%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET067+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 02:09:09 PM UTC 2026
% Result : Theorem 0.03s 0.40s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 18 unt; 0 def)
% Number of atoms : 84 ( 19 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 87 ( 38 ~; 32 |; 13 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 60 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : subclass(X,universal_class),
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(f44,conjecture,
! [X,Y] : subclass(unordered_pair(X,X),unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y] : subclass(unordered_pair(X,X),unordered_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(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(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(f63,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ member(X0,universal_class)
| 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(f191,plain,
? [X,Y] : ~ subclass(unordered_pair(X,X),unordered_pair(X,Y)),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
~ subclass(unordered_pair(sK7_skl,sK7_skl),unordered_pair(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,
~ subclass(unordered_pair(sK7_skl,sK7_skl),unordered_pair(sK7_skl,sK8_skl)),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f196,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f204,plain,
~ subclass(singleton(sK7_skl),unordered_pair(sK7_skl,sK8_skl)),
inference(backward_demodulation,[status(thm)],[f66,f193]) ).
fof(f205,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f66,f62]) ).
fof(f207,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f205]) ).
fof(f212,plain,
~ member(sK0_skl(unordered_pair(sK7_skl,sK8_skl),singleton(sK7_skl)),unordered_pair(sK7_skl,sK8_skl)),
inference(resolution,[status(thm)],[f204,f52]) ).
fof(f213,plain,
member(sK0_skl(unordered_pair(sK7_skl,sK8_skl),singleton(sK7_skl)),singleton(sK7_skl)),
inference(resolution,[status(thm)],[f204,f51]) ).
fof(f219,plain,
sK0_skl(unordered_pair(sK7_skl,sK8_skl),singleton(sK7_skl)) = sK7_skl,
inference(resolution,[status(thm)],[f207,f213]) ).
fof(f248,plain,
~ member(sK7_skl,unordered_pair(sK7_skl,sK8_skl)),
inference(backward_demodulation,[status(thm)],[f219,f212]) ).
fof(f249,plain,
member(sK7_skl,singleton(sK7_skl)),
inference(backward_demodulation,[status(thm)],[f219,f213]) ).
fof(f251,plain,
~ member(sK7_skl,universal_class),
inference(resolution,[status(thm)],[f248,f196]) ).
fof(f254,plain,
! [X0] :
( ~ member(sK7_skl,X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[status(thm)],[f251,f50]) ).
fof(f255,plain,
! [X0] : ~ member(sK7_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f254,f53]) ).
fof(f257,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f249,f255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET067+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:49:26 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.03/0.37 % Drodi V4.1.1
% 0.03/0.40 % Refutation found
% 0.03/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.42 % Elapsed time: 0.063329 seconds
% 0.03/0.42 % CPU time: 0.157820 seconds
% 0.03/0.42 % Total memory used: 104.912 MB
% 0.03/0.42 % Net memory used: 104.804 MB
%------------------------------------------------------------------------------