TSTP Solution File: SET095+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET095+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 20:39:05 EDT 2024
% Result : Theorem 0.14s 0.34s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 9 unt; 0 def)
% Number of atoms : 119 ( 28 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 123 ( 46 ~; 48 |; 20 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 72 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(X,Y)
& subclass(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [X,Y] :
( member(X,Y)
=> subclass(singleton(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y] :
( member(X,Y)
=> subclass(singleton(X),Y) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( ~ member(U,X)
| member(U,Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f47,plain,
! [X,Y] :
( ( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ( member(sk0_0(Y,X),X)
& ~ member(sk0_0(Y,X),Y) ) ) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f54,plain,
! [X,Y] :
( ( X != Y
| ( subclass(X,Y)
& subclass(Y,X) ) )
& ( X = Y
| ~ subclass(X,Y)
| ~ subclass(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f55,plain,
( ! [X,Y] :
( X != Y
| ( subclass(X,Y)
& subclass(Y,X) ) )
& ! [X,Y] :
( X = Y
| ~ subclass(X,Y)
| ~ subclass(Y,X) ) ),
inference(miniscoping,[status(esa)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f59,plain,
! [U,X,Y] :
( ( ~ member(U,unordered_pair(X,Y))
| ( member(U,universal_class)
& ( U = X
| U = Y ) ) )
& ( member(U,unordered_pair(X,Y))
| ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f60,plain,
( ! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( member(U,universal_class)
& ( U = X
| U = Y ) ) )
& ! [U,X,Y] :
( member(U,unordered_pair(X,Y))
| ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f66,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f191,plain,
? [X,Y] :
( member(X,Y)
& ~ subclass(singleton(X),Y) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f192,plain,
( member(sk0_7,sk0_8)
& ~ subclass(singleton(sk0_7),sk0_8) ),
inference(skolemization,[status(esa)],[f191]) ).
fof(f193,plain,
member(sk0_7,sk0_8),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f194,plain,
~ subclass(singleton(sk0_7),sk0_8),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f195,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f56]) ).
fof(f237,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| X0 = X2
| ~ subclass(X3,unordered_pair(X1,X2))
| ~ member(X0,X3) ),
inference(resolution,[status(thm)],[f62,f50]) ).
fof(f255,plain,
! [X0,X1,X2] :
( X0 = X1
| X0 = X1
| ~ subclass(X2,singleton(X1))
| ~ member(X0,X2) ),
inference(paramodulation,[status(thm)],[f66,f237]) ).
fof(f256,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ subclass(X2,singleton(X1))
| ~ member(X0,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f255]) ).
fof(f258,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[f256,f195]) ).
fof(f260,plain,
! [X0,X1] :
( sk0_0(X0,singleton(X1)) = X1
| subclass(singleton(X1),X0) ),
inference(resolution,[status(thm)],[f258,f51]) ).
fof(f271,plain,
sk0_0(sk0_8,singleton(sk0_7)) = sk0_7,
inference(resolution,[status(thm)],[f260,f194]) ).
fof(f279,plain,
( spl0_4
<=> subclass(singleton(sk0_7),sk0_8) ),
introduced(split_symbol_definition) ).
fof(f280,plain,
( subclass(singleton(sk0_7),sk0_8)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f287,plain,
( spl0_6
<=> member(sk0_7,sk0_8) ),
introduced(split_symbol_definition) ).
fof(f289,plain,
( ~ member(sk0_7,sk0_8)
| spl0_6 ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,plain,
( subclass(singleton(sk0_7),sk0_8)
| ~ member(sk0_7,sk0_8) ),
inference(paramodulation,[status(thm)],[f271,f52]) ).
fof(f291,plain,
( spl0_4
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f290,f279,f287]) ).
fof(f297,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f194]) ).
fof(f298,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f297]) ).
fof(f299,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f289,f193]) ).
fof(f300,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f301,plain,
$false,
inference(sat_refutation,[status(thm)],[f291,f298,f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET095+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33 % Computer : n016.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Mon Apr 29 22:14:40 EDT 2024
% 0.09/0.33 % CPUTime :
% 0.09/0.34 % Drodi V3.6.0
% 0.14/0.34 % Refutation found
% 0.14/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.36 % Elapsed time: 0.020084 seconds
% 0.14/0.36 % CPU time: 0.032113 seconds
% 0.14/0.36 % Total memory used: 13.598 MB
% 0.14/0.36 % Net memory used: 13.573 MB
%------------------------------------------------------------------------------