TPTP Problem File: SET143+3.p
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- Solve Problem
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% File : SET143+3 : TPTP v8.2.0. Released v2.2.0.
% Domain : Set Theory
% Problem : Associativity of intersection
% Version : [Try90] axioms : Reduced > Incomplete.
% English : The intersection of (the intersection of X and Y) and Z is the
% intersection of X and (the intersection of Y and Z).
% Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% Source : [ILF]
% Names : BOOLE (67) [TS89]
% Status : Theorem
% Rating : 0.39 v8.2.0, 0.33 v7.5.0, 0.44 v7.4.0, 0.27 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.22 v7.0.0, 0.27 v6.4.0, 0.23 v6.3.0, 0.29 v6.2.0, 0.40 v6.1.0, 0.57 v5.5.0, 0.63 v5.4.0, 0.57 v5.3.0, 0.63 v5.2.0, 0.45 v5.1.0, 0.48 v5.0.0, 0.50 v4.1.0, 0.52 v4.0.0, 0.50 v3.5.0, 0.53 v3.3.0, 0.50 v3.2.0, 0.55 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.62 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 15 ( 4 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 8 ( 0 ~; 0 |; 2 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
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%---- line(boole - df(3),1833060)
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
%---- line(boole - df(8),1833103)
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
%---- property(commutativity,op(intersection,2,function))
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
%---- line(tarski - df(3),1832749)
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
%---- property(reflexivity,op(subset,2,predicate))
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B) ).
%---- line(hidden - axiom108,1832615)
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ) ).
%---- line(boole - th(67),1833740)
fof(prove_associativity_of_intersection,conjecture,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)) ).
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