%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET063+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:09:07 PM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 8 unt; 2 def)
% Number of atoms : 76 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 25 |; 13 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] : ~ member(X,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [X] :
( subclass(X,null_class)
=> X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X] :
( subclass(X,null_class)
=> X = null_class ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,Y)
| ~ member(U,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f47,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
( ! [X,Y] :
( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ! [X,Y] :
( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [X,Y] :
( ( ~ member(sK0_skl(Y,X),Y)
& member(sK0_skl(Y,X),X) )
| subclass(X,Y) )
& ! [X,Y] :
( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(U,sK0_skl(Y,X))],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
! [X,Y] :
( ( ~ subclass(Y,X)
| ~ subclass(X,Y)
| X = Y )
& ( ( subclass(Y,X)
& subclass(X,Y) )
| X != Y ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f55,plain,
( ! [X,Y] :
( ~ subclass(Y,X)
| ~ subclass(X,Y)
| X = Y )
& ! [X,Y] :
( ( subclass(Y,X)
& subclass(X,Y) )
| X != Y ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f96,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f191,plain,
? [X] :
( X != null_class
& subclass(X,null_class) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
( sK7_skl != null_class
& subclass(sK7_skl,null_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(X,sK7_skl)],[f191]) ).
fof(f193,plain,
subclass(sK7_skl,null_class),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
sK7_skl != null_class,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f204,plain,
( ~ subclass(null_class,sK7_skl)
| null_class = sK7_skl ),
inference(resolution,[status(thm)],[f58,f193]) ).
fof(f207,definition,
( sQ0_spl
<=> null_class = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ0_spl
| null_class = sK7_skl ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,definition,
( sQ1_spl
<=> subclass(null_class,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( sQ1_spl
| ~ subclass(null_class,sK7_skl) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f204,f207,f210]) ).
fof(f214,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f194]) ).
fof(f215,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f214]) ).
fof(f221,plain,
! [X0] : subclass(null_class,X0),
inference(resolution,[status(thm)],[f51,f96]) ).
fof(f223,plain,
( sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f212,f221]) ).
fof(f226,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f223]) ).
fof(f227,plain,
$false,
inference(sat_refutation,[status(thm)],[f213,f215,f226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET063+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:51:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.43 % Elapsed time: 0.061759 seconds
% 0.08/0.43 % CPU time: 0.162211 seconds
% 0.08/0.43 % Total memory used: 104.453 MB
% 0.08/0.43 % Net memory used: 104.360 MB
%------------------------------------------------------------------------------