TSTP Solution File: SET252-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET252-6 : 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 : n025.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 10:56:16 EDT 2023
% Result : Unsatisfiable 13.13s 4.15s
% Output : CNFRefutation 13.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 64
% Syntax : Number of formulae : 73 ( 7 unt; 59 typ; 0 def)
% Number of atoms : 21 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 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 : 49 ( 49 usr; 15 con; 0-3 aty)
% Number of variables : 28 (; 28 !; 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 > z > y > x > 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(x,type,
x: $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(y,type,
y: $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(z,type,
z: $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_239,axiom,
! [X,Y,Xr] : ( intersection(cross_product(X,Y),Xr) = 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_779,axiom,
~ subclass(restrict(x,y,z),x),
file(unknown,unknown) ).
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_4,plain,
! [X_4,Y_5] :
( subclass(X_4,Y_5)
| member(not_subclass_element(X_4,Y_5),X_4) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_585,plain,
! [Z_301,Y_302,X_303] :
( member(Z_301,Y_302)
| ~ member(Z_301,intersection(X_303,Y_302)) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_9089,plain,
! [X_803,Y_804,Y_805] :
( member(not_subclass_element(intersection(X_803,Y_804),Y_805),Y_804)
| subclass(intersection(X_803,Y_804),Y_805) ),
inference(resolution,[status(thm)],[c_4,c_585]) ).
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_9224,plain,
! [X_806,Y_807] : subclass(intersection(X_806,Y_807),Y_807),
inference(resolution,[status(thm)],[c_9089,c_6]) ).
tff(c_9277,plain,
! [Xr_68,X_66,Y_67] : subclass(restrict(Xr_68,X_66,Y_67),Xr_68),
inference(superposition,[status(thm),theory(equality)],[c_58,c_9224]) ).
tff(c_226,plain,
~ subclass(restrict(x,y,z),x),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_9297,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9277,c_226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET252-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n025.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 16:22:19 EDT 2023
% 0.14/0.36 % CPUTime :
% 13.13/4.15 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.13/4.16
% 13.13/4.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.53/4.18
% 13.53/4.18 Inference rules
% 13.53/4.18 ----------------------
% 13.53/4.18 #Ref : 0
% 13.53/4.18 #Sup : 2242
% 13.53/4.18 #Fact : 0
% 13.53/4.18 #Define : 0
% 13.53/4.18 #Split : 64
% 13.53/4.18 #Chain : 0
% 13.53/4.18 #Close : 0
% 13.53/4.18
% 13.53/4.18 Ordering : KBO
% 13.53/4.18
% 13.53/4.18 Simplification rules
% 13.53/4.18 ----------------------
% 13.53/4.18 #Subsume : 513
% 13.53/4.18 #Demod : 714
% 13.53/4.18 #Tautology : 411
% 13.53/4.18 #SimpNegUnit : 30
% 13.53/4.18 #BackRed : 125
% 13.53/4.18
% 13.53/4.18 #Partial instantiations: 0
% 13.53/4.18 #Strategies tried : 1
% 13.53/4.18
% 13.53/4.18 Timing (in seconds)
% 13.53/4.18 ----------------------
% 13.53/4.19 Preprocessing : 0.74
% 13.53/4.19 Parsing : 0.39
% 13.53/4.19 CNF conversion : 0.05
% 13.53/4.19 Main loop : 2.38
% 13.53/4.19 Inferencing : 0.74
% 13.53/4.19 Reduction : 0.81
% 13.53/4.19 Demodulation : 0.54
% 13.53/4.19 BG Simplification : 0.07
% 13.53/4.19 Subsumption : 0.55
% 13.53/4.19 Abstraction : 0.06
% 13.53/4.19 MUC search : 0.00
% 13.53/4.19 Cooper : 0.00
% 13.53/4.19 Total : 3.16
% 13.53/4.19 Index Insertion : 0.00
% 13.53/4.19 Index Deletion : 0.00
% 13.53/4.19 Index Matching : 0.00
% 13.53/4.19 BG Taut test : 0.00
%------------------------------------------------------------------------------