%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET015-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 0.12s 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 49 ( 20 ~; 29 |; 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 : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Xs,Ys] :
( member(X,union(Xs,Ys))
| ~ member(X,Xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Ys,Xs] :
( member(X,union(Xs,Ys))
| ~ member(X,Ys) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Xs,Ys] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Set1,Set2] :
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ equal_sets(union(as,bs),union(bs,as)),
file('/export/starexec/sandbox/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(f30,plain,
! [X,Xs] :
( ! [Ys] : member(X,union(Xs,Ys))
| ~ member(X,Xs) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f31,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X,Ys] :
( ! [Xs] : member(X,union(Xs,Ys))
| ~ member(X,Ys) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f33,plain,
! [X0,X1,X2] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X,Ys] :
( member(X,Ys)
| ! [Xs] :
( member(X,Xs)
| ~ member(X,union(Xs,Ys)) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f35,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
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(union(as,bs),union(bs,as)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f60,plain,
! [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)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[f26,f35]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ member(member_of_1_not_of_2(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f27,f33]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ member(member_of_1_not_of_2(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f27,f31]) ).
fof(f100,plain,
! [X0,X1,X2] :
( member(member_of_1_not_of_2(union(X0,X1),union(X1,X2)),X0)
| subset(union(X0,X1),union(X1,X2))
| subset(union(X0,X1),union(X1,X2)) ),
inference(resolution,[status(thm)],[f68,f60]) ).
fof(f106,plain,
! [X0,X1,X2] :
( member(member_of_1_not_of_2(union(X0,X1),union(X1,X2)),X0)
| subset(union(X0,X1),union(X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f100]) ).
fof(f606,plain,
! [X0,X1] :
( subset(union(X0,X1),union(X1,X0))
| subset(union(X0,X1),union(X1,X0)) ),
inference(resolution,[status(thm)],[f106,f67]) ).
fof(f619,plain,
! [X0,X1] : subset(union(X0,X1),union(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f606]) ).
fof(f663,plain,
! [X0,X1] :
( equal_sets(union(X1,X0),union(X0,X1))
| ~ subset(union(X0,X1),union(X1,X0)) ),
inference(resolution,[status(thm)],[f619,f43]) ).
fof(f665,plain,
! [X0,X1] : equal_sets(union(X0,X1),union(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f663,f619]) ).
fof(f671,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f52,f665]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET015-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 04:45:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.48 % Refutation found
% 0.12/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.51 % Elapsed time: 0.138542 seconds
% 0.12/0.51 % CPU time: 0.901690 seconds
% 0.12/0.51 % Total memory used: 27.246 MB
% 0.12/0.51 % Net memory used: 25.716 MB
%------------------------------------------------------------------------------