%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET205-6 : 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 02:09:38 PM UTC 2026
% Result : Unsatisfiable 10.23s 11.81s
% Output : CNFRefutation 11.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 78 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 33 ~; 37 |; 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 : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 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(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/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/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(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
cross_product(x,null_class) != null_class,
file('/export/starexec/sandbox/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(f133,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
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(f143,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f144,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f188,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f245,plain,
cross_product(x,null_class) != null_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f427,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(f432,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = null_class ),
inference(resolution,[status(thm)],[f188,f115]) ).
fof(f443,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f142,f188]) ).
fof(f511,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f146,f188]) ).
fof(f2329,plain,
! [X0] :
( member(regular(X0),universal_class)
| X0 = null_class ),
inference(resolution,[status(thm)],[f432,f118]) ).
fof(f2497,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f511,f2329]) ).
fof(f2502,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f2497]) ).
fof(f2514,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f2502,f146]) ).
fof(f3670,plain,
! [X0,X1,X2,X3] :
( cross_product(X0,X1) = null_class
| member(second(regular(cross_product(X0,X1))),X3)
| ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3)) ),
inference(paramodulation,[status(thm)],[f427,f134]) ).
fof(f3945,plain,
! [X0] :
( ~ member(regular(intersection(null_class,X0)),universal_class)
| intersection(null_class,X0) = null_class ),
inference(resolution,[status(thm)],[f443,f2514]) ).
fof(f3986,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f3945,f2329]) ).
fof(f4133,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f3986,f144]) ).
fof(f4140,plain,
! [X0] : ~ member(X0,null_class),
inference(backward_subsumption_resolution,[status(thm)],[f2514,f4133]) ).
fof(f5837,plain,
! [X0,X1] :
( cross_product(X0,X1) = null_class
| cross_product(X0,X1) = null_class
| member(second(regular(cross_product(X0,X1))),X1) ),
inference(resolution,[status(thm)],[f3670,f188]) ).
fof(f5838,plain,
! [X0,X1] :
( cross_product(X0,X1) = null_class
| member(second(regular(cross_product(X0,X1))),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f5837]) ).
fof(f5924,plain,
! [X0] : cross_product(X0,null_class) = null_class,
inference(resolution,[status(thm)],[f5838,f4140]) ).
fof(f5975,plain,
null_class != null_class,
inference(backward_demodulation,[status(thm)],[f5924,f245]) ).
fof(f6005,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f5975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET205-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n018.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Mon Sep 21 05:02:39 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.39 % Drodi V4.1.1
% 10.23/11.81 % Refutation found
% 10.23/11.81 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.23/11.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.11/11.88 % Elapsed time: 1.505919 seconds
% 11.11/11.88 % CPU time: 11.459282 seconds
% 11.11/11.88 % Total memory used: 232.738 MB
% 11.11/11.88 % Net memory used: 209.677 MB
%------------------------------------------------------------------------------