TSTP Solution File: SET005-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 03:30:57 EDT 2022
% Result : Unsatisfiable 0.48s 0.69s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of clauses : 92 ( 12 unt; 32 nHn; 70 RR)
% Number of literals : 215 ( 0 equ; 83 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 92 ( 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(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_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(a_intersection_b,axiom,
intersection(a,b,aIb) ).
cnf(b_intersection_c,axiom,
intersection(b,c,bIc) ).
cnf(a_intersection_bIc,axiom,
intersection(a,bIc,aIbIc) ).
cnf(prove_aIb_intersection_c_is_aIbIc,negated_conjecture,
~ intersection(aIb,c,aIbIc) ).
cnf(refute_0_0,plain,
( ~ intersection(b,c,bIc)
| ~ member(X_51,bIc)
| member(X_51,c) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Element,$fot(X_51)),bind(Intersection,$fot(bIc)),bind(Set1,$fot(b)),bind(Set2,$fot(c))]]) ).
cnf(refute_0_1,plain,
( ~ member(X_51,bIc)
| member(X_51,c) ),
inference(resolve,[$cnf( intersection(b,c,bIc) )],[b_intersection_c,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),c) ),
inference(subst,[],[refute_0_1:[bind(X_51,$fot(h(aIb,c,aIbIc)))]]) ).
cnf(refute_0_3,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_51,aIb)
| member(X_51,b) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Element,$fot(X_51)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_4,plain,
( ~ member(X_51,aIb)
| member(X_51,b) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ member(h(aIb,X_276,aIbIc),aIb)
| member(h(aIb,X_276,aIbIc),b) ),
inference(subst,[],[refute_0_4:[bind(X_51,$fot(h(aIb,X_276,aIbIc)))]]) ).
cnf(refute_0_6,plain,
( intersection(Set1,Set2,aIbIc)
| member(h(Set1,Set2,aIbIc),Set1)
| member(h(Set1,Set2,aIbIc),aIbIc) ),
inference(subst,[],[intersection_axiom1:[bind(Intersection,$fot(aIbIc))]]) ).
cnf(refute_0_7,plain,
( ~ member(Element,aIbIc)
| ~ subset(aIbIc,aIb)
| member(Element,aIb) ),
inference(subst,[],[membership_in_subsets:[bind(Subset,$fot(aIbIc)),bind(Superset,$fot(aIb))]]) ).
cnf(refute_0_8,plain,
( ~ member(member_of_1_not_of_2(aIbIc,aIb),aIb)
| subset(aIbIc,aIb) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(aIbIc)),bind(Superset,$fot(aIb))]]) ).
cnf(refute_0_9,plain,
( member(member_of_1_not_of_2(aIbIc,Superset),aIbIc)
| subset(aIbIc,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(aIbIc))]]) ).
cnf(refute_0_10,plain,
( ~ intersection(a,bIc,aIbIc)
| ~ member(X_35,aIbIc)
| member(X_35,a) ),
inference(subst,[],[member_of_intersection_is_member_of_set1:[bind(Element,$fot(X_35)),bind(Intersection,$fot(aIbIc)),bind(Set1,$fot(a)),bind(Set2,$fot(bIc))]]) ).
cnf(refute_0_11,plain,
( ~ member(X_35,aIbIc)
| member(X_35,a) ),
inference(resolve,[$cnf( intersection(a,bIc,aIbIc) )],[a_intersection_bIc,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(member_of_1_not_of_2(aIbIc,Superset),aIbIc)
| member(member_of_1_not_of_2(aIbIc,Superset),a) ),
inference(subst,[],[refute_0_11:[bind(X_35,$fot(member_of_1_not_of_2(aIbIc,Superset)))]]) ).
cnf(refute_0_13,plain,
( member(member_of_1_not_of_2(aIbIc,Superset),a)
| subset(aIbIc,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIbIc,Superset),aIbIc) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( member(member_of_1_not_of_2(aIbIc,X_267),a)
| subset(aIbIc,X_267) ),
inference(subst,[],[refute_0_13:[bind(Superset,$fot(X_267))]]) ).
cnf(refute_0_15,plain,
( ~ intersection(b,c,bIc)
| ~ member(X_35,bIc)
| member(X_35,b) ),
inference(subst,[],[member_of_intersection_is_member_of_set1:[bind(Element,$fot(X_35)),bind(Intersection,$fot(bIc)),bind(Set1,$fot(b)),bind(Set2,$fot(c))]]) ).
cnf(refute_0_16,plain,
( ~ member(X_35,bIc)
| member(X_35,b) ),
inference(resolve,[$cnf( intersection(b,c,bIc) )],[b_intersection_c,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(member_of_1_not_of_2(aIbIc,X_59),bIc)
| member(member_of_1_not_of_2(aIbIc,X_59),b) ),
inference(subst,[],[refute_0_16:[bind(X_35,$fot(member_of_1_not_of_2(aIbIc,X_59)))]]) ).
cnf(refute_0_18,plain,
( ~ intersection(a,bIc,aIbIc)
| ~ member(X_51,aIbIc)
| member(X_51,bIc) ),
inference(subst,[],[member_of_intersection_is_member_of_set2:[bind(Element,$fot(X_51)),bind(Intersection,$fot(aIbIc)),bind(Set1,$fot(a)),bind(Set2,$fot(bIc))]]) ).
cnf(refute_0_19,plain,
( ~ member(X_51,aIbIc)
| member(X_51,bIc) ),
inference(resolve,[$cnf( intersection(a,bIc,aIbIc) )],[a_intersection_bIc,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ member(member_of_1_not_of_2(aIbIc,Superset),aIbIc)
| member(member_of_1_not_of_2(aIbIc,Superset),bIc) ),
inference(subst,[],[refute_0_19:[bind(X_51,$fot(member_of_1_not_of_2(aIbIc,Superset)))]]) ).
cnf(refute_0_21,plain,
( member(member_of_1_not_of_2(aIbIc,Superset),bIc)
| subset(aIbIc,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIbIc,Superset),aIbIc) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
( member(member_of_1_not_of_2(aIbIc,X_59),bIc)
| subset(aIbIc,X_59) ),
inference(subst,[],[refute_0_21:[bind(Superset,$fot(X_59))]]) ).
cnf(refute_0_23,plain,
( member(member_of_1_not_of_2(aIbIc,X_59),b)
| subset(aIbIc,X_59) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIbIc,X_59),bIc) )],[refute_0_22,refute_0_17]) ).
cnf(refute_0_24,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_218,a)
| ~ member(X_218,b)
| member(X_218,aIb) ),
inference(subst,[],[member_of_both_is_member_of_intersection:[bind(Element,$fot(X_218)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_25,plain,
( ~ member(X_218,a)
| ~ member(X_218,b)
| member(X_218,aIb) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ member(member_of_1_not_of_2(aIbIc,X_59),a)
| ~ member(member_of_1_not_of_2(aIbIc,X_59),b)
| member(member_of_1_not_of_2(aIbIc,X_59),aIb) ),
inference(subst,[],[refute_0_25:[bind(X_218,$fot(member_of_1_not_of_2(aIbIc,X_59)))]]) ).
cnf(refute_0_27,plain,
( ~ member(member_of_1_not_of_2(aIbIc,X_59),a)
| member(member_of_1_not_of_2(aIbIc,X_59),aIb)
| subset(aIbIc,X_59) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIbIc,X_59),b) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ member(member_of_1_not_of_2(aIbIc,X_267),a)
| member(member_of_1_not_of_2(aIbIc,X_267),aIb)
| subset(aIbIc,X_267) ),
inference(subst,[],[refute_0_27:[bind(X_59,$fot(X_267))]]) ).
cnf(refute_0_29,plain,
( member(member_of_1_not_of_2(aIbIc,X_267),aIb)
| subset(aIbIc,X_267) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIbIc,X_267),a) )],[refute_0_14,refute_0_28]) ).
cnf(refute_0_30,plain,
( member(member_of_1_not_of_2(aIbIc,aIb),aIb)
| subset(aIbIc,aIb) ),
inference(subst,[],[refute_0_29:[bind(X_267,$fot(aIb))]]) ).
cnf(refute_0_31,plain,
subset(aIbIc,aIb),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIbIc,aIb),aIb) )],[refute_0_30,refute_0_8]) ).
cnf(refute_0_32,plain,
( ~ member(Element,aIbIc)
| member(Element,aIb) ),
inference(resolve,[$cnf( subset(aIbIc,aIb) )],[refute_0_31,refute_0_7]) ).
cnf(refute_0_33,plain,
( ~ member(h(Set1,Set2,aIbIc),aIbIc)
| member(h(Set1,Set2,aIbIc),aIb) ),
inference(subst,[],[refute_0_32:[bind(Element,$fot(h(Set1,Set2,aIbIc)))]]) ).
cnf(refute_0_34,plain,
( intersection(Set1,Set2,aIbIc)
| member(h(Set1,Set2,aIbIc),Set1)
| member(h(Set1,Set2,aIbIc),aIb) ),
inference(resolve,[$cnf( member(h(Set1,Set2,aIbIc),aIbIc) )],[refute_0_6,refute_0_33]) ).
cnf(refute_0_35,plain,
( intersection(aIb,X_276,aIbIc)
| member(h(aIb,X_276,aIbIc),aIb) ),
inference(subst,[],[refute_0_34:[bind(Set1,$fot(aIb)),bind(Set2,$fot(X_276))]]) ).
cnf(refute_0_36,plain,
( intersection(aIb,X_276,aIbIc)
| member(h(aIb,X_276,aIbIc),b) ),
inference(resolve,[$cnf( member(h(aIb,X_276,aIbIc),aIb) )],[refute_0_35,refute_0_5]) ).
cnf(refute_0_37,plain,
( intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),b) ),
inference(subst,[],[refute_0_36:[bind(X_276,$fot(c))]]) ).
cnf(refute_0_38,plain,
( ~ intersection(b,c,bIc)
| ~ member(X_218,b)
| ~ member(X_218,c)
| member(X_218,bIc) ),
inference(subst,[],[member_of_both_is_member_of_intersection:[bind(Element,$fot(X_218)),bind(Intersection,$fot(bIc)),bind(Set1,$fot(b)),bind(Set2,$fot(c))]]) ).
cnf(refute_0_39,plain,
( ~ member(X_218,b)
| ~ member(X_218,c)
| member(X_218,bIc) ),
inference(resolve,[$cnf( intersection(b,c,bIc) )],[b_intersection_c,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ member(h(X_395,c,aIbIc),b)
| ~ member(h(X_395,c,aIbIc),c)
| member(h(X_395,c,aIbIc),bIc) ),
inference(subst,[],[refute_0_39:[bind(X_218,$fot(h(X_395,c,aIbIc)))]]) ).
cnf(refute_0_41,plain,
( ~ member(Element,aIbIc)
| ~ subset(aIbIc,c)
| member(Element,c) ),
inference(subst,[],[membership_in_subsets:[bind(Subset,$fot(aIbIc)),bind(Superset,$fot(c))]]) ).
cnf(refute_0_42,plain,
( ~ member(member_of_1_not_of_2(aIbIc,c),c)
| subset(aIbIc,c) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(aIbIc)),bind(Superset,$fot(c))]]) ).
cnf(refute_0_43,plain,
( ~ member(member_of_1_not_of_2(aIbIc,X_59),bIc)
| member(member_of_1_not_of_2(aIbIc,X_59),c) ),
inference(subst,[],[refute_0_1:[bind(X_51,$fot(member_of_1_not_of_2(aIbIc,X_59)))]]) ).
cnf(refute_0_44,plain,
( member(member_of_1_not_of_2(aIbIc,X_59),c)
| subset(aIbIc,X_59) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIbIc,X_59),bIc) )],[refute_0_22,refute_0_43]) ).
cnf(refute_0_45,plain,
( member(member_of_1_not_of_2(aIbIc,c),c)
| subset(aIbIc,c) ),
inference(subst,[],[refute_0_44:[bind(X_59,$fot(c))]]) ).
cnf(refute_0_46,plain,
subset(aIbIc,c),
inference(resolve,[$cnf( member(member_of_1_not_of_2(aIbIc,c),c) )],[refute_0_45,refute_0_42]) ).
cnf(refute_0_47,plain,
( ~ member(Element,aIbIc)
| member(Element,c) ),
inference(resolve,[$cnf( subset(aIbIc,c) )],[refute_0_46,refute_0_41]) ).
cnf(refute_0_48,plain,
( ~ member(h(X_107,X_108,aIbIc),aIbIc)
| member(h(X_107,X_108,aIbIc),c) ),
inference(subst,[],[refute_0_47:[bind(Element,$fot(h(X_107,X_108,aIbIc)))]]) ).
cnf(refute_0_49,plain,
( intersection(X_107,X_108,aIbIc)
| member(h(X_107,X_108,aIbIc),X_108)
| member(h(X_107,X_108,aIbIc),aIbIc) ),
inference(subst,[],[intersection_axiom2:[bind(Intersection,$fot(aIbIc)),bind(Set1,$fot(X_107)),bind(Set2,$fot(X_108))]]) ).
cnf(refute_0_50,plain,
( intersection(X_107,X_108,aIbIc)
| member(h(X_107,X_108,aIbIc),X_108)
| member(h(X_107,X_108,aIbIc),c) ),
inference(resolve,[$cnf( member(h(X_107,X_108,aIbIc),aIbIc) )],[refute_0_49,refute_0_48]) ).
cnf(refute_0_51,plain,
( intersection(X_395,c,aIbIc)
| member(h(X_395,c,aIbIc),c) ),
inference(subst,[],[refute_0_50:[bind(X_107,$fot(X_395)),bind(X_108,$fot(c))]]) ).
cnf(refute_0_52,plain,
( ~ member(h(X_395,c,aIbIc),b)
| intersection(X_395,c,aIbIc)
| member(h(X_395,c,aIbIc),bIc) ),
inference(resolve,[$cnf( member(h(X_395,c,aIbIc),c) )],[refute_0_51,refute_0_40]) ).
cnf(refute_0_53,plain,
( ~ member(h(aIb,c,aIbIc),b)
| intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),bIc) ),
inference(subst,[],[refute_0_52:[bind(X_395,$fot(aIb))]]) ).
cnf(refute_0_54,plain,
( intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),bIc) ),
inference(resolve,[$cnf( member(h(aIb,c,aIbIc),b) )],[refute_0_37,refute_0_53]) ).
cnf(refute_0_55,plain,
member(h(aIb,c,aIbIc),bIc),
inference(resolve,[$cnf( intersection(aIb,c,aIbIc) )],[refute_0_54,prove_aIb_intersection_c_is_aIbIc]) ).
cnf(refute_0_56,plain,
member(h(aIb,c,aIbIc),c),
inference(resolve,[$cnf( member(h(aIb,c,aIbIc),bIc) )],[refute_0_55,refute_0_2]) ).
cnf(refute_0_57,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),aIbIc)
| ~ member(h(aIb,c,aIbIc),c)
| intersection(aIb,c,aIbIc) ),
inference(subst,[],[intersection_axiom3:[bind(Intersection,$fot(aIbIc)),bind(Set1,$fot(aIb)),bind(Set2,$fot(c))]]) ).
cnf(refute_0_58,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),aIbIc)
| intersection(aIb,c,aIbIc) ),
inference(resolve,[$cnf( member(h(aIb,c,aIbIc),c) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),aIb) ),
inference(subst,[],[refute_0_32:[bind(Element,$fot(h(aIb,c,aIbIc)))]]) ).
cnf(refute_0_60,plain,
( ~ member(h(aIb,X_168,aIbIc),aIbIc)
| member(h(aIb,X_168,aIbIc),a) ),
inference(subst,[],[refute_0_11:[bind(X_35,$fot(h(aIb,X_168,aIbIc)))]]) ).
cnf(refute_0_61,plain,
( ~ intersection(a,b,aIb)
| ~ member(X_35,aIb)
| member(X_35,a) ),
inference(subst,[],[member_of_intersection_is_member_of_set1:[bind(Element,$fot(X_35)),bind(Intersection,$fot(aIb)),bind(Set1,$fot(a)),bind(Set2,$fot(b))]]) ).
cnf(refute_0_62,plain,
( ~ member(X_35,aIb)
| member(X_35,a) ),
inference(resolve,[$cnf( intersection(a,b,aIb) )],[a_intersection_b,refute_0_61]) ).
cnf(refute_0_63,plain,
( ~ member(h(aIb,X_85,X_83),aIb)
| member(h(aIb,X_85,X_83),a) ),
inference(subst,[],[refute_0_62:[bind(X_35,$fot(h(aIb,X_85,X_83)))]]) ).
cnf(refute_0_64,plain,
( intersection(aIb,X_85,X_83)
| member(h(aIb,X_85,X_83),X_83)
| member(h(aIb,X_85,X_83),aIb) ),
inference(subst,[],[intersection_axiom1:[bind(Intersection,$fot(X_83)),bind(Set1,$fot(aIb)),bind(Set2,$fot(X_85))]]) ).
cnf(refute_0_65,plain,
( intersection(aIb,X_85,X_83)
| member(h(aIb,X_85,X_83),X_83)
| member(h(aIb,X_85,X_83),a) ),
inference(resolve,[$cnf( member(h(aIb,X_85,X_83),aIb) )],[refute_0_64,refute_0_63]) ).
cnf(refute_0_66,plain,
( intersection(aIb,X_168,aIbIc)
| member(h(aIb,X_168,aIbIc),a)
| member(h(aIb,X_168,aIbIc),aIbIc) ),
inference(subst,[],[refute_0_65:[bind(X_83,$fot(aIbIc)),bind(X_85,$fot(X_168))]]) ).
cnf(refute_0_67,plain,
( intersection(aIb,X_168,aIbIc)
| member(h(aIb,X_168,aIbIc),a) ),
inference(resolve,[$cnf( member(h(aIb,X_168,aIbIc),aIbIc) )],[refute_0_66,refute_0_60]) ).
cnf(refute_0_68,plain,
( intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),a) ),
inference(subst,[],[refute_0_67:[bind(X_168,$fot(c))]]) ).
cnf(refute_0_69,plain,
( ~ intersection(a,bIc,aIbIc)
| ~ member(X_218,a)
| ~ member(X_218,bIc)
| member(X_218,aIbIc) ),
inference(subst,[],[member_of_both_is_member_of_intersection:[bind(Element,$fot(X_218)),bind(Intersection,$fot(aIbIc)),bind(Set1,$fot(a)),bind(Set2,$fot(bIc))]]) ).
cnf(refute_0_70,plain,
( ~ member(X_218,a)
| ~ member(X_218,bIc)
| member(X_218,aIbIc) ),
inference(resolve,[$cnf( intersection(a,bIc,aIbIc) )],[a_intersection_bIc,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ member(h(aIb,c,aIbIc),a)
| ~ member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(subst,[],[refute_0_70:[bind(X_218,$fot(h(aIb,c,aIbIc)))]]) ).
cnf(refute_0_72,plain,
( ~ member(h(aIb,c,aIbIc),a)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolve,[$cnf( member(h(aIb,c,aIbIc),bIc) )],[refute_0_55,refute_0_71]) ).
cnf(refute_0_73,plain,
( intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolve,[$cnf( member(h(aIb,c,aIbIc),a) )],[refute_0_68,refute_0_72]) ).
cnf(refute_0_74,plain,
member(h(aIb,c,aIbIc),aIbIc),
inference(resolve,[$cnf( intersection(aIb,c,aIbIc) )],[refute_0_73,prove_aIb_intersection_c_is_aIbIc]) ).
cnf(refute_0_75,plain,
member(h(aIb,c,aIbIc),aIb),
inference(resolve,[$cnf( member(h(aIb,c,aIbIc),aIbIc) )],[refute_0_74,refute_0_59]) ).
cnf(refute_0_76,plain,
( ~ member(h(aIb,c,aIbIc),aIbIc)
| intersection(aIb,c,aIbIc) ),
inference(resolve,[$cnf( member(h(aIb,c,aIbIc),aIb) )],[refute_0_75,refute_0_58]) ).
cnf(refute_0_77,plain,
intersection(aIb,c,aIbIc),
inference(resolve,[$cnf( member(h(aIb,c,aIbIc),aIbIc) )],[refute_0_74,refute_0_76]) ).
cnf(refute_0_78,plain,
$false,
inference(resolve,[$cnf( intersection(aIb,c,aIbIc) )],[refute_0_77,prove_aIb_intersection_c_is_aIbIc]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n018.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 12:41:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.69
% 0.48/0.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.48/0.70
%------------------------------------------------------------------------------