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Proof that closure pair(s, f) is closed under f

----> UNIT CONFLICT at   7.47 sec ----> 919 [binary,917.1,19.1] $F.

Length of proof is 12.  Level of proof is 6.

Proof



1 [reference] k(x) y=x.
2 [reference] p1 pair(x,y)=x.
3 [reference] p2 pair(x,y)=y.
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).
16 [reference] x=y|eq pair(x,y) =p2.
19 [reference] p2!=p1.
45 [reference] closedunder pair(xs,xf)=p2|xs x !=p1|xs (xf x) =p1.
46 [reference] closedunder pair(xs,xf)=p1|xs notclosed(xs,xf) =p1.
47 [reference] closedunder pair(xs,xf)=p1|xs (xf notclosed(xs,xf)) !=p1.
48 [reference] charq eq=p1.
51 [reference] abst k(x) k(y)=k(x y).
53 [reference] pair(x1,y1)!=pair(x2,y2)|y1=y2.
66 [reference] closedunder pair(kintersection x y,z)=p1|x notinint(x,z notclosed(kintersection x y,z)) =p1.
67 [reference] closedunder pair(kintersection x y,z)=p1|closedunder pair(notinint(x,z notclosed(kintersection x y,z)),z) =p2.
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).
74 [assumption to refute] p.
75 [assumption to refute] -p|closedunder pair(closure pair(bads,badf),badf) !=p1.
76 [ur,75,74,demod,72,6,6,1,6,1,4,1,4,6,1,4,51,2,1,6,1,4,1,51,3,4,2,3] closedunder pair(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf)!=p1.
78,77 [ur,76,67] closedunder pair(notinint(abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf)))),badf notclosed(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf)),badf)=p2.
79 [ur,76,66,demod,6,1,4,1,4,6,1,4,1,4,5,6,1,4,4,5,1,78] eq pair(pair(p1,p1),pair(subset pair(bads,notinint(abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf)))),badf notclosed(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf))),p2))=p1.
89 [ur,76,47] kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf) (badf notclosed(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf))!=p1.
90 [ur,76,46] kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf) notclosed(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf)=p1.
119 [para_into,76.1.2,48.1.2] closedunder pair(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf)!=charq eq.
202 [ur,119,53] pair(x,closedunder pair(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf))!=pair(y,charq eq).
256 [para_into,79.1.1.2.1.2,48.1.2] eq pair(pair(p1,charq eq),pair(subset pair(bads,notinint(abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf)))),badf notclosed(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf))),p2))=p1.
671,670 [ur,90,45,89] closedunder pair(kintersection (abst k(eq) pair(k(pair(p1,p1)),pair(abst k(subset) pair(k(bads),pair(p1,p2)),abst k(closedunder) pair(pair(p1,p2),k(badf))))) pair(bads,badf),badf)=p2.
707 [back_demod,202,demod,671,flip.1] pair(x,charq eq)!=pair(y,p2).
916,915 [ur,707,16] eq pair(pair(x,charq eq),pair(y,p2))=p2.
917 [back_demod,256,demod,916] p2=p1.
919 [binary,917.1,19.1] $F.



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