%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:08:52 PM UTC 2026
% Result : Unsatisfiable 2.60s 0.83s
% Output : CNFRefutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 14 unt; 0 def)
% Number of atoms : 193 ( 45 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 165 ( 49 ~; 116 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( little_set(X)
| ~ member(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( X = Y
| little_set(f1(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( X = Y
| ~ member(f1(X,Y),Y)
| ~ member(f1(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Z,X,Y] :
( ~ member(Z,Y)
| ~ member(Z,X)
| member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Z,X] :
( member(Z,X)
| ~ little_set(Z)
| member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : union(X,Y) = complement(intersection(complement(X),complement(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
union(as,bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
union(bs,as) = ds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X] :
( little_set(X)
| ! [Y] : ~ member(X,Y) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| little_set(f1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [Z,Y] :
( ~ member(Z,Y)
| ! [X] :
( ~ member(Z,X)
| member(Z,intersection(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
union(as,bs) = cs,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
union(bs,as) = ds,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
cs != ds,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(complement(X1),complement(X2)))
| ~ member(X0,union(X1,X2)) ),
inference(paramodulation,[status(thm)],[f29,f27]) ).
fof(f42,plain,
! [X0] :
( ~ member(X0,intersection(complement(bs),complement(as)))
| ~ member(X0,ds) ),
inference(paramodulation,[status(thm)],[f33,f40]) ).
fof(f43,plain,
! [X0] :
( ~ member(X0,intersection(complement(as),complement(bs)))
| ~ member(X0,cs) ),
inference(paramodulation,[status(thm)],[f32,f40]) ).
fof(f78,plain,
! [X0,X1,X2] :
( X0 = X1
| member(f1(X0,X1),X2)
| member(f1(X0,X1),complement(X2)) ),
inference(resolution,[status(thm)],[f28,f18]) ).
fof(f88,plain,
! [X0] :
( ~ member(f1(ds,X0),intersection(complement(bs),complement(as)))
| ds = X0
| member(f1(ds,X0),X0) ),
inference(resolution,[status(thm)],[f19,f42]) ).
fof(f102,plain,
! [X0] :
( ~ member(f1(X0,cs),intersection(complement(as),complement(bs)))
| X0 = cs
| member(f1(X0,cs),X0) ),
inference(resolution,[status(thm)],[f19,f43]) ).
fof(f120,plain,
! [X0] :
( ~ member(f1(ds,X0),complement(as))
| ~ member(f1(ds,X0),complement(bs))
| ds = X0
| member(f1(ds,X0),X0) ),
inference(resolution,[status(thm)],[f88,f26]) ).
fof(f123,plain,
! [X0] :
( ~ member(f1(X0,cs),complement(bs))
| ~ member(f1(X0,cs),complement(as))
| X0 = cs
| member(f1(X0,cs),X0) ),
inference(resolution,[status(thm)],[f102,f26]) ).
fof(f209,plain,
! [X0] :
( ~ member(f1(ds,X0),complement(as))
| ds = X0
| member(f1(ds,X0),X0)
| ds = X0
| member(f1(ds,X0),bs) ),
inference(resolution,[status(thm)],[f78,f120]) ).
fof(f212,plain,
! [X0] :
( ~ member(f1(X0,cs),complement(as))
| X0 = cs
| member(f1(X0,cs),X0)
| X0 = cs
| member(f1(X0,cs),bs) ),
inference(resolution,[status(thm)],[f78,f123]) ).
fof(f223,plain,
! [X0] :
( ~ member(f1(ds,X0),complement(as))
| member(f1(ds,X0),X0)
| ds = X0
| member(f1(ds,X0),bs) ),
inference(duplicate_literals_removal,[status(thm)],[f209]) ).
fof(f226,plain,
! [X0] :
( ~ member(f1(X0,cs),complement(as))
| member(f1(X0,cs),X0)
| X0 = cs
| member(f1(X0,cs),bs) ),
inference(duplicate_literals_removal,[status(thm)],[f212]) ).
fof(f232,plain,
! [X0] :
( ds = X0
| member(f1(ds,X0),as)
| member(f1(ds,X0),X0)
| ds = X0
| member(f1(ds,X0),bs) ),
inference(resolution,[status(thm)],[f223,f78]) ).
fof(f234,plain,
! [X0] :
( member(f1(ds,X0),as)
| member(f1(ds,X0),X0)
| ds = X0
| member(f1(ds,X0),bs) ),
inference(duplicate_literals_removal,[status(thm)],[f232]) ).
fof(f247,plain,
! [X0] :
( ds = X0
| ~ member(f1(ds,X0),ds)
| member(f1(ds,X0),as)
| ds = X0
| member(f1(ds,X0),bs) ),
inference(resolution,[status(thm)],[f234,f20]) ).
fof(f270,plain,
! [X0] :
( ~ member(f1(ds,X0),ds)
| member(f1(ds,X0),as)
| ds = X0
| member(f1(ds,X0),bs) ),
inference(duplicate_literals_removal,[status(thm)],[f247]) ).
fof(f330,plain,
! [X0] :
( X0 = cs
| member(f1(X0,cs),as)
| member(f1(X0,cs),X0)
| X0 = cs
| member(f1(X0,cs),bs) ),
inference(resolution,[status(thm)],[f226,f78]) ).
fof(f332,plain,
! [X0] :
( member(f1(X0,cs),as)
| member(f1(X0,cs),X0)
| X0 = cs
| member(f1(X0,cs),bs) ),
inference(duplicate_literals_removal,[status(thm)],[f330]) ).
fof(f355,plain,
( member(f1(ds,cs),as)
| ds = cs
| member(f1(ds,cs),bs)
| member(f1(ds,cs),as)
| ds = cs
| member(f1(ds,cs),bs) ),
inference(resolution,[status(thm)],[f332,f270]) ).
fof(f368,plain,
( member(f1(ds,cs),as)
| ds = cs
| member(f1(ds,cs),bs) ),
inference(duplicate_literals_removal,[status(thm)],[f355]) ).
fof(f369,plain,
( member(f1(ds,cs),as)
| member(f1(ds,cs),bs) ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f34]) ).
fof(f380,plain,
( little_set(f1(ds,cs))
| member(f1(ds,cs),as) ),
inference(resolution,[status(thm)],[f369,f17]) ).
fof(f381,plain,
little_set(f1(ds,cs)),
inference(forward_subsumption_resolution,[status(thm)],[f380,f17]) ).
fof(f1142,plain,
! [X0] :
( member(f1(ds,cs),X0)
| member(f1(ds,cs),complement(X0)) ),
inference(resolution,[status(thm)],[f381,f28]) ).
fof(f1717,plain,
! [X0,X1] :
( member(f1(ds,cs),intersection(complement(X0),complement(X1)))
| member(f1(ds,cs),union(X0,X1)) ),
inference(paramodulation,[status(thm)],[f29,f1142]) ).
fof(f1721,plain,
! [X0,X1] :
( member(f1(ds,cs),complement(X1))
| member(f1(ds,cs),union(X0,X1)) ),
inference(resolution,[status(thm)],[f1717,f24]) ).
fof(f1722,plain,
! [X0,X1] :
( member(f1(ds,cs),complement(X0))
| member(f1(ds,cs),union(X0,X1)) ),
inference(resolution,[status(thm)],[f1717,f22]) ).
fof(f1745,plain,
( member(f1(ds,cs),complement(as))
| member(f1(ds,cs),ds) ),
inference(paramodulation,[status(thm)],[f33,f1721]) ).
fof(f1746,plain,
( member(f1(ds,cs),complement(bs))
| member(f1(ds,cs),cs) ),
inference(paramodulation,[status(thm)],[f32,f1721]) ).
fof(f1752,plain,
( member(f1(ds,cs),ds)
| ds = cs
| member(f1(ds,cs),bs)
| member(f1(ds,cs),ds) ),
inference(resolution,[status(thm)],[f1745,f226]) ).
fof(f1755,plain,
( ds = cs
| member(f1(ds,cs),bs)
| member(f1(ds,cs),ds) ),
inference(duplicate_literals_removal,[status(thm)],[f1752]) ).
fof(f1756,plain,
( member(f1(ds,cs),bs)
| member(f1(ds,cs),ds) ),
inference(forward_subsumption_resolution,[status(thm)],[f1755,f34]) ).
fof(f1763,plain,
( ~ member(f1(ds,cs),bs)
| member(f1(ds,cs),cs) ),
inference(resolution,[status(thm)],[f1746,f27]) ).
fof(f1803,plain,
( member(f1(ds,cs),complement(bs))
| member(f1(ds,cs),ds) ),
inference(paramodulation,[status(thm)],[f33,f1722]) ).
fof(f1804,plain,
( member(f1(ds,cs),complement(as))
| member(f1(ds,cs),cs) ),
inference(paramodulation,[status(thm)],[f32,f1722]) ).
fof(f1813,plain,
( ~ member(f1(ds,cs),bs)
| member(f1(ds,cs),ds) ),
inference(resolution,[status(thm)],[f1803,f27]) ).
fof(f1817,plain,
member(f1(ds,cs),ds),
inference(forward_subsumption_resolution,[status(thm)],[f1813,f1756]) ).
fof(f1818,plain,
( member(f1(ds,cs),cs)
| ds = cs
| member(f1(ds,cs),bs)
| member(f1(ds,cs),cs) ),
inference(resolution,[status(thm)],[f1804,f223]) ).
fof(f1822,plain,
( ds = cs
| member(f1(ds,cs),bs)
| member(f1(ds,cs),cs) ),
inference(duplicate_literals_removal,[status(thm)],[f1818]) ).
fof(f1823,plain,
( member(f1(ds,cs),bs)
| member(f1(ds,cs),cs) ),
inference(forward_subsumption_resolution,[status(thm)],[f1822,f34]) ).
fof(f1824,plain,
( ds = cs
| ~ member(f1(ds,cs),ds)
| member(f1(ds,cs),bs) ),
inference(resolution,[status(thm)],[f1823,f20]) ).
fof(f1827,plain,
( ds = cs
| member(f1(ds,cs),bs) ),
inference(forward_subsumption_resolution,[status(thm)],[f1824,f1756]) ).
fof(f1828,plain,
member(f1(ds,cs),bs),
inference(forward_subsumption_resolution,[status(thm)],[f1827,f34]) ).
fof(f3112,plain,
member(f1(ds,cs),cs),
inference(forward_subsumption_resolution,[status(thm)],[f1763,f1828]) ).
fof(f3113,plain,
( ds = cs
| ~ member(f1(ds,cs),ds) ),
inference(resolution,[status(thm)],[f3112,f20]) ).
fof(f3116,plain,
ds = cs,
inference(forward_subsumption_resolution,[status(thm)],[f3113,f1817]) ).
fof(f3117,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3116,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:42:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 2.60/0.83 % Refutation found
% 2.60/0.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.60/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.66/0.86 % Elapsed time: 0.488408 seconds
% 2.66/0.86 % CPU time: 3.549704 seconds
% 2.66/0.86 % Total memory used: 170.047 MB
% 2.66/0.86 % Net memory used: 166.045 MB
%------------------------------------------------------------------------------