%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 01:38:34 PM UTC 2026
% Result : Unsatisfiable 0.23s 10.95s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 45 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 17 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 46 ( 46 !; 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(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),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(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [X,Y] :
( irreflexive(X,Y)
| ~ subclass(restrict(X,Y,Y),complement(identity_relation)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
subclass(x,complement(identity_relation)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,negated_conjecture,
~ irreflexive(x,domain_of(symmetrization_of(x))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f161,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f162,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f163,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f164,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f188,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f189,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f197,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f294,plain,
! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(restrict(X0,X1,X1),complement(identity_relation)) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f348,plain,
subclass(x,complement(identity_relation)),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f349,plain,
~ irreflexive(x,domain_of(symmetrization_of(x))),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f356,plain,
! [X0] :
( member(X0,complement(identity_relation))
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[f162,f348]) ).
fof(f374,plain,
! [X0] :
( subclass(X0,complement(identity_relation))
| ~ member(not_subclass_element(X0,complement(identity_relation)),x) ),
inference(resolution,[status(thm)],[f356,f164]) ).
fof(f551,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f189,f163]) ).
fof(f3709,plain,
! [X0] :
( subclass(intersection(x,X0),complement(identity_relation))
| subclass(intersection(x,X0),complement(identity_relation)) ),
inference(resolution,[status(thm)],[f551,f374]) ).
fof(f3771,plain,
! [X0] : subclass(intersection(x,X0),complement(identity_relation)),
inference(duplicate_literals_removal,[status(thm)],[f3709]) ).
fof(f3788,plain,
! [X0,X1] : subclass(restrict(x,X0,X1),complement(identity_relation)),
inference(paramodulation,[status(thm)],[f197,f3771]) ).
fof(f3790,plain,
! [X0] : irreflexive(x,X0),
inference(resolution,[status(thm)],[f3788,f294]) ).
fof(f3794,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f349,f3790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/10.47 % Computer : n026.cluster.edu
% 0.18/10.47 % Model : x86_64 x86_64
% 0.18/10.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.47 % Memory : 8046.5625MB
% 0.18/10.47 % OS : Linux 6.8.0-71-generic
% 0.18/10.47 % CPULimit : 300
% 0.18/10.47 % WCLimit : 300
% 0.18/10.47 % DateTime : Mon Sep 21 02:02:32 UTC 2026
% 0.18/10.47 % CPUTime :
% 0.23/10.50 % Drodi V4.1.1
% 0.23/10.95 % Refutation found
% 0.23/10.95 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/10.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/10.97 % Elapsed time: 0.477177 seconds
% 0.23/10.97 % CPU time: 3.418012 seconds
% 0.23/10.97 % Total memory used: 146.323 MB
% 0.23/10.97 % Net memory used: 142.694 MB
%------------------------------------------------------------------------------