TSTP Solution File: SET506-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET506-6 : 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 : n018.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 10:56:31 EDT 2023
% Result : Unsatisfiable 6.22s 2.45s
% Output : CNFRefutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 67
% Syntax : Number of formulae : 101 ( 24 unt; 56 typ; 0 def)
% Number of atoms : 69 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 24 ~; 24 |; 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 : 72 ( 44 >; 28 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 46 ( 46 usr; 12 con; 0-3 aty)
% Number of variables : 49 (; 49 !; 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 > 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(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(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_778,axiom,
universal_class = null_class,
file(unknown,unknown) ).
tff(f_80,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_132,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_128,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_483,axiom,
! [X] :
( ( X = null_class )
| ( intersection(X,regular(X)) = null_class ) ),
file(unknown,unknown) ).
tff(f_194,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_523,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file(unknown,unknown) ).
tff(f_200,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_383,axiom,
member(omega,universal_class),
file(unknown,unknown) ).
tff(f_216,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(c_226,plain,
universal_class = null_class,
inference(cnfTransformation,[status(thm)],[f_778]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_265,plain,
! [X_8] : subclass(X_8,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_226,c_8]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_22,plain,
! [X_22,Y_23] : member(unordered_pair(X_22,Y_23),universal_class),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_299,plain,
! [X_224,Y_225] : member(unordered_pair(X_224,Y_225),null_class),
inference(demodulation,[status(thm),theory(equality)],[c_226,c_22]) ).
tff(c_301,plain,
! [X_24] : member(singleton(X_24),null_class),
inference(superposition,[status(thm),theory(equality)],[c_24,c_299]) ).
tff(c_134,plain,
! [X_132] :
( ( intersection(X_132,regular(X_132)) = null_class )
| ( null_class = X_132 ) ),
inference(cnfTransformation,[status(thm)],[f_483]) ).
tff(c_411,plain,
! [Z_265,X_266,Y_267] :
( member(Z_265,X_266)
| ~ member(Z_265,intersection(X_266,Y_267)) ),
inference(cnfTransformation,[status(thm)],[f_194]) ).
tff(c_943,plain,
! [Z_328,X_329] :
( member(Z_328,X_329)
| ~ member(Z_328,null_class)
| ( null_class = X_329 ) ),
inference(superposition,[status(thm),theory(equality)],[c_134,c_411]) ).
tff(c_980,plain,
! [X_24,X_329] :
( member(singleton(X_24),X_329)
| ( null_class = X_329 ) ),
inference(resolution,[status(thm)],[c_301,c_943]) ).
tff(c_150,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(cnfTransformation,[status(thm)],[f_523]) ).
tff(c_584,plain,
! [Z_294,Y_295,X_296] :
( member(Z_294,Y_295)
| ~ member(Z_294,intersection(X_296,Y_295)) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_597,plain,
! [Z_294] :
( member(Z_294,subset_relation)
| ~ member(Z_294,identity_relation) ),
inference(superposition,[status(thm),theory(equality)],[c_150,c_584]) ).
tff(c_104,plain,
member(omega,universal_class),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_245,plain,
member(omega,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_226,c_104]) ).
tff(c_984,plain,
! [X_330] :
( member(omega,X_330)
| ( null_class = X_330 ) ),
inference(resolution,[status(thm)],[c_245,c_943]) ).
tff(c_48,plain,
! [Z_55,X_56] :
( ~ member(Z_55,X_56)
| ~ member(Z_55,complement(X_56)) ),
inference(cnfTransformation,[status(thm)],[f_216]) ).
tff(c_1055,plain,
! [X_336] :
( ~ member(omega,X_336)
| ( complement(X_336) = null_class ) ),
inference(resolution,[status(thm)],[c_984,c_48]) ).
tff(c_1094,plain,
( ( complement(subset_relation) = null_class )
| ~ member(omega,identity_relation) ),
inference(resolution,[status(thm)],[c_597,c_1055]) ).
tff(c_1414,plain,
~ member(omega,identity_relation),
inference(splitLeft,[status(thm)],[c_1094]) ).
tff(c_983,plain,
! [X_329] :
( member(omega,X_329)
| ( null_class = X_329 ) ),
inference(resolution,[status(thm)],[c_245,c_943]) ).
tff(c_1418,plain,
null_class = identity_relation,
inference(resolution,[status(thm)],[c_983,c_1414]) ).
tff(c_1468,plain,
member(omega,identity_relation),
inference(demodulation,[status(thm),theory(equality)],[c_1418,c_245]) ).
tff(c_1471,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1414,c_1468]) ).
tff(c_1472,plain,
complement(subset_relation) = null_class,
inference(splitRight,[status(thm)],[c_1094]) ).
tff(c_1632,plain,
! [Z_348] :
( ~ member(Z_348,subset_relation)
| ~ member(Z_348,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1472,c_48]) ).
tff(c_1636,plain,
! [X_24] :
( ~ member(singleton(X_24),null_class)
| ( subset_relation = null_class ) ),
inference(resolution,[status(thm)],[c_980,c_1632]) ).
tff(c_1666,plain,
subset_relation = null_class,
inference(demodulation,[status(thm),theory(equality)],[c_301,c_1636]) ).
tff(c_753,plain,
! [U_316,Y_317,X_318] :
( member(U_316,Y_317)
| ~ member(U_316,X_318)
| ~ subclass(X_318,Y_317) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_804,plain,
! [X_24,Y_317] :
( member(singleton(X_24),Y_317)
| ~ subclass(null_class,Y_317) ),
inference(resolution,[status(thm)],[c_301,c_753]) ).
tff(c_1648,plain,
! [X_24] :
( ~ member(singleton(X_24),null_class)
| ~ subclass(null_class,subset_relation) ),
inference(resolution,[status(thm)],[c_804,c_1632]) ).
tff(c_1675,plain,
~ subclass(null_class,subset_relation),
inference(demodulation,[status(thm),theory(equality)],[c_301,c_1648]) ).
tff(c_1734,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_265,c_1666,c_1675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET506-6 : 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
% 0.14/0.36 % Computer : n018.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 16:39:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 6.22/2.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.22/2.45
% 6.22/2.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.22/2.48
% 6.22/2.48 Inference rules
% 6.22/2.48 ----------------------
% 6.22/2.48 #Ref : 0
% 6.22/2.48 #Sup : 348
% 6.22/2.48 #Fact : 0
% 6.22/2.48 #Define : 0
% 6.22/2.48 #Split : 6
% 6.22/2.49 #Chain : 0
% 6.22/2.49 #Close : 0
% 6.22/2.49
% 6.22/2.49 Ordering : KBO
% 6.22/2.49
% 6.22/2.49 Simplification rules
% 6.22/2.49 ----------------------
% 6.22/2.49 #Subsume : 21
% 6.22/2.49 #Demod : 207
% 6.22/2.49 #Tautology : 119
% 6.22/2.49 #SimpNegUnit : 1
% 6.22/2.49 #BackRed : 59
% 6.22/2.49
% 6.22/2.49 #Partial instantiations: 0
% 6.22/2.49 #Strategies tried : 1
% 6.22/2.49
% 6.22/2.49 Timing (in seconds)
% 6.22/2.49 ----------------------
% 6.22/2.49 Preprocessing : 0.73
% 6.22/2.49 Parsing : 0.39
% 6.22/2.49 CNF conversion : 0.05
% 6.22/2.49 Main loop : 0.68
% 6.22/2.49 Inferencing : 0.21
% 6.22/2.49 Reduction : 0.24
% 6.22/2.49 Demodulation : 0.18
% 6.22/2.49 BG Simplification : 0.05
% 6.22/2.49 Subsumption : 0.14
% 6.22/2.49 Abstraction : 0.02
% 6.22/2.49 MUC search : 0.00
% 6.22/2.49 Cooper : 0.00
% 6.22/2.49 Total : 1.46
% 6.22/2.49 Index Insertion : 0.00
% 6.22/2.49 Index Deletion : 0.00
% 6.22/2.49 Index Matching : 0.00
% 6.22/2.49 BG Taut test : 0.00
%------------------------------------------------------------------------------