Predicate logic; 3 variables; implications (arrows)

https://commons.wikimedia.org/wiki/File:Predicate_logic;_3_variables;_implications.png

a3e12 --> e123
a2e13 --> e123
a1e23 --> e123
e2a3e1 --> a3e12
e2a3e1 --> e1(23)
e1a3e2 --> a3e12
e1a3e2 --> e(13)2
e3a2e1 --> a2e13
e3a2e1 --> e1(23)
e1a2e3 --> a2e13
e1a2e3 --> e(12)3
e3a1e2 --> a1e23
e3a1e2 --> e(13)2
e2a1e3 --> a1e23
e2a1e3 --> e(12)3
e12a3 --> e2a3e1
e12a3 --> e1a3e2
e13a2 --> e3a2e1
e13a2 --> e1a2e3
e23a1 --> e3a1e2
e23a1 --> e2a1e3
a23e1 --> e2a3e1
a23e1 --> e3a2e1
a23e1 --> a(23)e1
a13e2 --> e1a3e2
a13e2 --> e3a1e2
a13e2 --> a(13)e2
a12e3 --> e1a2e3
a12e3 --> e2a1e3
a12e3 --> a(12)e3
a2e1a3 --> e12a3
a2e1a3 --> a23e1
a2e1a3 --> a2e(13)
a3e1a2 --> e13a2
a3e1a2 --> a23e1
a3e1a2 --> a3e(12)
a1e2a3 --> e12a3
a1e2a3 --> a13e2
a1e2a3 --> a1e(23)
a3e2a1 --> e23a1
a3e2a1 --> a13e2
a3e2a1 --> a3e(12)
a1e3a2 --> e13a2
a1e3a2 --> a12e3
a1e3a2 --> a1e(23)
a2e3a1 --> e23a1
a2e3a1 --> a12e3
a2e3a1 --> a2e(13)
e1a23 --> a2e1a3
e1a23 --> a3e1a2
e1a23 --> e(12)a3
e1a23 --> e(13)a2
e1a23 --> e1a(23)
e2a13 --> a1e2a3
e2a13 --> a3e2a1
e2a13 --> e(12)a3
e2a13 --> e2a(13)
e2a13 --> e(23)a1
e3a12 --> a1e3a2
e3a12 --> a2e3a1
e3a12 --> e3a(12)
e3a12 --> e(13)a2
e3a12 --> e(23)a1
a123 --> e1a23
a123 --> e2a13
a123 --> e3a12
a123 --> a(12)3
a123 --> a(13)2
a123 --> a1(23)
e(12)3 --> e123
a3e(12) --> a3e12
a3e(12) --> e(12)3
a(12)e3 --> a2e13
a(12)e3 --> a1e23
a(12)e3 --> e(12)3
e(12)a3 --> e12a3
e(12)a3 --> a3e(12)
e(12)a3 --> e(123)
e3a(12) --> e3a2e1
e3a(12) --> e3a1e2
e3a(12) --> a(12)e3
e3a(12) --> a2e(13)
e3a(12) --> a1e(23)
e3a(12) --> e(123)
a(12)3 --> a2e1a3
a(12)3 --> a1e2a3
a(12)3 --> e(12)a3
a(12)3 --> e3a(12)
a(12)3 --> a(123)
e(13)2 --> e123
a2e(13) --> a2e13
a2e(13) --> e(13)2
a(13)e2 --> a3e12
a(13)e2 --> a1e23
a(13)e2 --> e(13)2
e(13)a2 --> e13a2
e(13)a2 --> a2e(13)
e(13)a2 --> e(123)
e2a(13) --> e2a3e1
e2a(13) --> e2a1e3
e2a(13) --> a3e(12)
e2a(13) --> a(13)e2
e2a(13) --> a1e(23)
e2a(13) --> e(123)
a(13)2 --> a3e1a2
a(13)2 --> a1e3a2
a(13)2 --> e(13)a2
a(13)2 --> e2a(13)
a(13)2 --> a(123)
e1(23) --> e123
a1e(23) --> a1e23
a1e(23) --> e1(23)
a(23)e1 --> a3e12
a(23)e1 --> a2e13
a(23)e1 --> e1(23)
e(23)a1 --> e23a1
e(23)a1 --> a1e(23)
e(23)a1 --> e(123)
e1a(23) --> e1a3e2
e1a(23) --> e1a2e3
e1a(23) --> a3e(12)
e1a(23) --> a2e(13)
e1a(23) --> a(23)e1
e1a(23) --> e(123)
a1(23) --> a3e2a1
a1(23) --> a2e3a1
a1(23) --> e(23)a1
a1(23) --> e1a(23)
a1(23) --> a(123)
e(123) --> e(12)3
e(123) --> e(13)2
e(123) --> e1(23)
a(123) --> a3e(12)
a(123) --> a(12)e3
a(123) --> a2e(13)
a(123) --> a(13)e2
a(123) --> a1e(23)
a(123) --> a(23)e1
a(123) --> e(123)