TSTP Solution File: SET006-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:30:58 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 4 unt; 4 nHn; 11 RR)
% Number of literals : 26 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 1 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_intersection_is_member_of_set2,axiom,
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) ) ).
cnf(d_intersection_a_is_d,hypothesis,
intersection(d,a,d) ).
cnf(prove_d_is_a_subset_of_a,negated_conjecture,
~ subset(d,a) ).
cnf(refute_0_0,plain,
( ~ member(member_of_1_not_of_2(d,a),a)
| subset(d,a) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(d)),bind(Superset,$fot(a))]]) ).
cnf(refute_0_1,plain,
( member(member_of_1_not_of_2(d,Superset),d)
| subset(d,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(d))]]) ).
cnf(refute_0_2,plain,
( ~ intersection(d,a,d)
| ~ member(X_39,d)
| member(X_39,a) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Element,$fot(X_39)),bind(Intersection,$fot(d)),bind(Set1,$fot(d)),bind(Set2,$fot(a))]]) ).
cnf(refute_0_3,plain,
( ~ member(X_39,d)
| member(X_39,a) ),
inference(resolve,[$cnf( intersection(d,a,d) )],[d_intersection_a_is_d,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ member(member_of_1_not_of_2(d,Superset),d)
| member(member_of_1_not_of_2(d,Superset),a) ),
inference(subst,[],[refute_0_3:[bind(X_39,$fot(member_of_1_not_of_2(d,Superset)))]]) ).
cnf(refute_0_5,plain,
( member(member_of_1_not_of_2(d,Superset),a)
| subset(d,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(d,Superset),d) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
( member(member_of_1_not_of_2(d,a),a)
| subset(d,a) ),
inference(subst,[],[refute_0_5:[bind(Superset,$fot(a))]]) ).
cnf(refute_0_7,plain,
subset(d,a),
inference(resolve,[$cnf( member(member_of_1_not_of_2(d,a),a) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( subset(d,a) )],[refute_0_7,prove_d_is_a_subset_of_a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 04:21:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------