%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET246-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:09:43 PM UTC 2026
% Result : Unsatisfiable 30.81s 4.41s
% Output : CNFRefutation 30.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 15 unt; 0 def)
% Number of atoms : 91 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 36 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 111 ( 111 !; 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(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(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(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
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(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(f113,negated_conjecture,
restrict(xr,null_class,y) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f131,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f136,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f141,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f152,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f188,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f245,plain,
restrict(xr,null_class,y) != null_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f411,plain,
! [X0,X1] :
( ordered_pair(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))) = regular(cross_product(X0,X1))
| cross_product(X0,X1) = null_class ),
inference(resolution,[status(thm)],[f188,f137]) ).
fof(f416,plain,
! [X0] :
( restrict(X0,singleton(regular(domain_of(X0))),universal_class) != null_class
| domain_of(X0) = null_class ),
inference(resolution,[status(thm)],[f188,f152]) ).
fof(f423,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f142,f188]) ).
fof(f427,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f150,f142]) ).
fof(f433,plain,
! [X0,X1,X2] :
( restrict(X0,X1,X2) = null_class
| member(regular(restrict(X0,X1,X2)),X0) ),
inference(resolution,[status(thm)],[f427,f188]) ).
fof(f490,plain,
! [X0,X1,X2] :
( ~ member(regular(restrict(complement(X0),X1,X2)),X0)
| restrict(complement(X0),X1,X2) = null_class ),
inference(resolution,[status(thm)],[f433,f146]) ).
fof(f497,plain,
! [X0,X1,X2,X3] :
( member(regular(restrict(X0,X1,X2)),X3)
| ~ subclass(X0,X3)
| restrict(X0,X1,X2) = null_class ),
inference(resolution,[status(thm)],[f433,f115]) ).
fof(f995,plain,
! [X0,X1,X2] :
( member(regular(restrict(X0,X1,X2)),universal_class)
| restrict(X0,X1,X2) = null_class ),
inference(resolution,[status(thm)],[f497,f118]) ).
fof(f998,plain,
! [X0,X1] :
( restrict(complement(universal_class),X0,X1) = null_class
| restrict(complement(universal_class),X0,X1) = null_class ),
inference(resolution,[status(thm)],[f995,f490]) ).
fof(f1008,plain,
! [X0,X1] : restrict(complement(universal_class),X0,X1) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f998]) ).
fof(f1013,plain,
domain_of(complement(universal_class)) = null_class,
inference(resolution,[status(thm)],[f1008,f416]) ).
fof(f1064,plain,
! [X0] :
( ~ member(X0,null_class)
| restrict(complement(universal_class),singleton(X0),universal_class) != null_class ),
inference(paramodulation,[status(thm)],[f1013,f152]) ).
fof(f1065,plain,
! [X0] :
( ~ member(X0,null_class)
| null_class != null_class ),
inference(forward_demodulation,[status(thm)],[f1008,f1064]) ).
fof(f1066,plain,
! [X0] : ~ member(X0,null_class),
inference(trivial_equality_resolution,[status(thm)],[f1065]) ).
fof(f1944,plain,
! [X0,X1,X2,X3] :
( cross_product(X0,X1) = null_class
| member(first(regular(cross_product(X0,X1))),X2)
| ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3)) ),
inference(paramodulation,[status(thm)],[f411,f132]) ).
fof(f2147,plain,
! [X0,X1,X2] :
( intersection(cross_product(X1,X2),X0) = null_class
| member(regular(restrict(X0,X1,X2)),cross_product(X1,X2)) ),
inference(paramodulation,[status(thm)],[f151,f423]) ).
fof(f2166,plain,
! [X0,X1,X2] :
( restrict(X0,X1,X2) = null_class
| member(regular(restrict(X0,X1,X2)),cross_product(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f151,f2147]) ).
fof(f19456,plain,
! [X0,X1] :
( cross_product(X0,X1) = null_class
| cross_product(X0,X1) = null_class
| member(first(regular(cross_product(X0,X1))),X0) ),
inference(resolution,[status(thm)],[f1944,f188]) ).
fof(f19458,plain,
! [X0,X1] :
( cross_product(X0,X1) = null_class
| member(first(regular(cross_product(X0,X1))),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f19456]) ).
fof(f21221,plain,
! [X0] : cross_product(null_class,X0) = null_class,
inference(resolution,[status(thm)],[f19458,f1066]) ).
fof(f21366,plain,
! [X0,X1] :
( restrict(X0,null_class,X1) = null_class
| member(regular(restrict(X0,null_class,X1)),null_class) ),
inference(paramodulation,[status(thm)],[f21221,f2166]) ).
fof(f21583,plain,
! [X0,X1] : restrict(X0,null_class,X1) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f21366,f1066]) ).
fof(f21621,plain,
null_class != null_class,
inference(backward_demodulation,[status(thm)],[f21583,f245]) ).
fof(f21729,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f21621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET246-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:58:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 30.81/4.41 % Refutation found
% 30.81/4.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 30.81/4.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 30.81/4.47 % Elapsed time: 4.097868 seconds
% 30.81/4.47 % CPU time: 32.219937 seconds
% 30.81/4.47 % Total memory used: 416.690 MB
% 30.81/4.47 % Net memory used: 375.737 MB
%------------------------------------------------------------------------------