%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET103+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:09:22 PM UTC 2026
% Result : Theorem 0.23s 0.53s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 101 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 99 ( 36 ~; 36 |; 22 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 64 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [X] :
( X != null_class
=> ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [X,Y] :
( member(Y,universal_class)
| unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y] :
( member(Y,universal_class)
| unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(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(f50,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f2]) ).
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(f67,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[status(thm)],[f7]) ).
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] :
( ~ member(Y,universal_class)
& unordered_pair(singleton(X),unordered_pair(X,null_class)) != ordered_pair(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
? [Y] :
( ~ member(Y,universal_class)
& ? [X] : unordered_pair(singleton(X),unordered_pair(X,null_class)) != ordered_pair(X,Y) ),
inference(miniscoping,[status(thm)],[f191]) ).
fof(f193,plain,
( ~ member(sK7_skl,universal_class)
& unordered_pair(singleton(sK8_skl),unordered_pair(sK8_skl,null_class)) != ordered_pair(sK8_skl,sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(Y,sK7_skl),skolemize(X,sK8_skl)],[f192]) ).
fof(f194,plain,
unordered_pair(singleton(sK8_skl),unordered_pair(sK8_skl,null_class)) != ordered_pair(sK8_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f195,plain,
~ member(sK7_skl,universal_class),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f204,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f66,f62]) ).
fof(f205,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f204]) ).
fof(f217,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f50,f53]) ).
fof(f266,plain,
! [X0] :
( sK5_skl(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f184,f205]) ).
fof(f271,plain,
! [X0] : ~ member(sK7_skl,X0),
inference(resolution,[status(thm)],[f217,f195]) ).
fof(f288,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f266,f184]) ).
fof(f290,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f288]) ).
fof(f291,plain,
singleton(sK7_skl) = null_class,
inference(resolution,[status(thm)],[f290,f271]) ).
fof(f299,plain,
! [X0] : ordered_pair(X0,sK7_skl) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)),
inference(paramodulation,[status(thm)],[f291,f67]) ).
fof(f384,plain,
ordered_pair(sK8_skl,sK7_skl) != ordered_pair(sK8_skl,sK7_skl),
inference(backward_demodulation,[status(thm)],[f299,f194]) ).
fof(f396,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f384]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET103+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 % Computer : n015.cluster.edu
% 0.20/0.48 % Model : x86_64 x86_64
% 0.20/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.48 % Memory : 8046.5625MB
% 0.20/0.48 % OS : Linux 6.8.0-71-generic
% 0.20/0.48 % CPULimit : 300
% 0.20/0.48 % WCLimit : 300
% 0.20/0.48 % DateTime : Mon Sep 21 04:56:05 UTC 2026
% 0.20/0.49 % CPUTime :
% 0.20/0.51 % Drodi V4.1.1
% 0.23/0.53 % Refutation found
% 0.23/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.61 % Elapsed time: 0.110297 seconds
% 0.23/0.61 % CPU time: 0.165823 seconds
% 0.23/0.61 % Total memory used: 27.242 MB
% 0.23/0.61 % Net memory used: 27.182 MB
%------------------------------------------------------------------------------