TSTP Solution File: SET096-6 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET096-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 12:33:58 EDT 2023
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 67 ( 17 unt; 0 def)
% Number of atoms : 134 ( 37 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 117 ( 50 ~; 61 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 61 (; 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( X != Y
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| U = X
| U = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( ~ inductive(X)
| member(null_class,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( X = null_class
| member(regular(X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
subclass(x,singleton(y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
singleton(y) != x,
file('/export/starexec/sandbox2/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(f98,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f99,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f100,plain,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f102,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
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(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f150,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f153,plain,
inductive(omega),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f169,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f200,plain,
subclass(x,singleton(y)),
inference(cnf_transformation,[status(esa)],[f92]) ).
fof(f201,plain,
x != null_class,
inference(cnf_transformation,[status(esa)],[f93]) ).
fof(f202,plain,
singleton(y) != x,
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f203,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f100]) ).
fof(f206,plain,
( spl0_0
<=> subclass(singleton(y),x) ),
introduced(split_symbol_definition) ).
fof(f208,plain,
( ~ subclass(singleton(y),x)
| spl0_0 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( spl0_1
<=> singleton(y) = x ),
introduced(split_symbol_definition) ).
fof(f210,plain,
( singleton(y) = x
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( ~ subclass(singleton(y),x)
| singleton(y) = x ),
inference(resolution,[status(thm)],[f102,f200]) ).
fof(f213,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f212,f206,f209]) ).
fof(f243,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| X0 = X2
| ~ subclass(X3,unordered_pair(X1,X2))
| ~ member(X0,X3) ),
inference(resolution,[status(thm)],[f104,f96]) ).
fof(f253,plain,
! [X0,X1,X2] :
( X0 = X1
| X0 = X1
| ~ subclass(X2,singleton(X1))
| ~ member(X0,X2) ),
inference(paramodulation,[status(thm)],[f110,f243]) ).
fof(f254,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ subclass(X2,singleton(X1))
| ~ member(X0,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f253]) ).
fof(f255,plain,
! [X0] :
( X0 = y
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[f254,f200]) ).
fof(f256,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[f254,f203]) ).
fof(f257,plain,
( spl0_6
<=> regular(x) = y ),
introduced(split_symbol_definition) ).
fof(f258,plain,
( regular(x) = y
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( spl0_7
<=> x = null_class ),
introduced(split_symbol_definition) ).
fof(f261,plain,
( x = null_class
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( regular(x) = y
| x = null_class ),
inference(resolution,[status(thm)],[f255,f169]) ).
fof(f264,plain,
( spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f263,f257,f260]) ).
fof(f275,plain,
( spl0_10
<=> member(y,x) ),
introduced(split_symbol_definition) ).
fof(f278,plain,
( x = null_class
| member(y,x)
| ~ spl0_6 ),
inference(paramodulation,[status(thm)],[f258,f169]) ).
fof(f279,plain,
( spl0_7
| spl0_10
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f278,f260,f275,f257]) ).
fof(f280,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f201]) ).
fof(f281,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f466,plain,
! [X0,X1] :
( not_subclass_element(singleton(X0),X1) = X0
| subclass(singleton(X0),X1) ),
inference(resolution,[status(thm)],[f256,f97]) ).
fof(f479,plain,
( not_subclass_element(singleton(y),x) = y
| spl0_0 ),
inference(resolution,[status(thm)],[f466,f208]) ).
fof(f515,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f202]) ).
fof(f516,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f677,plain,
( spl0_55
<=> member(null_class,universal_class) ),
introduced(split_symbol_definition) ).
fof(f679,plain,
( ~ member(null_class,universal_class)
| spl0_55 ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f723,plain,
! [X0] :
( ~ subclass(X0,universal_class)
| ~ member(null_class,X0)
| spl0_55 ),
inference(resolution,[status(thm)],[f679,f96]) ).
fof(f724,plain,
! [X0] :
( ~ member(null_class,X0)
| spl0_55 ),
inference(forward_subsumption_resolution,[status(thm)],[f723,f99]) ).
fof(f727,plain,
! [X0] :
( ~ inductive(X0)
| spl0_55 ),
inference(backward_subsumption_resolution,[status(thm)],[f150,f724]) ).
fof(f734,plain,
( $false
| spl0_55 ),
inference(backward_subsumption_resolution,[status(thm)],[f153,f727]) ).
fof(f735,plain,
spl0_55,
inference(contradiction_clause,[status(thm)],[f734]) ).
fof(f787,plain,
( ~ member(y,x)
| subclass(singleton(y),x)
| spl0_0 ),
inference(paramodulation,[status(thm)],[f479,f98]) ).
fof(f788,plain,
( ~ spl0_10
| spl0_0 ),
inference(split_clause,[status(thm)],[f787,f275,f206]) ).
fof(f794,plain,
$false,
inference(sat_refutation,[status(thm)],[f213,f264,f279,f281,f516,f735,f788]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET096-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n015.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 May 30 10:29:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.38 % Elapsed time: 0.034548 seconds
% 0.19/0.38 % CPU time: 0.105057 seconds
% 0.19/0.38 % Memory used: 15.801 MB
%------------------------------------------------------------------------------