%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET056+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 : n002.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 02:09:05 PM UTC 2026
% Result : Theorem 0.10s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 85 ( 12 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 94 ( 36 ~; 35 |; 19 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 45 !; 8 ?)
% 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(f44,conjecture,
! [X,Y] :
( ? [W] :
( ~ member(W,X)
& member(W,Y) )
| ? [U] :
( ~ member(U,Y)
& member(U,X) )
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y] :
( ? [W] :
( ~ member(W,X)
& member(W,Y) )
| ? [U] :
( ~ member(U,Y)
& member(U,X) )
| X = Y ),
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(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(f191,plain,
? [X,Y] :
( ! [W] :
( member(W,X)
| ~ member(W,Y) )
& ! [U] :
( member(U,Y)
| ~ member(U,X) )
& X != Y ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
( ! [W] :
( member(W,sK7_skl)
| ~ member(W,sK8_skl) )
& ! [U] :
( member(U,sK8_skl)
| ~ member(U,sK7_skl) )
& sK7_skl != 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,
sK7_skl != sK8_skl,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
! [X0] :
( member(X0,sK8_skl)
| ~ member(X0,sK7_skl) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f195,plain,
! [X0] :
( member(X0,sK7_skl)
| ~ member(X0,sK8_skl) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f206,plain,
! [X0] :
( member(sK0_skl(X0,sK8_skl),sK7_skl)
| subclass(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f51,f195]) ).
fof(f212,plain,
( subclass(sK8_skl,sK7_skl)
| subclass(sK8_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f52,f206]) ).
fof(f214,plain,
! [X0] :
( ~ member(sK0_skl(sK8_skl,X0),sK7_skl)
| subclass(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f52,f194]) ).
fof(f215,plain,
subclass(sK8_skl,sK7_skl),
inference(duplicate_literals_removal,[status(thm)],[f212]) ).
fof(f224,plain,
( ~ subclass(sK7_skl,sK8_skl)
| sK7_skl = sK8_skl ),
inference(resolution,[status(thm)],[f215,f58]) ).
fof(f226,plain,
~ subclass(sK7_skl,sK8_skl),
inference(forward_subsumption_resolution,[status(thm)],[f224,f193]) ).
fof(f228,plain,
( subclass(sK7_skl,sK8_skl)
| subclass(sK7_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f214,f51]) ).
fof(f230,plain,
subclass(sK7_skl,sK8_skl),
inference(duplicate_literals_removal,[status(thm)],[f228]) ).
fof(f231,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f230,f226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET056+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n002.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 04:51:06 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.10/5.40 % Refutation found
% 0.10/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.43 % Elapsed time: 0.049592 seconds
% 0.14/5.43 % CPU time: 0.145808 seconds
% 0.14/5.43 % Total memory used: 104.728 MB
% 0.14/5.43 % Net memory used: 104.619 MB
%------------------------------------------------------------------------------