@prefix : <#> .
     @prefix daml: <http://www.daml.org/2001/03/daml+oil#> .
     @prefix log: <http://www.w3.org/2000/10/swap/log#> .
    
    @forAll :a,
                :b,
                :p .
    
    :ancestor     a daml:TransitiveProperty .
    
    :bill     :ancestor :granpa,
                :pa .
    
    :pa     :ancestor :granpa .
    {
        :a     :means :b .
        
        }     :means {:a     log:implies :b .
        :b     log:implies :a .
        };
         log:implies {:a     log:implies :b .
        :b     log:implies :a .
        } .
    {
        :p     a daml:TransitiveProperty .
        
        }     :means {{
            @forAll :x,
                        :y,
                        :z .
            {
                :x     :p :y .
                :y     :p :z .
                
                }     log:implies {:x     :p :z .
                } .
            
            }     a log:Truth .
        };
         log:implies {{
            @forAll :x,
                        :y,
                        :z .
            {
                :x     :p :y .
                :y     :p :z .
                
                }     log:implies {:x     :p :z .
                } .
            
            }     a log:Truth .
        } .
    {
        {
            @forAll :x,
                        :y,
                        :z .
            {
                :x     :p :y .
                :y     :p :z .
                
                }     log:implies {:x     :p :z .
                } .
            
            }     a log:Truth .
        
        }     :means {:p     a daml:TransitiveProperty .
        };
         log:implies {:p     a daml:TransitiveProperty .
        } .
    {
        @forAll :x,
                    :y,
                    :z .
        {
            :x     :ancestor :y .
            :y     :ancestor :z .
            
            }     log:implies {:x     :ancestor :z .
            } .
        
        }     a log:Truth .
    {
        :a     log:implies :b .
        :b     log:implies :a .
        
        }     :means {:a     :means :b .
        };
         log:implies {:a     :means :b .
        } .