Dave is big. Dave is kind. Dave is nice. Dave is white. Harry is big. Harry is kind. Harry is nice. Harry is quiet. Harry is rough. Harry is white. All kind, smart people are nice. All kind, nice people are rough. If someone is kind and big then they are rough. If someone is white then they are kind. White, nice people are kind. If someone is rough and nice then they are smart. Kind people are white. Kind, nice people are quiet.
Dave is big.
("Dave" "is" "big" "+")
Dave is kind.
("Dave" "is" "kind" "+")
Dave is nice.
("Dave" "is" "nice" "+")
Dave is white.
("Dave" "is" "white" "+")
Harry is big.
("Harry" "is" "big" "+")
Harry is kind.
("Harry" "is" "kind" "+")
Harry is nice.
("Harry" "is" "nice" "+")
Harry is quiet.
("Harry" "is" "quiet" "+")
Harry is rough.
("Harry" "is" "rough" "+")
Harry is white.
("Harry" "is" "white" "+")
All kind, smart people are nice.
((("someone" "is" "kind" "+") ("someone" "is" "smart" "+")) -> ("someone" "is" "nice" "+"))
All kind, nice people are rough.
((("someone" "is" "kind" "+") ("someone" "is" "nice" "+")) -> ("someone" "is" "rough" "+"))
If someone is kind and big then they are rough.
((("someone" "is" "kind" "+") ("someone" "is" "big" "+")) -> ("someone" "is" "rough" "+"))
If someone is white then they are kind.
((("someone" "is" "white" "+")) -> ("someone" "is" "kind" "+"))
White, nice people are kind.
((("someone" "is" "white" "+") ("someone" "is" "nice" "+")) -> ("someone" "is" "kind" "+"))
If someone is rough and nice then they are smart.
((("someone" "is" "rough" "+") ("someone" "is" "nice" "+")) -> ("someone" "is" "smart" "+"))
Kind people are white.
((("someone" "is" "kind" "+")) -> ("someone" "is" "white" "+"))
Kind, nice people are quiet.
((("someone" "is" "kind" "+") ("someone" "is" "nice" "+")) -> ("someone" "is" "quiet" "+"))
Dave is big.
True
1
proof
[(triple1)]
("Dave" "is" "big" "+")
triple1
Dave is not big.
False
1
inv-proof
[(triple1)]
("Dave" "is" "big" "-")
triple1
@0: Dave is big.[(triple1)] Dave is kind.[(triple2 OR ((triple4) -> rule4) OR ((triple4 triple3) -> rule5))] Dave is nice.[(triple3)] Dave is white.[(triple4 OR ((triple2) -> rule7))] Harry is big.[(triple5)] Harry is kind.[(triple6 OR ((triple10) -> rule4) OR ((triple10 triple7) -> rule5))] Harry is nice.[(triple7)] Harry is quiet.[(triple8 OR ((triple6 triple7) -> rule8) OR ((((triple10) -> rule4) triple7) -> rule8) OR ((((triple10 triple7) -> rule5) triple7) -> rule8))] Harry is rough.[(triple9 OR ((triple6 triple5) -> rule3) OR ((triple6 triple7) -> rule2) OR ((((triple10) -> rule4) triple5) -> rule3) OR ((((triple10) -> rule4) triple7) -> rule2) OR ((((triple10 triple7) -> rule5) triple5) -> rule3) OR ((((triple10 triple7) -> rule5) triple7) -> rule2))] Harry is white.[(triple10 OR ((triple6) -> rule7))] @1: Dave is quiet.[(((triple2 triple3) -> rule8) OR ((((triple4) -> rule4) triple3) -> rule8) OR ((((triple4 triple3) -> rule5) triple3) -> rule8))] Dave is rough.[(((triple2 triple1) -> rule3) OR ((triple2 triple3) -> rule2) OR ((((triple4) -> rule4) triple1) -> rule3) OR ((((triple4) -> rule4) triple3) -> rule2) OR ((((triple4 triple3) -> rule5) triple1) -> rule3) OR ((((triple4 triple3) -> rule5) triple3) -> rule2))] Harry is smart.[(((triple9 triple7) -> rule6) OR ((((triple6 triple5) -> rule3) triple7) -> rule6) OR ((((triple6 triple7) -> rule2) triple7) -> rule6) OR ((((((triple10) -> rule4) triple5) -> rule3) triple7) -> rule6) OR ((((((triple10) -> rule4) triple7) -> rule2) triple7) -> rule6) OR ((((((triple10 triple7) -> rule5) triple5) -> rule3) triple7) -> rule6) OR ((((((triple10 triple7) -> rule5) triple7) -> rule2) triple7) -> rule6))] @2: Dave is smart.[(((((triple2 triple1) -> rule3) triple3) -> rule6) OR ((((triple2 triple3) -> rule2) triple3) -> rule6) OR ((((((triple4) -> rule4) triple1) -> rule3) triple3) -> rule6) OR ((((((triple4) -> rule4) triple3) -> rule2) triple3) -> rule6) OR ((((((triple4 triple3) -> rule5) triple1) -> rule3) triple3) -> rule6) OR ((((((triple4 triple3) -> rule5) triple3) -> rule2) triple3) -> rule6))]
Dave is big.
("Dave" "is" "big" "+")
triple1
Dave is kind.
("Dave" "is" "kind" "+")
triple2
((triple4) -> (rule4 % int1))
Dave is kind.
("Dave" "is" "kind" "+")
int1
((triple4 triple3) -> (rule5 % int1))
Dave is kind.
("Dave" "is" "kind" "+")
int1
Dave is nice.
("Dave" "is" "nice" "+")
triple3
Dave is white.
("Dave" "is" "white" "+")
triple4
((triple2) -> (rule7 % int1))
Dave is white.
("Dave" "is" "white" "+")
int1
Harry is big.
("Harry" "is" "big" "+")
triple5
Harry is kind.
("Harry" "is" "kind" "+")
triple6
((triple10) -> (rule4 % int1))
Harry is kind.
("Harry" "is" "kind" "+")
int1
((triple10 triple7) -> (rule5 % int1))
Harry is kind.
("Harry" "is" "kind" "+")
int1
Harry is nice.
("Harry" "is" "nice" "+")
triple7
Harry is quiet.
("Harry" "is" "quiet" "+")
triple8
((triple6 triple7) -> (rule8 % int1))
Harry is quiet.
("Harry" "is" "quiet" "+")
int1
((((triple10) -> (rule4 % int2)) triple7) -> (rule8 % int1))
Harry is quiet.
("Harry" "is" "quiet" "+")
int1
Harry is kind.
("Harry" "is" "kind" "+")
int2
((((triple10 triple7) -> (rule5 % int2)) triple7) -> (rule8 % int1))
Harry is quiet.
("Harry" "is" "quiet" "+")
int1
Harry is kind.
("Harry" "is" "kind" "+")
int2
Harry is rough.
("Harry" "is" "rough" "+")
triple9
((triple6 triple5) -> (rule3 % int1))
Harry is rough.
("Harry" "is" "rough" "+")
int1
((triple6 triple7) -> (rule2 % int1))
Harry is rough.
("Harry" "is" "rough" "+")
int1
((((triple10) -> (rule4 % int2)) triple5) -> (rule3 % int1))
Harry is rough.
("Harry" "is" "rough" "+")
int1
Harry is kind.
("Harry" "is" "kind" "+")
int2
((((triple10) -> (rule4 % int2)) triple7) -> (rule2 % int1))
Harry is rough.
("Harry" "is" "rough" "+")
int1
Harry is kind.
("Harry" "is" "kind" "+")
int2
((((triple10 triple7) -> (rule5 % int2)) triple5) -> (rule3 % int1))
Harry is rough.
("Harry" "is" "rough" "+")
int1
Harry is kind.
("Harry" "is" "kind" "+")
int2
((((triple10 triple7) -> (rule5 % int2)) triple7) -> (rule2 % int1))
Harry is rough.
("Harry" "is" "rough" "+")
int1
Harry is kind.
("Harry" "is" "kind" "+")
int2
Harry is white.
("Harry" "is" "white" "+")
triple10
((triple6) -> (rule7 % int1))
Harry is white.
("Harry" "is" "white" "+")
int1
Dave is quiet.
("Dave" "is" "quiet" "+")
((triple2 triple3) -> (rule8 % int1))
Dave is quiet.
("Dave" "is" "quiet" "+")
int1
((((triple4) -> (rule4 % int2)) triple3) -> (rule8 % int1))
Dave is quiet.
("Dave" "is" "quiet" "+")
int1
Dave is kind.
("Dave" "is" "kind" "+")
int2
((((triple4 triple3) -> (rule5 % int2)) triple3) -> (rule8 % int1))
Dave is quiet.
("Dave" "is" "quiet" "+")
int1
Dave is kind.
("Dave" "is" "kind" "+")
int2
Dave is rough.
("Dave" "is" "rough" "+")
((triple2 triple1) -> (rule3 % int1))
Dave is rough.
("Dave" "is" "rough" "+")
int1
((triple2 triple3) -> (rule2 % int1))
Dave is rough.
("Dave" "is" "rough" "+")
int1
((((triple4) -> (rule4 % int2)) triple1) -> (rule3 % int1))
Dave is rough.
("Dave" "is" "rough" "+")
int1
Dave is kind.
("Dave" "is" "kind" "+")
int2
((((triple4) -> (rule4 % int2)) triple3) -> (rule2 % int1))
Dave is rough.
("Dave" "is" "rough" "+")
int1
Dave is kind.
("Dave" "is" "kind" "+")
int2
((((triple4 triple3) -> (rule5 % int2)) triple1) -> (rule3 % int1))
Dave is rough.
("Dave" "is" "rough" "+")
int1
Dave is kind.
("Dave" "is" "kind" "+")
int2
((((triple4 triple3) -> (rule5 % int2)) triple3) -> (rule2 % int1))
Dave is rough.
("Dave" "is" "rough" "+")
int1
Dave is kind.
("Dave" "is" "kind" "+")
int2
Harry is smart.
("Harry" "is" "smart" "+")
((triple9 triple7) -> (rule6 % int1))
Harry is smart.
("Harry" "is" "smart" "+")
int1
((((triple6 triple5) -> (rule3 % int2)) triple7) -> (rule6 % int1))
Harry is smart.
("Harry" "is" "smart" "+")
int1
Harry is rough.
("Harry" "is" "rough" "+")
int2
((((triple6 triple7) -> (rule2 % int2)) triple7) -> (rule6 % int1))
Harry is smart.
("Harry" "is" "smart" "+")
int1
Harry is rough.
("Harry" "is" "rough" "+")
int2
((((((triple10) -> (rule4 % int3)) triple5) -> (rule3 % int2)) triple7) -> (rule6 % int1))
Harry is smart.
("Harry" "is" "smart" "+")
int1
Harry is rough.
("Harry" "is" "rough" "+")
int2
Harry is kind.
("Harry" "is" "kind" "+")
int3
((((((triple10) -> (rule4 % int3)) triple7) -> (rule2 % int2)) triple7) -> (rule6 % int1))
Harry is smart.
("Harry" "is" "smart" "+")
int1
Harry is rough.
("Harry" "is" "rough" "+")
int2
Harry is kind.
("Harry" "is" "kind" "+")
int3
((((((triple10 triple7) -> (rule5 % int3)) triple5) -> (rule3 % int2)) triple7) -> (rule6 % int1))
Harry is smart.
("Harry" "is" "smart" "+")
int1
Harry is rough.
("Harry" "is" "rough" "+")
int2
Harry is kind.
("Harry" "is" "kind" "+")
int3
((((((triple10 triple7) -> (rule5 % int3)) triple7) -> (rule2 % int2)) triple7) -> (rule6 % int1))
Harry is smart.
("Harry" "is" "smart" "+")
int1
Harry is rough.
("Harry" "is" "rough" "+")
int2
Harry is kind.
("Harry" "is" "kind" "+")
int3
Dave is smart.
("Dave" "is" "smart" "+")
((((triple2 triple1) -> (rule3 % int2)) triple3) -> (rule6 % int1))
Dave is smart.
("Dave" "is" "smart" "+")
int1
Dave is rough.
("Dave" "is" "rough" "+")
int2
((((triple2 triple3) -> (rule2 % int2)) triple3) -> (rule6 % int1))
Dave is smart.
("Dave" "is" "smart" "+")
int1
Dave is rough.
("Dave" "is" "rough" "+")
int2
((((((triple4) -> (rule4 % int3)) triple1) -> (rule3 % int2)) triple3) -> (rule6 % int1))
Dave is smart.
("Dave" "is" "smart" "+")
int1
Dave is rough.
("Dave" "is" "rough" "+")
int2
Dave is kind.
("Dave" "is" "kind" "+")
int3
((((((triple4) -> (rule4 % int3)) triple3) -> (rule2 % int2)) triple3) -> (rule6 % int1))
Dave is smart.
("Dave" "is" "smart" "+")
int1
Dave is rough.
("Dave" "is" "rough" "+")
int2
Dave is kind.
("Dave" "is" "kind" "+")
int3
((((((triple4 triple3) -> (rule5 % int3)) triple1) -> (rule3 % int2)) triple3) -> (rule6 % int1))
Dave is smart.
("Dave" "is" "smart" "+")
int1
Dave is rough.
("Dave" "is" "rough" "+")
int2
Dave is kind.
("Dave" "is" "kind" "+")
int3
((((((triple4 triple3) -> (rule5 % int3)) triple3) -> (rule2 % int2)) triple3) -> (rule6 % int1))
Dave is smart.
("Dave" "is" "smart" "+")
int1
Dave is rough.
("Dave" "is" "rough" "+")
int2
Dave is kind.
("Dave" "is" "kind" "+")
int3