F(0 U ((0 U c) & (b <=> 0)))
!(G(b | (b ^ c)) <=> Fa)
G(1) | (a ^ (F(0) R G(1)))
(c <=> G(X(0) => a)) U Fb
(Fb & !a) R !(0 U 0)
(a <=> 0) => (1 U (F(1) => b))
b <=> (a => (0 R F(a => 0)))
G(Xc R F(0 => FGa))
F(((0 R 1) ^ (0 => c)) <=> 1)
!F(a U ((b U a) => !1))
Fb & (c | G(0))
(G(1) ^ Xa) U G(a | b)
!c ^ ((c <=> c) | (1 <=> 0))
(0 | (a ^ Fc)) => 0
X((a <=> X(0)) ^ (a <=> Fb))
GXF(!!b & !!0)
F!(Xa | ((1 ^ 0) <=> 1))
(c R b) | (!b U (c & 1))
(b U X(0)) & ((b <=> 0) <=> 1)
X(1) R F(Gb R b)
F(a ^ (Fa ^ 0)) ^ Xb
(!0 U Xa) => (a ^ !a)
XGXFX(Fb => !b)
G(b | ((b U Ga) ^ X(0)))
!((b ^ X(1)) R !c)
(b U a) | ((a | 1) ^ Fa)
1 U X(!a | (b <=> X(1)))
(c ^ F(Fc => 1)) R !a
((a ^ 0) U c) ^ (Xb => 0)
(X(0) => G!!a) <=> Gb
X(1 & Ga & G(b ^ 0))
F(a ^ (c => (b R !Ga)))
!X((c => (b | c)) R !0)
0 & (G(1) => G(a | X(1)))
(GXb => G(1)) U GGa
F!Gc R (b | FFa)
b => ((b <=> !a) R FGc)
(a U ((c U b) <=> 0)) <=> Fa
G(X(1) => ((1 | !c) ^ 0))
FG(1 & FG!(1 ^ 0))
!((c => b) | (!0 ^ F(0)))
(b <=> c) & (1 U (a ^ !a))
(0 => 0) U F(b <=> (c & 1))
c ^ (a & (1 | (F(0) ^ 1)))
X(!F(0) => Fa) => Ga
X((b U c) => (a & (0 => a)))
GF!X!(!a R Xa)
F(Gc & (a | b | !1))
((b | c) ^ 1) | (c => !b)
(1 R a) & X((b & c) R c)
((0 R Ga) | (1 => 0)) R a
(1 U 1) ^ (1 | (c ^ Ga))
(1 => Fa) <=> (c => (a | c))
XFG(XX(1 R 1) => c)
G(((b R c) <=> (a | b)) U c)
!((b ^ (a | c)) => (1 => 0))
!b | ((Gb & !1) <=> 1)
(a & (1 | F!Xa)) U b
(FX(1) R 1) R (1 | Fb)
XF(0) ^ (F(1) R (b & 1))
a <=> (X(0) <=> (a <=> (c U 0)))
X(0 U G(1 & XXG(0)))
F((c & (a <=> (a ^ 1))) <=> 0)
!F(X(1) ^ Xa)
Fc & F(0) & (c => Fc)
(1 & FF(0)) U FFX(1)
FFb R (Xb & (c <=> 0))
(!b U (0 & (a ^ a))) => a
XG(0) <=> (F(1) => (1 R 1))
G(b <=> (G(1) | GXG(1)))
F!((b R b) U (!c U c))
G(1) | (b U (G(1) & !1))
G(b <=> !1) & (!c => b)
Xa U !(G(1) & (c U b))
X((b R Gc) R Fc) ^ 0
(Fc | Ga) => (X(1) => 0)
XXGG(b R X(a ^ 1))
G!(Gc | G(a <=> Ga))
F(X(1 & !b) R FG(0))
(0 & F(0)) | (Xa <=> G(1))
0 & FF(XF!c ^ 1)
X(Xc & F!b) R Xb
(G!0 R b) ^ (c R Ga)
((1 ^ 1) <=> (b ^ 1)) <=> Xa
X(b | 1 | (b => c))
G(F(1 U (a <=> Gc)) R b)
!X(b ^ X(a & FFa))
1 | X(GFa <=> (a ^ 0))
((b <=> G(1)) => Fa) U !1
!!Xc R (1 U (0 => 0))
Gc => (X(c U 1) ^ Ga)
(G(a U b) <=> X(0)) <=> Fb
X(((b R a) R (1 R b)) ^ 1)
FX(1 U (G(0 <=> 0) => 0))
!((a ^ !c) | (Gb => c))
(G(0) U FXa) & G!a
X(c <=> 1) U (Fa | !b)
c R (a R ((a & b) <=> G(0)))
(!1 | X(1 U c)) => Fb
G(c | 1) <=> (a R !!c)
GG(c | d | (!d <=> 0))
F(((b => 0) => a) | (c & e))
(e <=> F(0)) | XF(b U b)
(a | e) & F(!c & !e)
0 U (Gc & XGG!c)
(c ^ d) ^ (c | (Ff U 0))
(e ^ Gc) => (XGb <=> 0)
XFF(Xb R (1 & Gb))
G(!a & G(Xd => Xa))
!((c ^ e) ^ (f <=> XF(1)))
X!X(a => 0) | !Ge
d & G((c | !f) U Fe)
!X(b & G(1)) R (f U f)
(X(1) => G!d) ^ (b U 1)
X(Ff | (d <=> !0)) <=> 0
X(a U (Ge <=> (Gd ^ 0)))
G(F(!f => Xe) => Xf)
!G((d <=> d) => G!Gc)
e | GGF(a R !Ff)
(0 R (d => 1)) U (b | !d)
(c U 1) R ((a | e) R !a)
c => (F(f | X(1)) <=> Xd)
FG(1 & !c) <=> GGa
X(a <=> X(a ^ (e U Xf)))
FF((d ^ F(1)) R FGc)
!((1 U 0) & !F(d U c))
F(e => 1) & X!(b => d)
!e U (b & (c ^ GGb))
c ^ !(d <=> (d | GFf))
(X(1) ^ GGf) => XXd
(1 U e) <=> F((a & e) <=> 1)
G!(a & (a ^ !F!b))
F((Fc ^ 1) U X!Fc)
X(c U Ga) | (1 & !f)
F(1) & !G(e | XXe)
(!G(0) | X!d) U Xf
!G(a ^ d) ^ (1 => Xa)
(c => c) => G((c => 0) R d)
X(0 | F(!f | (b => f)))
G((GXa U Xa) R G(1))
!(FFG(0) <=> !(c | e))
1 | G(!(f => !a) => d)
X(1) & (b | c) & !Gf
((d | 1) ^ 0) R (b R Xd)
Gc ^ ((a & e & 1) <=> 1)
c <=> (c & ((c R e) => X(0)))
X((Fd & !FXd) ^ 0)
FX(Gc R (Gd & G(0)))
!!(Xa <=> (Gf <=> Xe))
Xb | X!a | F!0
(1 | Ff) U (0 & F!c)
Fd R (d ^ (Gd U Fb))
(FF!Gc ^ 0) => Fe
(X(1) => X(0)) <=> !FX(0)
XG((c <=> !e) U (f U 1))
F((b U G(0)) | !(a U e))
!((b ^ b) R (XGd => f))
!(c | d | 0) & (1 => 0)
e U ((b => 1) U (Gf R 1))
G(1) ^ (1 R (a => GGb))
FFFe => GX(0 R 1)
(d | (!a <=> !0)) <=> Gc
G(Fe & (e | (c & !1)))
F((Fe U 1) ^ (f | Fb))
(a <=> e) | GG(f R Xd)
f & (Gc | Gf | !0)
((e & 0) ^ Xd) R (1 R d)
(Fb <=> G(0)) ^ (Ge => d)
a => F!(f ^ (a | Gf))
X(d & X(!Gc <=> Fc))
G(!(1 & Fe) => !Gf)
!G((e ^ X(1)) <=> GXe)
f | (X(Gd R !d) => 1)
a & f & (1 => !XXe)
F!d R (c ^ (e & Xc))
XX((f <=> 0) => Fb) ^ 0
!0 <=> (F!Xa => X(0))
X((!Gb <=> Gf) => Fa)
FF(!(c & Gf) => Ff)
!(Fa & G(Xd => Fe))
(Xf ^ Gf) | !(d R f)
(d U 1) U (a U (f <=> Gb))
(c <=> (F(0) & GFd)) R d
XFX(b <=> f) => G!b
(b | Xf) <=> (Ff | Xa)
GF(X(c <=> (f R 1)) R e)
F((0 | Xa) U (1 => X(0)))
!(Gc => (Xc | FFe))
Fd & (G(1) | X(d <=> e))
X((d & Xb) ^ G(1)) U f
(Ga => Xa) ^ (F(0) <=> 0)
X!0 => F(b U !Fb)
f <=> (Gb & XG(d U a))
G((b ^ (d U e)) U (a R b))
F(G!1 <=> FX(1 R 1))
!1 | F(Xe R (e & 0))
Xb & F(d U (0 R Xa))
(e ^ (a U d)) R (b ^ F(0))
X!G(c ^ e) ^ (b & d)
G(Fa U !XFa) => d
F(c U ((Gb <=> X(1)) & (0 U c)))
!(G(Fb | F!Xb) <=> Fa)
Xc | (Gc ^ (Xc ^ (c => b)))
(G(Gc => !c) <=> !c) U Fb
(c <=> !GFb) R !(G(1) U 0)
X!0 => (F(0) U (GX(1) => b))
b <=> (a => (a R F(F!0 => 0)))
G((a => b) R F(X(1) => FGa))
F((F(0 | 1) ^ (G(0) => c)) <=> 0)
!F(b U ((Fa U Ga) => !1))
(c ^ (0 => X(0))) & (0 => c)
(a <=> (G(0) => 1)) U G(b | !a)
!F(0) ^ (XXc | (a <=> G(1)))
(((a <=> 1) ^ 1) | (F(1) R 0)) => 0
X((Fb <=> (a U a)) ^ G!!c)
GXF((c U 0) & !F(0 R a))
F!(((X(0) ^ 1) <=> 1) | F!c)
(c R b) | (!c U (a & (b => 1)))
(a U (a | b)) & ((G(0) <=> 0) <=> 1)
X(0) R F((1 => c) R (0 & !b))
Xb ^ F((XGb U b) ^ Fb)
(a <=> !(c R b)) => (Fc ^ Fa)
XGXFX(GG(1) => !!b)
G(c | ((0 U (c R a)) ^ GF(1)))
!((Xc ^ (Fc | !0)) R !c)
(X!c ^ (0 U c)) | XX!b
b U X(Ga | (G(0) <=> (a & c)))
!F(1 => Xb) R !Fb
((c => 0) U b) ^ ((a ^ Xc) U c)
Fb <=> ((c R b) => G!!Fc)
X(X(0) & G(b ^ 0) & (a <=> 0))
F(a ^ (1 => (b R !(c => !b))))
!X((!1 => (b | G(1))) R !0)
0 & (Xa => G(0 | (a & G(1))))
(X(a ^ c) => (b R c)) U GGa
!(0 U X(1)) R (a | FX!b)
F(0) => ((b <=> !Fa) R FGc)
(a U ((!1 U b) <=> Ga)) <=> Fa
G(X(1) => (a ^ (1 | Xb)))
FG(0 & FG!(b ^ (b | 1)))
!((1 => Fa) | ((a <=> 1) ^ !0))
(Xb U (a ^ !a)) & (b <=> !1)
(1 => X(0)) U F(b <=> (1 & F(0)))
b ^ (a & (0 | (F(1) ^ (1 <=> 1))))
(X!X(b ^ 0) <=> 0) => (a ^ c)
X(FF(1) => (0 & ((b R c) => a)))
GF!X!(GXc R a)
F(Gc & (!X(1) | (F(0) R b)))
(1 => !!a) | ((c | Fa) ^ 1)
(c R c) & X((c & FF(0)) R c)
((0 => G(1)) | X(1 U !0)) R a
!((a ^ 0) ^ Xa) ^ (X(1) U 1)
X(a & b) <=> (b => (a | (a <=> c)))
XFG(XX(X(1) R X(1)) => c)
G(((b <=> Xb) <=> (c | Fa)) U c)
!(((1 | (a <=> b)) ^ 0) => (1 => 0))
(b ^ 1) | ((Ga & GXa) <=> 1)
(c & (Xa | (!a & !c))) U b
((0 & G(0)) R Xc) R (1 | Fb)
(b R !b) ^ (Xb R (1 & !b))
b <=> (X(0) <=> ((Fa => c) <=> Fc))
X(F(0) U G(1 & XX(a R 0)))
F(G(1) <=> F(a <=> (a ^ (b & 0))))
!F(F(1) ^ (c & Fc & Xb))
F(0) & (b <=> 1) & (!b <=> Gc)
(b & X(b ^ c)) U FF(0 U 1)
(1 R 0) R ((0 U b) & (b U Xa))
((c => 1) U (b & (c ^ !b))) => a
(X(b | !c) => 1) <=> X(0 => b)
G((G(1) | GX(b ^ G(0))) <=> 0)
F!((!0 R b) U (G!1 U c))
(a => (a & Xb)) | (c => 0)
F(c => F(1)) & G(b <=> FXb)
Xb U !(G(1) & ((a <=> 1) U b))
((b ^ 0) U ((b <=> c) <=> 0)) ^ Gc
XX(a & !b) => ((0 | 1) => 0)
XXGG(Ga R X(b ^ Xa))
G!((b R 1) | (G(0 => c) ^ 1))
F(X(1 & G!F(1)) R FG(0))
((c & 1) <=> G(1)) | (Fc R Xb)
Gc & FF(XF!F(1) ^ 1)
X(Xc & FF(a <=> c)) R Xb
(!0 R (a => c)) ^ (0 R (b ^ 0))
((Gc ^ 1) <=> (1 ^ 1)) <=> (c ^ c)
X(b | 1 | Fc | (!c => c))
G((X(0) U (G(0) <=> Fc)) R Fa)
!X(b ^ X(Fb & FX!b))
c | X((b => Xa) <=> (a ^ Xb))
X!!((1 R b) <=> 1) U !Xc
(F(0) & X(1)) R (Xa U (0 => 0))
Fc => (Ga ^ X(Gc U Xc))
Fb <=> (G(!c U !a) <=> X(0))
X(a ^ ((b ^ F(1)) R (0 R Gc)))
FX(!c U (G(X(1) <=> 0) => 0))
!(!c | X(0) | (Fb ^ !c))
GFFc & (b <=> (Gb U !0))
(1 & !b) U ((a <=> b) | XFb)
c R (b R ((b & (c => a)) <=> G(0)))
(!(b | 0) U FX(1)) => (a => c)
G(1 | !0) <=> (a R !FF(1))
GG((!d <=> X(1)) | X(0 U c))
F((c & e) | ((X(1) => Xb) => a))
(e <=> F(0)) | XF(F!f U b)
F(Gf & !Ga) & (a | Ga)
f U (XGG!!d & GF(0))
(c ^ d) ^ (c | (f U Xd))
(Fa => Gd) => (a <=> X(c R e))
XFF((c | 1) R (1 & (b R f)))
G(!a & G((b => 0) => (d & f)))
!(FXX(c & 0) ^ (c ^ Fa))
X!X(d => (e U a)) | G!e
d & G((e => (e ^ f)) U (a <=> f))
!X(b & (1 U c)) R (f U F(1))
((b | 1) => G!d) ^ FXFf
d <=> X(Gd | (G(f U c) <=> 0))
X(d U (Xb <=> (Xb ^ (a => e))))
G((e ^ F(Xe => d)) => (c & 0))
!G(XG(0) => G!(d R Fc))
!0 | GGF(!b R !Ff)
F(X(0) => Xd) U (d | FFc)
F(d | 1) R ((e | Fe) R !a)
e => (F(G(1) | (d & 1)) <=> Gc)
GGa <=> FG(Xd & XFa)
X(a <=> X(a ^ (F(1) U (e | 0))))
FF((Fd R F(1)) R F(d ^ 0))
!((Xe U 1) & !F(Fe U c))
(c => F(a ^ b)) & F(a => Xe)
(c ^ 1) U (b & (GGb ^ Ga))
c ^ !(e <=> (c | GX(d => d)))
(Ff & (b R Xc)) => X(d | f)
F((a & !0) <=> 1) <=> (X(1) U e)
G!(!d & (F(d ^ e) U !a))
F(((c <=> e) ^ Xd) U X!Fc)
G(e <=> Xd) | X(f U (e => c))
Xf & !G(0 | !c | F(1))
(XGGa | (Gf U d)) U Xf
(b => (b | f)) ^ F(!Fa ^ 1)
FFf => G(((c <=> c) => 0) R d)
X(0 | F((b => G(1)) | !!0))
G((c R G(d & !0)) R (e ^ 0))
!(F(Fc U d) <=> !(b | !d))
f | G(!(X(1) => !Fd) => d)
X(1) & (F(0) => c) & !(1 R 1)
(1 & Gb) R (Fd R Xd)
((a & 1 & !0) <=> 1) ^ (0 => f)
c <=> (c & (F(d <=> f) => (b | e)))
X(((f R 0) & !F(c & d)) ^ 0)
FX(G!e R (G(0) & (c U d)))
!!(Xa <=> (Gf <=> (b | Xb)))
b | c | F!0 | !XXa
(XXc U 1) U (Xa & (b ^ 1))
F(0) R ((!c U (d => d)) ^ Gc)
(FF!(!f U f) ^ 0) => Fe
((d | Ga) U 1) <=> !F(1 U c)
XG(FX!!0 U (f U Xf))
F(((0 R f) <=> 0) | !(e U Fe))
!(GGd R (X(d ^ e) => F(1)))
!(Gf | (c => f)) & (!1 U 1)
a U ((0 | Fe) U ((a ^ 1) R 1))
(b => a) ^ G(Gc => XX!1)
G(Fb => 1) => GX(a R X(0))
Gc <=> (Gc | (1 => (c U Ge)))
G((0 | (Gd & !1)) & XG(0))
F((a | b | c) ^ (X(1) U Xe))
F(d R e) | GG(c R (d | 1))
e & ((b ^ f) | (GX(1) U G(1)))
(XG(1) ^ (0 & !e)) R (1 R d)
(G(0) <=> (a <=> c)) ^ (G(1) => Fc)
!1 => F!(a ^ (a | (f => 1)))
X(d & X(!(c R c) <=> (e <=> 0)))
G(XX(!0 R 1) => !(f ^ 1))
!G((Fb ^ 1) <=> (e ^ (e U f)))
f | (X(FGe R F!d) => 1)
1 & Gc & (X(0) => !XXe)
FGFa R (c ^ (Xc & F(0)))
d ^ XX((Xb U 1) => (c <=> 0))
!Xe <=> (!e & !F(e U a))
X((!(f R d) <=> (0 => 1)) => Fa)
FF(X(Xc ^ Xd) => (f => 0))
!(G(Fc => (1 <=> 0)) & F!b)
!(d R G(0)) | ((d & 1) ^ X(1))
(c R c) U (f U (f <=> (0 => Fa)))
(d <=> ((b <=> d) & (e R Fb))) R d
FX((b => b) <=> 0) => G!Fc
((0 <=> 0) | F!1) <=> (f U !0)
GF(X(e <=> ((a U c) R 1)) R e)
F(X(1 U !0) U (X(1) => X(0)))
!(!c => (FXG(0) | (c & d)))
!X(1) & ((f R a) | X(d <=> e))
X((Fd & !f) ^ (f | 1)) U f
(F(0) <=> 0) ^ (XFf => (a U e))
F(1 U a) => F(Fb U !Fb)
c <=> ((b ^ f) & XG(!d U a))
G(F((d => b) U e) U (d R Fc))
F(FX(Xa R 1) <=> (f | !f))
!d | F(!1 R (e & (1 ^ 0)))
Xb & F(Xd U (Xd R Xa))
(!G(0) U Ga) R (!b ^ Xa)
(b <=> e) ^ X!G(c ^ (1 U 0))
G(!e U !XX(b ^ e)) => d
F(!b U ((b U (c <=> 1)) & (Gb U c)))
!(G(Fb | F!(b | Gc)) <=> Fa)
Fc | (((c | 0) ^ (Xc => c)) ^ Gc)
(F(1) <=> G((1 R Xb) => !c)) U Fb
!GX(!a => c) R !(Xa U G(0))
F(1 <=> 0) => (Gc U (G(a & c) => b))
b <=> (b => (c R F(F!(b U b) => 0)))
G(XFa R F(G(1) => F(1 R !0)))
F((F(1 | X(0)) ^ (G(0) => F(1))) <=> 0)
!F(b U (X(b ^ XFa) => FX(0)))
(c ^ (a => (0 | !a))) & (0 => c)
(0 U F(G(0) => 1)) U G(Gb | !a)
GX(0) ^ (1 | !c | (G(1) <=> Fa))
((G(0) | (1 => 1)) <=> F(a <=> 1)) => G(1)
X(((0 U c) ^ 1) ^ ((a <=> a) <=> (a U a)))
GXF(!F(0 R !b) & X(a U 1))
F!((Xa <=> (X(0) ^ 1)) | X(a U 1))
(!F(1) U (a & (b => 1))) | (!1 R b)
X(b | F!a) & (X(0) <=> (G(0) <=> 0))
Ga R F((a | 0) R (c & F(a => 0)))
Xb ^ F(((c R Gc) U Fa) ^ Fb)
FF!(c R !0) => ((c <=> 0) ^ Fa)
XGXFX(G(!c => 0) => !!b)
G(a | ((b U (0 R !Fc)) ^ (a & 1)))
!(((!0 | XG(0)) ^ 1) R !c)
XXGFc | (X!c ^ (0 U !1))
0 U X((a ^ c) | (!!c <=> (1 => 1)))
!F((X(1) U b) => c) R !Fb
(Fc | (c ^ c)) ^ ((a ^ (0 U 1)) U c)
((0 R b) => G!!(0 <=> 0)) <=> X!c
X(Ga & G(FF(0) ^ 1) & !!0)
F(a ^ (0 => (1 R !(b => FGGc))))
!X(((c <=> c) | (0 => G(1))) R GGa)
c & ((1 R 1) => G(a | (a & (0 ^ 0))))
(!b & !c & (c ^ c)) U G(c R b)
((a U 1) <=> 1) R (c | FX!FGa)
G(1) => (!GFGFb R F(a ^ 0))
X(!(!a | GG(1)) U b) <=> (b <=> c)
G(X(1) => (Xa ^ (a | c | 0 | 1)))
FG(a & FG!((1 | XGb) ^ 0))
!((c => (b <=> c)) | (X(c <=> 0) <=> Xa))
(b <=> !X(1)) & G(FG!a ^ Xb)
(Fb U Xb) U F(a <=> (Xb & F(0)))
b ^ (!c & F((Xc <=> 1) ^ (b R 0)))
(c <=> X!X(b ^ (0 U 0))) => (a ^ c)
X(F(1 <=> 0) => (0 & ((b R !0) => a)))
GF!X!((0 | Xc) R (a | Fb))
F((1 U 1) & ((0 | (1 => (0 ^ 0))) ^ 0))
(1 & F(c & Fc)) | (c => !FFc)
G!Xc & X((c & FXG(0)) R c)
((Gc => G(1)) | (0 => (F(1) ^ 0))) R a
(X(1) U 1) ^ !((a ^ X(1)) ^ (a ^ 1))
X(c & !b) <=> (b => (a | (a <=> G(0))))
XFG(XX((a U b) R 1) => c)
G(((a | XX!c) <=> (b U Gb)) U c)
!((!b | (a <=> (0 => 1))) => (Xa => 0))
(((b ^ 1) & G(a | b)) <=> 1) | XX(0)
F(Xa | (FXc & !!a)) U !c
((G(0) & (1 U a)) U c) R (1 | XFc)
(XF(0) R (Xb & F(1))) ^ G!Fa
a <=> (X(0) <=> ((!!b => a) <=> (c => 0)))
X(X(0) U G(1 & XX(F(0) R Xa)))
F(G(1) <=> F(a <=> (a ^ (a & (0 R b)))))
!F((b & 1 & Fc & !1) ^ F(0))
F(0) & (b <=> Xb) & (a R (b & Gc))
FX(b ^ GXb) U FF(X(1) U 1)
(1 & F(0)) R ((0 U b) & (0 U (a & 0)))
((b | 1) U (c & (F!a ^ Gb))) => a
(b | X(0) | F!1) <=> X(Gc => b)
G(c <=> ((0 R b) | ((1 U 0) & XG(0))))
F!((Fa U Fb) U (GGX(0) U c))
(c => 0) | (b => (Xb & (Fa | !a)))
G(Fa <=> (b | 0)) & F(G!b => c)
XFb U !(G(1) & ((!c <=> 1) U b))
Gc ^ ((b ^ Xc) U (XXb <=> Gb))
XX(Ga & XGb) => ((0 | 1) => 0)
XXGG(Ga R X((a | c) ^ Fa))
G!((b R 1) | (G(1 => GX(0)) ^ 0))
F(!((1 U (b => 1)) => 1) R F(a R c))
X(0 => !1) | ((0 & F(0)) <=> (a R 1))
!1 & FF(XF!(Gc <=> 1) ^ 1)
(FF(XXa <=> G(1)) R c) R (c | 0)
X(b => !(0 R a)) ^ (0 R (Fc ^ 0))
(X(Xa ^ 1) <=> (X(0) ^ 1)) <=> GXc
X(c | Gc | Xb | X(b U F(1)))
G((G(0) U ((1 U b) <=> (c <=> 0))) R Fa)
!X(b ^ X(F(0) & FXGFFa))
0 | X((XGc ^ 1) <=> (a ^ (c U b)))
X!!(a <=> ((0 | 1) R b)) U !Xc
X((a ^ b) U c) R (!c U (1 => X(0)))
!c => (((Xb ^ Ga) R c) ^ (0 => a))
Fb <=> ((a | c) <=> (c <=> !Fb))
X(c ^ (G(c ^ Xa) R (b R (1 ^ 0))))
FX(!b U (G((c | 0) <=> G(0)) => 0))
!(Fa | (b & 1) | (!F(1) ^ Fb))
((Fa U GG(0)) <=> Fb) & GFFc
(1 & (c <=> 1)) U ((a <=> b) | X(c <=> 1))
G(1) R (b R (G(0) <=> (b & (0 => Fb))))
(X(Gc <=> 0) U F(c & 0)) => (a => c)
G(X(0) | !0) <=> G!FX(a & c)
GG((b R (e <=> 0)) | (GGf <=> Xe))
F((FFe & (b ^ X(1))) | (c & Ga))
(!0 <=> F(0)) | XF(FGF(1) U b)
!!Ga & F(d & !(f R e))
b U (0 & 1 & XGG!!XGc)
(GFXf | (e <=> Ff)) ^ (c ^ Gf)
(!c <=> F!0) => (Gc <=> X(c R e))
XFF(FFb R (Xb & Xf))
G(!a & G((Gc => 0) => (d & !1)))
!(XX(d & e) ^ (a ^ XGc))
G!Ge | X!X(b => (e U !d))
d & G((c => (e ^ (f => e))) U (a <=> f))
(b & ((c & !0) U c)) R (b U GXf)
X(Gd <=> 1) ^ ((b | f) => GGGf)
a <=> X((c U a) | (G(F(1) U c) <=> 0))
X(c U (((b R !1) ^ (d & e)) <=> Ge))
G((F((e & 0) => d) ^ F(0)) => (c & 0))
!G((e <=> X(1)) => G!(f R (a <=> b)))
!0 | GGF(!b R !GGXa)
F(!c => (f | Xf)) U (d | FFc)
(b ^ G(1)) R ((f | X!Ge) R !a)
c => (F(a | Gc | (1 ^ 1)) <=> Gd)
G(e R a) <=> (XX(f U (e U e)) => d)
X(a <=> X((f <=> F(b U Xf)) ^ Ge))
FF(X(Fa | Xa) R F(d ^ Fe))
!(((a & b) U 1) & !F(G(0) U !c))
(XF(0) ^ G!b) & F(a => (b | c))
GFf U (b & (G(d ^ !c) ^ X(1)))
c ^ !(d <=> (e | GX(!Gc => d)))
(F(1) & (Fc R Xc)) => X(1 | Gd)
((a & d) U 1) <=> F(e <=> (1 & GXa))
G!(!d & ((b ^ FGd) U F!a))
F(((c <=> FGc) U d) U X!X!d)
X(f U (F(0) => c)) | G(e <=> (1 U d))
Xd & !G(f | 1 | Xf | !c)
(((1 R X(0)) U d) | XGGa) U Xf
(b => (b | !1)) ^ F(b ^ !(f <=> f))
(Xf <=> 0) => G(((b <=> Gd) => 0) R d)
X(b | F(((c U b) R b) | !FXc))
G((a R G(Ga & !Xd)) R (e ^ 0))
!(!(a | !Fe) <=> ((a <=> Fe) U d))
Gf | G(!(Xf => !X!f) => d)
(G!a R (d | (d <=> F(0)))) & (a | 1)
(b | Gb | Gd) R (X(0) R (b & d))
((f & 0 & G(a U a)) <=> 1) ^ XFf
F(F(d <=> F(1)) => (b | G(0))) <=> !f
X((e & 1 & !F(Ga & Ge)) ^ 0)
FX(!(b => 1) R ((d => a) & (e => a)))
!!((G(Ga U Fb) <=> 1) <=> (c & e))
FGX(1) | (X!X!XXa => b)
(G(0) & (b U e)) U (Xa & (f ^ Xb))
!1 R (((c R d) U (a => !a)) ^ Xc)
(FF!(!F(1) U F(1)) ^ 0) => Fe
!F(X(0) U c) <=> (1 | G(!d ^ 1))
XG(!F(Xd U e) U (c U (f | 0)))
F((Xb <=> (Xe => 0)) | !(e U Fe))
!((c ^ G(1)) R (X(d ^ !b) => F(1)))
!(Gf | (c => G(0))) & (FXd U 1)
a U (XXXG(0) U ((Xa ^ 1) R 1))
G((f => f) => XX!Xc) ^ (b => a)
(G!b => Xa) => GX(!b R X(0))
XX(0) <=> (Gc | (b => (c U (f R a))))
G((f <=> (Fe | (c R c))) & X(f R 1))
F(((f U 1) U Xe) ^ XFG(c <=> d))
GG(!d R (c | Gf)) | F(b R e)
0 & ((b ^ F(1)) | (XGf U (1 U f)))
((d U e) & (a | (a & e))) R (c R Gf)
((c ^ Gc) <=> (b ^ c)) ^ (b ^ (d | 1))
!a => F!(c ^ (a | (f => (a | 1))))
X(Gb & (!(c R Fa) <=> (e & Gd)))
G(XX(!Xd R 1) => !(!1 ^ 1))
!G((X!f ^ 1) <=> ((e | 1) ^ Fe))
f | (X(F(c ^ Xf) R F!d) => 1)
Gc & Xb & !X(!d | (c R 0))
(f => (0 => e)) R (c ^ (F(0) & (a | c)))
XX(((d R d) U 0) => (Ff <=> 0)) ^ 0
!Xe <=> (!e & !F(Ge U !c))
X((f <=> ((0 & X(1)) R !d)) => GFc)
FF(X((d | f) ^ (a & f)) => (f => 0))
!(GXXb & G((b => a) => (1 <=> 0)))
!(Fd R G(0)) | (f <=> (X(1) ^ !c))
F(c => a) U (d U (f <=> (f => X!e)))
(e <=> (X(d => Fe) & (b <=> Ge))) R d
FX(((d R 0) => b) <=> 1) => G!Fc
XG(c U 1) <=> ((0 <=> 0) | F!X(0))
GF(X((((e R e) U c) R 1) <=> 1) R e)
F((e | (c ^ f)) U (!e => (1 | Xe)))
!((0 R f) => ((c => b) | FX(c ^ 1)))
a & b & (e | !f | X(e <=> Gd))
X((1 ^ 1) ^ (X!f & FG(0))) U f
((a | b) U !(b U c)) ^ (c <=> XX(0))
(!b R f) => F(Fe U !XFFb)
c <=> ((a ^ c) & XG((f => b) U !b))
G((d <=> GGFGd) U (f R (a => a)))
F(FX((b | !1) R 1) <=> (f <=> Fe))
X(0) | F((b | d) R (!a & (1 ^ 0)))
Xb & F(Xf U ((f U c) R (d & f)))
(c R !(c ^ !1)) R ((d & e) ^ !b)
(a <=> Fc) ^ X!G(c ^ (Xd U 0))
G(!!0 U !XX(Fa ^ 0)) => d
F(Xa U ((!(c => b) U c) & ((b U c) U c)))
!(((a <=> c) | F(c ^ (c U Ga))) <=> XGa)
XF(0) | (((Xc => F(1)) ^ (c | 0)) ^ Gc)
(G((c R c) => F!1) <=> X(0)) U Fb
(XFGa => XXa) R !(a U G(0))
F(1 <=> 0) => (G(0) U (G(c & X!0) => b))
b <=> (0 => (b R F(F!(c U XFb) => 0)))
G(X(0 => 1) R F((a => b) => F(1 R !0)))
F(c <=> ((0 & (1 R G(0))) ^ ((0 R c) => F(1))))
!F(c U (X(G(1) ^ X(b => b)) => FX(0)))
((!c => (0 | !a)) ^ (c | G(0))) & (0 => c)
FF((Fb ^ 0) => 1) U G(Gc | F!b)
(!X(0 R 1) | (G(1) <=> (c R a))) ^ (b <=> 1)
(((0 & Fc) R Gc) <=> F(Xa <=> 1)) => G(1)
X((XGa <=> (Fb U a)) ^ G((0 U c) ^ 1))
GXF(X(1 U Xa) & !F(0 R !!0))
F!((1 & !c) | ((!a ^ 1) <=> X(0)))
((a & c) U (a & (GFa => 1))) | (!1 R b)
(((1 ^ 0) <=> 0) <=> F(1)) & ((c | 0) U (b ^ b))
!c R F((0 | Fb) R (1 & F(Gb => 0)))
(a & 0) ^ ((!0 <=> !0) U F(XGb ^ 0))
!(!c R !(a ^ 1)) => (Fa ^ (a <=> Xc))
XGXFX((!FG(0) => 0) => !FFa)
G(G(1) | ((a & Xa) ^ (b U (0 R !Fc))))
!(((!0 | X(c ^ 1)) ^ (b & 0)) R !F(1))
XXGXG(1) | (XG!1 ^ (0 U !1))
0 U X(((1 => 1) <=> !FFXa) | G!c)
(F(!b ^ 1) => (1 & (1 => c))) R !(a <=> 0)
((a ^ (X(1) U 1)) U c) ^ X(FXb ^ F(0))
(X(a ^ 0) => G!!(X(0) <=> 0)) <=> XGa
X(!c & (a <=> F(1)) & G(a ^ F(1 <=> 0)))
F(a ^ (c => (c R !(0 => FG(1 R Xb)))))
!X(((c <=> G(1)) | (a => (a ^ 0))) R GGa)
b & ((b | 0) => G(1 | (a & ((0 U c) ^ 0))))
(!b & !c & (c ^ G(1))) U G(0 R !b)
((0 U Xa) <=> 1) R (!0 | FX!FGa)
!c => (GFG(F(0) <=> 1) R F(Fa ^ 0))
X(!(!a | G(!a ^ 0)) U b) <=> (b <=> c)
G((b | c) => ((a | c | 0 | X(1)) ^ !c))
FG(c & FG!(b ^ (Xb | F(c => a))))
!((F(a | Xc) <=> (a & b)) | (c => (b <=> c)))
(b <=> !(a & b)) & GGGF(Fa & F(1))
(Xc => Fb) U F(((b => 1) & (0 => 0)) <=> 1)
a ^ (!c & F(((0 & 1) <=> 1) ^ F(b ^ 0)))
(b <=> X!X(b ^ (Xc U 0))) => (!b ^ 0)
X(((1 R 0) U 1) => (b & ((0 R GGb) => a)))
GF!X!(F(c & X(0)) R (c | X!a))
F((1 U 1) & (c ^ (0 | (c => (X(0) ^ G(0))))))
(1 & F(Fc & F(1))) | (G(1) => !FFc)
F(a & b) & X((!0 & FX(1 R a)) R c)
((!0 => (GX(0) ^ 0)) | (Gc => G(1))) R a
((a ^ X!1) <=> (F(0) ^ 1)) ^ (Xb U X(1))
FX(!b => c) <=> (a => (c | (a <=> (b => a))))
XFG(XX(GF(1) R (1 | (a & b))) => c)
G((F(a ^ Fb) <=> (Fc | XX!c)) U c)
!((Xb | ((!b => 0) <=> Fb)) => (Xa => 0))
(1 U 0) | ((c & F(1) & G(b | !b)) <=> 1)
F(Xa | (1 & X(1) & !FFa)) U !c
(0 | (c ^ 0)) R (1 | X(0 <=> 0))
(G!b R (Xb & (b <=> 0))) ^ !(a => !0)
a <=> (((F(1) => !b) U (a U Xa)) <=> (a & c))
X(Gc U G(1 & XX(X(b U 0) R Xa)))
F(G(1) <=> F(a <=> (a ^ (0 & (a R XG(0))))))
!F((c & Fc & Gc & !1) ^ (0 | 1))
((!c => b) ^ F(Fb | (b R 1))) & XG(1)
((c & Ga) U (b ^ 1)) U FF((0 U a) U 1)
(1 & F(0)) R (G(0 & X!0) & (0 U Fc))
((1 | F(0)) U (1 & (F!Gc ^ !b))) => a
X(Gc => b) <=> (b | (1 U 1) | FFX(1))
G(((X(1 U 0) & (!c U c)) | (0 R b)) <=> 0)
F!(F(!1 ^ !a) U (GG(b U 0) U c))
(Fb => (Xb & (Fa | !a))) | (!1 => 0)
b & (c R GFc) & G((b | Gb) <=> Fa)
(c ^ c) U !(F(Fa => (a | 1)) & (1 ^ 0))
((Xc <=> 1) U (X(G(1) U 0) <=> Gb)) ^ Gc
(Ga & X(F(1) ^ Ga)) => ((1 | Ga) => 0)
XXGG(X(0) R X((a <=> b) ^ (0 | !b)))
G!(G(0 => G((b R c) U 1)) | (a R Xb))
F(!((1 U (Xb => Xb)) => 1) R F(a R c))
((0 & XXb) <=> (a R 1)) | XG(a & X(1))
G(0) & FF(XF!((Xc U 1) <=> 1) ^ 1)
(FF((a U c) <=> XXa) R !0) R (c | 0)
G!(!b R F!0) ^ (b R (G(0) ^ Fc))
(((b | c) ^ 1) <=> (!c | F(1))) <=> G(0 => c)
X(c | (c ^ 1) | !1 | F(b <=> (a | 0)))
G(((1 U b) U ((Xc U b) <=> (c <=> 0))) R Fa)
!X((FXGF(b <=> 0) & (0 => 0)) ^ Ga)
c | X((a ^ X(X(1) ^ 0)) <=> (a ^ (c U b)))
!(((1 | (b R !1)) R b) <=> 0) U !(a & 0)
(G(0) | (!a R 1)) R (F(1) U (1 => (a U 1)))
XF(1) => (((!c ^ (b R c)) R c) ^ (0 => a))
Fb <=> ((!F(b & XGc) <=> 0) <=> (a | c))
X(a ^ ((F(1) ^ (b & 0)) R (Ga R (1 ^ 0))))
FX(Fb U (((b ^ !c) => (1 U a)) => Xb))
!(X(!c & GFb) | (X!c ^ !F(1)))
GF(a => 0) & ((a => Gc) U G(!b U b))
(b & (c <=> X(1))) U ((F(1) <=> 1) | (a <=> !b))
X(1) R (a R (G((b ^ c) R !a) <=> (1 U 1)))
(X(G(0) <=> !Xa) U F(c & 0)) => (a => c)
G(Ga | FG(1)) <=> FX(X(1) & !!c)
GG((G(1 => 0) <=> Fd) | !(e <=> (e & f)))
F((Ff & Ga) | (c => ((b & !0) => Xb)))
((a <=> e) <=> X(0)) | (Ge => FGX(c | 1))
!!(b ^ b) & F(d & !(1 R !e))
c U (XGG!!X(f ^ f) & (d U !e))
((e <=> XG(0)) | GF(e | 1)) ^ (c ^ Gf)
(F!Xe <=> !c) => (X(c R F(0)) <=> Gc)
XFF(F(f <=> 1) R (Xb & X(f & !1)))
G(!a & G((Ff U Fa) => (e & !Xd)))
!((XGc ^ Fb) ^ X(b & Fc & Ge))
X!X(!a => (d U !!e)) | (d R Gb)
d & G((Ff => (e ^ (f => e))) U (a <=> G(1)))
(b & ((c & !b) U c)) R (b U GXf)
((f | !c) => GGGf) ^ ((a ^ Ga) <=> 1)
X((G(F(1) U c) <=> Xa) | (a ^ c)) <=> !c
X(e U (((d & e) ^ (Fe R !1)) <=> (c ^ e)))
G((((Xd U d) => Xe) <=> !f) => (e & Xc))
!G((F(0) <=> X(1)) => G!(0 R (d <=> Fd)))
!0 | GGF((a <=> 1) R !GGb)
(G!a => (Xf | G(0))) U (!a | FFc)
(G(1) ^ Ff) R (!X!(1 R b) R FGf)
e => (XFd <=> F(d | (e => c) | (1 ^ 1)))
G(0 R !b) <=> (XX(f U (F(0) U e)) => d)
X(a <=> X(Ge ^ (f <=> F(Xf U (b & 1)))))
FF(X((e ^ e) | (a => f)) R F(d ^ Fe))
!(!d & (b R b) & !F((e ^ 1) U !c))
F(d => (a | Ga)) & (Gc => !XFFe)
F(f ^ 0) U (b & (G(d ^ !c) ^ (f U c)))
c ^ !((e | GX(!(a => c) => d)) <=> !0)
X(Xa | (a <=> GFf)) => X(e | (1 R f))
F((e & G(e & !1)) <=> 1) <=> (Gb & Gf)
G!(!d & ((F(c U d) ^ Xb) U F!a))
F(((d R c) | (e => Xc)) U X!X!Fe)
X(c U (Xf => !c)) | (G(1) & (G(1) U d))
(a U f) & !G(!Gf | ((0 | Xf) U f))
(XG(e ^ 0) | ((e & !c) => Gf)) U Xf
F(e ^ !(f <=> !Xb)) ^ (b => (b | !1))
G(a | c) => G(((!1 <=> (c => c)) => 0) R d)
X(d | F(GG(!a U b) | !F(d & 1)))
G((0 R G(Ge & !(a U d))) R (G(0) ^ 0))
!(!(0 | !(b <=> e)) <=> X(!f => XFe))
Xd | G(!((b & 1) => !XFG(0)) => d)
(a | 1) & (!(b <=> b) R (d | (F(0) <=> Gb)))
((Fe => d) R GGb) R ((f & 1) R (b & d))
((c & f & G((0 => f) U a)) <=> 1) ^ (b R 0)
!f <=> F((Fb & (b ^ f)) => (b | (c U c)))
X(X(0) ^ X!F(0 & Xe & (!d ^ 0)))
FX((b & !b) R ((d <=> !e) & (Gd => a)))
!!(((Fc => (Ga <=> 0)) <=> Xe) <=> (c & e))
FGX(1) | (X!X!X(a | !d) => b)
(Xa & (Fe U e)) U (Xa & (Xb ^ G(0)))
(a | c) R (((c <=> e) U (d => GGd)) ^ Gb)
(FF!((a => c) U (1 => b)) ^ 0) => XG(0)
(Gb | (!d ^ X(1))) <=> !F(1 U c)
XG((!(c R d) U Ff) U (a U (c | Xf)))
F((!c R ((e | 0) => 0)) | !(f U (c => a)))
!((1 & Fd) R ((c ^ (1 R Gd)) => (d => d)))
!(Gf | (1 => (c ^ 0))) & (e | 1 | G(1))
!b U (X(Gc R a) U ((Xb ^ Xa) R 1))
((d & Xc) => XX!(b & c)) ^ (Fb => a)
(d <=> GFGFb) => GX(G(1) R (a | c))
(Gc | (0 => (e U (b R (c R f))))) <=> GFd
G((e <=> ((Fb <=> 1) | (c => 0))) & X(f R 1))
F(((!1 U 1) U Xe) ^ XFG(e <=> Gd))
GG(Ge R (e | (c ^ 1))) | (Fc ^ Gb)
f & ((b ^ F(1)) | (X(Xd R 1) U (1 U f)))
(X((b ^ Xe) ^ 0) R !e) R (0 R (c ^ 1))
(f R (1 | Fe)) ^ (((d => e) ^ 1) <=> (b ^ c))
!a => F!(a ^ (!d | G(c | (b & 1))))
X(Gb & (!(Ff R Fa) <=> (e & (a U d))))
G(XX((f ^ Gf) R Xe) => !(!1 ^ 1))
!G(((b | Xe) ^ Fe) <=> XFG(c | e))
f | (X(((1 U Xc) ^ 0) R FFGa) => 1)
Gc & Xb & !X(GGf | (Fa R 0))
!(!1 <=> 0) R (Gf ^ (XGd => (b & c)))
c ^ XX(((e R Ga) U 0) => (XF(0) <=> 0))
(Gd U !(f U F(b U !c))) <=> !(1 U 0)
X((e <=> (((1 U 1) => 1) R GGf)) => GFc)
FF((c <=> (e & 0 & (d R a))) => (d => Xf))
!(G(XF!b => (Xd <=> 0)) & X(a | b))
!(Fd R G(0)) | (f <=> ((d ^ e) ^ (b | c)))
(Ff => a) U (Gb U (f <=> (f => XF!0)))
(Fd <=> (G(G(0) => d) & (b <=> (b => c)))) R d
F((0 R G(1)) => b) => G!(a <=> c)
(Ga => (1 R c)) <=> (b | Xf | (Xa <=> 0))
GF(X(b <=> (((f R (1 => e)) U c) R 1)) R e)
F((e | (f ^ Fb)) U (G!0 => (1 | Xe)))
!((d => 0) => ((e ^ !c) | FX(Gd ^ 1)))
XGd & (X(e <=> (Fd => f)) | (a & X(1)))
X((X!f & FG(0)) ^ (X(0) ^ 1)) U G(0)
(Fe <=> XX(0)) ^ (e <=> (b U FX(a <=> 1)))
(!!c R f) => F(X!0 U !XFFb)
a <=> (XG((!0 => b) U !b) & (c ^ !c))
G((Fb <=> GF(Xc => d)) U (f R (a => a)))
F(FX(G!Xb R X(1)) <=> (f <=> X!e))
F(G!c R (!1 & (Xe ^ 0))) | XX(0)
a & 0 & G(F(1 => !1) R (Fe & !0))
(a R !(c ^ GXc)) R ((d ^ 0) ^ GFf)
(d => !1) ^ X!G(Fe ^ ((b <=> e) R 1))
G((Fa U b) U !XX(a ^ X!e)) => d
F(Xa U (((b U c) U F(1)) & (!(1 => Gb) U c)))
!(((a <=> c) | F(Gc ^ (c U (b ^ 1)))) <=> XGa)
((c ^ (X(c & XF(0)) => b)) ^ (0 ^ 0)) | XG(1)
FG(!(1 & (F(1) => c)) => F!X(0)) U XFb
((!F(1) <=> 1) => X(b U a)) R !(a U G(0))
(b ^ c) => (!a U (G(c & XFGc) => b))
b <=> (!c => (Fc R F(F!(c U XFb) => 0)))
G((!0 U 0) R F(XF(0) => F(a R F(b U c))))
F((((Fa U c) U Gb) ^ ((G(1) R c) => F(1))) <=> 0)
!F(a U ((!Gc => F(1 => G(0))) => F(a | b)))
((F(1) ^ (0 => 1)) | (b R FF!c)) & (Gb => c)
((Ga ^ (Ga ^ 1)) => 1) U G((a ^ 0) | F!b)
((G(1) <=> (c R a)) | !X(a R X(0))) ^ !(a ^ c)
(F((c & 0) <=> 0) <=> ((c U 1) R (1 & Gb))) => G(1)
X((Gc & (c R !c)) ^ ((c => a) <=> (!a U !b)))
GXF(!F(c R !!G(0)) & (a <=> (0 | Fa)))
F!(((F(1) ^ (1 & Xa)) <=> G(1)) | F!FG(1))
(FX(0) R b) | X(a & (G(G!c <=> Fc) => 1))
(!b <=> ((c | Gb) <=> Gb)) & F((c R Xc) <=> 1)
(a & b) R F((a & Ga) R (1 & F(G(1) => Ga)))
(a & 0) ^ (F(0 U Xb) U F(Gb ^ X(0 R a)))
!(G!1 R !(a ^ 1)) => (XFb ^ X(a U 1))
XGXFX((b R F(F(0) R a)) => !F(b <=> 1))
G(Ga | ((c U (1 R !G(b <=> 0))) ^ (Fb <=> 1)))
!(((FGb | (Xb U c)) ^ (Fb => 0)) R !F(1))
(X!(a & b) ^ XG!X(0)) | (b ^ (b ^ X(0)))
Ga U X(G!G(0) | (!FFXa <=> (1 => 1)))
((a | (b <=> F(0))) => (Xb & (1 => c))) R !(a <=> 0)
((Fc ^ (Xb => 0)) U c) ^ (Gb => (a R (c | 0)))
(XFXGa => G!!(c <=> (b U 0))) <=> (a | b)
X((a U 1) & G(a ^ F(Ga <=> 1)) & (b <=> Gc))
F(a ^ (0 => (c R !(!1 => FG(X(0) R Xb)))))
!X((((0 => G(1)) => c) <=> XX!a) R G(0 R c))
0 & ((c | Fb) => G(0 | (!b & (0 | GF(0)))))
((c ^ G(1)) & (1 ^ 0) & !!a) U G(0 R !b)
(!1 | FXG(0)) R (F(1) | FX!F(a ^ 0))
G(0) => (GFG(Gc <=> (b => 1)) R F(Fa ^ 0))
(b <=> c) <=> X(!(GFa | (F!!0 ^ 0)) U b)
G((c <=> 0) => ((a | 0 | F(1)) ^ Xa))
FG(1 & FG!(c ^ (Xb | F(XXb => a))))
!((c => (c <=> G(0))) | (F(a | (1 U 1)) <=> (a & b)))
(b <=> !(a & b)) & GGGF((b <=> 1) & (1 => 1))
(1 => Fb) U F((!X(0) & (Fb => 1)) <=> 1)
(!c & F((Fa ^ !c) ^ ((b & X(0)) <=> 1))) ^ 0
(X!X(b ^ ((b ^ 0) U G(0))) <=> 1) => (!b ^ 0)
X((Xc | F(0)) => (0 & ((1 R G(b U F(0))) => a)))
GF!X!(F(c & 0) R (1 | X!Fa))
F((1 U 1) & ((0 | (0 => ((1 ^ 0) ^ GXc))) ^ 1))
(1 & F(Ga & X!Xc)) | (G(1) => !FFc)
X((!0 & FX(Xc R a)) R c) & (a ^ FFb)
((F(!c ^ 0) & GX(0)) | (Fb => (c R 0))) R a
(G(X!(b | c) U a) ^ !a) ^ ((b | 0) U X(1))
(a => (1 | (Fb <=> (a U b)))) <=> FX(!Gb => c)
XFG(XX((!c => c) R (1 | (b & Ga))) => c)
G(((Fc | XXGF(0)) <=> F(b ^ (a <=> b))) U c)
!((((0 | 1) R b) U !(Gb => 1)) => ((b | c) => 0))
(a U G(1)) | ((c & F(1) & G(!b | !0)) <=> 1)
F(FG!F(F(0) & (0 | 1)) | (a & c)) U !c
F(0 | ((Xc <=> 0) ^ G(1))) R (1 | X(G(0) <=> 1))
(Fb => !Xa) ^ (G!Fa R (Xb & (b <=> 0)))
b <=> ((a & c) <=> ((a <=> GXF(1)) U (!b U Xa)))
X((b => a) U G(1 & XX((b | Gc) R (0 U b))))
F(G(1) <=> F(a <=> (a ^ (1 & (!a R X(0 R a))))))
!F(((F(0) <=> 1) & FXa & (b | c)) ^ (a & 1))
(F((c <=> c) | FGc) ^ F(b ^ !1)) & XG(1)
(G(0 R a) => G(0 | 1)) U FF((G(0) U a) U 1)
(Fa & X(1)) R ((c U (0 <=> 0)) & FXF(0 R 1))
((a | !b) U (b & (F!(b => 0) ^ (c => 1)))) => a
X(b | FF(0 & (1 | F(1)))) <=> X((1 R 1) => b)
G(((G(1) R b) | (!F(1) => ((1 & !1) U 0))) <=> 0)
F!((!!a ^ (a & b)) U (GG(Ga U 0) U c))
(!1 => 0) | (Fb => ((b | c) & !FFGFb))
G((Gb | !c) <=> Fa) & F(Fa R G(c <=> 0))
(b R 0) U !((!X(a & Fb) <=> 1) & (Xb ^ 0))
Gc ^ (((1 => a) ^ 1) U (X(Fc U Gc) <=> Gb))
((!c => X(0)) U F!F(0)) => ((0 & Fc) => G(1))
XXGG((1 U a) R X((a <=> F(0)) ^ (0 | !b)))
G!(G(F(0) => G((!b R c) U 1)) | (a R Xb))
F(((G(0) U ((0 | 1) => Xb)) => 1) R F(!a R c))
((0 & X(c U a)) <=> (a R 1)) | (!X(1) ^ X!0)
Xb & FF(XF!((!X(1) U X(1)) <=> 1) ^ 0)
(FF(X(1 U c) <=> X(c | 0)) R !0) R (c | 0)
(b R (XF(0) ^ G(0))) ^ G!(!Fb R F!0)
((!c | GXb) <=> ((b ^ 1) ^ X(1))) <=> (0 & G(1))
X(c | Xa | (c ^ 1) | F(b <=> (Gc | !1)))
G((((b & c) U b) => !((c R c) U G(1))) R (b <=> c))
!X(((1 U a) & FXGF(a <=> FF(0))) ^ Ga)
1 | X((a ^ (1 U Fa)) <=> (X(X(1) ^ 0) ^ Fa))
!(((1 | (0 R !Xb)) R b) <=> G(1)) U !(a & 0)
X(F(1 ^ 1) R Xa) R (XX(1) U (1 => (a U 1)))
XF(1) => ((0 => a) ^ (((b R !1) ^ G!1) R c))
X!b <=> (G(X(a ^ 0) U F(!!1 <=> 1)) U 0)
X((((a <=> a) & !F(0)) R (!b R (Gb ^ 1))) ^ 0)
FX((a <=> a) U (((b ^ FF(1)) => (1 U a)) => Xb))
!(G(b <=> !(c ^ Xb)) | (!GXa ^ (0 => c)))
GF(0 => Xa) & ((X(c => 0) U GGb) <=> !a)
(FGb ^ (b U 1)) U ((a <=> !b) | (b <=> (1 <=> 1)))
X(1) R (a R (G((G(1) U 0) R GFb) <=> (1 U 1)))
((Gc ^ XGFb) U F(c & Gb)) => (a => F(1))
G((c R a) | FG(1)) <=> (0 => !!(F!b R 1))
GG((a & G(b R 1)) | (G(Xe => 0) <=> (e R e)))
F((Ff & Ga) | (Fb => (GX!0 => (f & 1))))
FGX(1 | (Ge <=> Xa)) | ((e <=> Fe) <=> Xb)
F(!(X(1) R !e) & !Ga) & (d ^ !(b ^ b))
c U (XGG!!X(XXf ^ 0) & GF!d)
(c ^ (1 R 1)) ^ ((XFc ^ 1) => (f U Xd))
F!(F(0) U Gc) => (X(e R G(c U d)) <=> !c)
XFF((1 | (0 => b)) R (b & 0 & (b => (c | 1))))
G(FFb & ((FXc U XFc) => (e & !Xd)))
!((F(1) ^ X(b R c)) ^ !(XFc & (d <=> !0)))
X!X(!e => (Gb U !!e)) | (b <=> (d => 1))
d & G((X(Xb U Xc) R F(1)) U (f <=> (b R a)))
(X(Xa U c) | (c <=> 0)) R (0 U G(b | 1))
((1 U (c | f)) => GG(1 R 1)) ^ (c ^ (!e => e))
Gd <=> X((Gd <=> G(a U Gc)) | F!c)
X(e U (((c <=> (d & !d)) ^ (d & Ge)) <=> (d U e)))
G((!f <=> (!(d ^ !1) => (e & 0))) => (e & Xc))
!G(X(G(0) U 1) => G!(d R (X!b <=> G(0))))
!0 | GGF((1 & !1) R !GG(c | !a))
((f & !c) ^ F(d & Gb)) U (Ff | F(a => b))
(f <=> (e & f)) R (!X!((d | 1) R b) R FGf)
e => (F(F(FGd => c) | (X(1) ^ 1)) <=> XFd)
(X(b U ((f <=> Fe) U e)) => !c) <=> G(0 R !b)
X(!c <=> (Ge ^ (f <=> F(XXa U (0 & Xb)))))
FF(((e ^ Xa) <=> !(e R 0)) R F(f ^ (d => 0)))
!(X(d R GGGb) & !F((e ^ X(0)) U !c))
XFX(c <=> (Fe <=> 0)) & F(a => (d | (a R c)))
F(f ^ 0) U (b & (G(GGa ^ G(0)) ^ (d | 1)))
Ga ^ ((e | GX(!(!e => Fe) => d)) <=> Xb)
X(Xc | (G(a <=> 1) <=> Xa)) => X(e | (1 R f))
(Gb & (f => 1)) <=> F((e & G(G(0) & !1)) <=> 1)
G!((Xb R !FF(FGd ^ Gc)) & !!e)
F((c <=> F((e => f) R Fc)) U X!X!(d <=> f))
G(((c R f) => f) U d) | X(1 U ((c & 1) => !c))
!G(((d | 0 | 1) U F(1)) | !Gf) & (a <=> 1)
(G(!G(0) ^ (X(0) => a)) ^ (0 & !c)) U (1 U 1)
(d => (b | !Xb)) ^ !!(!1 <=> !(e & !e))
(!e U Fa) => G(((FXf <=> (c => c)) => 0) R d)
X(a | F(GG(!(d <=> 0) U b) | !F(d & 1)))
G((f R G(FG(0) & !(d U Gc))) R (G(0) ^ 0))
!(!(d | !(b <=> !e)) <=> ((c <=> (c U f)) <=> Gf))
!1 | G(((d => 1) => !XF(!1 ^ 1)) => !a)
X(d | (XG!b <=> X(b & !a))) & (1 | Fd)
G(!a R G(Fe => d)) R ((d U f) R (b & !f))
(X(1) <=> !(c & G((0 => F(0)) U a))) ^ (Xb R f)
!f <=> F((GGf <=> (b U 0)) => (b | (!f U c)))
X(X(0) ^ X!F((FGe ^ Xf) & (Xe => 0)))
FX((b & !!c) R ((d <=> FG(0)) & (Gd => a)))
!!((c & Gc) <=> (e & ((e & 0) => (b <=> (c ^ e)))))
X!X!X(0 | !G(e R b)) | FG(b U f)
((d <=> 1) R (a R Fe)) U ((f U d) & GX(e U 1))
G!b R ((X(c <=> f) U (d => G(c => a))) ^ Gc)
(FF!((1 R Gf) U (Xe => b)) ^ 0) => XG(0)
!F((1 | X(1)) U c) <=> G(!(1 ^ 1) ^ (b ^ c))
XG((Fd U ((c ^ e) R d)) U (0 U (a | (c & 0))))
F(!(G(0) U (c => a)) | (F(1) R ((a | Xe) => 0)))
!((Xa <=> Gd) R ((f ^ (0 R (c ^ f))) => (d => d)))
!((b R 1) | (c ^ (!1 U 1))) & F(!G(0) ^ 1)
!0 U (!F(d R Fa) U (((b & f) ^ Fe) R 1))
(Fb => a) ^ (F(f & Fd) => XX!(c & !f))
GFGX!GFe => GX(Xa R (a | Fe))
GXGb <=> (Gc | (0 => (F(0) U (b R (c R f)))))
G(X(!1 R 1) & (f <=> ((Gc => 0) | (e <=> Ff))))
F(((d <=> f) ^ (e U 1)) ^ ((a | b | c) U (e | 1)))
(Fe R !b) | GG(Gd R (Ga | (Fa ^ 1)))
0 & ((X(Gd R X(0)) ^ 1) | (F(1) ^ Ge))
(X(((d & Gb) ^ 0) ^ 0) R !e) R (0 R (c ^ 1))
(!(Ff => e) <=> (b ^ Fd)) ^ (!1 R (1 | Fe))
Xf => F!(a ^ (!d | G(!a | (c & !f))))
X(Gb & ((b ^ (1 => !e)) <=> !(Xe R (f => c))))
G((((0 | F(0)) ^ FXb) U e) => !(Fe ^ Xf))
!G(((b | (b & d)) ^ Fe) <=> (c | (f ^ (1 U e))))
f | (X(X(c | (!f => 0)) R FF(e => d)) => 1)
!f & (b => f) & X((!GGf <=> (d ^ 1)) R 0)
(f & (a | Xe)) R (Gf ^ ((e => a) => (c & !c)))
e ^ XX((Ff R (Xc R d)) => (X(f <=> 0) <=> 0))
!(1 U 0) <=> (Gf U !(d U F(!f U !!e)))
X((c <=> ((c | f | Gc) R G(e => 1))) => GFc)
FF((c <=> ((!f R a) & (e <=> !1))) => (d => Xf))
!((!a | !b) & G(F!!b => (Fc <=> X(1))))
!(Xf R (c R d)) | ((c | Fd) ^ GF(c ^ e))
(f <=> (a <=> 1)) U (!d U (f <=> (d => XFFXf)))
(((b <=> (Fb => c)) & (d => Fd)) <=> !b) R d
F((X(0) R (!a & (f ^ 0))) => b) => G!(a <=> c)
(0 R (!f R Xa)) <=> (b | (c U 1) | (Xa <=> 0))
GF(X((((0 R ((b & 1) => e)) U c) R 1) <=> 1) R e)
F((F(1) ^ XXF(0)) U ((e U 0) => (a | 0 | 1)))
!((e U b) => (F(G(1) <=> 0) | FX((b R d) ^ 1)))
((d & (e U a)) | X(e <=> (Fd => f))) & GFFf
X(G(d U a) ^ (F(f => b) & (X(0) ^ 1))) U G(0)
!FX((e | !b) <=> Ff) ^ (X(c & 0) <=> Fe)
F(a | !!d) => F(FXe U !XFXFb)
(F(c <=> 0) & XG(((a & c) => Ga) U !b)) <=> 0
G((GF(Gb => Gf) <=> Fb) U (G(1) R (a => a)))
F(FX(G!(c | 0) R X(1)) <=> X(!e & !0))
(a ^ f) | F((a <=> X(0)) R (!d & ((a | 1) ^ 0)))
a & 0 & G(X!(f & Gd) R (Xd & FXd))
!(Gb ^ (Fa | Fc)) R ((a ^ Xd) ^ GFf)
(c <=> e) ^ X!G(Fe ^ ((b <=> Fc) R 1))
G((Ge => c) U !XX(XGFXa ^ 0)) => d
F(F(1) U ((!(a => (1 => c)) U G(0)) & ((b U c) U F(1))))
!(XGa <=> (F((b U (c ^ !c)) ^ X(0)) | (Ga <=> 1)))
(1 => a) | ((c ^ ((c & X(Xb => c)) => Ga)) ^ (0 ^ 0))
FG((Gc | F(0) | X(1)) => F!(b | c)) U XFb
((b U !XFGa) ^ (0 | 1)) R !(!!b U (a R 1))
X(F(1) <=> 1) => (XG(1) U ((c & XF(b R 0)) => !a))
b <=> (!a => (G(1) R F((a U X((b <=> 0) <=> 0)) => Ga)))
G((c R (a ^ 0)) R F((0 => 1) => F(b R F(Fa U c))))
F(c <=> (((1 R X(0)) => XX(0)) ^ (((b => b) U c) U Gb)))
!F(1 U ((!a => F(Xc => G(0))) => F(a | b)))
(FFFGGXb | (F(1) ^ (0 => X(0)))) & (Gb => c)
(FF(b & c) | (Gb R a)) U G((a <=> c) | FF!b)
(G(!G(1) U a) | ((0 => a) <=> (F(1) R a))) ^ (1 => F(0))
(F((c & 0) <=> G(0)) <=> ((Fc & X(0 | 1)) => 1)) => G(1)
X(((1 => !b) <=> (!a U !b)) ^ (Gc & (c R G!1)))
GXF(!F(a R !!(c R c)) & (0 | (c => !Gb)))
F!(Fb | (a <=> b) | (((1 & Xa) ^ F(1)) <=> (c R a)))
(FX(0) R b) | X(a & (G(G!F(1) <=> (a <=> 0)) => 1))
((0 R (1 & Xc)) <=> 1) & (((c | Gb) <=> Gb) <=> F!a)
(c => b) R F((b <=> (a ^ c)) R (0 & F((1 => 1) => Ga)))
(a & 0) ^ (!(Gb & F(0)) U F(X(c R Gc) ^ Gb))
(a <=> (G(0) ^ (a | G!c))) => (XFb ^ X(c U Xa))
XGXFX(!F((b R b) R Fa) => !F(!c <=> 0))
G(X(0) | ((a U (c R !G(!c <=> 0))) ^ ((a ^ 0) <=> 1)))
!((((Fa => (a => 0)) ^ 1) | F(G(0) ^ 1)) R !XXa)
(c ^ 0) | (X!(a & !b) ^ XG!X(0)) | (a => 1)
F(1) U X((F(!a & G(0)) <=> (Xa => 1)) | (Xb U a))
((((a | (b <=> c)) U b) => c) & (Xb U a)) R !(b <=> Ga)
((Fc ^ ((b | c) => 0)) U c) ^ F((Gb => 0) | FG(0))
(XFXGa => G!!(G(0) <=> (b U 0))) <=> (a | G(0))
X((a <=> c) & (Fa => Gc) & G(c ^ F(Fa <=> X(0))))
F(a ^ (c => (1 R !(Xb => FG(GXc R (0 U c))))))
!X((((a => (a ^ 0)) => c) <=> F(c ^ G(1))) R G(0 R c))
a & ((Fb => a) => G(b | (!b & (Xa | (Xc R 1)))))
G(((c ^ !b) ^ !c) & (1 | F(1))) U G(1 R FGc)
!(b & X(Fc R 0)) R (X(0) | FX!F(c ^ !c))
(a R 0) => (G((!c => 1) <=> FX(0)) R F(!a ^ Ga))
(b <=> !0) <=> X(!(GFa | (F!!Gb ^ 0)) U b)
G((a <=> c) => ((1 | ((c | 1) U !1) | XX(0)) ^ !b))
FG(0 & FG!((b | 0 | (!Gc R GF(1))) ^ 1))
!(((a & !b) <=> (!c | (1 <=> 0))) | (c => (G(0) <=> !1)))
GGF(b & G(1) & (b <=> !c)) & (b <=> !(b & Fa))
X(c | (1 & Fa)) U F(b <=> (!(b U 1) & (Fb => 1)))
b ^ (!c & F((Gc <=> G!c) ^ (X(1) <=> Xb)))
X!X(Fc ^ ((F(1) U b) R (b U 1))) => (!b ^ Ga)
X((!0 R (b ^ c)) => (1 & ((X(0) R G(b U F(0))) => a)))
GF!X!((1 R (XF(1) U 0)) R (c | X!(c => c)))
F((a U X(1)) & (0 | (a => (((c U 1) ^ 1) ^ (F(0) R 1)))))
(X(1) => !F(c => 1)) | (1 & X!(0 & 1) & F!c)
X((!0 & FX(FX(0) R !c)) R c) & !FXF(0)
(((1 => 0) => (c R 0)) | ((b | (Ga => a)) ^ (a => b))) R a
(G(X!(a | !Gb) U a) ^ F(1)) ^ ((b | 0) U X(1))
(!(Fb ^ 0) => c) <=> (b => (a | (Fb <=> (F(1) U !b))))
XFG(XX(!(a & !1) R (1 | (b & (1 => b)))) => c)
G(((Xb | XXGXGa) <=> G(Fa <=> (b ^ 0))) U c)
!(((Fa | (c ^ 0)) U !(!b => X(0))) => ((b | c) => 0))
a | !c | ((G(Xb => c) & G(!0 | FFc)) <=> 1)
F((a & c) | FG!F(GG(1) & (1 | Xc))) U !c
F(0 | (G(1) ^ (a <=> (a | X(0))))) R (1 | X(G(0) <=> 1))
((c => !a) R ((b | 1) & XXGa)) ^ F!(a <=> Gc)
((c & Fc) <=> ((G!Fa => FGFc) => (a => a))) <=> 1
X(GFb U G(1 & XX((Fb | GGc) R (0 U b))))
F((1 U b) <=> GG(a ^ (G(1) & (F(1) R X(Gb R a)))))
!F((FXa & (b | c) & ((c => 1) <=> 1)) ^ XXGb)
(F((c <=> c) | F(b ^ 0)) ^ !!(0 & F(0))) & XG(1)
G((X(0) => GGa) ^ F(0)) U FF(((b ^ c) U a) U 1)
Gb R ((c U (0 <=> 0)) & FXF(Xc R X(0)))
((Gb => !a) U (1 & ((b | 1) ^ F!(c => Gb)))) => a
X((c R X(1)) => b) <=> (GGb | (b <=> F(0 & (c | 1))))
G(a <=> (((b R F(1)) => ((!c U c) U X(1))) | (G(1) R b)))
F!(FFF(c & !Ga) U (GG((a => b) U 0) U c))
(!FFGXXXFb & (b | F(1))) | (FXa => 0)
GG(Gb <=> (Fa U 0)) & G((!0 | (a ^ c)) <=> Fa)
F(1 U 0) U !((!X(Fb & Fc) <=> 1) & (Xb ^ 0))
((!a & (b | 1)) U (((c <=> 0) ^ G(1)) <=> (c R 0))) ^ Gc
((G(0) => (a | 1)) U F!F(0)) => ((0 & XF(1)) => G(1))
XXGG(G!1 R X((a | !!c) ^ X(!0 ^ 0)))
G!((Fb => G((a => b) U X(0))) | (Ga R Xb))
F(((Fa U (0 => (b U c))) => 1) R F(!a R F(1)))
((1 ^ 1) & X!Gb) | ((F(0) | XGa) <=> (Fc R 1))
FF(XF!(((1 R b) U (c | 1)) <=> 1) ^ 0) & (0 => 0)
(FF(X(1 U !0) <=> X(c | 0)) R !0) R (0 | F(1))
(0 R (XF(0) ^ (a R b))) ^ (b => F(0 U (Fa <=> Xc)))
((X(1) ^ (b ^ 1)) <=> (GXb | !!0)) <=> (X(0) & X(1))
X(F(0) | (c ^ 1) | (c & 0) | F(b <=> (Gc | !1)))
G(((F(1) | (1 U b)) => !(0 U (b R 0))) R (b <=> c))
!X(Ga ^ (FXGF(Gc <=> FF(0)) & (0 U !1)))
c | X(X((0 | XG!1) ^ 0) <=> (Fc ^ G(a => c)))
(((1 | (b R !(c | F(0)))) R b) <=> F(0)) U !(0 & Fa)
(F(0) U GF(X(1) ^ 1)) R (0 U (c => (!c U 1)))
c => ((0 => Fc) ^ (X(1) | (G(a <=> c) U (1 => a))))
X!b <=> (G((Fb R c) U F(c <=> !Fb)) U 0)
X(a ^ ((0 => (F(1) <=> G!a)) R (Gc R (Ga ^ X(0)))))
FX(!!c U ((FF(b <=> Fb) => (X(0) U a)) => Xb))
!(((Gb => c) ^ !GXa) | (F(1) U (a => (c ^ Xb))))
GF(0 => Xa) & ((X(a => Gc) U GGb) <=> !!c)
((G(1) => !b) <=> X(1)) U ((a <=> !b) | ((Xb <=> 1) <=> 0))
!0 R (0 R ((Xc => ((b ^ G(1)) <=> Fc)) <=> (Xb U 1)))
((Gc ^ XGXFF(0)) U F(c & Gb)) => (a => F(1))
G(F(a U 0) | FF(1)) <=> (0 => !!(FGF(0) R 1))
GG((a & G(!b R 1)) | (G(Xe => 0) <=> (e R F(0))))
F((Gc & (c ^ f)) | ((Xb & XF(e & Fd)) ^ Gf))
FGX(1 | ((a ^ f) <=> GFb)) | ((e <=> Fe) <=> Xb)
!G!GFc & F(!(Xe R FGf) & (d ^ Ga))
1 U (!(Fb U c) & XGG!!X(b ^ X(0 & 1)))
(c ^ (1 R 1)) ^ ((1 | (f <=> f)) => ((e & FXf) U Xd))
!((f R c) U (0 U c)) => (Gb <=> X(Fb R G(c U d)))
XFF((Xb | Xc) R (b & 0 & (X(1) => (b | Xc))))
G(FFb & ((b <=> (c <=> (b & Ff))) => (b & !(c | e))))
!((Xf ^ X(c R Fa)) ^ ((!1 <=> 1) => (Ge ^ Fd)))
X!X(Gb => (!c U !!(b => d))) | (!e => Xd)
d & G((X((1 | !c) U Xc) R F(1)) U (f <=> (b R a)))
((b => F(0)) => ((Xd & !b) U c)) R (1 U G(0 | Xb))
((1 | XFf) => GG(Xb R 1)) ^ ((!e => e) ^ Ga)
X((G((c U a) U (f ^ 0)) <=> Gb) | !(d <=> e)) <=> Xf
X(f U ((Gd ^ 0) <=> ((d & Ge) ^ (e <=> (c & FGe)))))
G(F(((c <=> f) & ((1 U a) U Xd)) => d) => (d & e & 0))
!G((Xd | (a ^ b)) => G!(1 R (X!b <=> (e => d))))
!0 | GGF(!!X(1) R !GG(0 | !G!c))
((f & !c) ^ F(c & (e R b))) U (F(1) | F(Gc => b))
(F(1) & GGf) R (!X!((b ^ f) R Gf) R FGf)
e => ((b ^ Gc) <=> F(F((c R b) => Fa) | (X(1) ^ 1)))
G(f R F!e) <=> F((!1 => d) => X(f U (F(0) U e)))
X((F(G(0) & (XXa U (0 & Xb))) ^ (f R 0)) <=> !c)
FF(((e ^ (d | 0)) <=> G(d U 0)) R F((Gc => 0) ^ 1))
!(!F(((b | e) U 0) U !Fd) & G(1 U G!G(0)))
FX((a | (e U d)) <=> Gc) & F(b => (b | (d R !a)))
(!e U X(0)) U (b & ((d | Ff) ^ G(GGa ^ G(0))))
((b | GX(!((e ^ 0) => XFa) => d)) <=> !f) ^ Ga
G(G(Xc <=> (a & f)) <=> (e R a)) => X(f | (Xe R f))
F((1 & G(G(0) & FXe)) <=> 1) <=> ((d & 1) => !!a)
G!((Xd R !FF(F(!f U d) ^ Ff)) & !!e)
F(((!0 => F(1)) & (c => Gc)) U X!X!(f <=> Fc))
X(e U ((c ^ 1) => !Fe)) | (((c <=> X(0)) R f) U Gf)
d & 1 & !G(X(f | ((Ff U f) <=> 0)) | !(e R 1))
(((a <=> f) U e) ^ G(!G(0) ^ (X(1) => Gf))) U (1 U 1)
(!a => (b | !Xb)) ^ !(!Xf <=> XG!(e U b))
(Xa <=> G!c) => G((((0 | 1) <=> (b => Gb)) => 0) R d)
X(0 | F((!(b <=> G(a ^ c)) U b) | !F(b & Ff)))
G(X!(!d U ((!d R f) R X!a)) R ((a ^ f) ^ 0))
!(((a R 0) <=> (c <=> (c U f))) <=> !(d | !(G(0) <=> Ga)))
X(0) | G(((a & Gf) => !XF(FXb ^ 1)) => !a)
X(d | (X(Fb & Ga) <=> GFGF(1))) & (1 | Fd)
(!Ge R G(!0 => Gc)) R ((Gb U f) R (b & !f))
GF!f ^ (!(0 & G((f => X(c & f)) U a)) <=> X(1))
F(((b U 0) <=> G(c ^ 1)) => (b | (!F(1) U c))) <=> !f
X(X!F(e & (c ^ c) & (FGe ^ (e & 1))) ^ X(0))
FX((!b => !f) R (((a => c) => a) & (d ^ (b & !b))))
!!((e & ((a R e) => ((b ^ !Xc) <=> 1))) <=> (c & Gc))
X!X!X(c | !G(0 R FFe)) | FG(b U f)
((c & e) R G(e U a)) U ((f U d) & GX(XXc U 1))
X!1 R (((c <=> !1) U (Gc => G(c => a))) ^ (e => b))
(FF!((f R (c & d)) U ((c | 0) => b)) ^ 0) => XG(0)
!F((a | d | 1) U c) <=> ((a & b) ^ X(b <=> G!0))
XG((((b R b) ^ (d R c)) R d) U (b U (0 | (a & Xc))))
F(((Fd | (b U (1 R c))) => 0) | !(Xb U (Ge => a)))
!((!e => G(1)) R ((c ^ (Xf R (c ^ G(1)))) => (d => d)))
(e | (X(1) U Xd)) & !((b R 1) | (c ^ (FXd U 1)))
!e U (!F(0 R (b <=> b)) U ((Fe ^ (b & !1)) R 1))
((Gd <=> X(0)) => XX!(Fb & GXf)) ^ (Fb => a)
X!GX((b ^ c) ^ 1) => GX(b R (a | Fe))
(d => !a) <=> ((e R c) | F(!d R (0 R (c <=> X!e))))
G(X(!1 R 1) & (((Fc => Xc) | (e => (d | 1))) <=> 0))
F(((d | !c) U (e | 1)) ^ (F(f R Fd) ^ !1))
GG(Gd R (!d | (!d ^ Xc))) | GXX(a => 0)
a & (G(e | (((b R e) R G(0)) ^ 0)) | ((b <=> 0) ^ Gf))
F((!GGe U !Xe) R XG(1)) R (e R (Gf ^ 1))
(!(G(1) => Fc) <=> (b ^ Fd)) ^ (Xe R (Xd | Xf))
(c U 1) => F!(a ^ (!d | G(!a | (c & F!1))))
X(Gb & (!((b & 0) R (f => c)) <=> (!a => F(b <=> 1))))
G((1 | ((Xb | F(0)) & (b => 0))) => !(XFe ^ Xf))
!G(((1 U e) & (!0 <=> 0)) <=> ((f | (a & Gb)) ^ Fe))
((!a ^ F(!(!f => 0) => F(f ^ 0))) => Xd) | !1
!F(1) & (b => f) & X((!GGf <=> (Ge ^ 1)) R 0)
(X(f | Ga) R f) R ((!Gc => (c & F!d)) ^ Gf)
e ^ XX((Xe R (XFe R !e)) => (X(f <=> 0) <=> 0))
F!(1 U F((d & f) U !!XGe)) <=> !(0 U X(1))
X(((c <=> c) R (G(e & !a) => (0 & X(1)))) => G(e => c))
FF(X(X!!(!Xf R e) => Ff) => (f => (d & 1)))
!(G(GX(a | b) => ((b => a) <=> X(1))) & (1 U !Fd))
c | !((d & 1) R (c R d)) | ((Fe ^ FGe) <=> !1)
!(Xa <=> G(1)) U (Fc U (f <=> (Gb => XFFXf)))
((((c ^ !d) <=> !d) & ((b ^ b) R (a => 0))) <=> !d) R d
((!1 R ((f ^ Xe) & FX(0))) => b) => G!(a <=> Fb)
((X(0) <=> !f) | (!1 U !0)) <=> (FF(0) => (a R Gf))
GF(X(d <=> (X(((1 => 0) U f) => FGb) R Xf)) R e)
F((XXXXb ^ F(1)) U ((F(0) U 0) => (a | 0 | 1)))
!(GGGe => (((d => 0) <=> 0) | FX((a R Gc) ^ 1)))
(X(e <=> (Fd => G(1))) | (b & (Fa U a))) & FXF(0)
X((((e | 1) ^ 1) & F(f => b)) ^ (b <=> XGa)) U G(0)
(Fe <=> X(c & 0)) ^ !FX(XXd <=> (c | !Fa))
(Fe <=> XFb) => F((!b R f) U !XFX(a <=> 0))
((!f <=> X(1)) & XG(((a ^ c) => Ff) U F!d)) <=> 1
G(((XXe ^ Xc) => GG!d) U (Xe R (e => Fd)))
F(FX(G!(f | !f) R X(1)) <=> XG(GXe R e))
(d & e) | F((a => Gc) R (((a | Gf) ^ 0) & (0 => f)))
a & 0 & G((c | d | XFe) R (Ff & F(d & e)))
((e <=> Xf) ^ G(a | Fa)) R ((e ^ (a U d)) ^ GFf)
X!G((((1 R a) <=> Fc) R 1) ^ Fe) ^ (Fc ^ G(0))
G((b U (c & 0)) U !XX(c ^ XGF(d U e))) => d
