%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET151-6 : TPTP v9.0.0. 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 : n023.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 : Wed Apr 9 08:38:07 PM UTC 2025
% Result : Unsatisfiable 35.30s 20.89s
% Output : CNFRefutation 35.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 92 ( 45 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 78 ( 78 !; 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,
complement(null_class) != universal_class,
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_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_238,axiom,
! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_480,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_195,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_217,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ 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_101,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(c_226,plain,
complement(null_class) != universal_class,
inference(cnfTransformation,[status(thm)],[f_780]) ).
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_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_96861,plain,
! [X_3252,X_3253] :
( subclass(X_3252,complement(X_3253))
| member(not_subclass_element(X_3252,complement(X_3253)),X_3253)
| ~ member(not_subclass_element(X_3252,complement(X_3253)),universal_class) ),
inference(resolution,[status(thm)],[c_1631,c_6]) ).
tff(c_96884,plain,
! [X_4,X_3253] :
( member(not_subclass_element(X_4,complement(X_3253)),X_3253)
| ~ subclass(X_4,universal_class)
| subclass(X_4,complement(X_3253)) ),
inference(resolution,[status(thm)],[c_859,c_96861]) ).
tff(c_96928,plain,
! [X_3254,X_3255] :
( member(not_subclass_element(X_3254,complement(X_3255)),X_3255)
| subclass(X_3254,complement(X_3255)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_96884]) ).
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_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_480]) ).
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_3965,plain,
! [X_614,Y_615] :
( member(regular(intersection(X_614,Y_615)),X_614)
| ( intersection(X_614,Y_615) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_371]) ).
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_4092,plain,
! [Y_616] : ( intersection(null_class,Y_616) = null_class ),
inference(resolution,[status(thm)],[c_3965,c_1549]) ).
tff(c_4153,plain,
! [X_64,Y_65] : ( restrict(null_class,X_64,Y_65) = null_class ),
inference(superposition,[status(thm),theory(equality)],[c_56,c_4092]) ).
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_77543,plain,
! [X_2711] :
( ( restrict(X_2711,singleton(regular(domain_of(X_2711))),universal_class) != null_class )
| ( domain_of(X_2711) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_1339]) ).
tff(c_77557,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm),theory(equality)],[c_4153,c_77543]) ).
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_77627,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_77557,c_60]) ).
tff(c_77669,plain,
! [Z_70] : ~ member(Z_70,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_4153,c_77627]) ).
tff(c_97159,plain,
! [X_3256] : subclass(X_3256,complement(null_class)),
inference(resolution,[status(thm)],[c_96928,c_77669]) ).
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_97369,plain,
complement(null_class) = universal_class,
inference(resolution,[status(thm)],[c_97159,c_459]) ).
tff(c_97445,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_226,c_97369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET151-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 20:11:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 35.30/20.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.30/20.90
% 35.30/20.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------