%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET096+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 : n010.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 02:09:19 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 129 ( 46 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 131 ( 46 ~; 49 |; 28 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 69 !; 6 ?)
% 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(f4,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [X] :
( X != null_class
=> ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [X,Y] :
( subclass(X,singleton(Y))
=> ( singleton(Y) = X
| X = null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y] :
( subclass(X,singleton(Y))
=> ( singleton(Y) = X
| 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(f50,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| 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(f59,plain,
! [U,X,Y] :
( ( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f60,plain,
( ! [U,X,Y] :
( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ! [U,X,Y] :
( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f66,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f181,plain,
! [X] :
( ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) )
| X = null_class ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f182,plain,
! [X] :
( ( disjoint(sK5_skl(X),X)
& member(sK5_skl(X),X)
& member(sK5_skl(X),universal_class) )
| X = null_class ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(U,sK5_skl(X))],[f181]) ).
fof(f184,plain,
! [X0] :
( member(sK5_skl(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f191,plain,
? [X,Y] :
( singleton(Y) != X
& X != null_class
& subclass(X,singleton(Y)) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
( singleton(sK8_skl) != sK7_skl
& sK7_skl != null_class
& subclass(sK7_skl,singleton(sK8_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(X,sK7_skl),skolemize(Y,sK8_skl)],[f191]) ).
fof(f193,plain,
subclass(sK7_skl,singleton(sK8_skl)),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
sK7_skl != null_class,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f195,plain,
singleton(sK8_skl) != sK7_skl,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f202,plain,
( ~ subclass(singleton(sK8_skl),sK7_skl)
| singleton(sK8_skl) = sK7_skl ),
inference(resolution,[status(thm)],[f58,f193]) ).
fof(f205,plain,
~ subclass(singleton(sK8_skl),sK7_skl),
inference(forward_subsumption_resolution,[status(thm)],[f202,f195]) ).
fof(f212,plain,
member(sK0_skl(sK7_skl,singleton(sK8_skl)),singleton(sK8_skl)),
inference(resolution,[status(thm)],[f205,f51]) ).
fof(f240,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f66,f62]) ).
fof(f241,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f240]) ).
fof(f269,plain,
sK0_skl(sK7_skl,singleton(sK8_skl)) = sK8_skl,
inference(resolution,[status(thm)],[f241,f212]) ).
fof(f277,plain,
! [X0,X1] :
( member(sK5_skl(X0),X1)
| ~ subclass(X0,X1)
| X0 = null_class ),
inference(resolution,[status(thm)],[f184,f50]) ).
fof(f300,plain,
( ~ member(sK8_skl,sK7_skl)
| subclass(singleton(sK8_skl),sK7_skl) ),
inference(paramodulation,[status(thm)],[f269,f52]) ).
fof(f302,plain,
~ member(sK8_skl,sK7_skl),
inference(forward_subsumption_resolution,[status(thm)],[f300,f205]) ).
fof(f316,plain,
! [X0,X1] :
( sK5_skl(X0) = X1
| ~ subclass(X0,singleton(X1))
| X0 = null_class ),
inference(resolution,[status(thm)],[f277,f241]) ).
fof(f768,plain,
( sK5_skl(sK7_skl) = sK8_skl
| sK7_skl = null_class ),
inference(resolution,[status(thm)],[f316,f193]) ).
fof(f772,plain,
sK5_skl(sK7_skl) = sK8_skl,
inference(forward_subsumption_resolution,[status(thm)],[f768,f194]) ).
fof(f784,plain,
( member(sK8_skl,sK7_skl)
| sK7_skl = null_class ),
inference(paramodulation,[status(thm)],[f772,f184]) ).
fof(f787,plain,
member(sK8_skl,sK7_skl),
inference(forward_subsumption_resolution,[status(thm)],[f784,f194]) ).
fof(f789,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f787,f302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:52:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.084819 seconds
% 0.14/0.46 % CPU time: 0.326638 seconds
% 0.14/0.46 % Total memory used: 107.599 MB
% 0.14/0.46 % Net memory used: 107.202 MB
%------------------------------------------------------------------------------