TSTP Solution File: NUM183-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM183-1 : 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 : n022.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 83.12s 67.39s
% Output : CNFRefutation 83.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 87
% Syntax : Number of formulae : 102 ( 12 unt; 79 typ; 0 def)
% Number of atoms : 44 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 63 ( 63 usr; 19 con; 0-3 aty)
% Number of variables : 21 (; 21 !; 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 > x > 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(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_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_1116,axiom,
~ member(x,kind_1_ordinals),
file(unknown,unknown) ).
tff(f_1118,axiom,
~ member(x,limit_ordinals),
file(unknown,unknown) ).
tff(f_1114,axiom,
member(x,ordinal_numbers),
file(unknown,unknown) ).
tff(f_77,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_220,axiom,
! [Z,X] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_995,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file(unknown,unknown) ).
tff(f_205,axiom,
! [Z,X,Y] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ),
file(unknown,unknown) ).
tff(c_320,plain,
~ member(x,kind_1_ordinals),
inference(cnfTransformation,[status(thm)],[f_1116]) ).
tff(c_322,plain,
~ member(x,limit_ordinals),
inference(cnfTransformation,[status(thm)],[f_1118]) ).
tff(c_318,plain,
member(x,ordinal_numbers),
inference(cnfTransformation,[status(thm)],[f_1114]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_9780,plain,
! [U_1177,Y_1178,X_1179] :
( member(U_1177,Y_1178)
| ~ member(U_1177,X_1179)
| ~ subclass(X_1179,Y_1178) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_9856,plain,
! [Y_1181] :
( member(x,Y_1181)
| ~ subclass(ordinal_numbers,Y_1181) ),
inference(resolution,[status(thm)],[c_318,c_9780]) ).
tff(c_9870,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c_8,c_9856]) ).
tff(c_50,plain,
! [Z_57,X_58] :
( member(Z_57,X_58)
| member(Z_57,complement(X_58))
| ~ member(Z_57,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_278,plain,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
inference(cnfTransformation,[status(thm)],[f_995]) ).
tff(c_11145,plain,
! [Z_1301,X_1302,Y_1303] :
( member(Z_1301,intersection(X_1302,Y_1303))
| ~ member(Z_1301,Y_1303)
| ~ member(Z_1301,X_1302) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_19167,plain,
! [Z_1615] :
( member(Z_1615,limit_ordinals)
| ~ member(Z_1615,ordinal_numbers)
| ~ member(Z_1615,complement(kind_1_ordinals)) ),
inference(superposition,[status(thm),theory(equality)],[c_278,c_11145]) ).
tff(c_223857,plain,
! [Z_4802] :
( member(Z_4802,limit_ordinals)
| ~ member(Z_4802,ordinal_numbers)
| member(Z_4802,kind_1_ordinals)
| ~ member(Z_4802,universal_class) ),
inference(resolution,[status(thm)],[c_50,c_19167]) ).
tff(c_224062,plain,
( member(x,limit_ordinals)
| ~ member(x,ordinal_numbers)
| member(x,kind_1_ordinals) ),
inference(resolution,[status(thm)],[c_9870,c_223857]) ).
tff(c_224206,plain,
( member(x,limit_ordinals)
| member(x,kind_1_ordinals) ),
inference(demodulation,[status(thm),theory(equality)],[c_318,c_224062]) ).
tff(c_224208,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_320,c_322,c_224206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM183-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 14:25:03 EDT 2023
% 0.14/0.34 % CPUTime :
% 83.12/67.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 83.12/67.39
% 83.12/67.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.12/67.42
% 83.12/67.42 Inference rules
% 83.12/67.42 ----------------------
% 83.12/67.42 #Ref : 1
% 83.12/67.42 #Sup : 58847
% 83.12/67.42 #Fact : 24
% 83.12/67.42 #Define : 0
% 83.12/67.42 #Split : 364
% 83.12/67.42 #Chain : 0
% 83.12/67.42 #Close : 0
% 83.12/67.42
% 83.12/67.42 Ordering : KBO
% 83.12/67.42
% 83.12/67.42 Simplification rules
% 83.12/67.42 ----------------------
% 83.12/67.42 #Subsume : 23289
% 83.12/67.43 #Demod : 26179
% 83.12/67.43 #Tautology : 10500
% 83.12/67.43 #SimpNegUnit : 5604
% 83.12/67.43 #BackRed : 1866
% 83.12/67.43
% 83.12/67.43 #Partial instantiations: 0
% 83.12/67.43 #Strategies tried : 1
% 83.12/67.43
% 83.12/67.43 Timing (in seconds)
% 83.12/67.43 ----------------------
% 83.26/67.43 Preprocessing : 0.81
% 83.26/67.43 Parsing : 0.43
% 83.26/67.43 CNF conversion : 0.06
% 83.26/67.43 Main loop : 65.61
% 83.26/67.43 Inferencing : 7.96
% 83.26/67.43 Reduction : 29.95
% 83.26/67.43 Demodulation : 21.43
% 83.26/67.43 BG Simplification : 0.29
% 83.26/67.43 Subsumption : 18.96
% 83.26/67.43 Abstraction : 0.47
% 83.26/67.43 MUC search : 0.00
% 83.26/67.43 Cooper : 0.00
% 83.26/67.43 Total : 66.48
% 83.26/67.43 Index Insertion : 0.00
% 83.26/67.43 Index Deletion : 0.00
% 83.26/67.43 Index Matching : 0.00
% 83.26/67.43 BG Taut test : 0.00
%------------------------------------------------------------------------------