TSTP Solution File: SET011-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 03:31:02 EDT 2022
% Result : Unsatisfiable 0.69s 0.86s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of clauses : 61 ( 9 unt; 25 nHn; 48 RR)
% Number of literals : 145 ( 0 equ; 57 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 : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 2 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(intersection_axiom1,axiom,
( member(h(Set1,Set2,Intersection),Intersection)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Set1) ) ).
cnf(intersection_axiom2,axiom,
( member(h(Set1,Set2,Intersection),Intersection)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Set2) ) ).
cnf(intersection_axiom3,axiom,
( ~ member(h(Set1,Set2,Intersection),Intersection)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection) ) ).
cnf(member_of_difference,axiom,
( ~ difference(Set1,Set2,Difference)
| ~ member(Element,Difference)
| member(Element,Set1) ) ).
cnf(not_member_of_difference,axiom,
( ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ difference(A_set,Set1,Set2) ) ).
cnf(member_of_difference_or_set2,axiom,
( ~ member(Element,Set1)
| ~ difference(Set1,Set2,Difference)
| member(Element,Difference)
| member(Element,Set2) ) ).
cnf(a_minus_b,hypothesis,
difference(a,b,aDb) ).
cnf(a_minus_aDb,hypothesis,
difference(a,aDb,aD_aDb) ).
cnf(prove_a_intersection_b_is_aD_aDb,negated_conjecture,
~ intersection(a,b,aD_aDb) ).
cnf(refute_0_0,plain,
( ~ member(Element,aD_aDb)
| ~ subset(aD_aDb,b)
| member(Element,b) ),
inference(subst,[],[membership_in_subsets:[bind(Subset,$fot(aD_aDb)),bind(Superset,$fot(b))]]) ).
cnf(refute_0_1,plain,
( member(member_of_1_not_of_2(aD_aDb,b),aD_aDb)
| subset(aD_aDb,b) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(aD_aDb)),bind(Superset,$fot(b))]]) ).
cnf(refute_0_2,plain,
( ~ difference(a,aDb,aD_aDb)
| ~ member(X_104,aD_aDb)
| ~ member(X_104,aDb) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(a)),bind(Element,$fot(X_104)),bind(Set1,$fot(aDb)),bind(Set2,$fot(aD_aDb))]]) ).
cnf(refute_0_3,plain,
( ~ member(X_104,aD_aDb)
| ~ member(X_104,aDb) ),
inference(resolve,[$cnf( difference(a,aDb,aD_aDb) )],[a_minus_aDb,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ member(member_of_1_not_of_2(aD_aDb,b),aD_aDb)
| ~ member(member_of_1_not_of_2(aD_aDb,b),aDb) ),
inference(subst,[],[refute_0_3:[bind(X_104,$fot(member_of_1_not_of_2(aD_aDb,b)))]]) ).
cnf(refute_0_5,plain,
( ~ member(member_of_1_not_of_2(aD_aDb,b),b)
| subset(aD_aDb,b) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(aD_aDb)),bind(Superset,$fot(b))]]) ).
cnf(refute_0_6,plain,
( member(member_of_1_not_of_2(aD_aDb,Superset),aD_aDb)
| subset(aD_aDb,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(aD_aDb))]]) ).
cnf(refute_0_7,plain,
( ~ difference(a,aDb,aD_aDb)
| ~ member(X_68,aD_aDb)
| member(X_68,a) ),
inference(subst,[],[member_of_difference:[bind(Difference,$fot(aD_aDb)),bind(Element,$fot(X_68)),bind(Set1,$fot(a)),bind(Set2,$fot(aDb))]]) ).
cnf(refute_0_8,plain,
( ~ member(X_68,aD_aDb)
| member(X_68,a) ),
inference(resolve,[$cnf( difference(a,aDb,aD_aDb) )],[a_minus_aDb,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ member(member_of_1_not_of_2(aD_aDb,Superset),aD_aDb)
| member(member_of_1_not_of_2(aD_aDb,Superset),a) ),
inference(subst,[],[refute_0_8:[bind(X_68,$fot(member_of_1_not_of_2(aD_aDb,Superset)))]]) ).
cnf(refute_0_10,plain,
( member(member_of_1_not_of_2(aD_aDb,Superset),a)
| subset(aD_aDb,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aD_aDb,Superset),aD_aDb) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ difference(a,b,aDb)
| ~ member(X_361,a)
| member(X_361,aDb)
| member(X_361,b) ),
inference(subst,[],[member_of_difference_or_set2:[bind(Difference,$fot(aDb)),bind(Element,$fot(X_361)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_12,plain,
( ~ member(X_361,a)
| member(X_361,aDb)
| member(X_361,b) ),
inference(resolve,[$cnf( difference(a,b,aDb) )],[a_minus_b,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ member(member_of_1_not_of_2(aD_aDb,Superset),a)
| member(member_of_1_not_of_2(aD_aDb,Superset),aDb)
| member(member_of_1_not_of_2(aD_aDb,Superset),b) ),
inference(subst,[],[refute_0_12:[bind(X_361,$fot(member_of_1_not_of_2(aD_aDb,Superset)))]]) ).
cnf(refute_0_14,plain,
( member(member_of_1_not_of_2(aD_aDb,Superset),aDb)
| member(member_of_1_not_of_2(aD_aDb,Superset),b)
| subset(aD_aDb,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aD_aDb,Superset),a) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( member(member_of_1_not_of_2(aD_aDb,b),aDb)
| member(member_of_1_not_of_2(aD_aDb,b),b)
| subset(aD_aDb,b) ),
inference(subst,[],[refute_0_14:[bind(Superset,$fot(b))]]) ).
cnf(refute_0_16,plain,
( member(member_of_1_not_of_2(aD_aDb,b),aDb)
| subset(aD_aDb,b) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aD_aDb,b),b) )],[refute_0_15,refute_0_5]) ).
cnf(refute_0_17,plain,
( ~ member(member_of_1_not_of_2(aD_aDb,b),aD_aDb)
| subset(aD_aDb,b) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aD_aDb,b),aDb) )],[refute_0_16,refute_0_4]) ).
cnf(refute_0_18,plain,
subset(aD_aDb,b),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aD_aDb,b),aD_aDb) )],[refute_0_1,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ member(Element,aD_aDb)
| member(Element,b) ),
inference(resolve,[$cnf( subset(aD_aDb,b) )],[refute_0_18,refute_0_0]) ).
cnf(refute_0_20,plain,
( ~ member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),b) ),
inference(subst,[],[refute_0_19:[bind(Element,$fot(h(a,b,aD_aDb)))]]) ).
cnf(refute_0_21,plain,
( ~ member(h(X_136,X_137,aD_aDb),aD_aDb)
| member(h(X_136,X_137,aD_aDb),a) ),
inference(subst,[],[refute_0_8:[bind(X_68,$fot(h(X_136,X_137,aD_aDb)))]]) ).
cnf(refute_0_22,plain,
( intersection(X_136,X_137,aD_aDb)
| member(h(X_136,X_137,aD_aDb),X_136)
| member(h(X_136,X_137,aD_aDb),aD_aDb) ),
inference(subst,[],[intersection_axiom1:[bind(Intersection,$fot(aD_aDb)),bind(Set1,$fot(X_136)),bind(Set2,$fot(X_137))]]) ).
cnf(refute_0_23,plain,
( intersection(X_136,X_137,aD_aDb)
| member(h(X_136,X_137,aD_aDb),X_136)
| member(h(X_136,X_137,aD_aDb),a) ),
inference(resolve,[$cnf( member(h(X_136,X_137,aD_aDb),aD_aDb) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
( intersection(a,X_137,aD_aDb)
| member(h(a,X_137,aD_aDb),a) ),
inference(subst,[],[refute_0_23:[bind(X_136,$fot(a))]]) ).
cnf(refute_0_25,plain,
( ~ difference(a,aDb,aD_aDb)
| ~ member(X_361,a)
| member(X_361,aD_aDb)
| member(X_361,aDb) ),
inference(subst,[],[member_of_difference_or_set2:[bind(Difference,$fot(aD_aDb)),bind(Element,$fot(X_361)),bind(Set1,$fot(a)),bind(Set2,$fot(aDb))]]) ).
cnf(refute_0_26,plain,
( ~ member(X_361,a)
| member(X_361,aD_aDb)
| member(X_361,aDb) ),
inference(resolve,[$cnf( difference(a,aDb,aD_aDb) )],[a_minus_aDb,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ member(h(a,X_137,aD_aDb),a)
| member(h(a,X_137,aD_aDb),aD_aDb)
| member(h(a,X_137,aD_aDb),aDb) ),
inference(subst,[],[refute_0_26:[bind(X_361,$fot(h(a,X_137,aD_aDb)))]]) ).
cnf(refute_0_28,plain,
( intersection(a,X_137,aD_aDb)
| member(h(a,X_137,aD_aDb),aD_aDb)
| member(h(a,X_137,aD_aDb),aDb) ),
inference(resolve,[$cnf( member(h(a,X_137,aD_aDb),a) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
( intersection(a,b,aD_aDb)
| member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),aDb) ),
inference(subst,[],[refute_0_28:[bind(X_137,$fot(b))]]) ).
cnf(refute_0_30,plain,
( ~ difference(a,b,aDb)
| ~ member(X_104,aDb)
| ~ member(X_104,b) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(a)),bind(Element,$fot(X_104)),bind(Set1,$fot(b)),bind(Set2,$fot(aDb))]]) ).
cnf(refute_0_31,plain,
( ~ member(X_104,aDb)
| ~ member(X_104,b) ),
inference(resolve,[$cnf( difference(a,b,aDb) )],[a_minus_b,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ member(h(X_387,b,aD_aDb),aDb)
| ~ member(h(X_387,b,aD_aDb),b) ),
inference(subst,[],[refute_0_31:[bind(X_104,$fot(h(X_387,b,aD_aDb)))]]) ).
cnf(refute_0_33,plain,
( intersection(Set1,Set2,aD_aDb)
| member(h(Set1,Set2,aD_aDb),Set2)
| member(h(Set1,Set2,aD_aDb),aD_aDb) ),
inference(subst,[],[intersection_axiom2:[bind(Intersection,$fot(aD_aDb))]]) ).
cnf(refute_0_34,plain,
( ~ member(h(Set1,Set2,aD_aDb),aD_aDb)
| member(h(Set1,Set2,aD_aDb),b) ),
inference(subst,[],[refute_0_19:[bind(Element,$fot(h(Set1,Set2,aD_aDb)))]]) ).
cnf(refute_0_35,plain,
( intersection(Set1,Set2,aD_aDb)
| member(h(Set1,Set2,aD_aDb),Set2)
| member(h(Set1,Set2,aD_aDb),b) ),
inference(resolve,[$cnf( member(h(Set1,Set2,aD_aDb),aD_aDb) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( intersection(X_387,b,aD_aDb)
| member(h(X_387,b,aD_aDb),b) ),
inference(subst,[],[refute_0_35:[bind(Set1,$fot(X_387)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_37,plain,
( ~ member(h(X_387,b,aD_aDb),aDb)
| intersection(X_387,b,aD_aDb) ),
inference(resolve,[$cnf( member(h(X_387,b,aD_aDb),b) )],[refute_0_36,refute_0_32]) ).
cnf(refute_0_38,plain,
( ~ member(h(a,b,aD_aDb),aDb)
| intersection(a,b,aD_aDb) ),
inference(subst,[],[refute_0_37:[bind(X_387,$fot(a))]]) ).
cnf(refute_0_39,plain,
( intersection(a,b,aD_aDb)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolve,[$cnf( member(h(a,b,aD_aDb),aDb) )],[refute_0_29,refute_0_38]) ).
cnf(refute_0_40,plain,
member(h(a,b,aD_aDb),aD_aDb),
inference(resolve,[$cnf( intersection(a,b,aD_aDb) )],[refute_0_39,prove_a_intersection_b_is_aD_aDb]) ).
cnf(refute_0_41,plain,
member(h(a,b,aD_aDb),b),
inference(resolve,[$cnf( member(h(a,b,aD_aDb),aD_aDb) )],[refute_0_40,refute_0_20]) ).
cnf(refute_0_42,plain,
( ~ member(h(a,b,aD_aDb),a)
| ~ member(h(a,b,aD_aDb),aD_aDb)
| ~ member(h(a,b,aD_aDb),b)
| intersection(a,b,aD_aDb) ),
inference(subst,[],[intersection_axiom3:[bind(Intersection,$fot(aD_aDb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_43,plain,
( ~ member(h(a,b,aD_aDb),a)
| ~ member(h(a,b,aD_aDb),aD_aDb)
| intersection(a,b,aD_aDb) ),
inference(resolve,[$cnf( member(h(a,b,aD_aDb),b) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),a) ),
inference(subst,[],[refute_0_8:[bind(X_68,$fot(h(a,b,aD_aDb)))]]) ).
cnf(refute_0_45,plain,
member(h(a,b,aD_aDb),a),
inference(resolve,[$cnf( member(h(a,b,aD_aDb),aD_aDb) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ member(h(a,b,aD_aDb),aD_aDb)
| intersection(a,b,aD_aDb) ),
inference(resolve,[$cnf( member(h(a,b,aD_aDb),a) )],[refute_0_45,refute_0_43]) ).
cnf(refute_0_47,plain,
intersection(a,b,aD_aDb),
inference(resolve,[$cnf( member(h(a,b,aD_aDb),aD_aDb) )],[refute_0_40,refute_0_46]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( intersection(a,b,aD_aDb) )],[refute_0_47,prove_a_intersection_b_is_aD_aDb]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.09 % Command : metis --show proof --show saturation %s
% 0.09/0.29 % Computer : n020.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sat Jul 9 23:59:43 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.69/0.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.86
% 0.69/0.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.69/0.86
%------------------------------------------------------------------------------