%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET137-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 54.56s 7.33s
% Output : CNFRefutation 54.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 84 ( 30 unt; 0 def)
% Number of atoms : 150 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 132 ( 66 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 150 ( 150 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [X] : intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))) = cantor(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,negated_conjecture,
member(w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
set_builder(u,set_builder(v,set_builder(w,null_class))) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f98,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f100,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f101,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f104,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| X1 = X0
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f109,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f110,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f112,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f124,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f127,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f130,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f131,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f134,plain,
! [X0,X1,X2] : restrict(X0,X1,X2) = intersection(cross_product(X1,X2),X0),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f135,plain,
! [X0,X1] :
( null_class != restrict(X1,singleton(X0),universal_class)
| ~ member(X0,domain_of(X1)) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f171,plain,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f172,plain,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f182,plain,
! [X0] : cantor(X0) = intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f202,plain,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f205,plain,
member(w,x),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f206,plain,
null_class = set_builder(u,set_builder(v,set_builder(w,null_class))),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f228,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f112,f110]) ).
fof(f270,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f99,f125]) ).
fof(f271,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f99,f127]) ).
fof(f287,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| ~ member(X0,cantor(X1)) ),
inference(paramodulation,[status(thm)],[f182,f125]) ).
fof(f322,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[status(thm)],[f98,f101]) ).
fof(f334,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,complement(X1)) ),
inference(resolution,[status(thm)],[f98,f129]) ).
fof(f398,plain,
! [X0] :
( cantor(X0) = null_class
| member(regular(cantor(X0)),domain_of(X0)) ),
inference(resolution,[status(thm)],[f287,f171]) ).
fof(f576,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,universal_class)
| member(X0,intersection(complement(X1),complement(X2))) ),
inference(paramodulation,[status(thm)],[f131,f130]) ).
fof(f1209,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f271,f100]) ).
fof(f1241,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(thm)],[f1209]) ).
fof(f1246,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f270,f100]) ).
fof(f1275,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f1246]) ).
fof(f1308,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,intersection(X1,complement(X2))) ),
inference(resolution,[status(thm)],[f1241,f334]) ).
fof(f1317,plain,
! [X0,X1,X2] : subclass(restrict(X0,X1,X2),X0),
inference(paramodulation,[status(thm)],[f134,f1241]) ).
fof(f1329,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(complement(X1),X2))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f1275,f334]) ).
fof(f1342,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(paramodulation,[status(thm)],[f172,f1275]) ).
fof(f1393,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[status(thm)],[f1342,f104]) ).
fof(f1396,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f1393]) ).
fof(f1401,plain,
! [X0,X1] : null_class = restrict(null_class,X0,X1),
inference(resolution,[status(thm)],[f1396,f1317]) ).
fof(f1487,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(paramodulation,[status(thm)],[f1401,f135]) ).
fof(f1498,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_equality_resolution,[status(thm)],[f1487]) ).
fof(f1503,plain,
cantor(null_class) = null_class,
inference(resolution,[status(thm)],[f1498,f398]) ).
fof(f1516,plain,
! [X0] :
( member(X0,domain_of(null_class))
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f1503,f287]) ).
fof(f1517,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f1516,f1498]) ).
fof(f4939,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f576,f1329]) ).
fof(f4940,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f576,f1308]) ).
fof(f4953,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f4939,f322]) ).
fof(f4960,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f4940,f322]) ).
fof(f5050,plain,
! [X0,X1,X2] :
( ~ member(X0,singleton(X1))
| member(X0,set_builder(X1,X2)) ),
inference(paramodulation,[status(thm)],[f202,f4953]) ).
fof(f5142,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,set_builder(X1,X2)) ),
inference(paramodulation,[status(thm)],[f202,f4960]) ).
fof(f5154,plain,
! [X0] :
( ~ member(X0,set_builder(v,set_builder(w,null_class)))
| member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f206,f5142]) ).
fof(f5156,plain,
! [X0] : ~ member(X0,set_builder(v,set_builder(w,null_class))),
inference(forward_subsumption_resolution,[status(thm)],[f5154,f1517]) ).
fof(f5169,plain,
! [X0] : ~ member(X0,set_builder(w,null_class)),
inference(resolution,[status(thm)],[f5156,f5142]) ).
fof(f5178,plain,
null_class = set_builder(w,null_class),
inference(resolution,[status(thm)],[f5169,f171]) ).
fof(f5813,plain,
! [X0] :
( ~ member(X0,singleton(w))
| member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f5178,f5050]) ).
fof(f5815,plain,
! [X0] : ~ member(X0,singleton(w)),
inference(forward_subsumption_resolution,[status(thm)],[f5813,f1517]) ).
fof(f5836,plain,
~ member(w,universal_class),
inference(resolution,[status(thm)],[f5815,f228]) ).
fof(f5933,plain,
! [X0] :
( ~ subclass(X0,universal_class)
| ~ member(w,X0) ),
inference(resolution,[status(thm)],[f5836,f98]) ).
fof(f5934,plain,
! [X0] : ~ member(w,X0),
inference(forward_subsumption_resolution,[status(thm)],[f5933,f101]) ).
fof(f5936,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f205,f5934]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET137-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:58:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 54.56/7.33 % Refutation found
% 54.56/7.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 54.56/7.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 54.03/8.10 % Elapsed time: 7.712578 seconds
% 54.03/8.10 % CPU time: 56.167421 seconds
% 54.03/8.10 % Total memory used: 701.040 MB
% 54.03/8.10 % Net memory used: 631.560 MB
%------------------------------------------------------------------------------