TSTP Solution File: SET002-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 03:30:54 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 27 ( 6 unt; 8 nHn; 22 RR)
% Number of literals : 55 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 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(subsets_are_set_equal_sets,axiom,
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( ~ union(Set1,Set2,Union)
| ~ member(Element,Union)
| member(Element,Set1)
| member(Element,Set2) ) ).
cnf(member_of_set1_is_member_of_union,axiom,
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1)
| member(Element,Union) ) ).
cnf(a_union_a_is_aUa,hypothesis,
union(a,a,aUa) ).
cnf(prove_a_equals_aUa,negated_conjecture,
~ equal_sets(aUa,a) ).
cnf(refute_0_0,plain,
( ~ subset(a,aUa)
| ~ subset(aUa,a)
| equal_sets(aUa,a) ),
inference(subst,[],[subsets_are_set_equal_sets:[bind(Set1,$fot(a)),bind(Set2,$fot(aUa))]]) ).
cnf(refute_0_1,plain,
( ~ member(member_of_1_not_of_2(aUa,a),a)
| subset(aUa,a) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(aUa)),bind(Superset,$fot(a))]]) ).
cnf(refute_0_2,plain,
( member(member_of_1_not_of_2(aUa,Superset),aUa)
| subset(aUa,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(aUa))]]) ).
cnf(refute_0_3,plain,
( ~ member(X_69,aUa)
| ~ union(a,a,aUa)
| member(X_69,a) ),
inference(subst,[],[member_of_union_is_member_of_one_set:[bind(Element,$fot(X_69)),bind(Set1,$fot(a)),bind(Set2,$fot(a)),bind(Union,$fot(aUa))]]) ).
cnf(refute_0_4,plain,
( ~ member(X_69,aUa)
| member(X_69,a) ),
inference(resolve,[$cnf( union(a,a,aUa) )],[a_union_a_is_aUa,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ member(member_of_1_not_of_2(aUa,Superset),aUa)
| member(member_of_1_not_of_2(aUa,Superset),a) ),
inference(subst,[],[refute_0_4:[bind(X_69,$fot(member_of_1_not_of_2(aUa,Superset)))]]) ).
cnf(refute_0_6,plain,
( member(member_of_1_not_of_2(aUa,Superset),a)
| subset(aUa,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aUa,Superset),aUa) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( member(member_of_1_not_of_2(aUa,a),a)
| subset(aUa,a) ),
inference(subst,[],[refute_0_6:[bind(Superset,$fot(a))]]) ).
cnf(refute_0_8,plain,
subset(aUa,a),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aUa,a),a) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( ~ subset(a,aUa)
| equal_sets(aUa,a) ),
inference(resolve,[$cnf( subset(aUa,a) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
( ~ member(member_of_1_not_of_2(a,aUa),aUa)
| subset(a,aUa) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(a)),bind(Superset,$fot(aUa))]]) ).
cnf(refute_0_11,plain,
( member(member_of_1_not_of_2(a,Superset),a)
| subset(a,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(a))]]) ).
cnf(refute_0_12,plain,
( ~ member(X_35,a)
| ~ union(a,a,aUa)
| member(X_35,aUa) ),
inference(subst,[],[member_of_set1_is_member_of_union:[bind(Element,$fot(X_35)),bind(Set1,$fot(a)),bind(Set2,$fot(a)),bind(Union,$fot(aUa))]]) ).
cnf(refute_0_13,plain,
( ~ member(X_35,a)
| member(X_35,aUa) ),
inference(resolve,[$cnf( union(a,a,aUa) )],[a_union_a_is_aUa,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ member(member_of_1_not_of_2(a,Superset),a)
| member(member_of_1_not_of_2(a,Superset),aUa) ),
inference(subst,[],[refute_0_13:[bind(X_35,$fot(member_of_1_not_of_2(a,Superset)))]]) ).
cnf(refute_0_15,plain,
( member(member_of_1_not_of_2(a,Superset),aUa)
| subset(a,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(a,Superset),a) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( member(member_of_1_not_of_2(a,aUa),aUa)
| subset(a,aUa) ),
inference(subst,[],[refute_0_15:[bind(Superset,$fot(aUa))]]) ).
cnf(refute_0_17,plain,
subset(a,aUa),
inference(resolve,[$cnf( member(member_of_1_not_of_2(a,aUa),aUa) )],[refute_0_16,refute_0_10]) ).
cnf(refute_0_18,plain,
equal_sets(aUa,a),
inference(resolve,[$cnf( subset(a,aUa) )],[refute_0_17,refute_0_9]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( equal_sets(aUa,a) )],[refute_0_18,prove_a_equals_aUa]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n021.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 : Mon Jul 11 10:00:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.38
% 0.19/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39
%------------------------------------------------------------------------------