TSTP Solution File: SET097-7 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET097-7 : 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 : Tue Apr 30 20:39:07 EDT 2024
% Result : Unsatisfiable 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 80 ( 16 unt; 0 def)
% Number of atoms : 167 ( 40 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 159 ( 72 ~; 80 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 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(f23,axiom,
! [Z,X,Y] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [Z] : ~ member(Z,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [X] :
( ~ subclass(X,null_class)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f106,axiom,
! [Z] :
( Z = null_class
| member(not_subclass_element(Z,null_class),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f123,axiom,
! [X] :
( ~ member(X,universal_class)
| singleton(X) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f125,axiom,
! [Y,X] :
( ~ member(Y,singleton(X))
| Y = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f126,axiom,
! [X] :
( member(X,universal_class)
| singleton(X) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f140,axiom,
! [X,Y] :
( ~ subclass(X,singleton(Y))
| X = null_class
| singleton(Y) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f141,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f142,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f143,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f144,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f147,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f148,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f177,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,complement(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f265,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f267,plain,
! [X0] :
( ~ subclass(X0,null_class)
| X0 = null_class ),
inference(cnf_transformation,[status(esa)],[f105]) ).
fof(f268,plain,
! [X0] :
( X0 = null_class
| member(not_subclass_element(X0,null_class),X0) ),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f293,plain,
! [X0] :
( ~ member(X0,universal_class)
| singleton(X0) != null_class ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f295,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f296,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
inference(cnf_transformation,[status(esa)],[f126]) ).
fof(f311,plain,
! [X0,X1] :
( ~ subclass(X0,singleton(X1))
| X0 = null_class
| singleton(X1) = X0 ),
inference(cnf_transformation,[status(esa)],[f140]) ).
fof(f312,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f313,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[status(esa)],[f142]) ).
fof(f314,plain,
x != null_class,
inference(cnf_transformation,[status(esa)],[f143]) ).
fof(f317,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[status(thm)],[f146,f312]) ).
fof(f319,plain,
intersection(complement(singleton(not_subclass_element(x,null_class))),x) = null_class,
inference(resolution,[status(thm)],[f317,f267]) ).
fof(f367,plain,
! [X0] :
( singleton(X0) = null_class
| not_subclass_element(singleton(X0),null_class) = X0 ),
inference(resolution,[status(thm)],[f268,f295]) ).
fof(f368,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f367,f268]) ).
fof(f369,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f368]) ).
fof(f374,plain,
! [X0] :
( ~ member(X0,complement(singleton(not_subclass_element(x,null_class))))
| ~ member(X0,x)
| member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f319,f175]) ).
fof(f375,plain,
! [X0] :
( ~ member(X0,complement(singleton(not_subclass_element(x,null_class))))
| ~ member(X0,x) ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f265]) ).
fof(f386,plain,
! [X0] :
( ~ member(X0,x)
| ~ member(X0,universal_class)
| member(X0,singleton(not_subclass_element(x,null_class))) ),
inference(resolution,[status(thm)],[f375,f177]) ).
fof(f387,plain,
! [X0] :
( ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),x)
| ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),universal_class)
| subclass(X0,singleton(not_subclass_element(x,null_class))) ),
inference(resolution,[status(thm)],[f386,f147]) ).
fof(f389,plain,
( spl0_7
<=> member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),universal_class) ),
introduced(split_symbol_definition) ).
fof(f391,plain,
( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),universal_class)
| spl0_7 ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,plain,
( spl0_8
<=> subclass(x,singleton(not_subclass_element(x,null_class))) ),
introduced(split_symbol_definition) ).
fof(f393,plain,
( subclass(x,singleton(not_subclass_element(x,null_class)))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f395,plain,
( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),universal_class)
| subclass(x,singleton(not_subclass_element(x,null_class)))
| subclass(x,singleton(not_subclass_element(x,null_class))) ),
inference(resolution,[status(thm)],[f387,f146]) ).
fof(f396,plain,
( ~ spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f395,f389,f392]) ).
fof(f397,plain,
( singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) = null_class
| spl0_7 ),
inference(resolution,[status(thm)],[f391,f296]) ).
fof(f398,plain,
( spl0_9
<=> singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) = null_class ),
introduced(split_symbol_definition) ).
fof(f399,plain,
( singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) = null_class
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,plain,
( spl0_10
<=> member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),null_class) ),
introduced(split_symbol_definition) ).
fof(f402,plain,
( member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),null_class)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f404,plain,
( singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) = null_class
| member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),null_class)
| spl0_7 ),
inference(paramodulation,[status(thm)],[f397,f369]) ).
fof(f405,plain,
( spl0_9
| spl0_10
| spl0_7 ),
inference(split_clause,[status(thm)],[f404,f398,f401,f389]) ).
fof(f437,plain,
( spl0_13
<=> member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),x) ),
introduced(split_symbol_definition) ).
fof(f438,plain,
( member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),x)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f439,plain,
( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),x)
| spl0_13 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f486,plain,
( subclass(x,singleton(not_subclass_element(x,null_class)))
| spl0_13 ),
inference(resolution,[status(thm)],[f439,f146]) ).
fof(f487,plain,
( spl0_22
<=> x = null_class ),
introduced(split_symbol_definition) ).
fof(f488,plain,
( x = null_class
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,plain,
( spl0_23
<=> singleton(not_subclass_element(x,null_class)) = x ),
introduced(split_symbol_definition) ).
fof(f491,plain,
( singleton(not_subclass_element(x,null_class)) = x
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( x = null_class
| singleton(not_subclass_element(x,null_class)) = x
| spl0_13 ),
inference(resolution,[status(thm)],[f486,f311]) ).
fof(f494,plain,
( spl0_22
| spl0_23
| spl0_13 ),
inference(split_clause,[status(thm)],[f493,f487,f490,f437]) ).
fof(f495,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f313]) ).
fof(f496,plain,
~ spl0_23,
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f497,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f314]) ).
fof(f498,plain,
~ spl0_22,
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f528,plain,
( x = null_class
| singleton(not_subclass_element(x,null_class)) = x
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f393,f311]) ).
fof(f529,plain,
( spl0_22
| spl0_23
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f528,f487,f490,f392]) ).
fof(f719,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f402,f265]) ).
fof(f720,plain,
~ spl0_10,
inference(contradiction_clause,[status(thm)],[f719]) ).
fof(f1266,plain,
! [X0,X1] :
( ~ subclass(X0,universal_class)
| ~ member(X1,X0)
| singleton(X1) != null_class ),
inference(resolution,[status(thm)],[f145,f293]) ).
fof(f1267,plain,
! [X0,X1] :
( ~ member(X0,X1)
| singleton(X0) != null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f1266,f148]) ).
fof(f1292,plain,
( singleton(not_subclass_element(x,singleton(not_subclass_element(x,null_class)))) != null_class
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f1267,f438]) ).
fof(f1293,plain,
( null_class != null_class
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f399,f1292]) ).
fof(f1294,plain,
( $false
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_equality_resolution,[status(esa)],[f1293]) ).
fof(f1295,plain,
( ~ spl0_9
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f1294]) ).
fof(f1296,plain,
$false,
inference(sat_refutation,[status(thm)],[f396,f405,f494,f496,f498,f529,f720,f1295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET097-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:48:16 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.37 % Drodi V3.6.0
% 0.20/0.52 % Refutation found
% 0.20/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.54 % Elapsed time: 0.175529 seconds
% 0.20/0.54 % CPU time: 1.261963 seconds
% 0.20/0.54 % Total memory used: 82.423 MB
% 0.20/0.54 % Net memory used: 81.635 MB
%------------------------------------------------------------------------------