%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:08:49 PM UTC 2026
% Result : Unsatisfiable 20.26s 18.08s
% Output : CNFRefutation 20.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 20 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 83 ( 36 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [Element,Subset,Superset] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f5,axiom,
! [X,Xs] :
( member(X,complement(Xs))
| member(X,Xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Xs] :
( ~ member(X,complement(Xs))
| ~ member(X,Xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ equal_sets(Subset,Superset) ),
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(complement(a),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
equal_sets(complement(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ equal_sets(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [Element,Superset] :
( member(Element,Superset)
| ! [Subset] :
( ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
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(f30,plain,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
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(complement(a),b),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
equal_sets(complement(b),c),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
~ equal_sets(a,c),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f58,plain,
equal_sets(b,complement(a)),
inference(resolution,[status(thm)],[f54,f47]) ).
fof(f62,plain,
equal_sets(c,complement(b)),
inference(resolution,[status(thm)],[f55,f47]) ).
fof(f65,plain,
! [X0] :
( equal_sets(c,X0)
| ~ equal_sets(complement(b),X0) ),
inference(resolution,[status(thm)],[f62,f49]) ).
fof(f78,plain,
subset(b,complement(a)),
inference(resolution,[status(thm)],[f43,f58]) ).
fof(f80,plain,
subset(complement(a),b),
inference(resolution,[status(thm)],[f43,f54]) ).
fof(f89,plain,
! [X0,X1] :
( subset(X0,complement(X1))
| member(member_of_1_not_of_2(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[f30,f29]) ).
fof(f90,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ subset(complement(X1),X2)
| member(X0,X1) ),
inference(resolution,[status(thm)],[f30,f27]) ).
fof(f91,plain,
! [X0,X1] :
( subset(complement(X0),X1)
| ~ member(member_of_1_not_of_2(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[f31,f28]) ).
fof(f118,plain,
! [X0] :
( member(X0,b)
| member(X0,a) ),
inference(resolution,[status(thm)],[f90,f80]) ).
fof(f204,plain,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,complement(complement(X1))),X1)
| subset(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[f89,f31]) ).
fof(f209,plain,
! [X0,X1,X2] :
( member(member_of_1_not_of_2(X0,complement(X1)),X2)
| ~ subset(X1,X2)
| subset(X0,complement(X1)) ),
inference(resolution,[status(thm)],[f89,f27]) ).
fof(f214,plain,
! [X0] :
( member(member_of_1_not_of_2(complement(b),X0),a)
| subset(complement(b),X0) ),
inference(resolution,[status(thm)],[f91,f118]) ).
fof(f221,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(complement(complement(X0)),X1),X0)
| subset(complement(complement(X0)),X1) ),
inference(resolution,[status(thm)],[f91,f30]) ).
fof(f2946,plain,
( subset(complement(b),complement(complement(a)))
| subset(complement(b),complement(complement(a))) ),
inference(resolution,[status(thm)],[f204,f214]) ).
fof(f2965,plain,
! [X0] :
( subset(X0,complement(complement(X0)))
| subset(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[f204,f28]) ).
fof(f3016,plain,
subset(complement(b),complement(complement(a))),
inference(duplicate_literals_removal,[status(thm)],[f2946]) ).
fof(f3035,plain,
! [X0] : subset(X0,complement(complement(X0))),
inference(duplicate_literals_removal,[status(thm)],[f2965]) ).
fof(f3761,plain,
! [X0] :
( member(member_of_1_not_of_2(X0,complement(b)),complement(a))
| subset(X0,complement(b)) ),
inference(resolution,[status(thm)],[f209,f78]) ).
fof(f4108,plain,
! [X0] :
( subset(complement(complement(X0)),X0)
| subset(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f221,f29]) ).
fof(f4134,plain,
! [X0] : subset(complement(complement(X0)),X0),
inference(duplicate_literals_removal,[status(thm)],[f4108]) ).
fof(f4489,plain,
! [X0] :
( equal_sets(X0,complement(complement(X0)))
| ~ subset(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[f4134,f45]) ).
fof(f4490,plain,
! [X0] : equal_sets(X0,complement(complement(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f4489,f3035]) ).
fof(f4509,plain,
! [X0,X1] :
( equal_sets(X0,X1)
| ~ equal_sets(complement(complement(X0)),X1) ),
inference(resolution,[status(thm)],[f4490,f49]) ).
fof(f5858,plain,
( subset(complement(complement(a)),complement(b))
| subset(complement(complement(a)),complement(b)) ),
inference(resolution,[status(thm)],[f3761,f91]) ).
fof(f5879,plain,
subset(complement(complement(a)),complement(b)),
inference(duplicate_literals_removal,[status(thm)],[f5858]) ).
fof(f6024,plain,
( equal_sets(complement(b),complement(complement(a)))
| ~ subset(complement(b),complement(complement(a))) ),
inference(resolution,[status(thm)],[f5879,f45]) ).
fof(f6025,plain,
equal_sets(complement(b),complement(complement(a))),
inference(forward_subsumption_resolution,[status(thm)],[f6024,f3016]) ).
fof(f6032,plain,
equal_sets(c,complement(complement(a))),
inference(resolution,[status(thm)],[f6025,f65]) ).
fof(f6047,plain,
equal_sets(complement(complement(a)),c),
inference(resolution,[status(thm)],[f6032,f47]) ).
fof(f6340,plain,
equal_sets(a,c),
inference(resolution,[status(thm)],[f6047,f4509]) ).
fof(f6348,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6340,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.45 % CPULimit : 300
% 0.09/15.45 % WCLimit : 300
% 0.09/15.45 % DateTime : Mon Sep 21 04:42:05 UTC 2026
% 0.09/15.45 % CPUTime :
% 0.09/15.46 % Drodi V4.1.1
% 20.26/18.08 % Refutation found
% 20.26/18.08 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 20.26/18.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.82/18.11 % Elapsed time: 2.641203 seconds
% 17.82/18.11 % CPU time: 20.688441 seconds
% 17.82/18.11 % Total memory used: 111.789 MB
% 17.82/18.11 % Net memory used: 92.396 MB
%------------------------------------------------------------------------------