TSTP Solution File: SET010-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 03:31:01 EDT 2022
% Result : Unsatisfiable 3.05s 3.28s
% Output : CNFRefutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 21
% Syntax : Number of clauses : 127 ( 17 unt; 45 nHn; 107 RR)
% Number of literals : 299 ( 0 equ; 133 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 127 ( 4 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(union_axiom1,axiom,
( union(Set1,Set2,Union)
| member(g(Set1,Set2,Union),Set1)
| member(g(Set1,Set2,Union),Set2)
| member(g(Set1,Set2,Union),Union) ) ).
cnf(union_axiom2,axiom,
( ~ member(g(Set1,Set2,Union),Set1)
| ~ member(g(Set1,Set2,Union),Union)
| union(Set1,Set2,Union) ) ).
cnf(union_axiom3,axiom,
( ~ member(g(Set1,Set2,Union),Set2)
| ~ member(g(Set1,Set2,Union),Union)
| union(Set1,Set2,Union) ) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set1) ) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) ) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Set2)
| ~ member(Element,Set1)
| member(Element,Intersection) ) ).
cnf(intersection_axiom1,axiom,
( member(h(Set1,Set2,Intersection),Intersection)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Set1) ) ).
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(difference_axiom2,axiom,
( difference(Set1,Set2,Difference)
| member(k(Set1,Set2,Difference),Set1)
| member(k(Set1,Set2,Difference),Difference) ) ).
cnf(difference_axiom3,axiom,
( ~ member(k(Set1,Set2,Difference),Difference)
| ~ member(k(Set1,Set2,Difference),Set1)
| member(k(Set1,Set2,Difference),Set2)
| difference(Set1,Set2,Difference) ) ).
cnf(a_intersection_b,hypothesis,
intersection(a,b,aIb) ).
cnf(c_minus_a,hypothesis,
difference(c,a,cDa) ).
cnf(c_minus_b,hypothesis,
difference(c,b,cDb) ).
cnf(c_minus_aIb,hypothesis,
difference(c,aIb,cD_aIb) ).
cnf(prove_cDa_union_cDb_is_cD_aIb,negated_conjecture,
~ union(cDa,cDb,cD_aIb) ).
cnf(refute_0_0,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa)
| union(cDa,cDb,cD_aIb) ),
inference(subst,[],[union_axiom2:[bind(Set1,$fot(cDa)),bind(Set2,$fot(cDb)),bind(Union,$fot(cD_aIb))]]) ).
cnf(refute_0_1,plain,
( ~ difference(c,a,cDa)
| ~ member(X_877,c)
| member(X_877,a)
| member(X_877,cDa) ),
inference(subst,[],[member_of_difference_or_set2:[bind(Difference,$fot(cDa)),bind(Element,$fot(X_877)),bind(Set1,$fot(c)),bind(Set2,$fot(a))]]) ).
cnf(refute_0_2,plain,
( ~ member(X_877,c)
| member(X_877,a)
| member(X_877,cDa) ),
inference(resolve,[$cnf( difference(c,a,cDa) )],[c_minus_a,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(subst,[],[refute_0_2:[bind(X_877,$fot(g(cDa,cDb,cD_aIb)))]]) ).
cnf(refute_0_4,plain,
( ~ difference(c,aIb,cD_aIb)
| ~ member(X_148,cD_aIb)
| member(X_148,c) ),
inference(subst,[],[member_of_difference:[bind(Difference,$fot(cD_aIb)),bind(Element,$fot(X_148)),bind(Set1,$fot(c)),bind(Set2,$fot(aIb))]]) ).
cnf(refute_0_5,plain,
( ~ member(X_148,cD_aIb)
| member(X_148,c) ),
inference(resolve,[$cnf( difference(c,aIb,cD_aIb) )],[c_minus_aIb,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),c) ),
inference(subst,[],[refute_0_5:[bind(X_148,$fot(g(cDa,cDb,cD_aIb)))]]) ).
cnf(refute_0_7,plain,
( ~ intersection(cDb,cD_aIb,cDb)
| ~ member(Element,cDb)
| member(Element,cD_aIb) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Intersection,$fot(cDb)),bind(Set1,$fot(cDb)),bind(Set2,$fot(cD_aIb))]]) ).
cnf(refute_0_8,plain,
( intersection(cDb,Set2,cDb)
| member(h(cDb,Set2,cDb),cDb) ),
inference(subst,[],[intersection_axiom1:[bind(Intersection,$fot(cDb)),bind(Set1,$fot(cDb))]]) ).
cnf(refute_0_9,plain,
( ~ difference(aIb,cDb,aIb)
| ~ member(Element,aIb)
| ~ member(Element,cDb) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(aIb)),bind(Set1,$fot(cDb)),bind(Set2,$fot(aIb))]]) ).
cnf(refute_0_10,plain,
( difference(aIb,Set2,aIb)
| member(k(aIb,Set2,aIb),aIb) ),
inference(subst,[],[difference_axiom2:[bind(Difference,$fot(aIb)),bind(Set1,$fot(aIb))]]) ).
cnf(refute_0_11,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_119,aIb)
| member(X_119,b) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Element,$fot(X_119)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_12,plain,
( ~ member(X_119,aIb)
| member(X_119,b) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ member(k(aIb,Set2,aIb),aIb)
| member(k(aIb,Set2,aIb),b) ),
inference(subst,[],[refute_0_12:[bind(X_119,$fot(k(aIb,Set2,aIb)))]]) ).
cnf(refute_0_14,plain,
( difference(aIb,Set2,aIb)
| member(k(aIb,Set2,aIb),b) ),
inference(resolve,[$cnf( member(k(aIb,Set2,aIb),aIb) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( difference(aIb,cDb,aIb)
| member(k(aIb,cDb,aIb),b) ),
inference(subst,[],[refute_0_14:[bind(Set2,$fot(cDb))]]) ).
cnf(refute_0_16,plain,
( difference(X_76,X_77,X_76)
| member(k(X_76,X_77,X_76),X_76) ),
inference(subst,[],[difference_axiom2:[bind(Difference,$fot(X_76)),bind(Set1,$fot(X_76)),bind(Set2,$fot(X_77))]]) ).
cnf(refute_0_17,plain,
( ~ member(k(X_76,X_77,X_76),X_76)
| difference(X_76,X_77,X_76)
| member(k(X_76,X_77,X_76),X_77) ),
inference(subst,[],[difference_axiom3:[bind(Difference,$fot(X_76)),bind(Set1,$fot(X_76)),bind(Set2,$fot(X_77))]]) ).
cnf(refute_0_18,plain,
( difference(X_76,X_77,X_76)
| member(k(X_76,X_77,X_76),X_77) ),
inference(resolve,[$cnf( member(k(X_76,X_77,X_76),X_76) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( difference(X_76,cDb,X_76)
| member(k(X_76,cDb,X_76),cDb) ),
inference(subst,[],[refute_0_18:[bind(X_77,$fot(cDb))]]) ).
cnf(refute_0_20,plain,
( ~ difference(c,b,cDb)
| ~ member(X_224,b)
| ~ member(X_224,cDb) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(c)),bind(Element,$fot(X_224)),bind(Set1,$fot(b)),bind(Set2,$fot(cDb))]]) ).
cnf(refute_0_21,plain,
( ~ member(X_224,b)
| ~ member(X_224,cDb) ),
inference(resolve,[$cnf( difference(c,b,cDb) )],[c_minus_b,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ member(k(X_76,cDb,X_76),b)
| ~ member(k(X_76,cDb,X_76),cDb) ),
inference(subst,[],[refute_0_21:[bind(X_224,$fot(k(X_76,cDb,X_76)))]]) ).
cnf(refute_0_23,plain,
( ~ member(k(X_76,cDb,X_76),b)
| difference(X_76,cDb,X_76) ),
inference(resolve,[$cnf( member(k(X_76,cDb,X_76),cDb) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ member(k(aIb,cDb,aIb),b)
| difference(aIb,cDb,aIb) ),
inference(subst,[],[refute_0_23:[bind(X_76,$fot(aIb))]]) ).
cnf(refute_0_25,plain,
difference(aIb,cDb,aIb),
inference(resolve,[$cnf( member(k(aIb,cDb,aIb),b) )],[refute_0_15,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ member(Element,aIb)
| ~ member(Element,cDb) ),
inference(resolve,[$cnf( difference(aIb,cDb,aIb) )],[refute_0_25,refute_0_9]) ).
cnf(refute_0_27,plain,
( ~ member(h(cDb,Set2,cDb),aIb)
| ~ member(h(cDb,Set2,cDb),cDb) ),
inference(subst,[],[refute_0_26:[bind(Element,$fot(h(cDb,Set2,cDb)))]]) ).
cnf(refute_0_28,plain,
( ~ member(h(cDb,Set2,cDb),aIb)
| intersection(cDb,Set2,cDb) ),
inference(resolve,[$cnf( member(h(cDb,Set2,cDb),cDb) )],[refute_0_8,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ member(h(cDb,cD_aIb,cDb),aIb)
| intersection(cDb,cD_aIb,cDb) ),
inference(subst,[],[refute_0_28:[bind(Set2,$fot(cD_aIb))]]) ).
cnf(refute_0_30,plain,
( intersection(X_66,X_67,X_66)
| member(h(X_66,X_67,X_66),X_66) ),
inference(subst,[],[intersection_axiom1:[bind(Intersection,$fot(X_66)),bind(Set1,$fot(X_66)),bind(Set2,$fot(X_67))]]) ).
cnf(refute_0_31,plain,
( ~ member(h(X_66,X_67,X_66),X_66)
| ~ member(h(X_66,X_67,X_66),X_67)
| intersection(X_66,X_67,X_66) ),
inference(subst,[],[intersection_axiom3:[bind(Intersection,$fot(X_66)),bind(Set1,$fot(X_66)),bind(Set2,$fot(X_67))]]) ).
cnf(refute_0_32,plain,
( ~ member(h(X_66,X_67,X_66),X_67)
| intersection(X_66,X_67,X_66) ),
inference(resolve,[$cnf( member(h(X_66,X_67,X_66),X_66) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ member(h(cDb,cD_aIb,cDb),cD_aIb)
| intersection(cDb,cD_aIb,cDb) ),
inference(subst,[],[refute_0_32:[bind(X_66,$fot(cDb)),bind(X_67,$fot(cD_aIb))]]) ).
cnf(refute_0_34,plain,
( ~ difference(c,b,cDb)
| ~ member(X_148,cDb)
| member(X_148,c) ),
inference(subst,[],[member_of_difference:[bind(Difference,$fot(cDb)),bind(Element,$fot(X_148)),bind(Set1,$fot(c)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_35,plain,
( ~ member(X_148,cDb)
| member(X_148,c) ),
inference(resolve,[$cnf( difference(c,b,cDb) )],[c_minus_b,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ member(h(cDb,Set2,cDb),cDb)
| member(h(cDb,Set2,cDb),c) ),
inference(subst,[],[refute_0_35:[bind(X_148,$fot(h(cDb,Set2,cDb)))]]) ).
cnf(refute_0_37,plain,
( intersection(cDb,Set2,cDb)
| member(h(cDb,Set2,cDb),c) ),
inference(resolve,[$cnf( member(h(cDb,Set2,cDb),cDb) )],[refute_0_8,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ difference(c,aIb,cD_aIb)
| ~ member(X_877,c)
| member(X_877,aIb)
| member(X_877,cD_aIb) ),
inference(subst,[],[member_of_difference_or_set2:[bind(Difference,$fot(cD_aIb)),bind(Element,$fot(X_877)),bind(Set1,$fot(c)),bind(Set2,$fot(aIb))]]) ).
cnf(refute_0_39,plain,
( ~ member(X_877,c)
| member(X_877,aIb)
| member(X_877,cD_aIb) ),
inference(resolve,[$cnf( difference(c,aIb,cD_aIb) )],[c_minus_aIb,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ member(h(cDb,Set2,cDb),c)
| member(h(cDb,Set2,cDb),aIb)
| member(h(cDb,Set2,cDb),cD_aIb) ),
inference(subst,[],[refute_0_39:[bind(X_877,$fot(h(cDb,Set2,cDb)))]]) ).
cnf(refute_0_41,plain,
( intersection(cDb,Set2,cDb)
| member(h(cDb,Set2,cDb),aIb)
| member(h(cDb,Set2,cDb),cD_aIb) ),
inference(resolve,[$cnf( member(h(cDb,Set2,cDb),c) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( intersection(cDb,cD_aIb,cDb)
| member(h(cDb,cD_aIb,cDb),aIb)
| member(h(cDb,cD_aIb,cDb),cD_aIb) ),
inference(subst,[],[refute_0_41:[bind(Set2,$fot(cD_aIb))]]) ).
cnf(refute_0_43,plain,
( intersection(cDb,cD_aIb,cDb)
| member(h(cDb,cD_aIb,cDb),aIb) ),
inference(resolve,[$cnf( member(h(cDb,cD_aIb,cDb),cD_aIb) )],[refute_0_42,refute_0_33]) ).
cnf(refute_0_44,plain,
intersection(cDb,cD_aIb,cDb),
inference(resolve,[$cnf( member(h(cDb,cD_aIb,cDb),aIb) )],[refute_0_43,refute_0_29]) ).
cnf(refute_0_45,plain,
( ~ member(Element,cDb)
| member(Element,cD_aIb) ),
inference(resolve,[$cnf( intersection(cDb,cD_aIb,cDb) )],[refute_0_44,refute_0_7]) ).
cnf(refute_0_46,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(subst,[],[refute_0_45:[bind(Element,$fot(g(cDa,cDb,cD_aIb)))]]) ).
cnf(refute_0_47,plain,
( ~ member(Element,cDa)
| ~ subset(cDa,cD_aIb)
| member(Element,cD_aIb) ),
inference(subst,[],[membership_in_subsets:[bind(Subset,$fot(cDa)),bind(Superset,$fot(cD_aIb))]]) ).
cnf(refute_0_48,plain,
( member(member_of_1_not_of_2(cDa,Superset),cDa)
| subset(cDa,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(cDa))]]) ).
cnf(refute_0_49,plain,
( ~ difference(aIb,cDa,aIb)
| ~ member(Element,aIb)
| ~ member(Element,cDa) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(aIb)),bind(Set1,$fot(cDa)),bind(Set2,$fot(aIb))]]) ).
cnf(refute_0_50,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_91,aIb)
| member(X_91,a) ),
inference(subst,[],[member_of_intersection_is_member_of_set1:[bind(Element,$fot(X_91)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_51,plain,
( ~ member(X_91,aIb)
| member(X_91,a) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ member(k(aIb,Set2,aIb),aIb)
| member(k(aIb,Set2,aIb),a) ),
inference(subst,[],[refute_0_51:[bind(X_91,$fot(k(aIb,Set2,aIb)))]]) ).
cnf(refute_0_53,plain,
( difference(aIb,Set2,aIb)
| member(k(aIb,Set2,aIb),a) ),
inference(resolve,[$cnf( member(k(aIb,Set2,aIb),aIb) )],[refute_0_10,refute_0_52]) ).
cnf(refute_0_54,plain,
( difference(aIb,cDa,aIb)
| member(k(aIb,cDa,aIb),a) ),
inference(subst,[],[refute_0_53:[bind(Set2,$fot(cDa))]]) ).
cnf(refute_0_55,plain,
( difference(X_76,cDa,X_76)
| member(k(X_76,cDa,X_76),cDa) ),
inference(subst,[],[refute_0_18:[bind(X_77,$fot(cDa))]]) ).
cnf(refute_0_56,plain,
( ~ difference(c,a,cDa)
| ~ member(X_224,a)
| ~ member(X_224,cDa) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(c)),bind(Element,$fot(X_224)),bind(Set1,$fot(a)),bind(Set2,$fot(cDa))]]) ).
cnf(refute_0_57,plain,
( ~ member(X_224,a)
| ~ member(X_224,cDa) ),
inference(resolve,[$cnf( difference(c,a,cDa) )],[c_minus_a,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ member(k(X_76,cDa,X_76),a)
| ~ member(k(X_76,cDa,X_76),cDa) ),
inference(subst,[],[refute_0_57:[bind(X_224,$fot(k(X_76,cDa,X_76)))]]) ).
cnf(refute_0_59,plain,
( ~ member(k(X_76,cDa,X_76),a)
| difference(X_76,cDa,X_76) ),
inference(resolve,[$cnf( member(k(X_76,cDa,X_76),cDa) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ member(k(aIb,cDa,aIb),a)
| difference(aIb,cDa,aIb) ),
inference(subst,[],[refute_0_59:[bind(X_76,$fot(aIb))]]) ).
cnf(refute_0_61,plain,
difference(aIb,cDa,aIb),
inference(resolve,[$cnf( member(k(aIb,cDa,aIb),a) )],[refute_0_54,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ member(Element,aIb)
| ~ member(Element,cDa) ),
inference(resolve,[$cnf( difference(aIb,cDa,aIb) )],[refute_0_61,refute_0_49]) ).
cnf(refute_0_63,plain,
( ~ member(member_of_1_not_of_2(cDa,Superset),aIb)
| ~ member(member_of_1_not_of_2(cDa,Superset),cDa) ),
inference(subst,[],[refute_0_62:[bind(Element,$fot(member_of_1_not_of_2(cDa,Superset)))]]) ).
cnf(refute_0_64,plain,
( ~ member(member_of_1_not_of_2(cDa,Superset),aIb)
| subset(cDa,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(cDa,Superset),cDa) )],[refute_0_48,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ member(member_of_1_not_of_2(cDa,cD_aIb),aIb)
| subset(cDa,cD_aIb) ),
inference(subst,[],[refute_0_64:[bind(Superset,$fot(cD_aIb))]]) ).
cnf(refute_0_66,plain,
( ~ member(member_of_1_not_of_2(cDa,cD_aIb),cD_aIb)
| subset(cDa,cD_aIb) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(cDa)),bind(Superset,$fot(cD_aIb))]]) ).
cnf(refute_0_67,plain,
( ~ difference(c,a,cDa)
| ~ member(X_148,cDa)
| member(X_148,c) ),
inference(subst,[],[member_of_difference:[bind(Difference,$fot(cDa)),bind(Element,$fot(X_148)),bind(Set1,$fot(c)),bind(Set2,$fot(a))]]) ).
cnf(refute_0_68,plain,
( ~ member(X_148,cDa)
| member(X_148,c) ),
inference(resolve,[$cnf( difference(c,a,cDa) )],[c_minus_a,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ member(member_of_1_not_of_2(cDa,Superset),cDa)
| member(member_of_1_not_of_2(cDa,Superset),c) ),
inference(subst,[],[refute_0_68:[bind(X_148,$fot(member_of_1_not_of_2(cDa,Superset)))]]) ).
cnf(refute_0_70,plain,
( member(member_of_1_not_of_2(cDa,Superset),c)
| subset(cDa,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(cDa,Superset),cDa) )],[refute_0_48,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ member(member_of_1_not_of_2(cDa,Superset),c)
| member(member_of_1_not_of_2(cDa,Superset),aIb)
| member(member_of_1_not_of_2(cDa,Superset),cD_aIb) ),
inference(subst,[],[refute_0_39:[bind(X_877,$fot(member_of_1_not_of_2(cDa,Superset)))]]) ).
cnf(refute_0_72,plain,
( member(member_of_1_not_of_2(cDa,Superset),aIb)
| member(member_of_1_not_of_2(cDa,Superset),cD_aIb)
| subset(cDa,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(cDa,Superset),c) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( member(member_of_1_not_of_2(cDa,cD_aIb),aIb)
| member(member_of_1_not_of_2(cDa,cD_aIb),cD_aIb)
| subset(cDa,cD_aIb) ),
inference(subst,[],[refute_0_72:[bind(Superset,$fot(cD_aIb))]]) ).
cnf(refute_0_74,plain,
( member(member_of_1_not_of_2(cDa,cD_aIb),aIb)
| subset(cDa,cD_aIb) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(cDa,cD_aIb),cD_aIb) )],[refute_0_73,refute_0_66]) ).
cnf(refute_0_75,plain,
subset(cDa,cD_aIb),
inference(resolve,[$cnf( member(member_of_1_not_of_2(cDa,cD_aIb),aIb) )],[refute_0_74,refute_0_65]) ).
cnf(refute_0_76,plain,
( ~ member(Element,cDa)
| member(Element,cD_aIb) ),
inference(resolve,[$cnf( subset(cDa,cD_aIb) )],[refute_0_75,refute_0_47]) ).
cnf(refute_0_77,plain,
( ~ member(g(cDa,X_3355,X_3356),cDa)
| member(g(cDa,X_3355,X_3356),cD_aIb) ),
inference(subst,[],[refute_0_76:[bind(Element,$fot(g(cDa,X_3355,X_3356)))]]) ).
cnf(refute_0_78,plain,
( member(g(cDa,X_3355,X_3356),X_3355)
| member(g(cDa,X_3355,X_3356),X_3356)
| member(g(cDa,X_3355,X_3356),cDa)
| union(cDa,X_3355,X_3356) ),
inference(subst,[],[union_axiom1:[bind(Set1,$fot(cDa)),bind(Set2,$fot(X_3355)),bind(Union,$fot(X_3356))]]) ).
cnf(refute_0_79,plain,
( member(g(cDa,X_3355,X_3356),X_3355)
| member(g(cDa,X_3355,X_3356),X_3356)
| member(g(cDa,X_3355,X_3356),cD_aIb)
| union(cDa,X_3355,X_3356) ),
inference(resolve,[$cnf( member(g(cDa,X_3355,X_3356),cDa) )],[refute_0_78,refute_0_77]) ).
cnf(refute_0_80,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDb)
| union(cDa,cDb,cD_aIb) ),
inference(subst,[],[refute_0_79:[bind(X_3355,$fot(cDb)),bind(X_3356,$fot(cD_aIb))]]) ).
cnf(refute_0_81,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| union(cDa,cDb,cD_aIb) ),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),cDb) )],[refute_0_80,refute_0_46]) ).
cnf(refute_0_82,plain,
member(g(cDa,cDb,cD_aIb),cD_aIb),
inference(resolve,[$cnf( union(cDa,cDb,cD_aIb) )],[refute_0_81,prove_cDa_union_cDb_is_cD_aIb]) ).
cnf(refute_0_83,plain,
member(g(cDa,cDb,cD_aIb),c),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),cD_aIb) )],[refute_0_82,refute_0_6]) ).
cnf(refute_0_84,plain,
( member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),c) )],[refute_0_83,refute_0_3]) ).
cnf(refute_0_85,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_871,a)
| ~ member(X_871,b)
| member(X_871,aIb) ),
inference(subst,[],[member_of_both_is_member_of_intersection:[bind(Element,$fot(X_871)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_86,plain,
( ~ member(X_871,a)
| ~ member(X_871,b)
| member(X_871,aIb) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_85]) ).
cnf(refute_0_87,plain,
( ~ member(g(cDa,cDb,cD_aIb),a)
| ~ member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),aIb) ),
inference(subst,[],[refute_0_86:[bind(X_871,$fot(g(cDa,cDb,cD_aIb)))]]) ).
cnf(refute_0_88,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDb)
| union(cDa,cDb,cD_aIb) ),
inference(subst,[],[union_axiom3:[bind(Set1,$fot(cDa)),bind(Set2,$fot(cDb)),bind(Union,$fot(cD_aIb))]]) ).
cnf(refute_0_89,plain,
( ~ difference(c,b,cDb)
| ~ member(X_877,c)
| member(X_877,b)
| member(X_877,cDb) ),
inference(subst,[],[member_of_difference_or_set2:[bind(Difference,$fot(cDb)),bind(Element,$fot(X_877)),bind(Set1,$fot(c)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_90,plain,
( ~ member(X_877,c)
| member(X_877,b)
| member(X_877,cDb) ),
inference(resolve,[$cnf( difference(c,b,cDb) )],[c_minus_b,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(subst,[],[refute_0_90:[bind(X_877,$fot(g(cDa,cDb,cD_aIb)))]]) ).
cnf(refute_0_92,plain,
( member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),c) )],[refute_0_83,refute_0_91]) ).
cnf(refute_0_93,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),b)
| union(cDa,cDb,cD_aIb) ),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),cDb) )],[refute_0_92,refute_0_88]) ).
cnf(refute_0_94,plain,
( member(g(cDa,cDb,cD_aIb),b)
| union(cDa,cDb,cD_aIb) ),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),cD_aIb) )],[refute_0_82,refute_0_93]) ).
cnf(refute_0_95,plain,
member(g(cDa,cDb,cD_aIb),b),
inference(resolve,[$cnf( union(cDa,cDb,cD_aIb) )],[refute_0_94,prove_cDa_union_cDb_is_cD_aIb]) ).
cnf(refute_0_96,plain,
( ~ member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),aIb) ),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),b) )],[refute_0_95,refute_0_87]) ).
cnf(refute_0_97,plain,
( ~ difference(c,aIb,cD_aIb)
| ~ member(X_224,aIb)
| ~ member(X_224,cD_aIb) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(c)),bind(Element,$fot(X_224)),bind(Set1,$fot(aIb)),bind(Set2,$fot(cD_aIb))]]) ).
cnf(refute_0_98,plain,
( ~ member(X_224,aIb)
| ~ member(X_224,cD_aIb) ),
inference(resolve,[$cnf( difference(c,aIb,cD_aIb) )],[c_minus_aIb,refute_0_97]) ).
cnf(refute_0_99,plain,
( ~ member(g(cDa,cDb,cD_aIb),aIb)
| ~ member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(subst,[],[refute_0_98:[bind(X_224,$fot(g(cDa,cDb,cD_aIb)))]]) ).
cnf(refute_0_100,plain,
~ member(g(cDa,cDb,cD_aIb),aIb),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),cD_aIb) )],[refute_0_82,refute_0_99]) ).
cnf(refute_0_101,plain,
~ member(g(cDa,cDb,cD_aIb),a),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),aIb) )],[refute_0_96,refute_0_100]) ).
cnf(refute_0_102,plain,
member(g(cDa,cDb,cD_aIb),cDa),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),a) )],[refute_0_84,refute_0_101]) ).
cnf(refute_0_103,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| union(cDa,cDb,cD_aIb) ),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),cDa) )],[refute_0_102,refute_0_0]) ).
cnf(refute_0_104,plain,
union(cDa,cDb,cD_aIb),
inference(resolve,[$cnf( member(g(cDa,cDb,cD_aIb),cD_aIb) )],[refute_0_82,refute_0_103]) ).
cnf(refute_0_105,plain,
$false,
inference(resolve,[$cnf( union(cDa,cDb,cD_aIb) )],[refute_0_104,prove_cDa_union_cDb_is_cD_aIb]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 14:57:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.05/3.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.05/3.28
% 3.05/3.28 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.05/3.29
%------------------------------------------------------------------------------