TSTP Solution File: SET230-6 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET230-6 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.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 10:56:13 EDT 2023
% Result : Unsatisfiable 26.63s 14.44s
% Output : CNFRefutation 26.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 74
% Syntax : Number of formulae : 182 ( 48 unt; 58 typ; 0 def)
% Number of atoms : 224 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 210 ( 110 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 151 (; 151 !; 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 > w > universal_class > u > 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(w,type,
w: $i ).
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(u,type,
u: $i ).
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_70,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_479,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_194,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_216,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(f_200,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_75,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_780,axiom,
u != w,
file(unknown,unknown) ).
tff(f_159,axiom,
! [U,X,V,Y] :
( ~ member(U,X)
| ~ member(V,Y)
| member(ordered_pair(U,V),cross_product(X,Y)) ),
file(unknown,unknown) ).
tff(f_778,axiom,
cross_product(u,u) = cross_product(w,w),
file(unknown,unknown) ).
tff(f_145,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file(unknown,unknown) ).
tff(f_151,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
file(unknown,unknown) ).
tff(f_100,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_523,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file(unknown,unknown) ).
tff(f_483,axiom,
! [X] :
( ( X = null_class )
| ( intersection(X,regular(X)) = null_class ) ),
file(unknown,unknown) ).
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_70]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_479]) ).
tff(c_414,plain,
! [Z_273,X_274,Y_275] :
( member(Z_273,X_274)
| ~ member(Z_273,intersection(X_274,Y_275)) ),
inference(cnfTransformation,[status(thm)],[f_194]) ).
tff(c_30421,plain,
! [X_1497,Y_1498] :
( member(regular(intersection(X_1497,Y_1498)),X_1497)
| ( intersection(X_1497,Y_1498) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_414]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_758,plain,
! [U_320,Y_321,X_322] :
( member(U_320,Y_321)
| ~ member(U_320,X_322)
| ~ subclass(X_322,Y_321) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_799,plain,
! [X_131,Y_321] :
( member(regular(X_131),Y_321)
| ~ subclass(X_131,Y_321)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_132,c_758]) ).
tff(c_1446,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_758]) ).
tff(c_340,plain,
! [Z_256,X_257] :
( ~ member(Z_256,X_257)
| ~ member(Z_256,complement(X_257)) ),
inference(cnfTransformation,[status(thm)],[f_216]) ).
tff(c_355,plain,
! [X_257] :
( ~ member(regular(complement(X_257)),X_257)
| ( complement(X_257) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_340]) ).
tff(c_1501,plain,
! [Y_384] :
( ~ subclass(complement(Y_384),Y_384)
| ( complement(Y_384) = null_class ) ),
inference(resolution,[status(thm)],[c_1446,c_355]) ).
tff(c_1523,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[c_8,c_1501]) ).
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_1580,plain,
! [Z_386] :
( ~ member(Z_386,universal_class)
| ~ member(Z_386,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1523,c_48]) ).
tff(c_1584,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ~ subclass(X_131,universal_class)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_799,c_1580]) ).
tff(c_1628,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ( null_class = X_131 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1584]) ).
tff(c_30538,plain,
! [Y_1499] : ( intersection(null_class,Y_1499) = null_class ),
inference(resolution,[status(thm)],[c_30421,c_1628]) ).
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_30825,plain,
! [Z_1506,Y_1507] :
( member(Z_1506,Y_1507)
| ~ member(Z_1506,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_30538,c_44]) ).
tff(c_41062,plain,
! [Y_1872,Y_1873] :
( member(not_subclass_element(null_class,Y_1872),Y_1873)
| subclass(null_class,Y_1872) ),
inference(resolution,[status(thm)],[c_4,c_30825]) ).
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_75]) ).
tff(c_41157,plain,
! [Y_1873] : subclass(null_class,Y_1873),
inference(resolution,[status(thm)],[c_41062,c_6]) ).
tff(c_228,plain,
w != u,
inference(cnfTransformation,[status(thm)],[f_780]) ).
tff(c_32,plain,
! [U_35,V_37,X_36,Y_38] :
( member(ordered_pair(U_35,V_37),cross_product(X_36,Y_38))
| ~ member(V_37,Y_38)
| ~ member(U_35,X_36) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_226,plain,
cross_product(w,w) = cross_product(u,u),
inference(cnfTransformation,[status(thm)],[f_778]) ).
tff(c_1647,plain,
! [U_387,X_388,V_389,Y_390] :
( member(U_387,X_388)
| ~ member(ordered_pair(U_387,V_389),cross_product(X_388,Y_390)) ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_3755,plain,
! [U_604,V_605] :
( member(U_604,w)
| ~ member(ordered_pair(U_604,V_605),cross_product(u,u)) ),
inference(superposition,[status(thm),theory(equality)],[c_226,c_1647]) ).
tff(c_3764,plain,
! [U_35,V_37] :
( member(U_35,w)
| ~ member(V_37,u)
| ~ member(U_35,u) ),
inference(resolution,[status(thm)],[c_32,c_3755]) ).
tff(c_3772,plain,
! [V_607] : ~ member(V_607,u),
inference(splitLeft,[status(thm)],[c_3764]) ).
tff(c_3811,plain,
u = null_class,
inference(resolution,[status(thm)],[c_132,c_3772]) ).
tff(c_3818,plain,
w != null_class,
inference(demodulation,[status(thm),theory(equality)],[c_3811,c_228]) ).
tff(c_3771,plain,
! [V_37] : ~ member(V_37,u),
inference(splitLeft,[status(thm)],[c_3764]) ).
tff(c_3813,plain,
! [V_37] : ~ member(V_37,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_3811,c_3771]) ).
tff(c_2597,plain,
! [U_479,V_480,X_481,Y_482] :
( member(ordered_pair(U_479,V_480),cross_product(X_481,Y_482))
| ~ member(V_480,Y_482)
| ~ member(U_479,X_481) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_2613,plain,
! [U_479,V_480] :
( member(ordered_pair(U_479,V_480),cross_product(u,u))
| ~ member(V_480,w)
| ~ member(U_479,w) ),
inference(superposition,[status(thm),theory(equality)],[c_226,c_2597]) ).
tff(c_30119,plain,
! [U_1493,V_1494] :
( member(ordered_pair(U_1493,V_1494),cross_product(null_class,null_class))
| ~ member(V_1494,w)
| ~ member(U_1493,w) ),
inference(demodulation,[status(thm),theory(equality)],[c_3811,c_3811,c_2613]) ).
tff(c_30,plain,
! [V_32,Y_34,U_31,X_33] :
( member(V_32,Y_34)
| ~ member(ordered_pair(U_31,V_32),cross_product(X_33,Y_34)) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_30132,plain,
! [V_1494,U_1493] :
( member(V_1494,null_class)
| ~ member(V_1494,w)
| ~ member(U_1493,w) ),
inference(resolution,[status(thm)],[c_30119,c_30]) ).
tff(c_30159,plain,
! [V_1494,U_1493] :
( ~ member(V_1494,w)
| ~ member(U_1493,w) ),
inference(negUnitSimplification,[status(thm)],[c_3813,c_30132]) ).
tff(c_30167,plain,
! [U_1495] : ~ member(U_1495,w),
inference(splitLeft,[status(thm)],[c_30159]) ).
tff(c_30259,plain,
w = null_class,
inference(resolution,[status(thm)],[c_132,c_30167]) ).
tff(c_30291,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3818,c_30259]) ).
tff(c_30295,plain,
! [V_1496] : ~ member(V_1496,w),
inference(splitRight,[status(thm)],[c_30159]) ).
tff(c_30387,plain,
w = null_class,
inference(resolution,[status(thm)],[c_132,c_30295]) ).
tff(c_30419,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3818,c_30387]) ).
tff(c_30798,plain,
! [U_1505] :
( member(U_1505,w)
| ~ member(U_1505,u) ),
inference(splitRight,[status(thm)],[c_3764]) ).
tff(c_30989,plain,
! [X_1511] :
( subclass(X_1511,w)
| ~ member(not_subclass_element(X_1511,w),u) ),
inference(resolution,[status(thm)],[c_30798,c_6]) ).
tff(c_30994,plain,
subclass(u,w),
inference(resolution,[status(thm)],[c_4,c_30989]) ).
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_100]) ).
tff(c_30999,plain,
( ( w = u )
| ~ subclass(w,u) ),
inference(resolution,[status(thm)],[c_30994,c_14]) ).
tff(c_31003,plain,
~ subclass(w,u),
inference(negUnitSimplification,[status(thm)],[c_228,c_30999]) ).
tff(c_67444,plain,
! [U_2576,V_2577] :
( member(ordered_pair(U_2576,V_2577),cross_product(u,u))
| ~ member(V_2577,w)
| ~ member(U_2576,w) ),
inference(superposition,[status(thm),theory(equality)],[c_226,c_2597]) ).
tff(c_67485,plain,
! [V_2577,U_2576] :
( member(V_2577,u)
| ~ member(V_2577,w)
| ~ member(U_2576,w) ),
inference(resolution,[status(thm)],[c_67444,c_30]) ).
tff(c_67493,plain,
! [U_2578] : ~ member(U_2578,w),
inference(splitLeft,[status(thm)],[c_67485]) ).
tff(c_67637,plain,
w = null_class,
inference(resolution,[status(thm)],[c_132,c_67493]) ).
tff(c_53997,plain,
! [U_2266,V_2267] :
( member(ordered_pair(U_2266,V_2267),cross_product(u,u))
| ~ member(V_2267,w)
| ~ member(U_2266,w) ),
inference(superposition,[status(thm),theory(equality)],[c_226,c_2597]) ).
tff(c_54032,plain,
! [V_2267,U_2266] :
( member(V_2267,u)
| ~ member(V_2267,w)
| ~ member(U_2266,w) ),
inference(resolution,[status(thm)],[c_53997,c_30]) ).
tff(c_54040,plain,
! [U_2268] : ~ member(U_2268,w),
inference(splitLeft,[status(thm)],[c_54032]) ).
tff(c_54164,plain,
w = null_class,
inference(resolution,[status(thm)],[c_132,c_54040]) ).
tff(c_44815,plain,
! [X_2002,Y_2003,Y_2004] :
( member(not_subclass_element(X_2002,Y_2003),Y_2004)
| ~ subclass(X_2002,Y_2004)
| subclass(X_2002,Y_2003) ),
inference(resolution,[status(thm)],[c_4,c_758]) ).
tff(c_150,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(cnfTransformation,[status(thm)],[f_523]) ).
tff(c_572,plain,
! [Z_298,Y_299,X_300] :
( member(Z_298,Y_299)
| ~ member(Z_298,intersection(X_300,Y_299)) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_594,plain,
! [Z_301] :
( member(Z_301,subset_relation)
| ~ member(Z_301,identity_relation) ),
inference(superposition,[status(thm),theory(equality)],[c_150,c_572]) ).
tff(c_599,plain,
! [X_6] :
( subclass(X_6,subset_relation)
| ~ member(not_subclass_element(X_6,subset_relation),identity_relation) ),
inference(resolution,[status(thm)],[c_594,c_6]) ).
tff(c_44992,plain,
! [X_2005] :
( ~ subclass(X_2005,identity_relation)
| subclass(X_2005,subset_relation) ),
inference(resolution,[status(thm)],[c_44815,c_599]) ).
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_66]) ).
tff(c_30821,plain,
! [U_1505,Y_2] :
( member(U_1505,Y_2)
| ~ subclass(w,Y_2)
| ~ member(U_1505,u) ),
inference(resolution,[status(thm)],[c_30798,c_2]) ).
tff(c_45051,plain,
! [U_1505] :
( member(U_1505,subset_relation)
| ~ member(U_1505,u)
| ~ subclass(w,identity_relation) ),
inference(resolution,[status(thm)],[c_44992,c_30821]) ).
tff(c_46391,plain,
~ subclass(w,identity_relation),
inference(splitLeft,[status(thm)],[c_45051]) ).
tff(c_54174,plain,
~ subclass(null_class,identity_relation),
inference(demodulation,[status(thm),theory(equality)],[c_54164,c_46391]) ).
tff(c_54193,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41157,c_54174]) ).
tff(c_54355,plain,
! [V_2270] :
( member(V_2270,u)
| ~ member(V_2270,w) ),
inference(splitRight,[status(thm)],[c_54032]) ).
tff(c_54613,plain,
! [Y_2272] :
( member(not_subclass_element(w,Y_2272),u)
| subclass(w,Y_2272) ),
inference(resolution,[status(thm)],[c_4,c_54355]) ).
tff(c_54623,plain,
subclass(w,u),
inference(resolution,[status(thm)],[c_54613,c_6]) ).
tff(c_54630,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31003,c_31003,c_54623]) ).
tff(c_54658,plain,
! [U_2274] :
( member(U_2274,subset_relation)
| ~ member(U_2274,u) ),
inference(splitRight,[status(thm)],[c_45051]) ).
tff(c_54750,plain,
( member(regular(u),subset_relation)
| ( u = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_54658]) ).
tff(c_54753,plain,
u = null_class,
inference(splitLeft,[status(thm)],[c_54750]) ).
tff(c_42339,plain,
! [U_1915,Y_1916] :
( member(U_1915,Y_1916)
| ~ subclass(w,Y_1916)
| ~ member(U_1915,u) ),
inference(resolution,[status(thm)],[c_30798,c_2]) ).
tff(c_42353,plain,
! [U_1918] :
( member(U_1918,universal_class)
| ~ member(U_1918,u) ),
inference(resolution,[status(thm)],[c_8,c_42339]) ).
tff(c_1566,plain,
! [Z_55] :
( ~ member(Z_55,universal_class)
| ~ member(Z_55,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1523,c_48]) ).
tff(c_42394,plain,
! [U_1919] :
( ~ member(U_1919,null_class)
| ~ member(U_1919,u) ),
inference(resolution,[status(thm)],[c_42353,c_1566]) ).
tff(c_42467,plain,
! [Y_5] :
( ~ member(not_subclass_element(u,Y_5),null_class)
| subclass(u,Y_5) ),
inference(resolution,[status(thm)],[c_4,c_42394]) ).
tff(c_44964,plain,
! [Y_2003] :
( ~ subclass(u,null_class)
| subclass(u,Y_2003) ),
inference(resolution,[status(thm)],[c_44815,c_42467]) ).
tff(c_45193,plain,
~ subclass(u,null_class),
inference(splitLeft,[status(thm)],[c_44964]) ).
tff(c_54762,plain,
~ subclass(null_class,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_54753,c_45193]) ).
tff(c_54783,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41157,c_54762]) ).
tff(c_54785,plain,
u != null_class,
inference(splitRight,[status(thm)],[c_54750]) ).
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_56204,plain,
! [X_2305,Y_2306,Y_2307] :
( member(not_subclass_element(intersection(X_2305,Y_2306),Y_2307),X_2305)
| subclass(intersection(X_2305,Y_2306),Y_2307) ),
inference(resolution,[status(thm)],[c_4,c_414]) ).
tff(c_30823,plain,
! [X_6] :
( subclass(X_6,w)
| ~ member(not_subclass_element(X_6,w),u) ),
inference(resolution,[status(thm)],[c_30798,c_6]) ).
tff(c_56569,plain,
! [Y_2314] : subclass(intersection(u,Y_2314),w),
inference(resolution,[status(thm)],[c_56204,c_30823]) ).
tff(c_58617,plain,
! [Y_2386] :
( ( intersection(u,Y_2386) = w )
| ~ subclass(w,intersection(u,Y_2386)) ),
inference(resolution,[status(thm)],[c_56569,c_14]) ).
tff(c_58629,plain,
( ( intersection(u,regular(u)) = w )
| ~ subclass(w,null_class)
| ( u = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_134,c_58617]) ).
tff(c_58632,plain,
( ( intersection(u,regular(u)) = w )
| ~ subclass(w,null_class) ),
inference(negUnitSimplification,[status(thm)],[c_54785,c_58629]) ).
tff(c_58633,plain,
~ subclass(w,null_class),
inference(splitLeft,[status(thm)],[c_58632]) ).
tff(c_67642,plain,
~ subclass(null_class,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_67637,c_58633]) ).
tff(c_67666,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41157,c_67642]) ).
tff(c_67848,plain,
! [V_2580] :
( member(V_2580,u)
| ~ member(V_2580,w) ),
inference(splitRight,[status(thm)],[c_67485]) ).
tff(c_68042,plain,
! [Y_2582] :
( member(not_subclass_element(w,Y_2582),u)
| subclass(w,Y_2582) ),
inference(resolution,[status(thm)],[c_4,c_67848]) ).
tff(c_68058,plain,
subclass(w,u),
inference(resolution,[status(thm)],[c_68042,c_6]) ).
tff(c_68067,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31003,c_31003,c_68058]) ).
tff(c_68069,plain,
subclass(w,null_class),
inference(splitRight,[status(thm)],[c_58632]) ).
tff(c_1824,plain,
! [X_412] :
( ~ member(regular(X_412),null_class)
| ( null_class = X_412 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1584]) ).
tff(c_1836,plain,
! [X_131] :
( ~ subclass(X_131,null_class)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_799,c_1824]) ).
tff(c_68091,plain,
w = null_class,
inference(resolution,[status(thm)],[c_68069,c_1836]) ).
tff(c_68113,plain,
~ subclass(null_class,u),
inference(demodulation,[status(thm),theory(equality)],[c_68091,c_31003]) ).
tff(c_68133,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41157,c_68113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET230-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Aug 3 16:15:36 EDT 2023
% 0.11/0.32 % CPUTime :
% 26.63/14.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.63/14.46
% 26.63/14.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.63/14.50
% 26.63/14.50 Inference rules
% 26.63/14.50 ----------------------
% 26.63/14.50 #Ref : 2
% 26.63/14.50 #Sup : 17063
% 26.63/14.50 #Fact : 0
% 26.63/14.50 #Define : 0
% 26.63/14.50 #Split : 330
% 26.63/14.50 #Chain : 0
% 26.63/14.50 #Close : 0
% 26.63/14.50
% 26.63/14.50 Ordering : KBO
% 26.63/14.50
% 26.63/14.50 Simplification rules
% 26.63/14.50 ----------------------
% 26.63/14.50 #Subsume : 4050
% 26.63/14.50 #Demod : 5348
% 26.63/14.50 #Tautology : 2237
% 26.63/14.50 #SimpNegUnit : 470
% 26.63/14.50 #BackRed : 809
% 26.63/14.50
% 26.63/14.50 #Partial instantiations: 0
% 26.63/14.50 #Strategies tried : 1
% 26.63/14.50
% 26.63/14.50 Timing (in seconds)
% 26.63/14.50 ----------------------
% 26.63/14.51 Preprocessing : 0.74
% 26.63/14.51 Parsing : 0.39
% 26.63/14.51 CNF conversion : 0.05
% 26.63/14.51 Main loop : 12.81
% 26.63/14.51 Inferencing : 2.75
% 26.63/14.51 Reduction : 5.39
% 26.63/14.51 Demodulation : 3.66
% 26.63/14.51 BG Simplification : 0.14
% 26.63/14.51 Subsumption : 3.63
% 26.63/14.51 Abstraction : 0.17
% 26.63/14.51 MUC search : 0.00
% 26.63/14.51 Cooper : 0.00
% 26.63/14.51 Total : 13.62
% 26.63/14.51 Index Insertion : 0.00
% 26.63/14.51 Index Deletion : 0.00
% 26.63/14.51 Index Matching : 0.00
% 26.63/14.51 BG Taut test : 0.00
%------------------------------------------------------------------------------