%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET075-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:09:12 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 14 unt; 0 def)
% Number of atoms : 92 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 84 ( 42 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 97 ( 97 !; 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(f10,axiom,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,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(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ 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(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(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f95,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f98,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f106,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f107,plain,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f116,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f121,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f122,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f126,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f132,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f169,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f199,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f200,plain,
unordered_pair(x,y) = null_class,
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f217,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f95,f98]) ).
fof(f237,plain,
member(y,v),
inference(resolution,[status(thm)],[f114,f199]) ).
fof(f286,plain,
ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y),
inference(resolution,[status(thm)],[f117,f199]) ).
fof(f296,plain,
! [X0,X1] :
( member(first(ordered_pair(x,y)),X0)
| ~ member(ordered_pair(x,y),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f286,f112]) ).
fof(f337,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X2,X0))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f217,f107]) ).
fof(f378,plain,
! [X0] :
( member(y,null_class)
| ~ member(y,X0) ),
inference(paramodulation,[status(thm)],[f200,f337]) ).
fof(f395,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f169,f122]) ).
fof(f415,plain,
member(first(ordered_pair(x,y)),u),
inference(resolution,[status(thm)],[f296,f199]) ).
fof(f684,plain,
! [X0,X1] :
( ~ member(y,X1)
| X0 = null_class
| member(y,X0) ),
inference(resolution,[status(thm)],[f395,f378]) ).
fof(f698,plain,
! [X0] :
( X0 = null_class
| member(y,X0) ),
inference(resolution,[status(thm)],[f684,f237]) ).
fof(f712,plain,
! [X0] :
( ~ member(y,X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f698,f126]) ).
fof(f808,plain,
! [X0] :
( X0 = null_class
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f712,f698]) ).
fof(f845,plain,
! [X0,X1] :
( X1 = null_class
| ~ member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f808,f126]) ).
fof(f847,plain,
! [X0,X1] :
( X1 = null_class
| ~ member(X0,null_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f845,f395]) ).
fof(f850,plain,
! [X0,X1] :
( ~ member(y,X1)
| X0 = null_class ),
inference(resolution,[status(thm)],[f847,f378]) ).
fof(f859,plain,
! [X0] : X0 = null_class,
inference(backward_subsumption_resolution,[status(thm)],[f698,f850]) ).
fof(f868,plain,
! [X0,X1] : ~ member(X0,domain_of(X1)),
inference(backward_subsumption_resolution,[status(thm)],[f132,f859]) ).
fof(f869,plain,
! [X0,X1] : X0 = X1,
inference(paramodulation,[status(thm)],[f859,f859]) ).
fof(f887,plain,
! [X0,X1] : ~ member(X0,X1),
inference(paramodulation,[status(thm)],[f869,f868]) ).
fof(f892,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f415,f887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET075-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:48:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.44 % Refutation found
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.46 % Elapsed time: 0.087844 seconds
% 0.10/0.46 % CPU time: 0.408352 seconds
% 0.10/0.46 % Total memory used: 111.615 MB
% 0.10/0.46 % Net memory used: 110.965 MB
%------------------------------------------------------------------------------