%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET287-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 02:09:46 PM UTC 2026
% Result : Unsatisfiable 8.85s 1.81s
% Output : CNFRefutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 62 ( 25 unt; 0 def)
% Number of atoms : 104 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 40 ~; 42 |; 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 : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 103 ( 103 !; 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(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(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = 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(f113,negated_conjecture,
subclass(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
domain_of(intersection(complement(y),x)) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f116,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f118,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f119,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f122,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f142,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f143,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f145,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f147,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f149,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f153,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f189,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f246,plain,
subclass(x,y),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
domain_of(intersection(complement(y),x)) != null_class,
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f250,plain,
! [X0] :
( member(X0,y)
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[f116,f246]) ).
fof(f252,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f119,f116]) ).
fof(f257,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f117,f143]) ).
fof(f258,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[f117,f252]) ).
fof(f270,plain,
! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[f147,f117]) ).
fof(f271,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f145,f117]) ).
fof(f337,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f257,f118]) ).
fof(f341,plain,
! [X0,X1,X2] :
( ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0)
| subclass(intersection(complement(X0),X1),X2) ),
inference(resolution,[status(thm)],[f257,f147]) ).
fof(f348,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f337]) ).
fof(f349,plain,
! [X0] :
( subclass(complement(universal_class),X0)
| subclass(complement(universal_class),X0) ),
inference(resolution,[status(thm)],[f270,f258]) ).
fof(f350,plain,
! [X0] : subclass(complement(universal_class),X0),
inference(duplicate_literals_removal,[status(thm)],[f349]) ).
fof(f351,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subclass(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[f348,f122]) ).
fof(f354,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(resolution,[status(thm)],[f350,f116]) ).
fof(f403,plain,
! [X0,X1] :
( member(not_subclass_element(intersection(X0,x),X1),y)
| subclass(intersection(X0,x),X1) ),
inference(resolution,[status(thm)],[f271,f250]) ).
fof(f464,plain,
! [X0] : intersection(complement(universal_class),X0) = complement(universal_class),
inference(resolution,[status(thm)],[f351,f350]) ).
fof(f524,plain,
! [X0] : complement(complement(universal_class)) = union(universal_class,X0),
inference(paramodulation,[status(thm)],[f464,f149]) ).
fof(f609,plain,
! [X0,X1] :
( ~ member(X0,complement(universal_class))
| ~ member(X0,union(universal_class,X1)) ),
inference(paramodulation,[status(thm)],[f524,f147]) ).
fof(f616,plain,
! [X0] : ~ member(X0,complement(universal_class)),
inference(forward_subsumption_resolution,[status(thm)],[f609,f354]) ).
fof(f636,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[f616,f189]) ).
fof(f647,plain,
! [X0] : intersection(complement(universal_class),X0) = null_class,
inference(backward_demodulation,[status(thm)],[f636,f464]) ).
fof(f648,plain,
! [X0] : subclass(null_class,X0),
inference(backward_demodulation,[status(thm)],[f636,f350]) ).
fof(f657,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(forward_demodulation,[status(thm)],[f636,f647]) ).
fof(f666,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class) ),
inference(resolution,[status(thm)],[f648,f122]) ).
fof(f699,plain,
! [X0] :
( domain_of(X0) = null_class
| restrict(X0,singleton(regular(domain_of(X0))),universal_class) != null_class ),
inference(resolution,[status(thm)],[f153,f189]) ).
fof(f735,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(paramodulation,[status(thm)],[f151,f657]) ).
fof(f4859,plain,
! [X0] :
( subclass(intersection(complement(y),x),X0)
| subclass(intersection(complement(y),x),X0) ),
inference(resolution,[status(thm)],[f341,f403]) ).
fof(f4875,plain,
! [X0] : subclass(intersection(complement(y),x),X0),
inference(duplicate_literals_removal,[status(thm)],[f4859]) ).
fof(f4996,plain,
null_class = intersection(complement(y),x),
inference(resolution,[status(thm)],[f4875,f666]) ).
fof(f5062,plain,
domain_of(null_class) != null_class,
inference(backward_demodulation,[status(thm)],[f4996,f247]) ).
fof(f7039,plain,
domain_of(null_class) = null_class,
inference(resolution,[status(thm)],[f699,f735]) ).
fof(f7046,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f7039,f5062]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET287-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n015.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:08:20 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 8.85/1.81 % Refutation found
% 8.85/1.81 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.85/1.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.85/1.86 % Elapsed time: 1.397706 seconds
% 8.85/1.86 % CPU time: 10.356332 seconds
% 8.85/1.86 % Total memory used: 188.582 MB
% 8.85/1.86 % Net memory used: 176.814 MB
%------------------------------------------------------------------------------