%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM049-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 01:38:35 PM UTC 2026
% Result : Unsatisfiable 5.24s 11.25s
% Output : CNFRefutation 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 21 unt; 0 def)
% Number of atoms : 73 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 32 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 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(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(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(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,axiom,
! [Y,X] :
( connected(X,Y)
| ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
subclass(cross_product(y,y),identity_relation),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,negated_conjecture,
~ connected(x,y),
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(f175,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f177,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f183,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
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(f193,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f194,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f195,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f296,plain,
! [X0,X1] :
( connected(X1,X0)
| ~ subclass(cross_product(X0,X0),union(identity_relation,symmetrization_of(X1))) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f348,plain,
subclass(cross_product(y,y),identity_relation),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f349,plain,
~ connected(x,y),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f394,plain,
! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
inference(paramodulation,[status(thm)],[f177,f175]) ).
fof(f427,plain,
! [X0,X1,X2] :
( subclass(cross_product(X0,X1),X2)
| ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2) ),
inference(resolution,[status(thm)],[f184,f163]) ).
fof(f536,plain,
! [X0,X1,X2] :
( member(X0,intersection(complement(X1),complement(X2)))
| member(X0,union(X1,X2))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f195,f194]) ).
fof(f1464,plain,
~ subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x))),
inference(resolution,[status(thm)],[f296,f349]) ).
fof(f1466,plain,
~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x))),
inference(resolution,[status(thm)],[f1464,f164]) ).
fof(f2189,plain,
ordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))) = not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),
inference(resolution,[status(thm)],[f427,f1464]) ).
fof(f2400,plain,
member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class),
inference(paramodulation,[status(thm)],[f2189,f394]) ).
fof(f2707,plain,
( member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class) ),
inference(resolution,[status(thm)],[f536,f1466]) ).
fof(f2717,plain,
member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x)))),
inference(forward_subsumption_resolution,[status(thm)],[f2707,f2400]) ).
fof(f2719,plain,
member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)),
inference(resolution,[status(thm)],[f2717,f189]) ).
fof(f2721,plain,
~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation),
inference(resolution,[status(thm)],[f2719,f193]) ).
fof(f2865,plain,
! [X0] :
( ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),X0)
| ~ subclass(X0,identity_relation) ),
inference(resolution,[status(thm)],[f2721,f162]) ).
fof(f3050,plain,
~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y)),
inference(resolution,[status(thm)],[f2865,f348]) ).
fof(f3173,plain,
subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x))),
inference(resolution,[status(thm)],[f3050,f163]) ).
fof(f3176,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3173,f1464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM049-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.43 % Computer : n017.cluster.edu
% 0.16/10.43 % Model : x86_64 x86_64
% 0.16/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.43 % Memory : 8046.5625MB
% 0.16/10.43 % OS : Linux 6.8.0-71-generic
% 0.16/10.43 % CPULimit : 300
% 0.16/10.43 % WCLimit : 300
% 0.16/10.43 % DateTime : Mon Sep 21 01:56:23 UTC 2026
% 0.16/10.44 % CPUTime :
% 0.16/10.45 % Drodi V4.1.1
% 5.24/11.25 % Refutation found
% 5.24/11.25 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.24/11.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.93/11.28 % Elapsed time: 0.841145 seconds
% 4.93/11.28 % CPU time: 6.389786 seconds
% 4.93/11.28 % Total memory used: 180.590 MB
% 4.93/11.28 % Net memory used: 168.580 MB
%------------------------------------------------------------------------------