TSTP Solution File: NUM190-1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM190-1 : 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 : n007.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 10:51:02 EDT 2023
% Result : Unsatisfiable 6.77s 2.51s
% Output : CNFRefutation 6.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 85
% Syntax : Number of formulae : 103 ( 10 unt; 78 typ; 0 def)
% Number of atoms : 41 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 60 >; 43 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 18 con; 0-3 aty)
% Number of variables : 22 (; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ section > maps > homomorphism > compatible > well_ordering > transitive > subclass > member > irreflexive > connected > asymmetric > single_valued_class > operation > one_to_one > inductive > function > segment > restrict > recursion > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordinal_multiply > ordinal_add > ordered_pair > not_well_ordering > not_subclass_element > least > intersection > image > cross_product > compose > apply > #nlpp > symmetrization_of > sum_class > successor > singleton > single_valued3 > single_valued2 > single_valued1 > second > rotate > rest_of > regular > recursion_equation_functions > range_of > power_class > inverse > integer_of > flip > first > domain_of > diagonalise > compose_class > complement > cantor > universal_class > union_of_range_map > successor_relation > subset_relation > singleton_relation > rest_relation > ordinal_numbers > omega > null_class > limit_ordinals > kind_1_ordinals > identity_relation > element_relation > domain_relation > composition_function > choice > application_function > add_relation
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(omega,type,
omega: $i ).
tff(null_class,type,
null_class: $i ).
tff(limit_ordinals,type,
limit_ordinals: $i ).
tff(kind_1_ordinals,type,
kind_1_ordinals: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff(rest_relation,type,
rest_relation: $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_of_range_map,type,
union_of_range_map: $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(transitive,type,
transitive: ( $i * $i ) > $o ).
tff(well_ordering,type,
well_ordering: ( $i * $i ) > $o ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(ordinal_numbers,type,
ordinal_numbers: $i ).
tff(choice,type,
choice: $i ).
tff(connected,type,
connected: ( $i * $i ) > $o ).
tff(subset_relation,type,
subset_relation: $i ).
tff(ordinal_multiply,type,
ordinal_multiply: ( $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(section,type,
section: ( $i * $i * $i ) > $o ).
tff(ordinal_add,type,
ordinal_add: ( $i * $i ) > $i ).
tff(recursion,type,
recursion: ( $i * $i * $i ) > $i ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(irreflexive,type,
irreflexive: ( $i * $i ) > $o ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(first,type,
first: $i > $i ).
tff(integer_of,type,
integer_of: $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(least,type,
least: ( $i * $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(recursion_equation_functions,type,
recursion_equation_functions: $i > $i ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff(add_relation,type,
add_relation: $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(rest_of,type,
rest_of: $i > $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(segment,type,
segment: ( $i * $i * $i ) > $i ).
tff(symmetrization_of,type,
symmetrization_of: $i > $i ).
tff(single_valued1,type,
single_valued1: $i > $i ).
tff(successor,type,
successor: $i > $i ).
tff(asymmetric,type,
asymmetric: ( $i * $i ) > $o ).
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(not_well_ordering,type,
not_well_ordering: ( $i * $i ) > $i ).
tff(f_1114,axiom,
omega = null_class,
file(unknown,unknown) ).
tff(f_374,axiom,
inductive(omega),
file(unknown,unknown) ).
tff(f_380,axiom,
member(omega,universal_class),
file(unknown,unknown) ).
tff(f_480,axiom,
! [X] :
( ( X = null_class )
| ( intersection(X,regular(X)) = null_class ) ),
file(unknown,unknown) ).
tff(f_355,axiom,
! [X] :
( ~ inductive(X)
| member(null_class,X) ),
file(unknown,unknown) ).
tff(f_191,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_213,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(c_318,plain,
omega = null_class,
inference(cnfTransformation,[status(thm)],[f_1114]) ).
tff(c_100,plain,
inductive(omega),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_323,plain,
inductive(null_class),
inference(demodulation,[status(thm),theory(equality)],[c_318,c_100]) ).
tff(c_104,plain,
member(omega,universal_class),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_321,plain,
member(null_class,universal_class),
inference(demodulation,[status(thm),theory(equality)],[c_318,c_104]) ).
tff(c_134,plain,
! [X_132] :
( ( intersection(X_132,regular(X_132)) = null_class )
| ( null_class = X_132 ) ),
inference(cnfTransformation,[status(thm)],[f_480]) ).
tff(c_94,plain,
! [X_106] :
( member(null_class,X_106)
| ~ inductive(X_106) ),
inference(cnfTransformation,[status(thm)],[f_355]) ).
tff(c_700,plain,
! [Z_389,X_390,Y_391] :
( member(Z_389,X_390)
| ~ member(Z_389,intersection(X_390,Y_391)) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_726,plain,
! [X_393,Y_394] :
( member(null_class,X_393)
| ~ inductive(intersection(X_393,Y_394)) ),
inference(resolution,[status(thm)],[c_94,c_700]) ).
tff(c_729,plain,
! [X_132] :
( member(null_class,X_132)
| ~ inductive(null_class)
| ( null_class = X_132 ) ),
inference(superposition,[status(thm),theory(equality)],[c_134,c_726]) ).
tff(c_738,plain,
! [X_395] :
( member(null_class,X_395)
| ( null_class = X_395 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_323,c_729]) ).
tff(c_48,plain,
! [Z_55,X_56] :
( ~ member(Z_55,X_56)
| ~ member(Z_55,complement(X_56)) ),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_890,plain,
! [X_409] :
( ~ member(null_class,X_409)
| ( complement(X_409) = null_class ) ),
inference(resolution,[status(thm)],[c_738,c_48]) ).
tff(c_941,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[c_321,c_890]) ).
tff(c_460,plain,
! [Z_346,X_347] :
( ~ member(Z_346,X_347)
| ~ member(Z_346,complement(X_347)) ),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_470,plain,
! [X_347] :
( ~ member(null_class,X_347)
| ~ inductive(complement(X_347)) ),
inference(resolution,[status(thm)],[c_94,c_460]) ).
tff(c_962,plain,
( ~ member(null_class,universal_class)
| ~ inductive(null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_941,c_470]) ).
tff(c_970,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_323,c_321,c_962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM190-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15 % 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
% 0.14/0.36 % Computer : n007.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
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 3 15:07:54 EDT 2023
% 0.14/0.37 % CPUTime :
% 6.77/2.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.77/2.52
% 6.77/2.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.77/2.55
% 6.77/2.55 Inference rules
% 6.77/2.55 ----------------------
% 6.77/2.55 #Ref : 0
% 6.77/2.55 #Sup : 135
% 6.77/2.55 #Fact : 2
% 6.77/2.55 #Define : 0
% 6.77/2.55 #Split : 8
% 6.77/2.55 #Chain : 0
% 6.77/2.55 #Close : 0
% 6.77/2.55
% 6.77/2.55 Ordering : KBO
% 6.77/2.55
% 6.77/2.55 Simplification rules
% 6.77/2.55 ----------------------
% 6.77/2.55 #Subsume : 14
% 6.77/2.55 #Demod : 32
% 6.77/2.55 #Tautology : 54
% 6.87/2.55 #SimpNegUnit : 2
% 6.87/2.55 #BackRed : 7
% 6.87/2.55
% 6.87/2.55 #Partial instantiations: 0
% 6.87/2.55 #Strategies tried : 1
% 6.87/2.55
% 6.87/2.55 Timing (in seconds)
% 6.87/2.55 ----------------------
% 6.87/2.55 Preprocessing : 0.81
% 6.87/2.55 Parsing : 0.43
% 6.87/2.55 CNF conversion : 0.06
% 6.87/2.55 Main loop : 0.60
% 6.87/2.55 Inferencing : 0.18
% 6.87/2.55 Reduction : 0.21
% 6.87/2.55 Demodulation : 0.15
% 6.87/2.55 BG Simplification : 0.05
% 6.87/2.55 Subsumption : 0.13
% 6.87/2.55 Abstraction : 0.02
% 6.87/2.55 MUC search : 0.00
% 6.87/2.55 Cooper : 0.00
% 6.87/2.55 Total : 1.46
% 6.87/2.55 Index Insertion : 0.00
% 6.87/2.55 Index Deletion : 0.00
% 6.87/2.55 Index Matching : 0.00
% 6.87/2.55 BG Taut test : 0.00
%------------------------------------------------------------------------------