TPTP Examples

Axioms/LIST-ROZEK.ax

@@ -0,0 +1,58 @@
+%--------------------------------------------------------------------------
+% File     : NUM-ROZEK : TPTP v8.1.2.
+% Domain   : Data Structures
+% Axioms   : Lists - Head, Tail, and Length
+%--------------------------------------------------------------------------
+
+%-- List Basics
+
+tff(list_t, type, list: $tType).
+
+tff(list_nil, type, nil : list).
+
+tff(list_cons, type,
+    cons: (
+        ($int * list) > list
+    )
+).
+
+%-- Head
+
+tff(head_t, type,
+    head: list > $int
+).
+
+tff(head_cons, axiom,
+    ![H: $int, T: list]: (
+        head(cons(H, T)) = H
+    )
+).
+
+%-- Tail
+
+tff(tail_t, type,
+    tail: list > list
+).
+
+tff(tail_cons, axiom,
+    ![H: $int, T: list]: (
+        tail(cons(H, T)) = T
+    )
+).
+
+% Note: The existence of head and tail definition shows that
+% cons is injective.
+
+%-- Length
+
+tff(length_t, type,
+    length: list > $int
+).
+
+tff(length_nil, axiom, length(nil) = 0).
+
+tff(length_cons, axiom,
+    ![H: $int, T: list]: (
+        length(cons(H, T)) = $sum(1, length(T))
+    )
+).

Axioms/NUM-ROZEK.ax

@@ -0,0 +1,42 @@
+%--------------------------------------------------------------------------
+% File     : NUM-ROZEK : TPTP v8.1.2.
+% Domain   : Number Theory
+% Axioms   : Number theory - Equality and Addition
+%--------------------------------------------------------------------------
+
+%-- Constants
+fof(c1, axiom, "one" = successor("zero")).
+fof(c1, axiom, "two" = successor("one")).
+fof(c1, axiom, "three" = successor("two")).
+fof(c1, axiom, "four" = successor("three")).
+fof(c1, axiom, "five" = successor("four")).
+
+%-- Equality with respect to natural numbers
+
+fof(zero, axiom,
+    ![X] : "zero" != successor(X)
+).
+
+fof(successor_equality, axiom,
+    ![A, B]: (
+        (successor(A) = successor(B)) =>
+        (A = B)
+    )
+).
+% Note: Also shows that successor is an injective function
+
+%-- Addition Axioms
+
+fof(adding_zero, axiom,
+    ![A]: add(A,"zero") = A
+).
+
+fof(addition, axiom,
+    ![A, B]:
+        (add(A,successor(B)) =
+        successor(add(A,B)))
+).
+
+
+
+%--------------------------------------------------------------------------