TSTP Solution File: SET244-6 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET244-6 : 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 10:56:15 EDT 2023
% Result : Unsatisfiable 225.47s 197.90s
% Output : CNFRefutation 225.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 67
% Syntax : Number of formulae : 87 ( 10 unt; 58 typ; 0 def)
% Number of atoms : 56 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 25 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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 : 48 ( 48 usr; 14 con; 0-3 aty)
% Number of variables : 60 (; 60 !; 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_81,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_209,axiom,
! [Z,X,Y] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ),
file(unknown,unknown) ).
tff(f_76,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_201,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_101,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_238,axiom,
! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_780,axiom,
restrict(universal_class,x,y) != cross_product(x,y),
file(unknown,unknown) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_4,plain,
! [X_4,Y_5] :
( subclass(X_4,Y_5)
| member(not_subclass_element(X_4,Y_5),X_4) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_859,plain,
! [U_335,Y_336,X_337] :
( member(U_335,Y_336)
| ~ member(U_335,X_337)
| ~ subclass(X_337,Y_336) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_896,plain,
! [X_4,Y_5,Y_336] :
( member(not_subclass_element(X_4,Y_5),Y_336)
| ~ subclass(X_4,Y_336)
| subclass(X_4,Y_5) ),
inference(resolution,[status(thm)],[c_4,c_859]) ).
tff(c_2205,plain,
! [Z_450,X_451,Y_452] :
( member(Z_450,intersection(X_451,Y_452))
| ~ member(Z_450,Y_452)
| ~ member(Z_450,X_451) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_6,plain,
! [X_6,Y_7] :
( subclass(X_6,Y_7)
| ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_745369,plain,
! [X_17353,X_17354,Y_17355] :
( subclass(X_17353,intersection(X_17354,Y_17355))
| ~ member(not_subclass_element(X_17353,intersection(X_17354,Y_17355)),Y_17355)
| ~ member(not_subclass_element(X_17353,intersection(X_17354,Y_17355)),X_17354) ),
inference(resolution,[status(thm)],[c_2205,c_6]) ).
tff(c_776735,plain,
! [X_18029,X_18030] :
( ~ member(not_subclass_element(X_18029,intersection(X_18030,X_18029)),X_18030)
| subclass(X_18029,intersection(X_18030,X_18029)) ),
inference(resolution,[status(thm)],[c_4,c_745369]) ).
tff(c_783186,plain,
! [X_18091,Y_18092] :
( ~ subclass(X_18091,Y_18092)
| subclass(X_18091,intersection(Y_18092,X_18091)) ),
inference(resolution,[status(thm)],[c_896,c_776735]) ).
tff(c_541,plain,
! [Z_287,Y_288,X_289] :
( member(Z_287,Y_288)
| ~ member(Z_287,intersection(X_289,Y_288)) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_522142,plain,
! [X_12023,Y_12024,Y_12025] :
( member(not_subclass_element(intersection(X_12023,Y_12024),Y_12025),Y_12024)
| subclass(intersection(X_12023,Y_12024),Y_12025) ),
inference(resolution,[status(thm)],[c_4,c_541]) ).
tff(c_522334,plain,
! [X_12026,Y_12027] : subclass(intersection(X_12026,Y_12027),Y_12027),
inference(resolution,[status(thm)],[c_522142,c_6]) ).
tff(c_14,plain,
! [Y_14,X_13] :
( ( Y_14 = X_13 )
| ~ subclass(Y_14,X_13)
| ~ subclass(X_13,Y_14) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_522421,plain,
! [X_12026,Y_12027] :
( ( intersection(X_12026,Y_12027) = Y_12027 )
| ~ subclass(Y_12027,intersection(X_12026,Y_12027)) ),
inference(resolution,[status(thm)],[c_522334,c_14]) ).
tff(c_783803,plain,
! [Y_18095,X_18096] :
( ( intersection(Y_18095,X_18096) = X_18096 )
| ~ subclass(X_18096,Y_18095) ),
inference(resolution,[status(thm)],[c_783186,c_522421]) ).
tff(c_784136,plain,
! [X_18097] : ( intersection(universal_class,X_18097) = X_18097 ),
inference(resolution,[status(thm)],[c_8,c_783803]) ).
tff(c_56,plain,
! [Xr_63,X_64,Y_65] : ( intersection(Xr_63,cross_product(X_64,Y_65)) = restrict(Xr_63,X_64,Y_65) ),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_784367,plain,
! [X_64,Y_65] : ( restrict(universal_class,X_64,Y_65) = cross_product(X_64,Y_65) ),
inference(superposition,[status(thm),theory(equality)],[c_784136,c_56]) ).
tff(c_226,plain,
restrict(universal_class,x,y) != cross_product(x,y),
inference(cnfTransformation,[status(thm)],[f_780]) ).
tff(c_788045,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_784367,c_226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET244-6 : 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
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 16:43:44 EDT 2023
% 0.15/0.36 % CPUTime :
% 225.47/197.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 225.47/197.91
% 225.47/197.91 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 225.47/197.94
% 225.47/197.94 Inference rules
% 225.47/197.94 ----------------------
% 225.47/197.94 #Ref : 5
% 225.47/197.94 #Sup : 211946
% 225.47/197.94 #Fact : 68
% 225.47/197.94 #Define : 0
% 225.47/197.94 #Split : 1368
% 225.47/197.94 #Chain : 0
% 225.47/197.94 #Close : 0
% 225.47/197.94
% 225.47/197.94 Ordering : KBO
% 225.47/197.94
% 225.47/197.94 Simplification rules
% 225.47/197.94 ----------------------
% 225.47/197.94 #Subsume : 61897
% 225.47/197.94 #Demod : 96734
% 225.47/197.94 #Tautology : 30891
% 225.47/197.94 #SimpNegUnit : 4542
% 225.47/197.94 #BackRed : 1932
% 225.47/197.94
% 225.47/197.94 #Partial instantiations: 0
% 225.47/197.94 #Strategies tried : 1
% 225.47/197.94
% 225.47/197.94 Timing (in seconds)
% 225.47/197.94 ----------------------
% 225.65/197.94 Preprocessing : 0.75
% 225.65/197.94 Parsing : 0.39
% 225.65/197.94 CNF conversion : 0.05
% 225.65/197.94 Main loop : 196.13
% 225.65/197.94 Inferencing : 23.63
% 225.65/197.94 Reduction : 90.36
% 225.65/197.94 Demodulation : 65.55
% 225.65/197.94 BG Simplification : 0.97
% 225.65/197.94 Subsumption : 61.60
% 225.65/197.94 Abstraction : 1.70
% 225.65/197.94 MUC search : 0.00
% 225.65/197.94 Cooper : 0.00
% 225.65/197.94 Total : 196.93
% 225.65/197.94 Index Insertion : 0.00
% 225.65/197.94 Index Deletion : 0.00
% 225.65/197.94 Index Matching : 0.00
% 225.65/197.94 BG Taut test : 0.00
%------------------------------------------------------------------------------