TSTP Solution File: SET451-6 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET451-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:34:52 EDT 2022
% Result : Unsatisfiable 86.74s 86.95s
% Output : CNFRefutation 86.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 40 ( 14 unt; 4 nHn; 33 RR)
% Number of literals : 74 ( 39 equ; 31 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ) ).
cnf(not_subclass_members2,axiom,
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ) ).
cnf(intersection2,axiom,
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) ).
cnf(restriction1,axiom,
intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ).
cnf(restriction2,axiom,
intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ).
cnf(subset_relation,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation ).
cnf(prove_subset_relation_alternate_defn1_1,negated_conjecture,
~ subclass(subset_relation,cross_product(universal_class,universal_class)) ).
cnf(refute_0_0,plain,
( ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class))
| subclass(subset_relation,cross_product(universal_class,universal_class)) ),
inference(subst,[],[not_subclass_members2:[bind(X,$fot(subset_relation)),bind(Y,$fot(cross_product(universal_class,universal_class)))]]) ).
cnf(refute_0_1,plain,
( member(not_subclass_element(subset_relation,Y),subset_relation)
| subclass(subset_relation,Y) ),
inference(subst,[],[not_subclass_members1:[bind(X,$fot(subset_relation))]]) ).
cnf(refute_0_2,plain,
( ~ member(X_1070,intersection(X_1068,cross_product(X,Y)))
| member(X_1070,cross_product(X,Y)) ),
inference(subst,[],[intersection2:[bind(X,$fot(X_1068)),bind(Y,$fot(cross_product(X,Y))),bind(Z,$fot(X_1070))]]) ).
cnf(refute_0_3,plain,
intersection(X_1068,cross_product(X,Y)) = restrict(X_1068,X,Y),
inference(subst,[],[restriction1:[bind(Xr,$fot(X_1068))]]) ).
cnf(refute_0_4,plain,
( intersection(X_1068,cross_product(X,Y)) != restrict(X_1068,X,Y)
| ~ member(X_1070,restrict(X_1068,X,Y))
| member(X_1070,intersection(X_1068,cross_product(X,Y))) ),
introduced(tautology,[equality,[$cnf( ~ member(X_1070,intersection(X_1068,cross_product(X,Y))) ),[1],$fot(restrict(X_1068,X,Y))]]) ).
cnf(refute_0_5,plain,
( ~ member(X_1070,restrict(X_1068,X,Y))
| member(X_1070,intersection(X_1068,cross_product(X,Y))) ),
inference(resolve,[$cnf( $equal(intersection(X_1068,cross_product(X,Y)),restrict(X_1068,X,Y)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ member(X_1070,restrict(X_1068,X,Y))
| member(X_1070,cross_product(X,Y)) ),
inference(resolve,[$cnf( member(X_1070,intersection(X_1068,cross_product(X,Y))) )],[refute_0_5,refute_0_2]) ).
cnf(refute_0_7,plain,
( ~ member(X_3355,restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class))
| member(X_3355,cross_product(universal_class,universal_class)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(universal_class)),bind(Y,$fot(universal_class)),bind(X_1068,$fot(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))),bind(X_1070,$fot(X_3355))]]) ).
cnf(refute_0_8,plain,
intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))) = restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),
inference(subst,[],[restriction2:[bind(X,$fot(universal_class)),bind(Xr,$fot(complement(compose(complement(element_relation),inverse(element_relation))))),bind(Y,$fot(universal_class))]]) ).
cnf(refute_0_9,plain,
restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class) = restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class),
introduced(tautology,[refl,[$fot(restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class))]]) ).
cnf(refute_0_10,plain,
( intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))) != restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)
| restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class) != restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class)
| restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class) = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) ),
introduced(tautology,[equality,[$cnf( $equal(restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class),restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class)) ),[1,0],$fot(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))]]) ).
cnf(refute_0_11,plain,
( intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))) != restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)
| restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class) = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) ),
inference(resolve,[$cnf( $equal(restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class),restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class) = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),
inference(resolve,[$cnf( $equal(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class),
inference(subst,[],[restriction2:[bind(X,$fot(universal_class)),bind(Xr,$fot(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))))),bind(Y,$fot(universal_class))]]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) != restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class)
| restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class) != restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))))),bind(Y0,$fot(restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class))),bind(Z0,$fot(restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)))]]) ).
cnf(refute_0_20,plain,
( restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class) != restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) ),
inference(resolve,[$cnf( $equal(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class)) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),
inference(resolve,[$cnf( $equal(restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class),restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) != restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)
| intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) != subset_relation
| restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) = subset_relation ),
introduced(tautology,[equality,[$cnf( $equal(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),subset_relation) ),[0],$fot(restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class))]]) ).
cnf(refute_0_23,plain,
( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) != subset_relation
| restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) = subset_relation ),
inference(resolve,[$cnf( $equal(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) = subset_relation,
inference(resolve,[$cnf( $equal(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),subset_relation) )],[subset_relation,refute_0_23]) ).
cnf(refute_0_25,plain,
( restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) != subset_relation
| ~ member(X_3355,subset_relation)
| member(X_3355,restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)) ),
introduced(tautology,[equality,[$cnf( ~ member(X_3355,restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)) ),[1],$fot(subset_relation)]]) ).
cnf(refute_0_26,plain,
( ~ member(X_3355,subset_relation)
| member(X_3355,restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)) ),
inference(resolve,[$cnf( $equal(restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),subset_relation) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ member(X_3355,subset_relation)
| member(X_3355,cross_product(universal_class,universal_class)) ),
inference(resolve,[$cnf( member(X_3355,restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)) )],[refute_0_26,refute_0_7]) ).
cnf(refute_0_28,plain,
( ~ member(not_subclass_element(subset_relation,Y),subset_relation)
| member(not_subclass_element(subset_relation,Y),cross_product(universal_class,universal_class)) ),
inference(subst,[],[refute_0_27:[bind(X_3355,$fot(not_subclass_element(subset_relation,Y)))]]) ).
cnf(refute_0_29,plain,
( member(not_subclass_element(subset_relation,Y),cross_product(universal_class,universal_class))
| subclass(subset_relation,Y) ),
inference(resolve,[$cnf( member(not_subclass_element(subset_relation,Y),subset_relation) )],[refute_0_1,refute_0_28]) ).
cnf(refute_0_30,plain,
( member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class))
| subclass(subset_relation,cross_product(universal_class,universal_class)) ),
inference(subst,[],[refute_0_29:[bind(Y,$fot(cross_product(universal_class,universal_class)))]]) ).
cnf(refute_0_31,plain,
subclass(subset_relation,cross_product(universal_class,universal_class)),
inference(resolve,[$cnf( member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)) )],[refute_0_30,refute_0_0]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( subclass(subset_relation,cross_product(universal_class,universal_class)) )],[refute_0_31,prove_subset_relation_alternate_defn1_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET451-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 03:16:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 86.74/86.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 86.74/86.95
% 86.74/86.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 86.74/86.96
%------------------------------------------------------------------------------