity_relation,Y_3927) ),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_119123]) ).
tff(c_2,plain,
! [U_3,Y_2,X_1] :
( member(U_3,Y_2)
| ~ member(U_3,X_1)
| ~ subclass(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_301481,plain,
! [Y_6746,Y_6747] :
( member(not_subclass_element(identity_relation,Y_6746),Y_6747)
| ~ subclass(subset_relation,Y_6747)
| subclass(identity_relation,Y_6746) ),
inference(resolution,[status(thm)],[c_119896,c_2]) ).
tff(c_301721,plain,
! [Y_6748] :
( ~ subclass(subset_relation,Y_6748)
| subclass(identity_relation,Y_6748) ),
inference(resolution,[status(thm)],[c_301481,c_6]) ).
tff(c_301732,plain,
subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(resolution,[status(thm)],[c_119924,c_301721]) ).
tff(c_301755,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_226,c_301732]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET454-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 16:49:05 EDT 2023
% 0.15/0.36 % CPUTime :
% 102.13/84.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 102.13/84.58
% 102.13/84.58 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 102.13/84.62
% 102.13/84.62 Inference rules
% 102.13/84.62 ----------------------
% 102.13/84.62 #Ref : 5
% 102.13/84.62 #Sup : 80400
% 102.13/84.62 #Fact : 22
% 102.13/84.62 #Define : 0
% 102.13/84.62 #Split : 711
% 102.13/84.62 #Chain : 0
% 102.13/84.62 #Close : 0
% 102.13/84.62
% 102.13/84.62 Ordering : KBO
% 102.13/84.62
% 102.13/84.62 Simplification rules
% 102.13/84.62 ----------------------
% 102.13/84.62 #Subsume : 25656
% 102.13/84.62 #Demod : 30973
% 102.13/84.62 #Tautology : 10038
% 102.13/84.62 #SimpNegUnit : 2594
% 102.13/84.62 #BackRed : 1260
% 102.13/84.62
% 102.13/84.62 #Partial instantiations: 0
% 102.13/84.62 #Strategies tried : 1
% 102.13/84.62
% 102.13/84.62 Timing (in seconds)
% 102.13/84.62 ----------------------
% 102.13/84.62 Preprocessing : 0.73
% 102.13/84.62 Parsing : 0.38
% 102.13/84.62 CNF conversion : 0.05
% 102.13/84.62 Main loop : 82.83
% 102.13/84.62 Inferencing : 10.48
% 102.13/84.62 Reduction : 38.98
% 102.13/84.62 Demodulation : 27.99
% 102.13/84.62 BG Simplification : 0.39
% 102.13/84.62 Subsumption : 26.27
% 102.13/84.62 Abstraction : 0.65
% 102.13/84.62 MUC search : 0.00
% 102.13/84.62 Cooper : 0.00
% 102.13/84.62 Total : 83.61
% 102.13/84.62 Index Insertion : 0.00
% 102.13/84.63 Index Deletion : 0.00
% 102.13/84.63 Index Matching : 0.00
% 102.13/84.63 BG Taut test : 0.00
%------------------------------------------------------------------------------