%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET012-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.16s 5.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 17 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 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(f5,axiom,
! [X,Xs] :
( member(X,complement(Xs))
| member(X,Xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Xs] :
( ~ member(X,complement(Xs))
| ~ member(X,Xs) ),
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(f17,axiom,
! [Xs,Ys] :
( equal_sets(Ys,Xs)
| ~ equal_sets(Xs,Ys) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ equal_sets(complement(complement(a)),a),
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(f28,plain,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
~ equal_sets(complement(complement(a)),a),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f61,plain,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(complement(X0),X1),X0)
| subset(complement(X0),X1) ),
inference(resolution,[status(thm)],[f26,f29]) ).
fof(f64,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,complement(X1)),X1)
| subset(X0,complement(X1)) ),
inference(resolution,[status(thm)],[f27,f28]) ).
fof(f78,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(complement(complement(X0)),X1),X0)
| subset(complement(complement(X0)),X1) ),
inference(resolution,[status(thm)],[f61,f28]) ).
fof(f82,plain,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,complement(complement(X1))),X1)
| subset(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[f64,f29]) ).
fof(f111,plain,
! [X0] :
( subset(complement(complement(X0)),X0)
| subset(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f78,f27]) ).
fof(f116,plain,
! [X0] : subset(complement(complement(X0)),X0),
inference(duplicate_literals_removal,[status(thm)],[f111]) ).
fof(f185,plain,
! [X0] :
( subset(X0,complement(complement(X0)))
| subset(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[f82,f26]) ).
fof(f193,plain,
! [X0] : subset(X0,complement(complement(X0))),
inference(duplicate_literals_removal,[status(thm)],[f185]) ).
fof(f214,plain,
! [X0] :
( equal_sets(X0,complement(complement(X0)))
| ~ subset(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f193,f43]) ).
fof(f215,plain,
! [X0] : equal_sets(X0,complement(complement(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f214,f116]) ).
fof(f219,plain,
! [X0] : equal_sets(complement(complement(X0)),X0),
inference(resolution,[status(thm)],[f215,f45]) ).
fof(f274,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f52,f219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n010.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 04:42:02 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.39 % Drodi V4.1.1
% 0.16/5.46 % Refutation found
% 0.16/5.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/5.47 % Elapsed time: 0.084483 seconds
% 0.16/5.47 % CPU time: 0.446541 seconds
% 0.16/5.47 % Total memory used: 20.413 MB
% 0.16/5.47 % Net memory used: 19.311 MB
%------------------------------------------------------------------------------