Anne is big. Anne is kind. Anne is round. Anne is young. Fiona is kind. Fiona is quiet. Fiona is smart. Fiona is white. Fiona is young. Gary is big. Gary is kind. Gary is quiet. Gary is round. Gary is smart. Gary is white. Gary is young. If something is quiet then it is smart. All kind, round things are white. If something is kind and young then it is quiet. All kind things are quiet. If Gary is white and Gary is young then Gary is kind. If Fiona is round and Fiona is big then Fiona is white. Smart things are big. If Fiona is big and Fiona is quiet then Fiona is kind.
Anne is big.
("Anne" "is" "big" "+")
Anne is kind.
("Anne" "is" "kind" "+")
Anne is round.
("Anne" "is" "round" "+")
Anne is young.
("Anne" "is" "young" "+")
Fiona is kind.
("Fiona" "is" "kind" "+")
Fiona is quiet.
("Fiona" "is" "quiet" "+")
Fiona is smart.
("Fiona" "is" "smart" "+")
Fiona is white.
("Fiona" "is" "white" "+")
Fiona is young.
("Fiona" "is" "young" "+")
Gary is big.
("Gary" "is" "big" "+")
Gary is kind.
("Gary" "is" "kind" "+")
Gary is quiet.
("Gary" "is" "quiet" "+")
Gary is round.
("Gary" "is" "round" "+")
Gary is smart.
("Gary" "is" "smart" "+")
Gary is white.
("Gary" "is" "white" "+")
Gary is young.
("Gary" "is" "young" "+")
If something is quiet then it is smart.
((("something" "is" "quiet" "+")) -> ("something" "is" "smart" "+"))
All kind, round things are white.
((("something" "is" "kind" "+") ("something" "is" "round" "+")) -> ("something" "is" "white" "+"))
If something is kind and young then it is quiet.
((("something" "is" "kind" "+") ("something" "is" "young" "+")) -> ("something" "is" "quiet" "+"))
All kind things are quiet.
((("something" "is" "kind" "+")) -> ("something" "is" "quiet" "+"))
If Gary is white and Gary is young then Gary is kind.
((("Gary" "is" "white" "+") ("Gary" "is" "young" "+")) -> ("Gary" "is" "kind" "+"))
If Fiona is round and Fiona is big then Fiona is white.
((("Fiona" "is" "round" "+") ("Fiona" "is" "big" "+")) -> ("Fiona" "is" "white" "+"))
Smart things are big.
((("something" "is" "smart" "+")) -> ("something" "is" "big" "+"))
If Fiona is big and Fiona is quiet then Fiona is kind.
((("Fiona" "is" "big" "+") ("Fiona" "is" "quiet" "+")) -> ("Fiona" "is" "kind" "+"))
Fiona is white.
True
1
proof
[(triple8)]
("Fiona" "is" "white" "+")
triple8
Anne is not young.
False
1
inv-proof
[(triple4)]
("Anne" "is" "young" "-")
triple4
Fiona is big.
True
2
proof
[(((triple7) -> rule7) OR ((((triple6) -> rule1)) -> rule7) OR ((((((triple5) -> rule4)) -> rule1)) -> rule7) OR ((((((triple5 triple9) -> rule3)) -> rule1)) -> rule7))]
("Fiona" "is" "big" "+")
((triple7) -> (rule7 % int1))
Fiona is big.
("Fiona" "is" "big" "+")
int1
((((triple6) -> (rule1 % int2))) -> (rule7 % int1))
Fiona is big.
("Fiona" "is" "big" "+")
int1
Fiona is smart.
("Fiona" "is" "smart" "+")
int2
((((((triple5) -> (rule4 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Fiona is big.
("Fiona" "is" "big" "+")
int1
Fiona is smart.
("Fiona" "is" "smart" "+")
int2
Fiona is quiet.
("Fiona" "is" "quiet" "+")
int3
((((((triple5 triple9) -> (rule3 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Fiona is big.
("Fiona" "is" "big" "+")
int1
Fiona is smart.
("Fiona" "is" "smart" "+")
int2
Fiona is quiet.
("Fiona" "is" "quiet" "+")
int3
Anne is not white.
False
3
inv-proof
[(((triple2 triple3) -> rule2))]
("Anne" "is" "white" "-")
((triple2 triple3) -> (rule2 % int1))
Anne is white.
("Anne" "is" "white" "+")
int1
@0: Anne is big.[(triple1 OR ((((((triple2) -> rule4)) -> rule1)) -> rule7) OR ((((((triple2 triple4) -> rule3)) -> rule1)) -> rule7))] Anne is kind.[(triple2)] Anne is round.[(triple3)] Anne is young.[(triple4)] Fiona is kind.[(triple5 OR ((((triple7) -> rule7) triple6) -> rule8) OR ((((((triple6) -> rule1)) -> rule7) triple6) -> rule8))] Fiona is quiet.[(triple6 OR ((triple5) -> rule4) OR ((triple5 triple9) -> rule3))] Fiona is smart.[(triple7 OR ((triple6) -> rule1) OR ((((triple5) -> rule4)) -> rule1) OR ((((triple5 triple9) -> rule3)) -> rule1))] Fiona is white.[(triple8)] Fiona is young.[(triple9)] Gary is big.[(triple10 OR ((triple14) -> rule7) OR ((((triple12) -> rule1)) -> rule7) OR ((((((triple11) -> rule4)) -> rule1)) -> rule7) OR ((((((triple11 triple16) -> rule3)) -> rule1)) -> rule7) OR ((((((((triple15 triple16) -> rule5)) -> rule4)) -> rule1)) -> rule7) OR ((((((((triple15 triple16) -> rule5) triple16) -> rule3)) -> rule1)) -> rule7))] Gary is kind.[(triple11 OR ((triple15 triple16) -> rule5))] Gary is quiet.[(triple12 OR ((triple11) -> rule4) OR ((triple11 triple16) -> rule3) OR ((((triple15 triple16) -> rule5)) -> rule4) OR ((((triple15 triple16) -> rule5) triple16) -> rule3))] Gary is round.[(triple13)] Gary is smart.[(triple14 OR ((triple12) -> rule1) OR ((((triple11) -> rule4)) -> rule1) OR ((((triple11 triple16) -> rule3)) -> rule1) OR ((((((triple15 triple16) -> rule5)) -> rule4)) -> rule1) OR ((((((triple15 triple16) -> rule5) triple16) -> rule3)) -> rule1))] Gary is white.[(triple15 OR ((triple11 triple13) -> rule2))] Gary is young.[(triple16)] @1: Anne is quiet.[(((triple2) -> rule4) OR ((triple2 triple4) -> rule3))] Anne is white.[(((triple2 triple3) -> rule2))] Fiona is big.[(((triple7) -> rule7) OR ((((triple6) -> rule1)) -> rule7) OR ((((((triple5) -> rule4)) -> rule1)) -> rule7) OR ((((((triple5 triple9) -> rule3)) -> rule1)) -> rule7))] @2: Anne is smart.[(((((triple2) -> rule4)) -> rule1) OR ((((triple2 triple4) -> rule3)) -> rule1))]
Anne is big.
("Anne" "is" "big" "+")
triple1
((((((triple2) -> (rule4 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Anne is big.
("Anne" "is" "big" "+")
int1
Anne is smart.
("Anne" "is" "smart" "+")
int2
Anne is quiet.
("Anne" "is" "quiet" "+")
int3
((((((triple2 triple4) -> (rule3 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Anne is big.
("Anne" "is" "big" "+")
int1
Anne is smart.
("Anne" "is" "smart" "+")
int2
Anne is quiet.
("Anne" "is" "quiet" "+")
int3
Anne is kind.
("Anne" "is" "kind" "+")
triple2
Anne is round.
("Anne" "is" "round" "+")
triple3
Anne is young.
("Anne" "is" "young" "+")
triple4
Fiona is kind.
("Fiona" "is" "kind" "+")
triple5
((((triple7) -> (rule7 % int2)) triple6) -> (rule8 % int1))
Fiona is kind.
("Fiona" "is" "kind" "+")
int1
Fiona is big.
("Fiona" "is" "big" "+")
int2
((((((triple6) -> (rule1 % int3))) -> (rule7 % int2)) triple6) -> (rule8 % int1))
Fiona is kind.
("Fiona" "is" "kind" "+")
int1
Fiona is big.
("Fiona" "is" "big" "+")
int2
Fiona is smart.
("Fiona" "is" "smart" "+")
int3
Fiona is quiet.
("Fiona" "is" "quiet" "+")
triple6
((triple5) -> (rule4 % int1))
Fiona is quiet.
("Fiona" "is" "quiet" "+")
int1
((triple5 triple9) -> (rule3 % int1))
Fiona is quiet.
("Fiona" "is" "quiet" "+")
int1
Fiona is smart.
("Fiona" "is" "smart" "+")
triple7
((triple6) -> (rule1 % int1))
Fiona is smart.
("Fiona" "is" "smart" "+")
int1
((((triple5) -> (rule4 % int2))) -> (rule1 % int1))
Fiona is smart.
("Fiona" "is" "smart" "+")
int1
Fiona is quiet.
("Fiona" "is" "quiet" "+")
int2
((((triple5 triple9) -> (rule3 % int2))) -> (rule1 % int1))
Fiona is smart.
("Fiona" "is" "smart" "+")
int1
Fiona is quiet.
("Fiona" "is" "quiet" "+")
int2
Fiona is white.
("Fiona" "is" "white" "+")
triple8
Fiona is young.
("Fiona" "is" "young" "+")
triple9
Gary is big.
("Gary" "is" "big" "+")
triple10
((triple14) -> (rule7 % int1))
Gary is big.
("Gary" "is" "big" "+")
int1
((((triple12) -> (rule1 % int2))) -> (rule7 % int1))
Gary is big.
("Gary" "is" "big" "+")
int1
Gary is smart.
("Gary" "is" "smart" "+")
int2
((((((triple11) -> (rule4 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Gary is big.
("Gary" "is" "big" "+")
int1
Gary is smart.
("Gary" "is" "smart" "+")
int2
Gary is quiet.
("Gary" "is" "quiet" "+")
int3
((((((triple11 triple16) -> (rule3 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Gary is big.
("Gary" "is" "big" "+")
int1
Gary is smart.
("Gary" "is" "smart" "+")
int2
Gary is quiet.
("Gary" "is" "quiet" "+")
int3
((((((((triple15 triple16) -> (rule5 % int4))) -> (rule4 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Gary is big.
("Gary" "is" "big" "+")
int1
Gary is smart.
("Gary" "is" "smart" "+")
int2
Gary is quiet.
("Gary" "is" "quiet" "+")
int3
Gary is kind.
("Gary" "is" "kind" "+")
int4
((((((((triple15 triple16) -> (rule5 % int4)) triple16) -> (rule3 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Gary is big.
("Gary" "is" "big" "+")
int1
Gary is smart.
("Gary" "is" "smart" "+")
int2
Gary is quiet.
("Gary" "is" "quiet" "+")
int3
Gary is kind.
("Gary" "is" "kind" "+")
int4
Gary is kind.
("Gary" "is" "kind" "+")
triple11
((triple15 triple16) -> (rule5 % int1))
Gary is kind.
("Gary" "is" "kind" "+")
int1
Gary is quiet.
("Gary" "is" "quiet" "+")
triple12
((triple11) -> (rule4 % int1))
Gary is quiet.
("Gary" "is" "quiet" "+")
int1
((triple11 triple16) -> (rule3 % int1))
Gary is quiet.
("Gary" "is" "quiet" "+")
int1
((((triple15 triple16) -> (rule5 % int2))) -> (rule4 % int1))
Gary is quiet.
("Gary" "is" "quiet" "+")
int1
Gary is kind.
("Gary" "is" "kind" "+")
int2
((((triple15 triple16) -> (rule5 % int2)) triple16) -> (rule3 % int1))
Gary is quiet.
("Gary" "is" "quiet" "+")
int1
Gary is kind.
("Gary" "is" "kind" "+")
int2
Gary is round.
("Gary" "is" "round" "+")
triple13
Gary is smart.
("Gary" "is" "smart" "+")
triple14
((triple12) -> (rule1 % int1))
Gary is smart.
("Gary" "is" "smart" "+")
int1
((((triple11) -> (rule4 % int2))) -> (rule1 % int1))
Gary is smart.
("Gary" "is" "smart" "+")
int1
Gary is quiet.
("Gary" "is" "quiet" "+")
int2
((((triple11 triple16) -> (rule3 % int2))) -> (rule1 % int1))
Gary is smart.
("Gary" "is" "smart" "+")
int1
Gary is quiet.
("Gary" "is" "quiet" "+")
int2
((((((triple15 triple16) -> (rule5 % int3))) -> (rule4 % int2))) -> (rule1 % int1))
Gary is smart.
("Gary" "is" "smart" "+")
int1
Gary is quiet.
("Gary" "is" "quiet" "+")
int2
Gary is kind.
("Gary" "is" "kind" "+")
int3
((((((triple15 triple16) -> (rule5 % int3)) triple16) -> (rule3 % int2))) -> (rule1 % int1))
Gary is smart.
("Gary" "is" "smart" "+")
int1
Gary is quiet.
("Gary" "is" "quiet" "+")
int2
Gary is kind.
("Gary" "is" "kind" "+")
int3
Gary is white.
("Gary" "is" "white" "+")
triple15
((triple11 triple13) -> (rule2 % int1))
Gary is white.
("Gary" "is" "white" "+")
int1
Gary is young.
("Gary" "is" "young" "+")
triple16
Anne is quiet.
("Anne" "is" "quiet" "+")
((triple2) -> (rule4 % int1))
Anne is quiet.
("Anne" "is" "quiet" "+")
int1
((triple2 triple4) -> (rule3 % int1))
Anne is quiet.
("Anne" "is" "quiet" "+")
int1
Anne is white.
("Anne" "is" "white" "+")
((triple2 triple3) -> (rule2 % int1))
Anne is white.
("Anne" "is" "white" "+")
int1
Fiona is big.
("Fiona" "is" "big" "+")
((triple7) -> (rule7 % int1))
Fiona is big.
("Fiona" "is" "big" "+")
int1
((((triple6) -> (rule1 % int2))) -> (rule7 % int1))
Fiona is big.
("Fiona" "is" "big" "+")
int1
Fiona is smart.
("Fiona" "is" "smart" "+")
int2
((((((triple5) -> (rule4 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Fiona is big.
("Fiona" "is" "big" "+")
int1
Fiona is smart.
("Fiona" "is" "smart" "+")
int2
Fiona is quiet.
("Fiona" "is" "quiet" "+")
int3
((((((triple5 triple9) -> (rule3 % int3))) -> (rule1 % int2))) -> (rule7 % int1))
Fiona is big.
("Fiona" "is" "big" "+")
int1
Fiona is smart.
("Fiona" "is" "smart" "+")
int2
Fiona is quiet.
("Fiona" "is" "quiet" "+")
int3
Anne is smart.
("Anne" "is" "smart" "+")
((((triple2) -> (rule4 % int2))) -> (rule1 % int1))
Anne is smart.
("Anne" "is" "smart" "+")
int1
Anne is quiet.
("Anne" "is" "quiet" "+")
int2
((((triple2 triple4) -> (rule3 % int2))) -> (rule1 % int1))
Anne is smart.
("Anne" "is" "smart" "+")
int1
Anne is quiet.
("Anne" "is" "quiet" "+")
int2