TSTP Solution File: SET012-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET012-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 03:31:03 EDT 2022
% Result : Unsatisfiable 0.23s 0.40s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 31 ( 8 unt; 10 nHn; 16 RR)
% Number of literals : 56 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subsets_axiom1,axiom,
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ) ).
cnf(subsets_axiom2,axiom,
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ) ).
cnf(member_of_set_or_complement,axiom,
( member(X,Xs)
| member(X,complement(Xs)) ) ).
cnf(not_member_of_set_and_complement,axiom,
( ~ member(X,Xs)
| ~ member(X,complement(Xs)) ) ).
cnf(subsets_are_set_equal_sets,axiom,
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ) ).
cnf(prove_involution,negated_conjecture,
~ equal_sets(complement(complement(a)),a) ).
cnf(refute_0_0,plain,
( ~ subset(X_72,complement(complement(X_72)))
| ~ subset(complement(complement(X_72)),X_72)
| equal_sets(complement(complement(X_72)),X_72) ),
inference(subst,[],[subsets_are_set_equal_sets:[bind(Set1,$fot(X_72)),bind(Set2,$fot(complement(complement(X_72))))]]) ).
cnf(refute_0_1,plain,
( ~ member(member_of_1_not_of_2(complement(complement(X_69)),X_69),X_69)
| subset(complement(complement(X_69)),X_69) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(complement(complement(X_69)))),bind(Superset,$fot(X_69))]]) ).
cnf(refute_0_2,plain,
( member(member_of_1_not_of_2(complement(complement(Xs)),X_30),Xs)
| member(member_of_1_not_of_2(complement(complement(Xs)),X_30),complement(Xs)) ),
inference(subst,[],[member_of_set_or_complement:[bind(X,$fot(member_of_1_not_of_2(complement(complement(Xs)),X_30)))]]) ).
cnf(refute_0_3,plain,
( ~ member(member_of_1_not_of_2(complement(Xs),X_17),Xs)
| ~ member(member_of_1_not_of_2(complement(Xs),X_17),complement(Xs)) ),
inference(subst,[],[not_member_of_set_and_complement:[bind(X,$fot(member_of_1_not_of_2(complement(Xs),X_17)))]]) ).
cnf(refute_0_4,plain,
( member(member_of_1_not_of_2(complement(Xs),X_17),complement(Xs))
| subset(complement(Xs),X_17) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(complement(Xs))),bind(Superset,$fot(X_17))]]) ).
cnf(refute_0_5,plain,
( ~ member(member_of_1_not_of_2(complement(Xs),X_17),Xs)
| subset(complement(Xs),X_17) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(complement(Xs),X_17),complement(Xs)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ member(member_of_1_not_of_2(complement(complement(Xs)),X_30),complement(Xs))
| subset(complement(complement(Xs)),X_30) ),
inference(subst,[],[refute_0_5:[bind(Xs,$fot(complement(Xs))),bind(X_17,$fot(X_30))]]) ).
cnf(refute_0_7,plain,
( member(member_of_1_not_of_2(complement(complement(Xs)),X_30),Xs)
| subset(complement(complement(Xs)),X_30) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(complement(complement(Xs)),X_30),complement(Xs)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( member(member_of_1_not_of_2(complement(complement(X_69)),X_69),X_69)
| subset(complement(complement(X_69)),X_69) ),
inference(subst,[],[refute_0_7:[bind(Xs,$fot(X_69)),bind(X_30,$fot(X_69))]]) ).
cnf(refute_0_9,plain,
subset(complement(complement(X_69)),X_69),
inference(resolve,[$cnf( member(member_of_1_not_of_2(complement(complement(X_69)),X_69),X_69) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
subset(complement(complement(X_72)),X_72),
inference(subst,[],[refute_0_9:[bind(X_69,$fot(X_72))]]) ).
cnf(refute_0_11,plain,
( ~ subset(X_72,complement(complement(X_72)))
| equal_sets(complement(complement(X_72)),X_72) ),
inference(resolve,[$cnf( subset(complement(complement(X_72)),X_72) )],[refute_0_10,refute_0_0]) ).
cnf(refute_0_12,plain,
( member(member_of_1_not_of_2(X_43,complement(complement(X_43))),X_43)
| subset(X_43,complement(complement(X_43))) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(X_43)),bind(Superset,$fot(complement(complement(X_43))))]]) ).
cnf(refute_0_13,plain,
( ~ member(member_of_1_not_of_2(X_27,complement(complement(Xs))),Xs)
| ~ member(member_of_1_not_of_2(X_27,complement(complement(Xs))),complement(Xs)) ),
inference(subst,[],[not_member_of_set_and_complement:[bind(X,$fot(member_of_1_not_of_2(X_27,complement(complement(Xs)))))]]) ).
cnf(refute_0_14,plain,
( member(member_of_1_not_of_2(X_19,complement(Xs)),Xs)
| member(member_of_1_not_of_2(X_19,complement(Xs)),complement(Xs)) ),
inference(subst,[],[member_of_set_or_complement:[bind(X,$fot(member_of_1_not_of_2(X_19,complement(Xs))))]]) ).
cnf(refute_0_15,plain,
( ~ member(member_of_1_not_of_2(X_19,complement(Xs)),complement(Xs))
| subset(X_19,complement(Xs)) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(X_19)),bind(Superset,$fot(complement(Xs)))]]) ).
cnf(refute_0_16,plain,
( member(member_of_1_not_of_2(X_19,complement(Xs)),Xs)
| subset(X_19,complement(Xs)) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(X_19,complement(Xs)),complement(Xs)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( member(member_of_1_not_of_2(X_27,complement(complement(Xs))),complement(Xs))
| subset(X_27,complement(complement(Xs))) ),
inference(subst,[],[refute_0_16:[bind(Xs,$fot(complement(Xs))),bind(X_19,$fot(X_27))]]) ).
cnf(refute_0_18,plain,
( ~ member(member_of_1_not_of_2(X_27,complement(complement(Xs))),Xs)
| subset(X_27,complement(complement(Xs))) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(X_27,complement(complement(Xs))),complement(Xs)) )],[refute_0_17,refute_0_13]) ).
cnf(refute_0_19,plain,
( ~ member(member_of_1_not_of_2(X_43,complement(complement(X_43))),X_43)
| subset(X_43,complement(complement(X_43))) ),
inference(subst,[],[refute_0_18:[bind(Xs,$fot(X_43)),bind(X_27,$fot(X_43))]]) ).
cnf(refute_0_20,plain,
subset(X_43,complement(complement(X_43))),
inference(resolve,[$cnf( member(member_of_1_not_of_2(X_43,complement(complement(X_43))),X_43) )],[refute_0_12,refute_0_19]) ).
cnf(refute_0_21,plain,
subset(X_72,complement(complement(X_72))),
inference(subst,[],[refute_0_20:[bind(X_43,$fot(X_72))]]) ).
cnf(refute_0_22,plain,
equal_sets(complement(complement(X_72)),X_72),
inference(resolve,[$cnf( subset(X_72,complement(complement(X_72))) )],[refute_0_21,refute_0_11]) ).
cnf(refute_0_23,plain,
equal_sets(complement(complement(a)),a),
inference(subst,[],[refute_0_22:[bind(X_72,$fot(a))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( equal_sets(complement(complement(a)),a) )],[refute_0_23,prove_involution]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : SET012-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.15 % Command : metis --show proof --show saturation %s
% 0.16/0.38 % Computer : n017.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 600
% 0.16/0.38 % DateTime : Sun Jul 10 19:44:48 EDT 2022
% 0.16/0.38 % CPUTime :
% 0.16/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.23/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.40
% 0.23/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.23/0.41
%------------------------------------------------------------------------------