%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.18s 0.67s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 50 ( 23 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 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(f10,axiom,
! [X,Xs,Ys] :
( member(X,intersection(Xs,Ys))
| ~ member(X,Ys)
| ~ member(X,Xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Xs,Ys] :
( member(X,Xs)
| ~ member(X,intersection(Xs,Ys)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Xs,Ys] :
( member(X,Ys)
| ~ member(X,intersection(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(f22,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f37,plain,
! [X,Xs] :
( member(X,Xs)
| ! [Ys] : ~ member(X,intersection(Xs,Ys)) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f38,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X,Ys] :
( member(X,Ys)
| ! [Xs] : ~ member(X,intersection(Xs,Ys)) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f40,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f52,plain,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f60,plain,
! [X0,X1,X2] :
( member(member_of_1_not_of_2(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f26,f40]) ).
fof(f61,plain,
! [X0,X1,X2] :
( member(member_of_1_not_of_2(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f26,f38]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ member(member_of_1_not_of_2(X0,intersection(X1,X2)),X2)
| ~ member(member_of_1_not_of_2(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[f27,f36]) ).
fof(f102,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),intersection(X2,X0))
| ~ member(member_of_1_not_of_2(intersection(X0,X1),intersection(X2,X0)),X2)
| subset(intersection(X0,X1),intersection(X2,X0)) ),
inference(resolution,[status(thm)],[f68,f61]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ member(member_of_1_not_of_2(intersection(X0,X1),intersection(X2,X0)),X2)
| subset(intersection(X0,X1),intersection(X2,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f102]) ).
fof(f430,plain,
! [X0,X1] :
( subset(intersection(X0,X1),intersection(X1,X0))
| subset(intersection(X0,X1),intersection(X1,X0)) ),
inference(resolution,[status(thm)],[f109,f60]) ).
fof(f444,plain,
! [X0,X1] : subset(intersection(X0,X1),intersection(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f430]) ).
fof(f453,plain,
! [X0,X1] :
( equal_sets(intersection(X1,X0),intersection(X0,X1))
| ~ subset(intersection(X0,X1),intersection(X1,X0)) ),
inference(resolution,[status(thm)],[f444,f43]) ).
fof(f455,plain,
! [X0,X1] : equal_sets(intersection(X0,X1),intersection(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f453,f444]) ).
fof(f457,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f52,f455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n013.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 04:41:06 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.67 % Refutation found
% 0.18/0.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.54/0.71 % Elapsed time: 0.233773 seconds
% 1.54/0.71 % CPU time: 1.538584 seconds
% 1.54/0.71 % Total memory used: 25.721 MB
% 1.54/0.71 % Net memory used: 24.518 MB
%------------------------------------------------------------------------------