%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET136-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.25s 1.06s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 18 unt; 2 def)
% Number of atoms : 111 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 43 ~; 49 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 80 ( 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
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,
set_builder(x,set_builder(y,set_builder(u,null_class))) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f96,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f99,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(f170,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
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,
set_builder(x,set_builder(y,set_builder(u,null_class))) = null_class,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f210,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f99,f96]) ).
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(f349,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f170,f123]) ).
fof(f368,plain,
! [X0] :
( member(u,X0)
| member(u,complement(X0)) ),
inference(resolution,[status(thm)],[f128,f201]) ).
fof(f420,plain,
! [X0,X1] :
( member(u,intersection(complement(X0),complement(X1)))
| member(u,union(X0,X1)) ),
inference(paramodulation,[status(thm)],[f129,f368]) ).
fof(f428,plain,
! [X0,X1] :
( member(u,complement(X1))
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f420,f125]) ).
fof(f429,plain,
! [X0,X1] :
( member(u,complement(X0))
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f420,f123]) ).
fof(f442,plain,
! [X0,X1] :
( ~ member(u,X1)
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f428,f127]) ).
fof(f449,plain,
! [X0,X1] :
( ~ member(u,X0)
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f429,f127]) ).
fof(f651,plain,
! [X0,X1] :
( ~ member(u,X1)
| member(u,set_builder(X0,X1)) ),
inference(paramodulation,[status(thm)],[f200,f442]) ).
fof(f660,plain,
( ~ member(u,set_builder(y,set_builder(u,null_class)))
| member(u,null_class) ),
inference(paramodulation,[status(thm)],[f202,f651]) ).
fof(f662,definition,
( sQ16_spl
<=> member(u,null_class) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f663,plain,
( ~ sQ16_spl
| member(u,null_class) ),
inference(component_clause,[status(thm)],[f662]) ).
fof(f665,definition,
( sQ17_spl
<=> member(u,set_builder(y,set_builder(u,null_class))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( sQ17_spl
| ~ member(u,set_builder(y,set_builder(u,null_class))) ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( ~ sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f660,f662,f665]) ).
fof(f670,plain,
! [X0] :
( ~ sQ16_spl
| X0 = null_class
| member(u,X0) ),
inference(resolution,[status(thm)],[f663,f349]) ).
fof(f704,plain,
! [X0] :
( ~ sQ16_spl
| ~ member(u,X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f670,f127]) ).
fof(f921,plain,
( sQ17_spl
| ~ member(u,set_builder(u,null_class)) ),
inference(resolution,[status(thm)],[f667,f651]) ).
fof(f923,plain,
! [X0,X1] :
( ~ member(u,singleton(X0))
| member(u,set_builder(X0,X1)) ),
inference(paramodulation,[status(thm)],[f200,f449]) ).
fof(f958,plain,
( ~ sQ16_spl
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f704,f201]) ).
fof(f1057,plain,
! [X0] : member(u,set_builder(u,X0)),
inference(resolution,[status(thm)],[f923,f234]) ).
fof(f1059,plain,
( sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f921,f1057]) ).
fof(f1064,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f1059]) ).
fof(f1298,plain,
! [X0] :
( ~ sQ16_spl
| ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f958,f127]) ).
fof(f1301,plain,
( ~ sQ16_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f663,f1310]) ).
fof(f1310,plain,
! [X0] :
( ~ sQ16_spl
| ~ member(X0,null_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f1298,f210]) ).
fof(f1311,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f1301]) ).
fof(f1312,plain,
$false,
inference(sat_refutation,[status(thm)],[f668,f1064,f1311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET136-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n009.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 04:55:43 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.49 % Drodi V4.1.1
% 0.25/1.06 % Refutation found
% 0.25/1.06 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.25/1.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.77/1.10 % Elapsed time: 0.626217 seconds
% 3.77/1.10 % CPU time: 4.440514 seconds
% 3.77/1.10 % Total memory used: 157.117 MB
% 3.77/1.10 % Net memory used: 151.252 MB
%------------------------------------------------------------------------------