TSTP Solution File: SET451-6 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET451-6 : 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/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 : n002.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 14.57s 4.85s
% Output : CNFRefutation 14.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 63
% Syntax : Number of formulae : 76 ( 13 unt; 56 typ; 0 def)
% Number of atoms : 27 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 34 (; 34 !; 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(subset_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(c_226,plain,
~ subclass(subset_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_11600,plain,
! [X_892,Y_893,Y_894] :
( member(not_subclass_element(intersection(X_892,Y_893),Y_894),Y_893)
| subclass(intersection(X_892,Y_893),Y_894) ),
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_11796,plain,
! [X_895,Y_896] : subclass(intersection(X_895,Y_896),Y_896),
inference(resolution,[status(thm)],[c_11600,c_6]) ).
tff(c_12183,plain,
! [Xr_908,X_909,Y_910] : subclass(restrict(Xr_908,X_909,Y_910),cross_product(X_909,Y_910)),
inference(superposition,[status(thm),theory(equality)],[c_56,c_11796]) ).
tff(c_12210,plain,
subclass(subset_relation,cross_product(universal_class,universal_class)),
inference(superposition,[status(thm),theory(equality)],[c_227,c_12183]) ).
tff(c_12222,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_226,c_12210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET451-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15 % 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
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.36 % CPULimit : 300
% 0.20/0.36 % WCLimit : 300
% 0.20/0.36 % DateTime : Thu Aug 3 16:36:46 EDT 2023
% 0.20/0.36 % CPUTime :
% 14.57/4.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.57/4.85
% 14.57/4.85 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.57/4.88
% 14.57/4.88 Inference rules
% 14.57/4.88 ----------------------
% 14.57/4.88 #Ref : 0
% 14.57/4.88 #Sup : 3004
% 14.57/4.88 #Fact : 0
% 14.57/4.88 #Define : 0
% 14.57/4.88 #Split : 82
% 14.57/4.88 #Chain : 0
% 14.57/4.88 #Close : 0
% 14.57/4.88
% 14.57/4.88 Ordering : KBO
% 14.57/4.88
% 14.57/4.88 Simplification rules
% 14.57/4.88 ----------------------
% 14.57/4.88 #Subsume : 735
% 14.57/4.88 #Demod : 918
% 14.57/4.88 #Tautology : 491
% 14.57/4.88 #SimpNegUnit : 50
% 14.57/4.88 #BackRed : 121
% 14.57/4.88
% 14.57/4.88 #Partial instantiations: 0
% 14.57/4.88 #Strategies tried : 1
% 14.57/4.88
% 14.57/4.88 Timing (in seconds)
% 14.57/4.88 ----------------------
% 14.67/4.89 Preprocessing : 0.78
% 14.67/4.89 Parsing : 0.41
% 14.67/4.89 CNF conversion : 0.05
% 14.67/4.89 Main loop : 2.93
% 14.67/4.89 Inferencing : 0.87
% 14.67/4.89 Reduction : 1.05
% 14.67/4.89 Demodulation : 0.72
% 14.67/4.89 BG Simplification : 0.08
% 14.67/4.89 Subsumption : 0.64
% 14.67/4.89 Abstraction : 0.08
% 14.67/4.89 MUC search : 0.00
% 14.67/4.89 Cooper : 0.00
% 14.67/4.89 Total : 3.75
% 14.67/4.89 Index Insertion : 0.00
% 14.67/4.89 Index Deletion : 0.00
% 14.67/4.89 Index Matching : 0.00
% 14.67/4.89 BG Taut test : 0.00
%------------------------------------------------------------------------------