Proof that closure x is a characteristic function

----> UNIT CONFLICT at 114.06 sec ----> 3075 [binary,3074.1,8.1] $F.

Length of proof is 5.  Level of proof is 3.

Proof

1 [reference] k(x) y=x.
4 [reference] pair(x,y) z=pair(x z,y z).
5 [reference] pair(p1 x,p2 x)=x.
6 [reference] abst x y z=x k(z) (y z).
8 [reference] x=x.
51 [reference] abst k(x) k(y)=k(x y).
54 [reference] kintersection xf y x=p2|xf z !=p1|z x =p1.
56 [reference] kintersection xf y x=p1|xf notinint(xf,x) =p1.
57 [reference] kintersection xf y x=p1|notinint(xf,x) x !=p1.
72 [reference] closure=abst (abst k(kintersection) (abst k(abst k(eq)) pair(k(k(pair(p1,p1))),pair(abst k(abst k(subset)) pair(abst k(p1),k(pair(p1,p2))),abst k(abst k(closedunder)) pair(k(pair(p1,p2)),abst k(p2)))))) pair(p1,p2).
76 [assumption to refute] p.
77 [assumption to refute] -p|closure bad1 bad2 !=p1.
78 [assumption to refute] -p|closure bad1 bad2 !=p2.
79 [ur,77,76,demod,72,6,6,1,6,1,4,1,4,6,1,4,51,1,6,1,4,1,51,4,5] kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset
) pair(k(p1 bad1),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(p2 bad1))))) bad1 bad2!=p1.
92 [ur,78,76,demod,72,6,6,1,6,1,4,1,4,6,1,4,51,1,6,1,4,1,51,4,5] kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset
) pair(k(p1 bad1),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(p2 bad1))))) bad1 bad2!=p2.
103 [ur,79,57] notinint(abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(p1 bad1),pair(p1,p2)),abst k(closedunder) pair(
pair(p1,p2),k(p2 bad1)))),bad2) bad2!=p1.
105,104 [ur,79,56,demod,6,1,4,1,4,6,1,4,1,4,5,6,1,4,4,5,1] eq pair(pair(p1,p1),pair(subset pair(p1 bad1,notinint(abst k(eq) pair(
k(pair(p1,p1)),pair(abst k(subset) pair(k(p1 bad1),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(p2 bad1)))),bad2)),closedu
nder pair(notinint(abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(p1 bad1),pair(p1,p2)),abst k(closedunder) pair(pair(
p1,p2),k(p2 bad1)))),bad2),p2 bad1)))=p1.
3074 [ur,103,54,92,demod,6,1,4,1,4,6,1,4,1,4,5,6,1,4,4,5,1,105] p1!=p1.
3075 [binary,3074.1,8.1] $F.