%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET015-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 02:08:51 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.84s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 30 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Xs,Ys] :
( member(X,union(Xs,Ys))
| ~ member(X,Xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Ys,Xs] :
( member(X,union(Xs,Ys))
| ~ member(X,Ys) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Xs,Ys] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Set1,Set2] :
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Xs,Ys] :
( equal_sets(Ys,Xs)
| ~ equal_sets(Xs,Ys) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Xs,Ys,Zs] :
( equal_sets(Xs,Zs)
| ~ equal_sets(Ys,Zs)
| ~ equal_sets(Xs,Ys) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
equal_sets(union(as,bs),cs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
equal_sets(union(bs,as),ds),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [X,Xs] :
( ! [Ys] : member(X,union(Xs,Ys))
| ~ member(X,Xs) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f33,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X,Ys] :
( ! [Xs] : member(X,union(Xs,Ys))
| ~ member(X,Ys) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f35,plain,
! [X0,X1,X2] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X,Ys] :
( member(X,Ys)
| ! [Xs] :
( member(X,Xs)
| ~ member(X,union(Xs,Ys)) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f45,plain,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f47,plain,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f48,plain,
! [Xs,Zs] :
( equal_sets(Xs,Zs)
| ! [Ys] :
( ~ equal_sets(Ys,Zs)
| ~ equal_sets(Xs,Ys) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f49,plain,
! [X0,X1,X2] :
( equal_sets(X0,X2)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f54,plain,
equal_sets(union(as,bs),cs),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
equal_sets(union(bs,as),ds),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
~ equal_sets(cs,ds),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
! [X0] :
( equal_sets(X0,cs)
| ~ equal_sets(X0,union(as,bs)) ),
inference(resolution,[status(thm)],[f54,f49]) ).
fof(f61,plain,
! [X0] :
( equal_sets(X0,ds)
| ~ equal_sets(X0,union(bs,as)) ),
inference(resolution,[status(thm)],[f55,f49]) ).
fof(f135,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(member_of_1_not_of_2(X0,union(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f33,f29]) ).
fof(f140,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(member_of_1_not_of_2(X0,union(X1,X2)),X2) ),
inference(resolution,[status(thm)],[f35,f29]) ).
fof(f147,plain,
! [X0,X1,X2] :
( subset(union(X0,X1),X2)
| member(member_of_1_not_of_2(union(X0,X1),X2),X1)
| member(member_of_1_not_of_2(union(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f37,f28]) ).
fof(f441,plain,
! [X0,X1,X2] :
( subset(union(X0,X1),union(X1,X2))
| subset(union(X0,X1),union(X1,X2))
| member(member_of_1_not_of_2(union(X0,X1),union(X1,X2)),X0) ),
inference(resolution,[status(thm)],[f147,f135]) ).
fof(f454,plain,
! [X0,X1,X2] :
( subset(union(X0,X1),union(X1,X2))
| member(member_of_1_not_of_2(union(X0,X1),union(X1,X2)),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f441]) ).
fof(f1697,plain,
! [X0,X1] :
( subset(union(X0,X1),union(X1,X0))
| subset(union(X0,X1),union(X1,X0)) ),
inference(resolution,[status(thm)],[f454,f140]) ).
fof(f1713,plain,
! [X0,X1] : subset(union(X0,X1),union(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f1697]) ).
fof(f3036,plain,
! [X0,X1] :
( equal_sets(union(X1,X0),union(X0,X1))
| ~ subset(union(X0,X1),union(X1,X0)) ),
inference(resolution,[status(thm)],[f1713,f45]) ).
fof(f3038,plain,
! [X0,X1] : equal_sets(union(X0,X1),union(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f3036,f1713]) ).
fof(f3179,plain,
equal_sets(union(bs,as),cs),
inference(resolution,[status(thm)],[f3038,f59]) ).
fof(f3512,plain,
equal_sets(cs,union(bs,as)),
inference(resolution,[status(thm)],[f3179,f47]) ).
fof(f3572,plain,
equal_sets(cs,ds),
inference(resolution,[status(thm)],[f3512,f61]) ).
fof(f3577,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3572,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET015-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.59 % Computer : n005.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Mon Sep 21 04:41:53 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.15/5.60 % Drodi V4.1.1
% 0.15/5.84 % Refutation found
% 0.15/5.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.87 % Elapsed time: 0.256179 seconds
% 0.15/5.87 % CPU time: 1.871544 seconds
% 0.15/5.87 % Total memory used: 36.806 MB
% 0.15/5.87 % Net memory used: 32.590 MB
%------------------------------------------------------------------------------