/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
 intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
 u'1'1(intersect'ii'out()) -> intersect'ii'out()
 intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
 u'2'1(intersect'ii'out()) -> intersect'ii'out()
 reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
 u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
 u'3'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
 u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
 u'4'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
 u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
 u'5'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
 u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
 u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
 u'6'2(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) -> u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
 u'7'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
 u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
 u'8'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
 u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
 u'9'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
 u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
 u'10'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
 u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
 u'11'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
 u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
 u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
 u'12'2(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
 u'13'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
 u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
 u'14'1(reduce'ii'out()) -> reduce'ii'out()
 reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
 u'15'1(intersect'ii'out()) -> reduce'ii'out()
 tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
 u'16'1(reduce'ii'out()) -> tautology'i'out()

Proof:
 DP Processor:
  DPs:
   intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys)
   intersect'ii'in#(Xs,cons(X0,Ys)) -> u'1'1#(intersect'ii'in(Xs,Ys))
   intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys)
   intersect'ii'in#(cons(X0,Xs),Ys) -> u'2'1#(intersect'ii'in(Xs,Ys))
   reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
   reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
   reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
   u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
   reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
   reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
   reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
   u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
   reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
   reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
   reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
   u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
   reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
   reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
   u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
   u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF)
   u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2#(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
   reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
   reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
   u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
   reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
   reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
   reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
   u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
   reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
   reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
   reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
   u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
   reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
   reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
   reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
   u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
   reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
   reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
   reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
   u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
   reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
   reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
   u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
   u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF)
   u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2#(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
   reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
   reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
   u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
   reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
   reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
   reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
   u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
   reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
   reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
   tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil()))
   tautology'i'in#(F) -> u'16'1#(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
  TRS:
   intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
   intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
   u'1'1(intersect'ii'out()) -> intersect'ii'out()
   intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
   u'2'1(intersect'ii'out()) -> intersect'ii'out()
   reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
   u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
   u'3'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
   u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
   u'4'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
   u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
   u'5'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
   u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
   u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
   u'6'2(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
   u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
   u'7'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
   u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
   u'8'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
   u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
   u'9'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
   u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
   u'10'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
   u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
   u'11'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
   u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
   u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
   u'12'2(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
   u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
   u'13'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
   u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
   u'14'1(reduce'ii'out()) -> reduce'ii'out()
   reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
   u'15'1(intersect'ii'out()) -> reduce'ii'out()
   tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
   u'16'1(reduce'ii'out()) -> tautology'i'out()
  TDG Processor:
   DPs:
    intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys)
    intersect'ii'in#(Xs,cons(X0,Ys)) -> u'1'1#(intersect'ii'in(Xs,Ys))
    intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys)
    intersect'ii'in#(cons(X0,Xs),Ys) -> u'2'1#(intersect'ii'in(Xs,Ys))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2#(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2#(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil()))
    tautology'i'in#(F) -> u'16'1#(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
   TRS:
    intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
    intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
    u'1'1(intersect'ii'out()) -> intersect'ii'out()
    intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
    u'2'1(intersect'ii'out()) -> intersect'ii'out()
    reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    u'3'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    u'4'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    u'5'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
    u'6'2(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    u'7'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    u'8'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    u'9'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    u'10'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    u'11'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
    u'12'2(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    u'13'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    u'14'1(reduce'ii'out()) -> reduce'ii'out()
    reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
    u'15'1(intersect'ii'out()) -> reduce'ii'out()
    tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
    u'16'1(reduce'ii'out()) -> tautology'i'out()
   graph:
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    tautology'i'in#(F) -> reduce'ii'in#(sequent(nil(),cons(F,nil())),sequent(nil(),nil())) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
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    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
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    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
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    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
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    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2) ->
    intersect'ii'in#(cons(X0,Xs),Ys) -> u'2'1#(intersect'ii'in(Xs,Ys))
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2) ->
    intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys)
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2) ->
    intersect'ii'in#(Xs,cons(X0,Ys)) -> u'1'1#(intersect'ii'in(Xs,Ys))
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2) ->
    intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF) ->
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2#(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF) ->
    u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF) ->
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2#(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF) ->
    u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1#(intersect'ii'in(F1,F2))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),nil()),sequent(F1,F2)) -> intersect'ii'in#(F1,F2)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    u'14'1#(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
    u'13'1#(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
    u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    u'11'1#(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    u'10'1#(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
    reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    u'9'1#(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    u'8'1#(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
    u'7'1#(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
    u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    u'5'1#(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    u'4'1#(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    u'3'1#(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
    reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
    reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
    reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
    reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
    intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys) ->
    intersect'ii'in#(cons(X0,Xs),Ys) -> u'2'1#(intersect'ii'in(Xs,Ys))
    intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys) ->
    intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys)
    intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys) ->
    intersect'ii'in#(Xs,cons(X0,Ys)) -> u'1'1#(intersect'ii'in(Xs,Ys))
    intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys) ->
    intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys)
    intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys) ->
    intersect'ii'in#(cons(X0,Xs),Ys) -> u'2'1#(intersect'ii'in(Xs,Ys))
    intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys) ->
    intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys)
    intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys) ->
    intersect'ii'in#(Xs,cons(X0,Ys)) -> u'1'1#(intersect'ii'in(Xs,Ys))
    intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys) ->
    intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys)
   SCC Processor:
    #sccs: 2
    #rules: 18
    #arcs: 406/1296
    DPs:
     reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
     reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
     reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
     reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
     reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
     reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
     reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
     reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
     reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
     u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
     u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF)
     reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
     reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
     reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
     reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
     reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
     reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
     reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
     reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
     reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
     reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
     reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
     reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
     u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
     u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF)
     reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
     reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
     reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
    TRS:
     intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
     intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
     u'1'1(intersect'ii'out()) -> intersect'ii'out()
     intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
     u'2'1(intersect'ii'out()) -> intersect'ii'out()
     reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
     u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
     u'3'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
     u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
     u'4'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
     u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
     u'5'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
     u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
     u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
     u'6'2(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
     u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
     u'7'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
     u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
     u'8'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
     u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
     u'9'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
     u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
     u'10'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
     u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
     u'11'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
     u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
     u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
     u'12'2(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
     u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
     u'13'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
     u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
     u'14'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
     u'15'1(intersect'ii'out()) -> reduce'ii'out()
     tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
     u'16'1(reduce'ii'out()) -> tautology'i'out()
    EDG Processor:
     DPs:
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
     TRS:
      intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
      intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
      u'1'1(intersect'ii'out()) -> intersect'ii'out()
      intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
      u'2'1(intersect'ii'out()) -> intersect'ii'out()
      reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
      u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
      u'3'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
      u'4'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
      u'5'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
      u'6'2(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
      u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
      u'7'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
      u'8'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
      u'9'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
      u'10'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
      u'11'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
      u'12'2(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
      u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
      u'13'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
      u'14'1(reduce'ii'out()) -> reduce'ii'out()
      reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
      u'15'1(intersect'ii'out()) -> reduce'ii'out()
      tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
      u'16'1(reduce'ii'out()) -> tautology'i'out()
     graph:
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF) ->
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))) ->
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)) ->
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF) ->
      u'6'1#(reduce'ii'out(),F2,Fs,Gs,NF) -> reduce'ii'in#(sequent(cons(F2,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      ->
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF) ->
      u'12'1#(reduce'ii'out(),Fs,G2,Gs,NF) -> reduce'ii'in#(sequent(Fs,cons(G2,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF) ->
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF) ->
      reduce'ii'in#(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
      u'12'1#(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      ->
      reduce'ii'in#(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> reduce'ii'in#(sequent(cons(G1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(if(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(iff(A,B),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,cons(F2,Fs)),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      reduce'ii'in#(sequent(cons(F1,Fs),Gs),NF)
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
      u'6'1#(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(x'2d(F1),Fs),Gs),NF) -> reduce'ii'in#(sequent(Fs,cons(F1,Gs)),NF)
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
      reduce'ii'in#(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
      reduce'ii'in#(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))
      reduce'ii'in#(sequent(Fs,cons(if(A,B),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
      reduce'ii'in#(sequent(Fs,cons(G1,cons(G2,Gs))),NF)
     Subterm Criterion Processor:
      simple projection:
       pi(cons) = [0,0,1]
       pi(if) = [0,0,0,1,1,1]
       pi(sequent) = [0,1]
       pi(x'2d) = [0,0]
       pi(x'2b) = [0,1,1]
       pi(x'2a) = [0,0,1,1]
       pi(u'13'1) = [0,0,0]
       pi(u'14'1) = [0,0,0]
       pi(reduce'ii'in#) = 0
       pi(u'6'1#) = [1,1,1,2,3]
       pi(u'12'1#) = [1,2,2,2,3]
      problem:
       DPs:
        
       TRS:
        intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
        intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
        u'1'1(intersect'ii'out()) -> intersect'ii'out()
        intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
        u'2'1(intersect'ii'out()) -> intersect'ii'out()
        reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
        u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
        u'3'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
        u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
        u'4'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
        u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
        u'5'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
        u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
        u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
        u'6'2(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
        u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
        u'7'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
        u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
        u'8'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
        u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
        u'9'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
        u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
        u'10'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
        u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
        u'11'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
        u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
        u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
        u'12'2(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
        u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
        u'13'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
        u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
        u'14'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
        u'15'1(intersect'ii'out()) -> reduce'ii'out()
        tautology'i'in(F) ->
        u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
        u'16'1(reduce'ii'out()) -> tautology'i'out()
      Qed
    
    DPs:
     intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys)
     intersect'ii'in#(cons(X0,Xs),Ys) -> intersect'ii'in#(Xs,Ys)
    TRS:
     intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
     intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
     u'1'1(intersect'ii'out()) -> intersect'ii'out()
     intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
     u'2'1(intersect'ii'out()) -> intersect'ii'out()
     reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
     u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
     u'3'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
     u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
     u'4'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
     u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
     u'5'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
     u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
     u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
     u'6'2(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
     u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
     u'7'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
     u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
     u'8'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
     u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
     u'9'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
     u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
     u'10'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
     u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
     u'11'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
     u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
     u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
     u'12'2(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
     u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
     u'13'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
     u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
     u'14'1(reduce'ii'out()) -> reduce'ii'out()
     reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
     u'15'1(intersect'ii'out()) -> reduce'ii'out()
     tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
     u'16'1(reduce'ii'out()) -> tautology'i'out()
    Subterm Criterion Processor:
     simple projection:
      pi(intersect'ii'in#) = 0
     problem:
      DPs:
       intersect'ii'in#(Xs,cons(X0,Ys)) -> intersect'ii'in#(Xs,Ys)
      TRS:
       intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
       intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
       u'1'1(intersect'ii'out()) -> intersect'ii'out()
       intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
       u'2'1(intersect'ii'out()) -> intersect'ii'out()
       reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
       u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
       u'3'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
       u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
       u'4'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
       u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
       u'5'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
       u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
       u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
       u'6'2(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
       u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
       u'7'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
       u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
       u'8'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
       u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
       u'9'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
       u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
       u'10'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
       u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
       u'11'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
       u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
       u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
       u'12'2(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
       u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
       u'13'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
       u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
       u'14'1(reduce'ii'out()) -> reduce'ii'out()
       reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
       u'15'1(intersect'ii'out()) -> reduce'ii'out()
       tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
       u'16'1(reduce'ii'out()) -> tautology'i'out()
     Subterm Criterion Processor:
      simple projection:
       pi(intersect'ii'in#) = 1
      problem:
       DPs:
        
       TRS:
        intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out()
        intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys))
        u'1'1(intersect'ii'out()) -> intersect'ii'out()
        intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys))
        u'2'1(intersect'ii'out()) -> intersect'ii'out()
        reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) ->
        u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF))
        u'3'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) ->
        u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF))
        u'4'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) ->
        u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF))
        u'5'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) ->
        u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF)
        u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF))
        u'6'2(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) ->
        u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF))
        u'7'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) ->
        u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF))
        u'8'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) ->
        u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF))
        u'9'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) ->
        u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right)))
        u'10'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) ->
        u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF))
        u'11'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) ->
        u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF)
        u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF))
        u'12'2(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) ->
        u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF))
        u'13'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) ->
        u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right))))
        u'14'1(reduce'ii'out()) -> reduce'ii'out()
        reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2))
        u'15'1(intersect'ii'out()) -> reduce'ii'out()
        tautology'i'in(F) ->
        u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil())))
        u'16'1(reduce'ii'out()) -> tautology'i'out()
      Qed