TSTP Solution File: SET130-6 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET130-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 May 31 12:34:05 EDT 2023
% Result : Unsatisfiable 9.75s 1.59s
% Output : CNFRefutation 9.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 81 ( 21 unt; 0 def)
% Number of atoms : 156 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 137 ( 62 ~; 70 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 95 (; 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| U = X
| U = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( X = null_class
| member(regular(X),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
~ member(u,set_builder(u,set_builder(y,set_builder(z,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f99,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f103,plain,
! [U,Y] :
( ! [X] :
( ~ member(U,unordered_pair(X,Y))
| U = X )
| U = Y ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f105,plain,
! [X] :
( ~ member(X,universal_class)
| ! [Y] : member(X,unordered_pair(X,Y)) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f105]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f122,plain,
! [Z,X] :
( ! [Y] : ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f127,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f128,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,complement(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f129,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f169,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f200,plain,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
inference(cnf_transformation,[status(esa)],[f92]) ).
fof(f201,plain,
member(u,universal_class),
inference(cnf_transformation,[status(esa)],[f93]) ).
fof(f202,plain,
~ member(u,set_builder(u,set_builder(y,set_builder(z,null_class)))),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f224,plain,
! [X0,X1] :
( X0 = null_class
| ~ subclass(X0,X1)
| member(regular(X0),X1) ),
inference(resolution,[status(thm)],[f169,f96]) ).
fof(f234,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f127,f169]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ subclass(X2,complement(X1))
| ~ member(X0,X2) ),
inference(resolution,[status(thm)],[f127,f96]) ).
fof(f248,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f110,f104]) ).
fof(f249,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f248]) ).
fof(f251,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f110,f106]) ).
fof(f255,plain,
! [X0,X1] :
( not_subclass_element(singleton(X0),X1) = X0
| subclass(singleton(X0),X1) ),
inference(resolution,[status(thm)],[f249,f97]) ).
fof(f562,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[status(thm)],[f96,f99]) ).
fof(f990,plain,
( spl0_78
<=> singleton(u) = null_class ),
introduced(split_symbol_definition) ).
fof(f991,plain,
( singleton(u) = null_class
| ~ spl0_78 ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f995,plain,
( spl0_79
<=> member(u,universal_class) ),
introduced(split_symbol_definition) ).
fof(f997,plain,
( ~ member(u,universal_class)
| spl0_79 ),
inference(component_clause,[status(thm)],[f995]) ).
fof(f1000,plain,
( $false
| spl0_79 ),
inference(forward_subsumption_resolution,[status(thm)],[f997,f201]) ).
fof(f1001,plain,
spl0_79,
inference(contradiction_clause,[status(thm)],[f1000]) ).
fof(f1068,plain,
! [X0] :
( complement(X0) = null_class
| ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f224,f234]) ).
fof(f1069,plain,
! [X0] :
( complement(X0) = null_class
| ~ subclass(complement(X0),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f1068]) ).
fof(f1081,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[f1069,f99]) ).
fof(f1103,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f1081,f127]) ).
fof(f1104,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f1103,f562]) ).
fof(f1105,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
inference(resolution,[status(thm)],[f1104,f224]) ).
fof(f1184,plain,
( spl0_97
<=> member(u,null_class) ),
introduced(split_symbol_definition) ).
fof(f1185,plain,
( member(u,null_class)
| ~ spl0_97 ),
inference(component_clause,[status(thm)],[f1184]) ).
fof(f1203,plain,
( ~ member(u,universal_class)
| member(u,null_class)
| ~ spl0_78 ),
inference(paramodulation,[status(thm)],[f991,f251]) ).
fof(f1204,plain,
( ~ spl0_79
| spl0_97
| ~ spl0_78 ),
inference(split_clause,[status(thm)],[f1203,f995,f1184,f990]) ).
fof(f1329,plain,
( $false
| ~ spl0_97 ),
inference(forward_subsumption_resolution,[status(thm)],[f1185,f1104]) ).
fof(f1330,plain,
~ spl0_97,
inference(contradiction_clause,[status(thm)],[f1329]) ).
fof(f3126,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(X1,null_class)
| ~ member(X0,X1) ),
inference(paramodulation,[status(thm)],[f1081,f236]) ).
fof(f3127,plain,
! [X0,X1] :
( ~ subclass(X0,null_class)
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3126,f562]) ).
fof(f3130,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| not_subclass_element(singleton(X1),null_class) = X1 ),
inference(resolution,[status(thm)],[f3127,f255]) ).
fof(f5929,plain,
! [X0] :
( not_subclass_element(singleton(X0),null_class) = X0
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f3130,f251]) ).
fof(f5971,plain,
! [X0,X1] :
( not_subclass_element(singleton(X0),null_class) = X0
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f5929,f562]) ).
fof(f8519,plain,
not_subclass_element(singleton(u),null_class) = u,
inference(resolution,[status(thm)],[f201,f5971]) ).
fof(f8526,plain,
( spl0_386
<=> subclass(singleton(u),null_class) ),
introduced(split_symbol_definition) ).
fof(f8527,plain,
( subclass(singleton(u),null_class)
| ~ spl0_386 ),
inference(component_clause,[status(thm)],[f8526]) ).
fof(f8536,plain,
( spl0_388
<=> member(u,singleton(u)) ),
introduced(split_symbol_definition) ).
fof(f8537,plain,
( member(u,singleton(u))
| ~ spl0_388 ),
inference(component_clause,[status(thm)],[f8536]) ).
fof(f8539,plain,
( member(u,singleton(u))
| subclass(singleton(u),null_class) ),
inference(paramodulation,[status(thm)],[f8519,f97]) ).
fof(f8540,plain,
( spl0_388
| spl0_386 ),
inference(split_clause,[status(thm)],[f8539,f8536,f8526]) ).
fof(f11769,plain,
! [X0] :
( member(u,complement(X0))
| member(u,X0) ),
inference(resolution,[status(thm)],[f128,f201]) ).
fof(f11822,plain,
( singleton(u) = null_class
| ~ spl0_386 ),
inference(resolution,[status(thm)],[f8527,f1105]) ).
fof(f11823,plain,
( spl0_78
| ~ spl0_386 ),
inference(split_clause,[status(thm)],[f11822,f990,f8526]) ).
fof(f11984,plain,
! [X0,X1] :
( member(u,union(X0,X1))
| member(u,intersection(complement(X0),complement(X1))) ),
inference(paramodulation,[status(thm)],[f129,f11769]) ).
fof(f12056,plain,
! [X0,X1] :
( member(u,union(X0,X1))
| member(u,complement(X0)) ),
inference(resolution,[status(thm)],[f11984,f123]) ).
fof(f12182,plain,
! [X0,X1] :
( member(u,set_builder(X0,X1))
| member(u,complement(singleton(X0))) ),
inference(paramodulation,[status(thm)],[f200,f12056]) ).
fof(f13111,plain,
member(u,complement(singleton(u))),
inference(resolution,[status(thm)],[f12182,f202]) ).
fof(f13155,plain,
~ member(u,singleton(u)),
inference(resolution,[status(thm)],[f13111,f127]) ).
fof(f13156,plain,
( $false
| ~ spl0_388 ),
inference(forward_subsumption_resolution,[status(thm)],[f13155,f8537]) ).
fof(f13157,plain,
~ spl0_388,
inference(contradiction_clause,[status(thm)],[f13156]) ).
fof(f13158,plain,
$false,
inference(sat_refutation,[status(thm)],[f1001,f1204,f1330,f8540,f11823,f13157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET130-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 10:21:42 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 9.75/1.59 % Refutation found
% 9.75/1.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.75/1.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.75/1.62 % Elapsed time: 1.278751 seconds
% 9.75/1.62 % CPU time: 10.014845 seconds
% 9.75/1.62 % Memory used: 156.399 MB
%------------------------------------------------------------------------------