TSTP Solution File: NUM228-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM228-1 : 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/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 : n029.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 10:51:04 EDT 2023
% Result : Unsatisfiable 5.10s 2.26s
% Output : CNFRefutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 83
% Syntax : Number of formulae : 90 ( 6 unt; 79 typ; 0 def)
% Number of atoms : 16 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 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 : 63 ( 63 usr; 19 con; 0-3 aty)
% Number of variables : 7 (; 7 !; 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 > z > 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(z,type,
z: $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_1117,axiom,
recursion_equation_functions(z) != null_class,
file(unknown,unknown) ).
tff(f_476,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_1039,axiom,
! [X,Z] :
( ~ member(X,recursion_equation_functions(Z))
| function(Z) ),
file(unknown,unknown) ).
tff(f_1115,axiom,
~ function(z),
file(unknown,unknown) ).
tff(c_320,plain,
recursion_equation_functions(z) != null_class,
inference(cnfTransformation,[status(thm)],[f_1117]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_413,plain,
! [Z_339,X_340] :
( function(Z_339)
| ~ member(X_340,recursion_equation_functions(Z_339)) ),
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_433,plain,
! [Z_342] :
( function(Z_342)
| ( recursion_equation_functions(Z_342) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_413]) ).
tff(c_318,plain,
~ function(z),
inference(cnfTransformation,[status(thm)],[f_1115]) ).
tff(c_436,plain,
recursion_equation_functions(z) = null_class,
inference(resolution,[status(thm)],[c_433,c_318]) ).
tff(c_440,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_320,c_436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM228-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % 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
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 15:25:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.10/2.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.10/2.26
% 5.10/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.10/2.29
% 5.10/2.29 Inference rules
% 5.10/2.29 ----------------------
% 5.10/2.29 #Ref : 0
% 5.10/2.29 #Sup : 23
% 5.10/2.29 #Fact : 0
% 5.10/2.29 #Define : 0
% 5.10/2.29 #Split : 1
% 5.10/2.29 #Chain : 0
% 5.10/2.29 #Close : 0
% 5.10/2.29
% 5.10/2.29 Ordering : KBO
% 5.10/2.29
% 5.10/2.29 Simplification rules
% 5.10/2.29 ----------------------
% 5.10/2.29 #Subsume : 1
% 5.10/2.29 #Demod : 5
% 5.10/2.29 #Tautology : 15
% 5.10/2.29 #SimpNegUnit : 1
% 5.10/2.29 #BackRed : 0
% 5.10/2.29
% 5.10/2.29 #Partial instantiations: 0
% 5.10/2.29 #Strategies tried : 1
% 5.10/2.29
% 5.10/2.29 Timing (in seconds)
% 5.10/2.29 ----------------------
% 5.10/2.29 Preprocessing : 0.82
% 5.10/2.29 Parsing : 0.43
% 5.10/2.29 CNF conversion : 0.06
% 5.10/2.29 Main loop : 0.41
% 5.10/2.29 Inferencing : 0.08
% 5.10/2.29 Reduction : 0.16
% 5.10/2.29 Demodulation : 0.12
% 5.10/2.29 BG Simplification : 0.05
% 5.10/2.29 Subsumption : 0.10
% 5.10/2.29 Abstraction : 0.02
% 5.10/2.29 MUC search : 0.00
% 5.10/2.29 Cooper : 0.00
% 5.10/2.29 Total : 1.28
% 5.10/2.29 Index Insertion : 0.00
% 5.10/2.29 Index Deletion : 0.00
% 5.10/2.29 Index Matching : 0.00
% 5.10/2.29 BG Taut test : 0.00
%------------------------------------------------------------------------------