%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET132-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 02:09:27 PM UTC 2026
% Result : Unsatisfiable 0.40s 0.68s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 16 unt; 0 def)
% Number of atoms : 60 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f106,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f122,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f123,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f125,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f128,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f129,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f200,plain,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f201,plain,
member(u,universal_class),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f202,plain,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f221,plain,
! [X0] : member(u,unordered_pair(u,X0)),
inference(resolution,[status(thm)],[f106,f201]) ).
fof(f234,plain,
member(u,singleton(u)),
inference(paramodulation,[status(thm)],[f110,f221]) ).
fof(f368,plain,
! [X0] :
( member(u,X0)
| member(u,complement(X0)) ),
inference(resolution,[status(thm)],[f128,f201]) ).
fof(f412,plain,
! [X0,X1] :
( member(u,intersection(complement(X0),complement(X1)))
| member(u,union(X0,X1)) ),
inference(paramodulation,[status(thm)],[f129,f368]) ).
fof(f420,plain,
! [X0,X1] :
( member(u,complement(X1))
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f412,f125]) ).
fof(f421,plain,
! [X0,X1] :
( member(u,complement(X0))
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f412,f123]) ).
fof(f434,plain,
! [X0,X1] :
( ~ member(u,X1)
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f420,f127]) ).
fof(f441,plain,
! [X0,X1] :
( ~ member(u,X0)
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f421,f127]) ).
fof(f652,plain,
! [X0,X1] :
( ~ member(u,X1)
| member(u,set_builder(X0,X1)) ),
inference(paramodulation,[status(thm)],[f200,f434]) ).
fof(f661,plain,
~ member(u,set_builder(y,set_builder(u,null_class))),
inference(resolution,[status(thm)],[f652,f202]) ).
fof(f663,plain,
~ member(u,set_builder(u,null_class)),
inference(resolution,[status(thm)],[f661,f652]) ).
fof(f691,plain,
! [X0,X1] :
( ~ member(u,singleton(X0))
| member(u,set_builder(X0,X1)) ),
inference(paramodulation,[status(thm)],[f200,f441]) ).
fof(f702,plain,
! [X0] : member(u,set_builder(u,X0)),
inference(resolution,[status(thm)],[f691,f234]) ).
fof(f705,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f663,f702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET132-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.52 % Computer : n018.cluster.edu
% 0.12/0.52 % Model : x86_64 x86_64
% 0.12/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.52 % Memory : 8046.5625MB
% 0.12/0.52 % OS : Linux 6.8.0-71-generic
% 0.12/0.53 % CPULimit : 300
% 0.12/0.53 % WCLimit : 300
% 0.12/0.53 % DateTime : Mon Sep 21 04:57:28 UTC 2026
% 0.12/0.53 % CPUTime :
% 0.12/0.54 % Drodi V4.1.1
% 0.40/0.68 % Refutation found
% 0.40/0.68 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.40/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.71 % Elapsed time: 0.175474 seconds
% 0.28/0.71 % CPU time: 1.070436 seconds
% 0.28/0.71 % Total memory used: 127.472 MB
% 0.28/0.71 % Net memory used: 124.920 MB
%------------------------------------------------------------------------------