%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 1.25s 1.41s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of clauses : 104 ( 13 unt; 37 nHn; 86 RR)
% Number of literals : 249 ( 0 equ; 102 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 : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 100 ( 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(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(member_of_set2_is_member_of_union,axiom,
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set2)
| member(Element,Union) ) ).
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(b_union_c,axiom,
union(b,c,bUc) ).
cnf(a_intersection_b,axiom,
intersection(a,b,aIb) ).
cnf(a_intersection_c,axiom,
intersection(a,c,aIc) ).
cnf(a_intersection_bUc,axiom,
intersection(a,bUc,aI_bUc) ).
cnf(prove_aIb_union_aIc_is_aI_bUc,negated_conjecture,
~ union(aIb,aIc,aI_bUc) ).
cnf(refute_0_0,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIb)
| union(aIb,aIc,aI_bUc) ),
inference(subst,[],[union_axiom2:[bind(Set1,$fot(aIb)),bind(Set2,$fot(aIc)),bind(Union,$fot(aI_bUc))]]) ).
cnf(refute_0_1,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIc)
| union(aIb,aIc,aI_bUc) ),
inference(subst,[],[union_axiom3:[bind(Set1,$fot(aIb)),bind(Set2,$fot(aIc)),bind(Union,$fot(aI_bUc))]]) ).
cnf(refute_0_2,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_473,a)
| ~ member(X_473,b)
| member(X_473,aIb) ),
inference(subst,[],[member_of_both_is_member_of_intersection:[bind(Element,$fot(X_473)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_3,plain,
( ~ member(X_473,a)
| ~ member(X_473,b)
| member(X_473,aIb) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),aIb) ),
inference(subst,[],[refute_0_3:[bind(X_473,$fot(g(aIb,aIc,aI_bUc)))]]) ).
cnf(refute_0_5,plain,
( ~ intersection(a,c,aIc)
| ~ member(X_473,a)
| ~ member(X_473,c)
| member(X_473,aIc) ),
inference(subst,[],[member_of_both_is_member_of_intersection:[bind(Element,$fot(X_473)),bind(Intersection,$fot(aIc)),bind(Set1,$fot(a)),bind(Set2,$fot(c))]]) ).
cnf(refute_0_6,plain,
( ~ member(X_473,a)
| ~ member(X_473,c)
| member(X_473,aIc) ),
inference(resolve,[$cnf( intersection(a,c,aIc) )],[a_intersection_c,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),c)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(subst,[],[refute_0_6:[bind(X_473,$fot(g(aIb,aIc,aI_bUc)))]]) ).
cnf(refute_0_8,plain,
( ~ member(X_468,bUc)
| ~ union(b,c,bUc)
| member(X_468,b)
| member(X_468,c) ),
inference(subst,[],[member_of_union_is_member_of_one_set:[bind(Element,$fot(X_468)),bind(Set1,$fot(b)),bind(Set2,$fot(c)),bind(Union,$fot(bUc))]]) ).
cnf(refute_0_9,plain,
( ~ member(X_468,bUc)
| member(X_468,b)
| member(X_468,c) ),
inference(resolve,[$cnf( union(b,c,bUc) )],[b_union_c,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),c) ),
inference(subst,[],[refute_0_9:[bind(X_468,$fot(g(aIb,aIc,aI_bUc)))]]) ).
cnf(refute_0_11,plain,
( ~ intersection(a,bUc,aI_bUc)
| ~ member(X_98,aI_bUc)
| member(X_98,bUc) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Element,$fot(X_98)),bind(Intersection,$fot(aI_bUc)),bind(Set1,$fot(a)),bind(Set2,$fot(bUc))]]) ).
cnf(refute_0_12,plain,
( ~ member(X_98,aI_bUc)
| member(X_98,bUc) ),
inference(resolve,[$cnf( intersection(a,bUc,aI_bUc) )],[a_intersection_bUc,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),bUc) ),
inference(subst,[],[refute_0_12:[bind(X_98,$fot(g(aIb,aIc,aI_bUc)))]]) ).
cnf(refute_0_14,plain,
( ~ member(Element,aIc)
| ~ subset(aIc,aI_bUc)
| member(Element,aI_bUc) ),
inference(subst,[],[membership_in_subsets:[bind(Subset,$fot(aIc)),bind(Superset,$fot(aI_bUc))]]) ).
cnf(refute_0_15,plain,
( ~ member(member_of_1_not_of_2(aIc,aI_bUc),aI_bUc)
| subset(aIc,aI_bUc) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(aIc)),bind(Superset,$fot(aI_bUc))]]) ).
cnf(refute_0_16,plain,
( member(member_of_1_not_of_2(aIc,Superset),aIc)
| subset(aIc,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(aIc))]]) ).
cnf(refute_0_17,plain,
( ~ intersection(a,c,aIc)
| ~ member(X_74,aIc)
| member(X_74,a) ),
inference(subst,[],[member_of_intersection_is_member_of_set1:[bind(Element,$fot(X_74)),bind(Intersection,$fot(aIc)),bind(Set1,$fot(a)),bind(Set2,$fot(c))]]) ).
cnf(refute_0_18,plain,
( ~ member(X_74,aIc)
| member(X_74,a) ),
inference(resolve,[$cnf( intersection(a,c,aIc) )],[a_intersection_c,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ member(member_of_1_not_of_2(aIc,Superset),aIc)
| member(member_of_1_not_of_2(aIc,Superset),a) ),
inference(subst,[],[refute_0_18:[bind(X_74,$fot(member_of_1_not_of_2(aIc,Superset)))]]) ).
cnf(refute_0_20,plain,
( member(member_of_1_not_of_2(aIc,Superset),a)
| subset(aIc,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIc,Superset),aIc) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( member(member_of_1_not_of_2(aIc,X_856),a)
| subset(aIc,X_856) ),
inference(subst,[],[refute_0_20:[bind(Superset,$fot(X_856))]]) ).
cnf(refute_0_22,plain,
( ~ member(X_62,c)
| ~ union(b,c,bUc)
| member(X_62,bUc) ),
inference(subst,[],[member_of_set2_is_member_of_union:[bind(Element,$fot(X_62)),bind(Set1,$fot(b)),bind(Set2,$fot(c)),bind(Union,$fot(bUc))]]) ).
cnf(refute_0_23,plain,
( ~ member(X_62,c)
| member(X_62,bUc) ),
inference(resolve,[$cnf( union(b,c,bUc) )],[b_union_c,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ member(member_of_1_not_of_2(aIc,X_111),c)
| member(member_of_1_not_of_2(aIc,X_111),bUc) ),
inference(subst,[],[refute_0_23:[bind(X_62,$fot(member_of_1_not_of_2(aIc,X_111)))]]) ).
cnf(refute_0_25,plain,
( ~ intersection(a,c,aIc)
| ~ member(X_98,aIc)
| member(X_98,c) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Element,$fot(X_98)),bind(Intersection,$fot(aIc)),bind(Set1,$fot(a)),bind(Set2,$fot(c))]]) ).
cnf(refute_0_26,plain,
( ~ member(X_98,aIc)
| member(X_98,c) ),
inference(resolve,[$cnf( intersection(a,c,aIc) )],[a_intersection_c,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ member(member_of_1_not_of_2(aIc,Superset),aIc)
| member(member_of_1_not_of_2(aIc,Superset),c) ),
inference(subst,[],[refute_0_26:[bind(X_98,$fot(member_of_1_not_of_2(aIc,Superset)))]]) ).
cnf(refute_0_28,plain,
( member(member_of_1_not_of_2(aIc,Superset),c)
| subset(aIc,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIc,Superset),aIc) )],[refute_0_16,refute_0_27]) ).
cnf(refute_0_29,plain,
( member(member_of_1_not_of_2(aIc,X_111),c)
| subset(aIc,X_111) ),
inference(subst,[],[refute_0_28:[bind(Superset,$fot(X_111))]]) ).
cnf(refute_0_30,plain,
( member(member_of_1_not_of_2(aIc,X_111),bUc)
| subset(aIc,X_111) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIc,X_111),c) )],[refute_0_29,refute_0_24]) ).
cnf(refute_0_31,plain,
( ~ intersection(a,bUc,aI_bUc)
| ~ member(X_473,a)
| ~ member(X_473,bUc)
| member(X_473,aI_bUc) ),
inference(subst,[],[member_of_both_is_member_of_intersection:[bind(Element,$fot(X_473)),bind(Intersection,$fot(aI_bUc)),bind(Set1,$fot(a)),bind(Set2,$fot(bUc))]]) ).
cnf(refute_0_32,plain,
( ~ member(X_473,a)
| ~ member(X_473,bUc)
| member(X_473,aI_bUc) ),
inference(resolve,[$cnf( intersection(a,bUc,aI_bUc) )],[a_intersection_bUc,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ member(member_of_1_not_of_2(aIc,X_111),a)
| ~ member(member_of_1_not_of_2(aIc,X_111),bUc)
| member(member_of_1_not_of_2(aIc,X_111),aI_bUc) ),
inference(subst,[],[refute_0_32:[bind(X_473,$fot(member_of_1_not_of_2(aIc,X_111)))]]) ).
cnf(refute_0_34,plain,
( ~ member(member_of_1_not_of_2(aIc,X_111),a)
| member(member_of_1_not_of_2(aIc,X_111),aI_bUc)
| subset(aIc,X_111) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIc,X_111),bUc) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ member(member_of_1_not_of_2(aIc,X_856),a)
| member(member_of_1_not_of_2(aIc,X_856),aI_bUc)
| subset(aIc,X_856) ),
inference(subst,[],[refute_0_34:[bind(X_111,$fot(X_856))]]) ).
cnf(refute_0_36,plain,
( member(member_of_1_not_of_2(aIc,X_856),aI_bUc)
| subset(aIc,X_856) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIc,X_856),a) )],[refute_0_21,refute_0_35]) ).
cnf(refute_0_37,plain,
( member(member_of_1_not_of_2(aIc,aI_bUc),aI_bUc)
| subset(aIc,aI_bUc) ),
inference(subst,[],[refute_0_36:[bind(X_856,$fot(aI_bUc))]]) ).
cnf(refute_0_38,plain,
subset(aIc,aI_bUc),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIc,aI_bUc),aI_bUc) )],[refute_0_37,refute_0_15]) ).
cnf(refute_0_39,plain,
( ~ member(Element,aIc)
| member(Element,aI_bUc) ),
inference(resolve,[$cnf( subset(aIc,aI_bUc) )],[refute_0_38,refute_0_14]) ).
cnf(refute_0_40,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(subst,[],[refute_0_39:[bind(Element,$fot(g(aIb,aIc,aI_bUc)))]]) ).
cnf(refute_0_41,plain,
( ~ member(Element,aIb)
| ~ subset(aIb,aI_bUc)
| member(Element,aI_bUc) ),
inference(subst,[],[membership_in_subsets:[bind(Subset,$fot(aIb)),bind(Superset,$fot(aI_bUc))]]) ).
cnf(refute_0_42,plain,
( ~ member(member_of_1_not_of_2(aIb,aI_bUc),aI_bUc)
| subset(aIb,aI_bUc) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(aIb)),bind(Superset,$fot(aI_bUc))]]) ).
cnf(refute_0_43,plain,
( member(member_of_1_not_of_2(aIb,Superset),aIb)
| subset(aIb,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(aIb))]]) ).
cnf(refute_0_44,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_74,aIb)
| member(X_74,a) ),
inference(subst,[],[member_of_intersection_is_member_of_set1:[bind(Element,$fot(X_74)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_45,plain,
( ~ member(X_74,aIb)
| member(X_74,a) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ member(member_of_1_not_of_2(aIb,Superset),aIb)
| member(member_of_1_not_of_2(aIb,Superset),a) ),
inference(subst,[],[refute_0_45:[bind(X_74,$fot(member_of_1_not_of_2(aIb,Superset)))]]) ).
cnf(refute_0_47,plain,
( member(member_of_1_not_of_2(aIb,Superset),a)
| subset(aIb,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIb,Superset),aIb) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( member(member_of_1_not_of_2(aIb,X_481),a)
| subset(aIb,X_481) ),
inference(subst,[],[refute_0_47:[bind(Superset,$fot(X_481))]]) ).
cnf(refute_0_49,plain,
( ~ member(X_51,b)
| ~ union(b,c,bUc)
| member(X_51,bUc) ),
inference(subst,[],[member_of_set1_is_member_of_union:[bind(Element,$fot(X_51)),bind(Set1,$fot(b)),bind(Set2,$fot(c)),bind(Union,$fot(bUc))]]) ).
cnf(refute_0_50,plain,
( ~ member(X_51,b)
| member(X_51,bUc) ),
inference(resolve,[$cnf( union(b,c,bUc) )],[b_union_c,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ member(member_of_1_not_of_2(aIb,X_107),b)
| member(member_of_1_not_of_2(aIb,X_107),bUc) ),
inference(subst,[],[refute_0_50:[bind(X_51,$fot(member_of_1_not_of_2(aIb,X_107)))]]) ).
cnf(refute_0_52,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_98,aIb)
| member(X_98,b) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Element,$fot(X_98)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_53,plain,
( ~ member(X_98,aIb)
| member(X_98,b) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ member(member_of_1_not_of_2(aIb,Superset),aIb)
| member(member_of_1_not_of_2(aIb,Superset),b) ),
inference(subst,[],[refute_0_53:[bind(X_98,$fot(member_of_1_not_of_2(aIb,Superset)))]]) ).
cnf(refute_0_55,plain,
( member(member_of_1_not_of_2(aIb,Superset),b)
| subset(aIb,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIb,Superset),aIb) )],[refute_0_43,refute_0_54]) ).
cnf(refute_0_56,plain,
( member(member_of_1_not_of_2(aIb,X_107),b)
| subset(aIb,X_107) ),
inference(subst,[],[refute_0_55:[bind(Superset,$fot(X_107))]]) ).
cnf(refute_0_57,plain,
( member(member_of_1_not_of_2(aIb,X_107),bUc)
| subset(aIb,X_107) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIb,X_107),b) )],[refute_0_56,refute_0_51]) ).
cnf(refute_0_58,plain,
( ~ member(member_of_1_not_of_2(aIb,X_107),a)
| ~ member(member_of_1_not_of_2(aIb,X_107),bUc)
| member(member_of_1_not_of_2(aIb,X_107),aI_bUc) ),
inference(subst,[],[refute_0_32:[bind(X_473,$fot(member_of_1_not_of_2(aIb,X_107)))]]) ).
cnf(refute_0_59,plain,
( ~ member(member_of_1_not_of_2(aIb,X_107),a)
| member(member_of_1_not_of_2(aIb,X_107),aI_bUc)
| subset(aIb,X_107) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIb,X_107),bUc) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ member(member_of_1_not_of_2(aIb,X_481),a)
| member(member_of_1_not_of_2(aIb,X_481),aI_bUc)
| subset(aIb,X_481) ),
inference(subst,[],[refute_0_59:[bind(X_107,$fot(X_481))]]) ).
cnf(refute_0_61,plain,
( member(member_of_1_not_of_2(aIb,X_481),aI_bUc)
| subset(aIb,X_481) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIb,X_481),a) )],[refute_0_48,refute_0_60]) ).
cnf(refute_0_62,plain,
( member(member_of_1_not_of_2(aIb,aI_bUc),aI_bUc)
| subset(aIb,aI_bUc) ),
inference(subst,[],[refute_0_61:[bind(X_481,$fot(aI_bUc))]]) ).
cnf(refute_0_63,plain,
subset(aIb,aI_bUc),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIb,aI_bUc),aI_bUc) )],[refute_0_62,refute_0_42]) ).
cnf(refute_0_64,plain,
( ~ member(Element,aIb)
| member(Element,aI_bUc) ),
inference(resolve,[$cnf( subset(aIb,aI_bUc) )],[refute_0_63,refute_0_41]) ).
cnf(refute_0_65,plain,
( ~ member(g(aIb,X_1311,X_1312),aIb)
| member(g(aIb,X_1311,X_1312),aI_bUc) ),
inference(subst,[],[refute_0_64:[bind(Element,$fot(g(aIb,X_1311,X_1312)))]]) ).
cnf(refute_0_66,plain,
( member(g(aIb,X_1311,X_1312),X_1311)
| member(g(aIb,X_1311,X_1312),X_1312)
| member(g(aIb,X_1311,X_1312),aIb)
| union(aIb,X_1311,X_1312) ),
inference(subst,[],[union_axiom1:[bind(Set1,$fot(aIb)),bind(Set2,$fot(X_1311)),bind(Union,$fot(X_1312))]]) ).
cnf(refute_0_67,plain,
( member(g(aIb,X_1311,X_1312),X_1311)
| member(g(aIb,X_1311,X_1312),X_1312)
| member(g(aIb,X_1311,X_1312),aI_bUc)
| union(aIb,X_1311,X_1312) ),
inference(resolve,[$cnf( member(g(aIb,X_1311,X_1312),aIb) )],[refute_0_66,refute_0_65]) ).
cnf(refute_0_68,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc)
| union(aIb,aIc,aI_bUc) ),
inference(subst,[],[refute_0_67:[bind(X_1311,$fot(aIc)),bind(X_1312,$fot(aI_bUc))]]) ).
cnf(refute_0_69,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| union(aIb,aIc,aI_bUc) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),aIc) )],[refute_0_68,refute_0_40]) ).
cnf(refute_0_70,plain,
member(g(aIb,aIc,aI_bUc),aI_bUc),
inference(resolve,[$cnf( union(aIb,aIc,aI_bUc) )],[refute_0_69,prove_aIb_union_aIc_is_aI_bUc]) ).
cnf(refute_0_71,plain,
member(g(aIb,aIc,aI_bUc),bUc),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),aI_bUc) )],[refute_0_70,refute_0_13]) ).
cnf(refute_0_72,plain,
( member(g(aIb,aIc,aI_bUc),b)
| member(g(aIb,aIc,aI_bUc),c) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),bUc) )],[refute_0_71,refute_0_10]) ).
cnf(refute_0_73,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),b) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),c) )],[refute_0_72,refute_0_7]) ).
cnf(refute_0_74,plain,
( ~ intersection(a,bUc,aI_bUc)
| ~ member(X_74,aI_bUc)
| member(X_74,a) ),
inference(subst,[],[member_of_intersection_is_member_of_set1:[bind(Element,$fot(X_74)),bind(Intersection,$fot(aI_bUc)),bind(Set1,$fot(a)),bind(Set2,$fot(bUc))]]) ).
cnf(refute_0_75,plain,
( ~ member(X_74,aI_bUc)
| member(X_74,a) ),
inference(resolve,[$cnf( intersection(a,bUc,aI_bUc) )],[a_intersection_bUc,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),a) ),
inference(subst,[],[refute_0_75:[bind(X_74,$fot(g(aIb,aIc,aI_bUc)))]]) ).
cnf(refute_0_77,plain,
member(g(aIb,aIc,aI_bUc),a),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),aI_bUc) )],[refute_0_70,refute_0_76]) ).
cnf(refute_0_78,plain,
( member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),b) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),a) )],[refute_0_77,refute_0_73]) ).
cnf(refute_0_79,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| member(g(aIb,aIc,aI_bUc),aIb)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),b) )],[refute_0_78,refute_0_4]) ).
cnf(refute_0_80,plain,
( member(g(aIb,aIc,aI_bUc),aIb)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),a) )],[refute_0_77,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIb)
| union(aIb,aIc,aI_bUc) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),aIc) )],[refute_0_80,refute_0_1]) ).
cnf(refute_0_82,plain,
( member(g(aIb,aIc,aI_bUc),aIb)
| union(aIb,aIc,aI_bUc) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),aI_bUc) )],[refute_0_70,refute_0_81]) ).
cnf(refute_0_83,plain,
member(g(aIb,aIc,aI_bUc),aIb),
inference(resolve,[$cnf( union(aIb,aIc,aI_bUc) )],[refute_0_82,prove_aIb_union_aIc_is_aI_bUc]) ).
cnf(refute_0_84,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| union(aIb,aIc,aI_bUc) ),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),aIb) )],[refute_0_83,refute_0_0]) ).
cnf(refute_0_85,plain,
union(aIb,aIc,aI_bUc),
inference(resolve,[$cnf( member(g(aIb,aIc,aI_bUc),aI_bUc) )],[refute_0_70,refute_0_84]) ).
cnf(refute_0_86,plain,
$false,
inference(resolve,[$cnf( union(aIb,aIc,aI_bUc) )],[refute_0_85,prove_aIb_union_aIc_is_aI_bUc]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.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 00:45:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.25/1.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.25/1.41
% 1.25/1.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.25/1.42
%------------------------------------------------------------------------------