TSTP Solution File: SET411-6 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET411-6 : 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/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 : n010.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 10:56:25 EDT 2023
% Result : Unsatisfiable 6.74s 2.54s
% Output : CNFRefutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 65
% Syntax : Number of formulae : 78 ( 12 unt; 58 typ; 0 def)
% Number of atoms : 30 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 48 ( 48 usr; 14 con; 0-3 aty)
% Number of variables : 20 (; 20 !; 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 > 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(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_780,axiom,
~ member(x,universal_class),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_778,axiom,
member(ordered_pair(x,y),singleton_relation),
file(unknown,unknown) ).
tff(f_729,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file(unknown,unknown) ).
tff(f_200,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_178,axiom,
! [X,Y] :
( ~ member(ordered_pair(X,Y),element_relation)
| member(X,Y) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(c_228,plain,
~ member(x,universal_class),
inference(cnfTransformation,[status(thm)],[f_780]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_226,plain,
member(ordered_pair(x,y),singleton_relation),
inference(cnfTransformation,[status(thm)],[f_778]) ).
tff(c_208,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(cnfTransformation,[status(thm)],[f_729]) ).
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_620,plain,
! [Z_304] :
( member(Z_304,element_relation)
| ~ member(Z_304,singleton_relation) ),
inference(superposition,[status(thm),theory(equality)],[c_208,c_44]) ).
tff(c_639,plain,
member(ordered_pair(x,y),element_relation),
inference(resolution,[status(thm)],[c_226,c_620]) ).
tff(c_38,plain,
! [X_42,Y_43] :
( member(X_42,Y_43)
| ~ member(ordered_pair(X_42,Y_43),element_relation) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_644,plain,
member(x,y),
inference(resolution,[status(thm)],[c_639,c_38]) ).
tff(c_1721,plain,
! [U_5720,Y_5721,X_5722] :
( member(U_5720,Y_5721)
| ~ member(U_5720,X_5722)
| ~ subclass(X_5722,Y_5721) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_1838,plain,
! [Y_5994] :
( member(x,Y_5994)
| ~ subclass(y,Y_5994) ),
inference(resolution,[status(thm)],[c_644,c_1721]) ).
tff(c_1846,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c_8,c_1838]) ).
tff(c_1855,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_228,c_1846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET411-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.14/0.35 % Computer : n010.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 16:05:29 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.74/2.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.74/2.54
% 6.74/2.54 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.92/2.57
% 6.92/2.57 Inference rules
% 6.92/2.57 ----------------------
% 6.92/2.57 #Ref : 0
% 6.92/2.57 #Sup : 340
% 6.92/2.57 #Fact : 0
% 6.92/2.57 #Define : 0
% 6.92/2.57 #Split : 10
% 6.92/2.57 #Chain : 0
% 6.92/2.57 #Close : 0
% 6.92/2.57
% 6.92/2.57 Ordering : KBO
% 6.92/2.57
% 6.92/2.57 Simplification rules
% 6.92/2.57 ----------------------
% 6.92/2.57 #Subsume : 21
% 6.92/2.57 #Demod : 82
% 6.92/2.57 #Tautology : 86
% 6.92/2.57 #SimpNegUnit : 1
% 6.92/2.57 #BackRed : 19
% 6.92/2.57
% 6.92/2.57 #Partial instantiations: 4160
% 6.92/2.57 #Strategies tried : 1
% 6.92/2.57
% 6.92/2.57 Timing (in seconds)
% 6.92/2.57 ----------------------
% 6.92/2.57 Preprocessing : 0.75
% 6.92/2.57 Parsing : 0.40
% 6.92/2.57 CNF conversion : 0.05
% 6.92/2.57 Main loop : 0.76
% 6.92/2.57 Inferencing : 0.31
% 6.92/2.57 Reduction : 0.22
% 6.92/2.57 Demodulation : 0.16
% 6.92/2.57 BG Simplification : 0.05
% 6.92/2.57 Subsumption : 0.13
% 6.92/2.57 Abstraction : 0.02
% 6.92/2.57 MUC search : 0.00
% 6.92/2.57 Cooper : 0.00
% 6.92/2.57 Total : 1.55
% 6.92/2.57 Index Insertion : 0.00
% 6.92/2.57 Index Deletion : 0.00
% 6.92/2.57 Index Matching : 0.00
% 6.92/2.57 BG Taut test : 0.00
%------------------------------------------------------------------------------