%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET098+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 : n016.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 02:09:20 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 80 ( 9 unt; 0 def)
% Number of atoms : 261 ( 49 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 299 ( 118 ~; 122 |; 49 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 186 ( 173 !; 13 ?)
% 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(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(f13,axiom,
! [X,Y,Z] :
( member(Z,intersection(X,Y))
<=> ( member(Z,Y)
& member(Z,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Z] :
( member(Z,complement(X))
<=> ( ~ member(Z,X)
& member(Z,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X,Y] :
( disjoint(X,Y)
<=> ! [U] :
~ ( member(U,Y)
& member(U,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] :
( ? [V] :
( ? [W] :
( member(W,X)
& member(W,intersection(complement(singleton(V)),X)) )
& member(V,X) )
| ? [Y] : singleton(Y) = X
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X] :
( ? [V] :
( ? [W] :
( member(W,X)
& member(W,intersection(complement(singleton(V)),X)) )
& member(V,X) )
| ? [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(f53,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f2]) ).
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(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(f85,plain,
! [X,Y,Z] :
( ( ~ member(Z,Y)
| ~ member(Z,X)
| member(Z,intersection(X,Y)) )
& ( ( member(Z,Y)
& member(Z,X) )
| ~ member(Z,intersection(X,Y)) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f86,plain,
( ! [X,Y,Z] :
( ~ member(Z,Y)
| ~ member(Z,X)
| member(Z,intersection(X,Y)) )
& ! [X,Y,Z] :
( ( member(Z,Y)
& member(Z,X) )
| ~ member(Z,intersection(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f90,plain,
! [X,Z] :
( ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
& ( ( ~ member(Z,X)
& member(Z,universal_class) )
| ~ member(Z,complement(X)) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f91,plain,
( ! [X,Z] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
& ! [X,Z] :
( ( ~ member(Z,X)
& member(Z,universal_class) )
| ~ member(Z,complement(X)) ) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f94,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f174,plain,
! [X,Y] :
( disjoint(X,Y)
<=> ! [U] :
( ~ member(U,Y)
| ~ member(U,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f175,plain,
! [X,Y] :
( ( ? [U] :
( member(U,Y)
& member(U,X) )
| disjoint(X,Y) )
& ( ! [U] :
( ~ member(U,Y)
| ~ member(U,X) )
| ~ disjoint(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
( ! [X,Y] :
( ? [U] :
( member(U,Y)
& member(U,X) )
| disjoint(X,Y) )
& ! [X,Y] :
( ! [U] :
( ~ member(U,Y)
| ~ member(U,X) )
| ~ disjoint(X,Y) ) ),
inference(miniscoping,[status(thm)],[f175]) ).
fof(f177,plain,
( ! [X,Y] :
( ( member(sK4_skl(Y,X),Y)
& member(sK4_skl(Y,X),X) )
| disjoint(X,Y) )
& ! [X,Y] :
( ! [U] :
( ~ member(U,Y)
| ~ member(U,X) )
| ~ disjoint(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(U,sK4_skl(Y,X))],[f176]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f177]) ).
fof(f179,plain,
! [X0,X1] :
( member(sK4_skl(X1,X0),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f177]) ).
fof(f180,plain,
! [X0,X1] :
( member(sK4_skl(X1,X0),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f177]) ).
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] :
( ! [V] :
( ! [W] :
( ~ member(W,X)
| ~ member(W,intersection(complement(singleton(V)),X)) )
| ~ member(V,X) )
& ! [Y] : singleton(Y) != X
& X != null_class ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
( ! [V] :
( ! [W] :
( ~ member(W,sK7_skl)
| ~ member(W,intersection(complement(singleton(V)),sK7_skl)) )
| ~ member(V,sK7_skl) )
& ! [Y] : singleton(Y) != sK7_skl
& sK7_skl != null_class ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(X,sK7_skl)],[f191]) ).
fof(f193,plain,
sK7_skl != null_class,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
! [X0] : singleton(X0) != sK7_skl,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f195,plain,
! [X0,X1] :
( ~ member(X1,sK7_skl)
| ~ member(X1,intersection(complement(singleton(X0)),sK7_skl))
| ~ member(X0,sK7_skl) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f198,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f202,plain,
! [X0,X1] :
( ~ member(X1,intersection(complement(singleton(X0)),sK7_skl))
| ~ member(X0,sK7_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f88]) ).
fof(f207,plain,
! [X0,X1] :
( ~ member(X1,sK7_skl)
| ~ member(X1,complement(singleton(X0)))
| ~ member(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f202,f89]) ).
fof(f208,plain,
! [X0,X1] :
( member(X1,singleton(X0))
| ~ member(X1,universal_class)
| ~ member(X1,sK7_skl)
| ~ member(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f207,f94]) ).
fof(f210,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f50,f53]) ).
fof(f302,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f66,f62]) ).
fof(f303,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f302]) ).
fof(f378,plain,
! [X0,X1] :
( subclass(singleton(X1),X0)
| sK0_skl(X0,singleton(X1)) = X1 ),
inference(resolution,[status(thm)],[f303,f51]) ).
fof(f391,plain,
! [X0,X1] :
( member(X1,singleton(X0))
| ~ member(X1,sK7_skl)
| ~ member(X0,sK7_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f208,f210]) ).
fof(f408,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f66,f198]) ).
fof(f422,plain,
! [X0,X1] :
( X1 = X0
| ~ member(X1,sK7_skl)
| ~ member(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f391,f303]) ).
fof(f463,plain,
! [X0] :
( sK7_skl = null_class
| sK5_skl(sK7_skl) = X0
| ~ member(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f422,f184]) ).
fof(f468,plain,
! [X0] :
( sK5_skl(sK7_skl) = X0
| ~ member(X0,sK7_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f193]) ).
fof(f473,plain,
! [X0] :
( subclass(sK7_skl,X0)
| sK5_skl(sK7_skl) = sK0_skl(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f468,f51]) ).
fof(f534,plain,
! [X0] :
( sK5_skl(sK7_skl) = sK4_skl(X0,sK7_skl)
| disjoint(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f179,f468]) ).
fof(f584,plain,
! [X0] :
( subclass(sK7_skl,X0)
| ~ member(sK5_skl(sK7_skl),X0)
| subclass(sK7_skl,X0) ),
inference(paramodulation,[status(thm)],[f473,f52]) ).
fof(f588,plain,
! [X0] :
( ~ member(sK5_skl(sK7_skl),X0)
| subclass(sK7_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f584]) ).
fof(f611,plain,
! [X0] :
( disjoint(sK7_skl,X0)
| member(sK5_skl(sK7_skl),X0)
| disjoint(sK7_skl,X0) ),
inference(paramodulation,[status(thm)],[f534,f180]) ).
fof(f613,plain,
! [X0] :
( member(sK5_skl(sK7_skl),X0)
| disjoint(sK7_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f611]) ).
fof(f615,plain,
! [X0] :
( subclass(sK7_skl,X0)
| disjoint(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f613,f588]) ).
fof(f965,plain,
! [X0,X1] :
( subclass(sK7_skl,X1)
| ~ member(X0,X1)
| ~ member(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f178,f615]) ).
fof(f1193,plain,
! [X0,X1] :
( ~ subclass(X1,sK7_skl)
| X1 = sK7_skl
| ~ member(X0,X1)
| ~ member(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f965,f58]) ).
fof(f1198,plain,
! [X0,X1] :
( ~ subclass(X1,sK7_skl)
| X1 = sK7_skl
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1193,f50]) ).
fof(f1732,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| ~ member(X0,X1)
| subclass(singleton(X0),X1) ),
inference(paramodulation,[status(thm)],[f378,f52]) ).
fof(f1736,plain,
! [X0,X1] :
( ~ member(X0,X1)
| subclass(singleton(X0),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1732]) ).
fof(f1739,plain,
! [X0,X1] :
( singleton(X0) = sK7_skl
| ~ member(X1,singleton(X0))
| ~ member(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f1736,f1198]) ).
fof(f1747,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| ~ member(X0,sK7_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1739,f194]) ).
fof(f1770,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f1747,f408]) ).
fof(f1771,plain,
! [X0] : ~ member(X0,sK7_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1770,f210]) ).
fof(f1812,plain,
sK7_skl = null_class,
inference(resolution,[status(thm)],[f1771,f184]) ).
fof(f1819,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1812,f193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET098+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:57:22 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.46 % Refutation found
% 0.15/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.49 % Elapsed time: 0.123995 seconds
% 0.15/0.49 % CPU time: 0.664737 seconds
% 0.15/0.49 % Total memory used: 112.592 MB
% 0.15/0.49 % Net memory used: 111.670 MB
%------------------------------------------------------------------------------