Bob is cold. Bob is furry. Bob is smart. Bob is young. Charlie is cold. Charlie is furry. Charlie is white. All furry people are blue. White, nice people are cold. If Bob is smart then Bob is furry. If someone is young then they are white. All furry, young people are nice. If someone is smart then they are young. If Bob is smart and Bob is white then Bob is nice. If someone is young and white then they are smart.
Bob is cold.
("Bob" "is" "cold" "+")
Bob is furry.
("Bob" "is" "furry" "+")
Bob is smart.
("Bob" "is" "smart" "+")
Bob is young.
("Bob" "is" "young" "+")
Charlie is cold.
("Charlie" "is" "cold" "+")
Charlie is furry.
("Charlie" "is" "furry" "+")
Charlie is white.
("Charlie" "is" "white" "+")
All furry people are blue.
((("someone" "is" "furry" "+")) -> ("someone" "is" "blue" "+"))
White, nice people are cold.
((("someone" "is" "white" "+") ("someone" "is" "nice" "+")) -> ("someone" "is" "cold" "+"))
If Bob is smart then Bob is furry.
((("Bob" "is" "smart" "+")) -> ("Bob" "is" "furry" "+"))
If someone is young then they are white.
((("someone" "is" "young" "+")) -> ("someone" "is" "white" "+"))
All furry, young people are nice.
((("someone" "is" "furry" "+") ("someone" "is" "young" "+")) -> ("someone" "is" "nice" "+"))
If someone is smart then they are young.
((("someone" "is" "smart" "+")) -> ("someone" "is" "young" "+"))
If Bob is smart and Bob is white then Bob is nice.
((("Bob" "is" "smart" "+") ("Bob" "is" "white" "+")) -> ("Bob" "is" "nice" "+"))
If someone is young and white then they are smart.
((("someone" "is" "young" "+") ("someone" "is" "white" "+")) -> ("someone" "is" "smart" "+"))
Bob is furry.
True
1
proof
[(triple2 OR ((triple3) -> rule3) OR ((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3))]
("Bob" "is" "furry" "+")
triple2
((triple3) -> (rule3 % int1))
Bob is furry.
("Bob" "is" "furry" "+")
int1
((((triple4 ((triple4) -> (rule4 % int3))) -> (rule8 % int2))) -> (rule3 % int1))
Bob is furry.
("Bob" "is" "furry" "+")
int1
Bob is smart.
("Bob" "is" "smart" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
Bob is not smart.
False
1
inv-proof
[(triple3 OR ((triple4 ((triple4) -> rule4)) -> rule8))]
("Bob" "is" "smart" "-")
triple3
((triple4 ((triple4) -> (rule4 % int2))) -> (rule8 % int1))
Bob is smart.
("Bob" "is" "smart" "+")
int1
Bob is white.
("Bob" "is" "white" "+")
int2
@0: Bob is cold.[(triple1 OR ((((triple4) -> rule4) ((triple2 triple4) -> rule5)) -> rule2) OR ((((triple4) -> rule4) ((triple2 ((triple3) -> rule6)) -> rule5)) -> rule2) OR ((((triple4) -> rule4) ((triple3 ((triple4) -> rule4)) -> rule7)) -> rule2) OR ((((triple4) -> rule4) ((((triple3) -> rule3) triple4) -> rule5)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((triple2 triple4) -> rule5)) -> rule2) OR ((((triple4) -> rule4) ((((triple3) -> rule3) ((triple3) -> rule6)) -> rule5)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((triple2 ((triple3) -> rule6)) -> rule5)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((triple3 ((triple4) -> rule4)) -> rule7)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((((triple3) -> rule3) triple4) -> rule5)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((((triple3) -> rule3) ((triple3) -> rule6)) -> rule5)) -> rule2) OR ((((triple4) -> rule4) ((triple3 ((((triple3) -> rule6)) -> rule4)) -> rule7)) -> rule2) OR ((((triple4) -> rule4) ((((triple4 ((triple4) -> rule4)) -> rule8) ((triple4) -> rule4)) -> rule7)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((triple3 ((((triple3) -> rule6)) -> rule4)) -> rule7)) -> rule2) OR ((((triple4) -> rule4) ((((triple4 ((triple4) -> rule4)) -> rule8) ((((triple3) -> rule6)) -> rule4)) -> rule7)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((((triple4 ((triple4) -> rule4)) -> rule8) ((triple4) -> rule4)) -> rule7)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((((triple4 ((triple4) -> rule4)) -> rule8) ((((triple3) -> rule6)) -> rule4)) -> rule7)) -> rule2) OR ((((triple4) -> rule4) ((((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3) triple4) -> rule5)) -> rule2) OR ((((triple4) -> rule4) ((((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3) ((triple3) -> rule6)) -> rule5)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3) triple4) -> rule5)) -> rule2) OR ((((((triple3) -> rule6)) -> rule4) ((((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3) ((triple3) -> rule6)) -> rule5)) -> rule2))] Bob is furry.[(triple2 OR ((triple3) -> rule3) OR ((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3))] Bob is smart.[(triple3 OR ((triple4 ((triple4) -> rule4)) -> rule8))] Bob is young.[(triple4 OR ((triple3) -> rule6))] Charlie is cold.[(triple5)] Charlie is furry.[(triple6)] Charlie is white.[(triple7)] @1: Bob is blue.[(((triple2) -> rule1) OR ((((triple3) -> rule3)) -> rule1) OR ((((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3)) -> rule1))] Bob is nice.[(((triple2 triple4) -> rule5) OR ((triple2 ((triple3) -> rule6)) -> rule5) OR ((triple3 ((triple4) -> rule4)) -> rule7) OR ((((triple3) -> rule3) triple4) -> rule5) OR ((((triple3) -> rule3) ((triple3) -> rule6)) -> rule5) OR ((triple3 ((((triple3) -> rule6)) -> rule4)) -> rule7) OR ((((triple4 ((triple4) -> rule4)) -> rule8) ((triple4) -> rule4)) -> rule7) OR ((((triple4 ((triple4) -> rule4)) -> rule8) ((((triple3) -> rule6)) -> rule4)) -> rule7) OR ((((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3) triple4) -> rule5) OR ((((((triple4 ((triple4) -> rule4)) -> rule8)) -> rule3) ((triple3) -> rule6)) -> rule5))] Bob is white.[(((triple4) -> rule4) OR ((((triple3) -> rule6)) -> rule4))] Charlie is blue.[(((triple6) -> rule1))]
Bob is cold.
("Bob" "is" "cold" "+")
triple1
((((triple4) -> (rule4 % int3)) ((triple2 triple4) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
((((triple4) -> (rule4 % int4)) ((triple2 ((triple3) -> (rule6 % int3))) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is young.
("Bob" "is" "young" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
((((triple4) -> (rule4 % int3)) ((triple3 ((triple4) -> (rule4 % int3))) -> (rule7 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
((((triple4) -> (rule4 % int4)) ((((triple3) -> (rule3 % int3)) triple4) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is furry.
("Bob" "is" "furry" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
((((((triple3) -> (rule6 % int4))) -> (rule4 % int3)) ((triple2 triple4) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
Bob is young.
("Bob" "is" "young" "+")
int4
((((triple4) -> (rule4 % int5)) ((((triple3) -> (rule3 % int4)) ((triple3) -> (rule6 % int3))) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is young.
("Bob" "is" "young" "+")
int3
Bob is furry.
("Bob" "is" "furry" "+")
int4
Bob is white.
("Bob" "is" "white" "+")
int5
((((((triple3) -> (rule6 % int4))) -> (rule4 % int3)) ((triple2 ((triple3) -> (rule6 % int4))) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
Bob is young.
("Bob" "is" "young" "+")
int4
((((((triple3) -> (rule6 % int4))) -> (rule4 % int3)) ((triple3 ((triple4) -> (rule4 % int3))) -> (rule7 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
Bob is young.
("Bob" "is" "young" "+")
int4
((((((triple3) -> (rule6 % int5))) -> (rule4 % int4)) ((((triple3) -> (rule3 % int3)) triple4) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is furry.
("Bob" "is" "furry" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
Bob is young.
("Bob" "is" "young" "+")
int5
((((((triple3) -> (rule6 % int5))) -> (rule4 % int4)) ((((triple3) -> (rule3 % int3)) ((triple3) -> (rule6 % int5))) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is furry.
("Bob" "is" "furry" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
Bob is young.
("Bob" "is" "young" "+")
int5
((((triple4) -> (rule4 % int4)) ((triple3 ((((triple3) -> (rule6 % int3))) -> (rule4 % int4))) -> (rule7 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is young.
("Bob" "is" "young" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
((((triple4) -> (rule4 % int4)) ((((triple4 ((triple4) -> (rule4 % int4))) -> (rule8 % int3)) ((triple4) -> (rule4 % int4))) -> (rule7 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is smart.
("Bob" "is" "smart" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
((((((triple3) -> (rule6 % int4))) -> (rule4 % int3)) ((triple3 ((((triple3) -> (rule6 % int4))) -> (rule4 % int3))) -> (rule7 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
Bob is young.
("Bob" "is" "young" "+")
int4
((((triple4) -> (rule4 % int5)) ((((triple4 ((triple4) -> (rule4 % int5))) -> (rule8 % int4)) ((((triple3) -> (rule6 % int3))) -> (rule4 % int5))) -> (rule7 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is young.
("Bob" "is" "young" "+")
int3
Bob is smart.
("Bob" "is" "smart" "+")
int4
Bob is white.
("Bob" "is" "white" "+")
int5
((((((triple3) -> (rule6 % int5))) -> (rule4 % int4)) ((((triple4 ((triple4) -> (rule4 % int4))) -> (rule8 % int3)) ((triple4) -> (rule4 % int4))) -> (rule7 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is smart.
("Bob" "is" "smart" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
Bob is young.
("Bob" "is" "young" "+")
int5
((((((triple3) -> (rule6 % int5))) -> (rule4 % int4)) ((((triple4 ((triple4) -> (rule4 % int4))) -> (rule8 % int3)) ((((triple3) -> (rule6 % int5))) -> (rule4 % int4))) -> (rule7 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is smart.
("Bob" "is" "smart" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
Bob is young.
("Bob" "is" "young" "+")
int5
((((triple4) -> (rule4 % int5)) ((((((triple4 ((triple4) -> (rule4 % int5))) -> (rule8 % int4))) -> (rule3 % int3)) triple4) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is furry.
("Bob" "is" "furry" "+")
int3
Bob is smart.
("Bob" "is" "smart" "+")
int4
Bob is white.
("Bob" "is" "white" "+")
int5
((((triple4) -> (rule4 % int6)) ((((((triple4 ((triple4) -> (rule4 % int6))) -> (rule8 % int5))) -> (rule3 % int4)) ((triple3) -> (rule6 % int3))) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is young.
("Bob" "is" "young" "+")
int3
Bob is furry.
("Bob" "is" "furry" "+")
int4
Bob is smart.
("Bob" "is" "smart" "+")
int5
Bob is white.
("Bob" "is" "white" "+")
int6
((((((triple3) -> (rule6 % int6))) -> (rule4 % int5)) ((((((triple4 ((triple4) -> (rule4 % int5))) -> (rule8 % int4))) -> (rule3 % int3)) triple4) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is furry.
("Bob" "is" "furry" "+")
int3
Bob is smart.
("Bob" "is" "smart" "+")
int4
Bob is white.
("Bob" "is" "white" "+")
int5
Bob is young.
("Bob" "is" "young" "+")
int6
((((((triple3) -> (rule6 % int6))) -> (rule4 % int5)) ((((((triple4 ((triple4) -> (rule4 % int5))) -> (rule8 % int4))) -> (rule3 % int3)) ((triple3) -> (rule6 % int6))) -> (rule5 % int2))) -> (rule2 % int1))
Bob is cold.
("Bob" "is" "cold" "+")
int1
Bob is nice.
("Bob" "is" "nice" "+")
int2
Bob is furry.
("Bob" "is" "furry" "+")
int3
Bob is smart.
("Bob" "is" "smart" "+")
int4
Bob is white.
("Bob" "is" "white" "+")
int5
Bob is young.
("Bob" "is" "young" "+")
int6
Bob is furry.
("Bob" "is" "furry" "+")
triple2
((triple3) -> (rule3 % int1))
Bob is furry.
("Bob" "is" "furry" "+")
int1
((((triple4 ((triple4) -> (rule4 % int3))) -> (rule8 % int2))) -> (rule3 % int1))
Bob is furry.
("Bob" "is" "furry" "+")
int1
Bob is smart.
("Bob" "is" "smart" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
Bob is smart.
("Bob" "is" "smart" "+")
triple3
((triple4 ((triple4) -> (rule4 % int2))) -> (rule8 % int1))
Bob is smart.
("Bob" "is" "smart" "+")
int1
Bob is white.
("Bob" "is" "white" "+")
int2
Bob is young.
("Bob" "is" "young" "+")
triple4
((triple3) -> (rule6 % int1))
Bob is young.
("Bob" "is" "young" "+")
int1
Charlie is cold.
("Charlie" "is" "cold" "+")
triple5
Charlie is furry.
("Charlie" "is" "furry" "+")
triple6
Charlie is white.
("Charlie" "is" "white" "+")
triple7
Bob is blue.
("Bob" "is" "blue" "+")
((triple2) -> (rule1 % int1))
Bob is blue.
("Bob" "is" "blue" "+")
int1
((((triple3) -> (rule3 % int2))) -> (rule1 % int1))
Bob is blue.
("Bob" "is" "blue" "+")
int1
Bob is furry.
("Bob" "is" "furry" "+")
int2
((((((triple4 ((triple4) -> (rule4 % int4))) -> (rule8 % int3))) -> (rule3 % int2))) -> (rule1 % int1))
Bob is blue.
("Bob" "is" "blue" "+")
int1
Bob is furry.
("Bob" "is" "furry" "+")
int2
Bob is smart.
("Bob" "is" "smart" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
Bob is nice.
("Bob" "is" "nice" "+")
((triple2 triple4) -> (rule5 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
((triple2 ((triple3) -> (rule6 % int2))) -> (rule5 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is young.
("Bob" "is" "young" "+")
int2
((triple3 ((triple4) -> (rule4 % int2))) -> (rule7 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is white.
("Bob" "is" "white" "+")
int2
((((triple3) -> (rule3 % int2)) triple4) -> (rule5 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is furry.
("Bob" "is" "furry" "+")
int2
((((triple3) -> (rule3 % int3)) ((triple3) -> (rule6 % int2))) -> (rule5 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is young.
("Bob" "is" "young" "+")
int2
Bob is furry.
("Bob" "is" "furry" "+")
int3
((triple3 ((((triple3) -> (rule6 % int3))) -> (rule4 % int2))) -> (rule7 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is white.
("Bob" "is" "white" "+")
int2
Bob is young.
("Bob" "is" "young" "+")
int3
((((triple4 ((triple4) -> (rule4 % int3))) -> (rule8 % int2)) ((triple4) -> (rule4 % int3))) -> (rule7 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is smart.
("Bob" "is" "smart" "+")
int2
Bob is white.
("Bob" "is" "white" "+")
int3
((((triple4 ((triple4) -> (rule4 % int4))) -> (rule8 % int3)) ((((triple3) -> (rule6 % int2))) -> (rule4 % int4))) -> (rule7 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is young.
("Bob" "is" "young" "+")
int2
Bob is smart.
("Bob" "is" "smart" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
((((((triple4 ((triple4) -> (rule4 % int4))) -> (rule8 % int3))) -> (rule3 % int2)) triple4) -> (rule5 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is furry.
("Bob" "is" "furry" "+")
int2
Bob is smart.
("Bob" "is" "smart" "+")
int3
Bob is white.
("Bob" "is" "white" "+")
int4
((((((triple4 ((triple4) -> (rule4 % int5))) -> (rule8 % int4))) -> (rule3 % int3)) ((triple3) -> (rule6 % int2))) -> (rule5 % int1))
Bob is nice.
("Bob" "is" "nice" "+")
int1
Bob is young.
("Bob" "is" "young" "+")
int2
Bob is furry.
("Bob" "is" "furry" "+")
int3
Bob is smart.
("Bob" "is" "smart" "+")
int4
Bob is white.
("Bob" "is" "white" "+")
int5
Bob is white.
("Bob" "is" "white" "+")
((triple4) -> (rule4 % int1))
Bob is white.
("Bob" "is" "white" "+")
int1
((((triple3) -> (rule6 % int2))) -> (rule4 % int1))
Bob is white.
("Bob" "is" "white" "+")
int1
Bob is young.
("Bob" "is" "young" "+")
int2
Charlie is blue.
("Charlie" "is" "blue" "+")
((triple6) -> (rule1 % int1))
Charlie is blue.
("Charlie" "is" "blue" "+")
int1