TSTP Solution File: SET012-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET012-2 : 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 0.47s 0.68s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 52 ( 10 unt; 14 nHn; 40 RR)
% Number of literals : 101 ( 0 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(membership_in_subsets,axiom,
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) ) ).
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(set_equal_sets_are_subsets1,axiom,
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ) ).
cnf(set_equal_sets_are_subsets2,axiom,
( ~ equal_sets(Superset,Subset)
| subset(Subset,Superset) ) ).
cnf(subsets_are_set_equal_sets,axiom,
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ) ).
cnf(transitivity_for_set_equal,axiom,
( ~ equal_sets(Xs,Ys)
| ~ equal_sets(Ys,Zs)
| equal_sets(Xs,Zs) ) ).
cnf(complement_of_a_is_b,hypothesis,
equal_sets(complement(a),b) ).
cnf(complement_of_b_is_c,hypothesis,
equal_sets(complement(b),c) ).
cnf(prove_a_equals_c,negated_conjecture,
~ equal_sets(a,c) ).
cnf(refute_0_0,plain,
( ~ equal_sets(X_284,complement(b))
| ~ equal_sets(complement(b),c)
| equal_sets(X_284,c) ),
inference(subst,[],[transitivity_for_set_equal:[bind(Xs,$fot(X_284)),bind(Ys,$fot(complement(b))),bind(Zs,$fot(c))]]) ).
cnf(refute_0_1,plain,
( ~ equal_sets(X_284,complement(b))
| equal_sets(X_284,c) ),
inference(resolve,[$cnf( equal_sets(complement(b),c) )],[complement_of_b_is_c,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ equal_sets(a,complement(b))
| equal_sets(a,c) ),
inference(subst,[],[refute_0_1:[bind(X_284,$fot(a))]]) ).
cnf(refute_0_3,plain,
( ~ subset(a,complement(b))
| ~ subset(complement(b),a)
| equal_sets(a,complement(b)) ),
inference(subst,[],[subsets_are_set_equal_sets:[bind(Set1,$fot(complement(b))),bind(Set2,$fot(a))]]) ).
cnf(refute_0_4,plain,
( ~ member(member_of_1_not_of_2(complement(b),a),a)
| subset(complement(b),a) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(complement(b))),bind(Superset,$fot(a))]]) ).
cnf(refute_0_5,plain,
( ~ member(member_of_1_not_of_2(complement(Xs),X_17),Xs)
| ~ member(member_of_1_not_of_2(complement(Xs),X_17),complement(Xs)) ),
inference(subst,[],[not_member_of_set_and_complement:[bind(X,$fot(member_of_1_not_of_2(complement(Xs),X_17)))]]) ).
cnf(refute_0_6,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_7,plain,
( ~ member(member_of_1_not_of_2(complement(Xs),X_17),Xs)
| subset(complement(Xs),X_17) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(complement(Xs),X_17),complement(Xs)) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ member(member_of_1_not_of_2(complement(b),X_17),b)
| subset(complement(b),X_17) ),
inference(subst,[],[refute_0_7:[bind(Xs,$fot(b))]]) ).
cnf(refute_0_9,plain,
( member(X_142,a)
| member(X_142,complement(a)) ),
inference(subst,[],[member_of_set_or_complement:[bind(X,$fot(X_142)),bind(Xs,$fot(a))]]) ).
cnf(refute_0_10,plain,
( ~ equal_sets(complement(a),b)
| subset(complement(a),b) ),
inference(subst,[],[set_equal_sets_are_subsets1:[bind(Subset,$fot(complement(a))),bind(Superset,$fot(b))]]) ).
cnf(refute_0_11,plain,
subset(complement(a),b),
inference(resolve,[$cnf( equal_sets(complement(a),b) )],[complement_of_a_is_b,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(X_137,complement(a))
| ~ subset(complement(a),b)
| member(X_137,b) ),
inference(subst,[],[membership_in_subsets:[bind(Element,$fot(X_137)),bind(Subset,$fot(complement(a))),bind(Superset,$fot(b))]]) ).
cnf(refute_0_13,plain,
( ~ member(X_137,complement(a))
| member(X_137,b) ),
inference(resolve,[$cnf( subset(complement(a),b) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ member(X_142,complement(a))
| member(X_142,b) ),
inference(subst,[],[refute_0_13:[bind(X_137,$fot(X_142))]]) ).
cnf(refute_0_15,plain,
( member(X_142,a)
| member(X_142,b) ),
inference(resolve,[$cnf( member(X_142,complement(a)) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
( member(member_of_1_not_of_2(complement(b),X_17),a)
| member(member_of_1_not_of_2(complement(b),X_17),b) ),
inference(subst,[],[refute_0_15:[bind(X_142,$fot(member_of_1_not_of_2(complement(b),X_17)))]]) ).
cnf(refute_0_17,plain,
( member(member_of_1_not_of_2(complement(b),X_17),a)
| subset(complement(b),X_17) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(complement(b),X_17),b) )],[refute_0_16,refute_0_8]) ).
cnf(refute_0_18,plain,
( member(member_of_1_not_of_2(complement(b),a),a)
| subset(complement(b),a) ),
inference(subst,[],[refute_0_17:[bind(X_17,$fot(a))]]) ).
cnf(refute_0_19,plain,
subset(complement(b),a),
inference(resolve,[$cnf( member(member_of_1_not_of_2(complement(b),a),a) )],[refute_0_18,refute_0_4]) ).
cnf(refute_0_20,plain,
( ~ subset(a,complement(b))
| equal_sets(a,complement(b)) ),
inference(resolve,[$cnf( subset(complement(b),a) )],[refute_0_19,refute_0_3]) ).
cnf(refute_0_21,plain,
( member(member_of_1_not_of_2(a,complement(b)),a)
| subset(a,complement(b)) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(a)),bind(Superset,$fot(complement(b)))]]) ).
cnf(refute_0_22,plain,
( ~ member(member_of_1_not_of_2(X_428,complement(b)),a)
| ~ member(member_of_1_not_of_2(X_428,complement(b)),complement(a)) ),
inference(subst,[],[not_member_of_set_and_complement:[bind(X,$fot(member_of_1_not_of_2(X_428,complement(b)))),bind(Xs,$fot(a))]]) ).
cnf(refute_0_23,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,$fot(member_of_1_not_of_2(X_19,complement(Xs))))]]) ).
cnf(refute_0_24,plain,
( ~ member(member_of_1_not_of_2(X_19,complement(Xs)),complement(Xs))
| subset(X_19,complement(Xs)) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(X_19)),bind(Superset,$fot(complement(Xs)))]]) ).
cnf(refute_0_25,plain,
( member(member_of_1_not_of_2(X_19,complement(Xs)),Xs)
| subset(X_19,complement(Xs)) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(X_19,complement(Xs)),complement(Xs)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( member(member_of_1_not_of_2(X_19,complement(b)),b)
| subset(X_19,complement(b)) ),
inference(subst,[],[refute_0_25:[bind(Xs,$fot(b))]]) ).
cnf(refute_0_27,plain,
( ~ equal_sets(complement(a),b)
| subset(b,complement(a)) ),
inference(subst,[],[set_equal_sets_are_subsets2:[bind(Subset,$fot(b)),bind(Superset,$fot(complement(a)))]]) ).
cnf(refute_0_28,plain,
subset(b,complement(a)),
inference(resolve,[$cnf( equal_sets(complement(a),b) )],[complement_of_a_is_b,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ member(X_137,b)
| ~ subset(b,complement(a))
| member(X_137,complement(a)) ),
inference(subst,[],[membership_in_subsets:[bind(Element,$fot(X_137)),bind(Subset,$fot(b)),bind(Superset,$fot(complement(a)))]]) ).
cnf(refute_0_30,plain,
( ~ member(X_137,b)
| member(X_137,complement(a)) ),
inference(resolve,[$cnf( subset(b,complement(a)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ member(member_of_1_not_of_2(X_19,complement(b)),b)
| member(member_of_1_not_of_2(X_19,complement(b)),complement(a)) ),
inference(subst,[],[refute_0_30:[bind(X_137,$fot(member_of_1_not_of_2(X_19,complement(b))))]]) ).
cnf(refute_0_32,plain,
( member(member_of_1_not_of_2(X_19,complement(b)),complement(a))
| subset(X_19,complement(b)) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(X_19,complement(b)),b) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
( member(member_of_1_not_of_2(X_428,complement(b)),complement(a))
| subset(X_428,complement(b)) ),
inference(subst,[],[refute_0_32:[bind(X_19,$fot(X_428))]]) ).
cnf(refute_0_34,plain,
( ~ member(member_of_1_not_of_2(X_428,complement(b)),a)
| subset(X_428,complement(b)) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(X_428,complement(b)),complement(a)) )],[refute_0_33,refute_0_22]) ).
cnf(refute_0_35,plain,
( ~ member(member_of_1_not_of_2(a,complement(b)),a)
| subset(a,complement(b)) ),
inference(subst,[],[refute_0_34:[bind(X_428,$fot(a))]]) ).
cnf(refute_0_36,plain,
subset(a,complement(b)),
inference(resolve,[$cnf( member(member_of_1_not_of_2(a,complement(b)),a) )],[refute_0_21,refute_0_35]) ).
cnf(refute_0_37,plain,
equal_sets(a,complement(b)),
inference(resolve,[$cnf( subset(a,complement(b)) )],[refute_0_36,refute_0_20]) ).
cnf(refute_0_38,plain,
equal_sets(a,c),
inference(resolve,[$cnf( equal_sets(a,complement(b)) )],[refute_0_37,refute_0_2]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( equal_sets(a,c) )],[refute_0_38,prove_a_equals_c]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET012-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 05:31:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.68
% 0.47/0.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.47/0.68
%------------------------------------------------------------------------------