TSTP Solution File: SET510-6 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET510-6 : 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 : n004.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 174.58s 150.37s
% Output : CNFRefutation 174.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 82
% Syntax : Number of formulae : 221 ( 63 unt; 56 typ; 0 def)
% Number of atoms : 308 ( 107 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 259 ( 116 ~; 143 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 46 ( 46 usr; 12 con; 0-3 aty)
% Number of variables : 220 (; 220 !; 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_780,axiom,
singleton(universal_class) != null_class,
file(unknown,unknown) ).
tff(f_492,axiom,
function(choice),
file(unknown,unknown) ).
tff(f_133,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_129,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_499,axiom,
! [Y] :
( ~ member(Y,universal_class)
| ( Y = null_class )
| member(apply(choice,Y),Y) ),
file(unknown,unknown) ).
tff(f_112,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_474,axiom,
! [Xf,X] :
( ~ function(Xf)
| ~ member(X,universal_class)
| member(image(Xf,X),universal_class) ),
file(unknown,unknown) ).
tff(f_488,axiom,
! [Xf,Y] : ( sum_class(image(Xf,singleton(Y))) = apply(Xf,Y) ),
file(unknown,unknown) ).
tff(f_400,axiom,
! [X] :
( ~ member(X,universal_class)
| member(sum_class(X),universal_class) ),
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_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_240,axiom,
! [X,Y,Xr] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_480,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_201,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_217,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(f_224,axiom,
! [Z,X] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_76,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_195,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_251,axiom,
! [X,Z] :
( ( restrict(X,singleton(Z),universal_class) != null_class )
| ~ member(Z,domain_of(X)) ),
file(unknown,unknown) ).
tff(f_528,axiom,
! [Xr] : ( complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr) ),
file(unknown,unknown) ).
tff(f_101,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_484,axiom,
! [X] :
( ( X = null_class )
| ( intersection(X,regular(X)) = null_class ) ),
file(unknown,unknown) ).
tff(f_229,axiom,
! [X,Y] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
file(unknown,unknown) ).
tff(f_233,axiom,
! [X,Y] : ( intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y)))) = symmetric_difference(X,Y) ),
file(unknown,unknown) ).
tff(c_226,plain,
singleton(universal_class) != null_class,
inference(cnfTransformation,[status(thm)],[f_780]) ).
tff(c_138,plain,
function(choice),
inference(cnfTransformation,[status(thm)],[f_492]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_259,plain,
! [X_224,Y_225] : member(unordered_pair(X_224,Y_225),universal_class),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_261,plain,
! [X_24] : member(singleton(X_24),universal_class),
inference(superposition,[status(thm),theory(equality)],[c_24,c_259]) ).
tff(c_1741,plain,
! [Y_409] :
( member(apply(choice,Y_409),Y_409)
| ( null_class = Y_409 )
| ~ member(Y_409,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_499]) ).
tff(c_705,plain,
! [Y_313,U_314,X_315] :
( ( Y_313 = U_314 )
| ( X_315 = U_314 )
| ~ member(U_314,unordered_pair(X_315,Y_313)) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_726,plain,
! [X_24,U_314] :
( ( X_24 = U_314 )
| ( X_24 = U_314 )
| ~ member(U_314,singleton(X_24)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_705]) ).
tff(c_1755,plain,
! [X_24] :
( ( apply(choice,singleton(X_24)) = X_24 )
| ( singleton(X_24) = null_class )
| ~ member(singleton(X_24),universal_class) ),
inference(resolution,[status(thm)],[c_1741,c_726]) ).
tff(c_1784,plain,
! [X_24] :
( ( apply(choice,singleton(X_24)) = X_24 )
| ( singleton(X_24) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_1755]) ).
tff(c_130,plain,
! [Xf_129,X_130] :
( member(image(Xf_129,X_130),universal_class)
| ~ member(X_130,universal_class)
| ~ function(Xf_129) ),
inference(cnfTransformation,[status(thm)],[f_474]) ).
tff(c_406,plain,
! [Xf_280,Y_281] : ( sum_class(image(Xf_280,singleton(Y_281))) = apply(Xf_280,Y_281) ),
inference(cnfTransformation,[status(thm)],[f_488]) ).
tff(c_108,plain,
! [X_111] :
( member(sum_class(X_111),universal_class)
| ~ member(X_111,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_400]) ).
tff(c_114570,plain,
! [Xf_3777,Y_3778] :
( member(apply(Xf_3777,Y_3778),universal_class)
| ~ member(image(Xf_3777,singleton(Y_3778)),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_406,c_108]) ).
tff(c_114581,plain,
! [Xf_129,Y_3778] :
( member(apply(Xf_129,Y_3778),universal_class)
| ~ member(singleton(Y_3778),universal_class)
| ~ function(Xf_129) ),
inference(resolution,[status(thm)],[c_130,c_114570]) ).
tff(c_114586,plain,
! [Xf_3779,Y_3780] :
( member(apply(Xf_3779,Y_3780),universal_class)
| ~ function(Xf_3779) ),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_114581]) ).
tff(c_114603,plain,
! [X_24] :
( member(X_24,universal_class)
| ~ function(choice)
| ( singleton(X_24) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_1784,c_114586]) ).
tff(c_114607,plain,
! [X_24] :
( member(X_24,universal_class)
| ( singleton(X_24) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_114603]) ).
tff(c_1832,plain,
! [X_417] :
( ( apply(choice,singleton(X_417)) = X_417 )
| ( singleton(X_417) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_1755]) ).
tff(c_140,plain,
! [Y_135] :
( member(apply(choice,Y_135),Y_135)
| ( null_class = Y_135 )
| ~ member(Y_135,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_499]) ).
tff(c_1838,plain,
! [X_417] :
( member(X_417,singleton(X_417))
| ( singleton(X_417) = null_class )
| ~ member(singleton(X_417),universal_class)
| ( singleton(X_417) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_1832,c_140]) ).
tff(c_1844,plain,
! [X_417] :
( member(X_417,singleton(X_417))
| ( singleton(X_417) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_1838]) ).
tff(c_46,plain,
! [Z_52,X_53,Y_54] :
( member(Z_52,intersection(X_53,Y_54))
| ~ member(Z_52,Y_54)
| ~ member(Z_52,X_53) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
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_825,plain,
! [U_327,Y_328,X_329] :
( member(U_327,Y_328)
| ~ member(U_327,X_329)
| ~ subclass(X_329,Y_328) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_859,plain,
! [X_4,Y_5,Y_328] :
( member(not_subclass_element(X_4,Y_5),Y_328)
| ~ subclass(X_4,Y_328)
| subclass(X_4,Y_5) ),
inference(resolution,[status(thm)],[c_4,c_825]) ).
tff(c_58,plain,
! [X_66,Y_67,Xr_68] : ( intersection(cross_product(X_66,Y_67),Xr_68) = restrict(Xr_68,X_66,Y_67) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_480]) ).
tff(c_559,plain,
! [Z_299,Y_300,X_301] :
( member(Z_299,Y_300)
| ~ member(Z_299,intersection(X_301,Y_300)) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_69862,plain,
! [X_2544,Y_2545] :
( member(regular(intersection(X_2544,Y_2545)),Y_2545)
| ( intersection(X_2544,Y_2545) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_559]) ).
tff(c_866,plain,
! [X_131,Y_328] :
( member(regular(X_131),Y_328)
| ~ subclass(X_131,Y_328)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_132,c_825]) ).
tff(c_1387,plain,
! [X_382,Y_383] :
( member(regular(X_382),Y_383)
| ~ subclass(X_382,Y_383)
| ( null_class = X_382 ) ),
inference(resolution,[status(thm)],[c_132,c_825]) ).
tff(c_344,plain,
! [Z_257,X_258] :
( ~ member(Z_257,X_258)
| ~ member(Z_257,complement(X_258)) ),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_359,plain,
! [X_258] :
( ~ member(regular(complement(X_258)),X_258)
| ( complement(X_258) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_344]) ).
tff(c_1442,plain,
! [Y_384] :
( ~ subclass(complement(Y_384),Y_384)
| ( complement(Y_384) = null_class ) ),
inference(resolution,[status(thm)],[c_1387,c_359]) ).
tff(c_1464,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[c_8,c_1442]) ).
tff(c_48,plain,
! [Z_55,X_56] :
( ~ member(Z_55,X_56)
| ~ member(Z_55,complement(X_56)) ),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_1501,plain,
! [Z_385] :
( ~ member(Z_385,universal_class)
| ~ member(Z_385,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1464,c_48]) ).
tff(c_1505,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ~ subclass(X_131,universal_class)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_866,c_1501]) ).
tff(c_1549,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ( null_class = X_131 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1505]) ).
tff(c_69987,plain,
! [X_2546] : ( intersection(X_2546,null_class) = null_class ),
inference(resolution,[status(thm)],[c_69862,c_1549]) ).
tff(c_70033,plain,
! [X_66,Y_67] : ( restrict(null_class,X_66,Y_67) = null_class ),
inference(superposition,[status(thm),theory(equality)],[c_58,c_69987]) ).
tff(c_1631,plain,
! [Z_398,X_399] :
( member(Z_398,X_399)
| member(Z_398,complement(X_399))
| ~ member(Z_398,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_224]) ).
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_139684,plain,
! [X_4463,X_4464] :
( subclass(X_4463,complement(X_4464))
| member(not_subclass_element(X_4463,complement(X_4464)),X_4464)
| ~ member(not_subclass_element(X_4463,complement(X_4464)),universal_class) ),
inference(resolution,[status(thm)],[c_1631,c_6]) ).
tff(c_139706,plain,
! [X_4,X_4464] :
( member(not_subclass_element(X_4,complement(X_4464)),X_4464)
| ~ subclass(X_4,universal_class)
| subclass(X_4,complement(X_4464)) ),
inference(resolution,[status(thm)],[c_859,c_139684]) ).
tff(c_142853,plain,
! [X_4498,X_4499] :
( member(not_subclass_element(X_4498,complement(X_4499)),X_4499)
| subclass(X_4498,complement(X_4499)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_139706]) ).
tff(c_371,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_195]) ).
tff(c_69634,plain,
! [X_2540,Y_2541] :
( member(regular(intersection(X_2540,Y_2541)),X_2540)
| ( intersection(X_2540,Y_2541) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_371]) ).
tff(c_69758,plain,
! [Y_2542] : ( intersection(null_class,Y_2542) = null_class ),
inference(resolution,[status(thm)],[c_69634,c_1549]) ).
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_201]) ).
tff(c_70263,plain,
! [Z_2553,Y_2554] :
( member(Z_2553,Y_2554)
| ~ member(Z_2553,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_69758,c_44]) ).
tff(c_113445,plain,
! [Y_3734,Y_3735] :
( member(not_subclass_element(null_class,Y_3734),Y_3735)
| subclass(null_class,Y_3734) ),
inference(resolution,[status(thm)],[c_4,c_70263]) ).
tff(c_512,plain,
! [X_291,Y_292] :
( subclass(X_291,Y_292)
| member(not_subclass_element(X_291,Y_292),X_291) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_108829,plain,
! [X_3585,Y_3586] :
( ~ member(not_subclass_element(complement(X_3585),Y_3586),X_3585)
| subclass(complement(X_3585),Y_3586) ),
inference(resolution,[status(thm)],[c_512,c_48]) ).
tff(c_108861,plain,
! [Y_3586] :
( ~ member(not_subclass_element(null_class,Y_3586),universal_class)
| subclass(complement(universal_class),Y_3586) ),
inference(superposition,[status(thm),theory(equality)],[c_1464,c_108829]) ).
tff(c_108892,plain,
! [Y_3586] :
( ~ member(not_subclass_element(null_class,Y_3586),universal_class)
| subclass(null_class,Y_3586) ),
inference(demodulation,[status(thm),theory(equality)],[c_1464,c_108861]) ).
tff(c_113539,plain,
! [Y_3734] : subclass(null_class,Y_3734),
inference(resolution,[status(thm)],[c_113445,c_108892]) ).
tff(c_1339,plain,
! [Z_378,X_379] :
( ~ member(Z_378,domain_of(X_379))
| ( restrict(X_379,singleton(Z_378),universal_class) != null_class ) ),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_116565,plain,
! [X_3842] :
( ( restrict(X_3842,singleton(regular(domain_of(X_3842))),universal_class) != null_class )
| ( domain_of(X_3842) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_1339]) ).
tff(c_116579,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm),theory(equality)],[c_70033,c_116565]) ).
tff(c_69737,plain,
! [Y_2541] : ( intersection(null_class,Y_2541) = null_class ),
inference(resolution,[status(thm)],[c_69634,c_1549]) ).
tff(c_152,plain,
! [Xr_139] : ( complement(domain_of(intersection(Xr_139,identity_relation))) = diagonalise(Xr_139) ),
inference(cnfTransformation,[status(thm)],[f_528]) ).
tff(c_70101,plain,
! [Z_2550,Xr_2551] :
( ~ member(Z_2550,domain_of(intersection(Xr_2551,identity_relation)))
| ~ member(Z_2550,diagonalise(Xr_2551)) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_344]) ).
tff(c_113221,plain,
! [Z_3726] :
( ~ member(Z_3726,domain_of(null_class))
| ~ member(Z_3726,diagonalise(null_class)) ),
inference(superposition,[status(thm),theory(equality)],[c_69737,c_70101]) ).
tff(c_113316,plain,
( ~ member(regular(domain_of(null_class)),diagonalise(null_class))
| ( domain_of(null_class) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_113221]) ).
tff(c_115193,plain,
~ member(regular(domain_of(null_class)),diagonalise(null_class)),
inference(splitLeft,[status(thm)],[c_113316]) ).
tff(c_115197,plain,
( ~ subclass(domain_of(null_class),diagonalise(null_class))
| ( domain_of(null_class) = null_class ) ),
inference(resolution,[status(thm)],[c_866,c_115193]) ).
tff(c_115198,plain,
~ subclass(domain_of(null_class),diagonalise(null_class)),
inference(splitLeft,[status(thm)],[c_115197]) ).
tff(c_116586,plain,
~ subclass(null_class,diagonalise(null_class)),
inference(demodulation,[status(thm),theory(equality)],[c_116579,c_115198]) ).
tff(c_116599,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_113539,c_116586]) ).
tff(c_116600,plain,
domain_of(null_class) = null_class,
inference(splitRight,[status(thm)],[c_115197]) ).
tff(c_60,plain,
! [Z_70,X_69] :
( ~ member(Z_70,domain_of(X_69))
| ( restrict(X_69,singleton(Z_70),universal_class) != null_class ) ),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_116664,plain,
! [Z_70] :
( ~ member(Z_70,null_class)
| ( restrict(null_class,singleton(Z_70),universal_class) != null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_116600,c_60]) ).
tff(c_116697,plain,
! [Z_70] : ~ member(Z_70,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_70033,c_116664]) ).
tff(c_143102,plain,
! [X_4500] : subclass(X_4500,complement(null_class)),
inference(resolution,[status(thm)],[c_142853,c_116697]) ).
tff(c_418,plain,
! [Y_282,X_283] :
( ( Y_282 = X_283 )
| ~ subclass(Y_282,X_283)
| ~ subclass(X_283,Y_282) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_459,plain,
! [X_8] :
( ( universal_class = X_8 )
| ~ subclass(universal_class,X_8) ),
inference(resolution,[status(thm)],[c_8,c_418]) ).
tff(c_143382,plain,
complement(null_class) = universal_class,
inference(resolution,[status(thm)],[c_143102,c_459]) ).
tff(c_739,plain,
! [X_319,U_320] :
( ( X_319 = U_320 )
| ( X_319 = U_320 )
| ~ member(U_320,singleton(X_319)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_705]) ).
tff(c_776,plain,
! [X_322] :
( ( regular(singleton(X_322)) = X_322 )
| ( singleton(X_322) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_739]) ).
tff(c_134,plain,
! [X_132] :
( ( intersection(X_132,regular(X_132)) = null_class )
| ( null_class = X_132 ) ),
inference(cnfTransformation,[status(thm)],[f_484]) ).
tff(c_170577,plain,
! [X_5066] :
( ( intersection(singleton(X_5066),X_5066) = null_class )
| ( singleton(X_5066) = null_class )
| ( singleton(X_5066) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_776,c_134]) ).
tff(c_69968,plain,
! [X_2544] : ( intersection(X_2544,null_class) = null_class ),
inference(resolution,[status(thm)],[c_69862,c_1549]) ).
tff(c_52,plain,
! [X_59,Y_60] : ( complement(intersection(complement(X_59),complement(Y_60))) = union(X_59,Y_60) ),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_1478,plain,
! [X_59] : ( complement(intersection(complement(X_59),null_class)) = union(X_59,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1464,c_52]) ).
tff(c_70051,plain,
! [X_2547] : ( union(X_2547,universal_class) = complement(null_class) ),
inference(demodulation,[status(thm),theory(equality)],[c_69968,c_1478]) ).
tff(c_54,plain,
! [X_61,Y_62] : ( intersection(complement(intersection(X_61,Y_62)),complement(intersection(complement(X_61),complement(Y_62)))) = symmetric_difference(X_61,Y_62) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_228,plain,
! [X_61,Y_62] : ( intersection(complement(intersection(X_61,Y_62)),union(X_61,Y_62)) = symmetric_difference(X_61,Y_62) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54]) ).
tff(c_70062,plain,
! [X_2547] : ( intersection(complement(intersection(X_2547,universal_class)),complement(null_class)) = symmetric_difference(X_2547,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_70051,c_228]) ).
tff(c_143387,plain,
! [X_2547] : ( intersection(complement(intersection(X_2547,universal_class)),universal_class) = symmetric_difference(X_2547,universal_class) ),
inference(demodulation,[status(thm),theory(equality)],[c_143382,c_70062]) ).
tff(c_170702,plain,
( ( symmetric_difference(singleton(universal_class),universal_class) = intersection(complement(null_class),universal_class) )
| ( singleton(universal_class) = null_class )
| ( singleton(universal_class) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_170577,c_143387]) ).
tff(c_171026,plain,
( ( symmetric_difference(singleton(universal_class),universal_class) = intersection(universal_class,universal_class) )
| ( singleton(universal_class) = null_class )
| ( singleton(universal_class) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143382,c_170702]) ).
tff(c_171027,plain,
symmetric_difference(singleton(universal_class),universal_class) = intersection(universal_class,universal_class),
inference(negUnitSimplification,[status(thm)],[c_226,c_226,c_171026]) ).
tff(c_42,plain,
! [Z_46,X_47,Y_48] :
( member(Z_46,X_47)
| ~ member(Z_46,intersection(X_47,Y_48)) ),
inference(cnfTransformation,[status(thm)],[f_195]) ).
tff(c_122601,plain,
! [X_4003,Y_4004,Y_4005] :
( member(not_subclass_element(intersection(X_4003,Y_4004),Y_4005),X_4003)
| subclass(intersection(X_4003,Y_4004),Y_4005) ),
inference(resolution,[status(thm)],[c_512,c_42]) ).
tff(c_122810,plain,
! [X_4006,Y_4007] : subclass(intersection(X_4006,Y_4007),X_4006),
inference(resolution,[status(thm)],[c_122601,c_6]) ).
tff(c_122872,plain,
! [X_61,Y_62] : subclass(symmetric_difference(X_61,Y_62),complement(intersection(X_61,Y_62))),
inference(superposition,[status(thm),theory(equality)],[c_228,c_122810]) ).
tff(c_171146,plain,
subclass(intersection(universal_class,universal_class),complement(intersection(singleton(universal_class),universal_class))),
inference(superposition,[status(thm),theory(equality)],[c_171027,c_122872]) ).
tff(c_1859,plain,
! [Z_419,X_420,Y_421] :
( member(Z_419,intersection(X_420,Y_421))
| ~ member(Z_419,Y_421)
| ~ member(Z_419,X_420) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_2,plain,
! [U_3,Y_2,X_1] :
( member(U_3,Y_2)
| ~ member(U_3,X_1)
| ~ subclass(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_1898,plain,
! [Z_419,Y_2,X_420,Y_421] :
( member(Z_419,Y_2)
| ~ subclass(intersection(X_420,Y_421),Y_2)
| ~ member(Z_419,Y_421)
| ~ member(Z_419,X_420) ),
inference(resolution,[status(thm)],[c_1859,c_2]) ).
tff(c_171290,plain,
! [Z_5071] :
( member(Z_5071,complement(intersection(singleton(universal_class),universal_class)))
| ~ member(Z_5071,universal_class) ),
inference(resolution,[status(thm)],[c_171146,c_1898]) ).
tff(c_171440,plain,
! [Z_5072] :
( ~ member(Z_5072,intersection(singleton(universal_class),universal_class))
| ~ member(Z_5072,universal_class) ),
inference(resolution,[status(thm)],[c_171290,c_48]) ).
tff(c_171730,plain,
! [Z_5073] :
( ~ member(Z_5073,universal_class)
| ~ member(Z_5073,singleton(universal_class)) ),
inference(resolution,[status(thm)],[c_46,c_171440]) ).
tff(c_171878,plain,
( ~ member(universal_class,universal_class)
| ( singleton(universal_class) = null_class ) ),
inference(resolution,[status(thm)],[c_1844,c_171730]) ).
tff(c_171983,plain,
~ member(universal_class,universal_class),
inference(negUnitSimplification,[status(thm)],[c_226,c_171878]) ).
tff(c_172008,plain,
singleton(universal_class) = null_class,
inference(resolution,[status(thm)],[c_114607,c_171983]) ).
tff(c_172016,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_226,c_172008]) ).
tff(c_172017,plain,
domain_of(null_class) = null_class,
inference(splitRight,[status(thm)],[c_113316]) ).
tff(c_172080,plain,
! [Z_70] :
( ~ member(Z_70,null_class)
| ( restrict(null_class,singleton(Z_70),universal_class) != null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_172017,c_60]) ).
tff(c_172113,plain,
! [Z_70] : ~ member(Z_70,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_70033,c_172080]) ).
tff(c_69813,plain,
complement(domain_of(null_class)) = diagonalise(null_class),
inference(superposition,[status(thm),theory(equality)],[c_69758,c_152]) ).
tff(c_172027,plain,
diagonalise(null_class) = complement(null_class),
inference(demodulation,[status(thm),theory(equality)],[c_172017,c_69813]) ).
tff(c_184845,plain,
! [Z_5459,Xr_5460] :
( member(Z_5459,domain_of(intersection(Xr_5460,identity_relation)))
| member(Z_5459,diagonalise(Xr_5460))
| ~ member(Z_5459,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_1631]) ).
tff(c_184916,plain,
! [Z_5459] :
( member(Z_5459,domain_of(null_class))
| member(Z_5459,diagonalise(null_class))
| ~ member(Z_5459,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_69737,c_184845]) ).
tff(c_184965,plain,
! [Z_5459] :
( member(Z_5459,null_class)
| member(Z_5459,complement(null_class))
| ~ member(Z_5459,universal_class) ),
inference(demodulation,[status(thm),theory(equality)],[c_172027,c_172017,c_184916]) ).
tff(c_184967,plain,
! [Z_5461] :
( member(Z_5461,complement(null_class))
| ~ member(Z_5461,universal_class) ),
inference(negUnitSimplification,[status(thm)],[c_172113,c_184965]) ).
tff(c_480956,plain,
! [X_9913] :
( subclass(X_9913,complement(null_class))
| ~ member(not_subclass_element(X_9913,complement(null_class)),universal_class) ),
inference(resolution,[status(thm)],[c_184967,c_6]) ).
tff(c_480968,plain,
! [X_4] :
( ~ subclass(X_4,universal_class)
| subclass(X_4,complement(null_class)) ),
inference(resolution,[status(thm)],[c_859,c_480956]) ).
tff(c_480998,plain,
! [X_9914] : subclass(X_9914,complement(null_class)),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_480968]) ).
tff(c_481310,plain,
complement(null_class) = universal_class,
inference(resolution,[status(thm)],[c_480998,c_459]) ).
tff(c_509239,plain,
! [X_10410] :
( ( intersection(singleton(X_10410),X_10410) = null_class )
| ( singleton(X_10410) = null_class )
| ( singleton(X_10410) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_776,c_134]) ).
tff(c_481323,plain,
! [X_2547] : ( intersection(complement(intersection(X_2547,universal_class)),universal_class) = symmetric_difference(X_2547,universal_class) ),
inference(demodulation,[status(thm),theory(equality)],[c_481310,c_70062]) ).
tff(c_509363,plain,
( ( symmetric_difference(singleton(universal_class),universal_class) = intersection(complement(null_class),universal_class) )
| ( singleton(universal_class) = null_class )
| ( singleton(universal_class) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_509239,c_481323]) ).
tff(c_509679,plain,
( ( symmetric_difference(singleton(universal_class),universal_class) = intersection(universal_class,universal_class) )
| ( singleton(universal_class) = null_class )
| ( singleton(universal_class) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_481310,c_509363]) ).
tff(c_509680,plain,
symmetric_difference(singleton(universal_class),universal_class) = intersection(universal_class,universal_class),
inference(negUnitSimplification,[status(thm)],[c_226,c_226,c_509679]) ).
tff(c_180672,plain,
! [X_5338,Y_5339,Y_5340] :
( member(not_subclass_element(intersection(X_5338,Y_5339),Y_5340),X_5338)
| subclass(intersection(X_5338,Y_5339),Y_5340) ),
inference(resolution,[status(thm)],[c_512,c_42]) ).
tff(c_180895,plain,
! [X_5341,Y_5342] : subclass(intersection(X_5341,Y_5342),X_5341),
inference(resolution,[status(thm)],[c_180672,c_6]) ).
tff(c_180959,plain,
! [X_61,Y_62] : subclass(symmetric_difference(X_61,Y_62),complement(intersection(X_61,Y_62))),
inference(superposition,[status(thm),theory(equality)],[c_228,c_180895]) ).
tff(c_509774,plain,
subclass(intersection(universal_class,universal_class),complement(intersection(singleton(universal_class),universal_class))),
inference(superposition,[status(thm),theory(equality)],[c_509680,c_180959]) ).
tff(c_509960,plain,
! [Z_10415] :
( member(Z_10415,complement(intersection(singleton(universal_class),universal_class)))
| ~ member(Z_10415,universal_class) ),
inference(resolution,[status(thm)],[c_509774,c_1898]) ).
tff(c_510125,plain,
! [Z_10416] :
( ~ member(Z_10416,intersection(singleton(universal_class),universal_class))
| ~ member(Z_10416,universal_class) ),
inference(resolution,[status(thm)],[c_509960,c_48]) ).
tff(c_510448,plain,
! [Z_10419] :
( ~ member(Z_10419,universal_class)
| ~ member(Z_10419,singleton(universal_class)) ),
inference(resolution,[status(thm)],[c_46,c_510125]) ).
tff(c_510596,plain,
( ~ member(universal_class,universal_class)
| ( singleton(universal_class) = null_class ) ),
inference(resolution,[status(thm)],[c_1844,c_510448]) ).
tff(c_510703,plain,
~ member(universal_class,universal_class),
inference(negUnitSimplification,[status(thm)],[c_226,c_510596]) ).
tff(c_510728,plain,
singleton(universal_class) = null_class,
inference(resolution,[status(thm)],[c_114607,c_510703]) ).
tff(c_510736,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_226,c_510728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET510-6 : 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 : n004.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 16:38:11 EDT 2023
% 0.14/0.34 % CPUTime :
% 174.58/150.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 174.58/150.40
% 174.58/150.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 174.82/150.45
% 174.82/150.45 Inference rules
% 174.82/150.45 ----------------------
% 174.82/150.45 #Ref : 6
% 174.82/150.45 #Sup : 137324
% 174.82/150.45 #Fact : 28
% 174.82/150.45 #Define : 0
% 174.82/150.45 #Split : 1061
% 174.82/150.45 #Chain : 0
% 174.82/150.45 #Close : 0
% 174.82/150.45
% 174.82/150.45 Ordering : KBO
% 174.82/150.45
% 174.82/150.45 Simplification rules
% 174.82/150.45 ----------------------
% 174.82/150.45 #Subsume : 43343
% 174.82/150.45 #Demod : 57408
% 174.82/150.45 #Tautology : 18026
% 174.82/150.45 #SimpNegUnit : 3400
% 174.82/150.45 #BackRed : 1571
% 174.82/150.45
% 174.82/150.45 #Partial instantiations: 0
% 174.82/150.45 #Strategies tried : 1
% 174.82/150.45
% 174.82/150.45 Timing (in seconds)
% 174.82/150.45 ----------------------
% 174.82/150.45 Preprocessing : 0.72
% 174.82/150.45 Parsing : 0.38
% 174.82/150.45 CNF conversion : 0.05
% 174.82/150.45 Main loop : 148.64
% 174.82/150.45 Inferencing : 17.62
% 174.82/150.45 Reduction : 69.49
% 174.82/150.45 Demodulation : 49.64
% 174.82/150.45 BG Simplification : 0.62
% 174.82/150.45 Subsumption : 47.02
% 174.82/150.45 Abstraction : 1.08
% 174.82/150.45 MUC search : 0.00
% 174.82/150.45 Cooper : 0.00
% 174.82/150.45 Total : 149.45
% 174.82/150.45 Index Insertion : 0.00
% 174.82/150.45 Index Deletion : 0.00
% 174.82/150.45 Index Matching : 0.00
% 174.82/150.45 BG Taut test : 0.00
%------------------------------------------------------------------------------