Beginnings of a new ML API

Signed-off-by: Christoph M. Wintersteiger <cwinter@microsoft.com>

src/api/ml/README

@@ -0,0 +1,3 @@
+This directory is work in progress.
+
+We are currently working on a brand new ML API.

src/api/ml/test_capi.regress.err

@@ -1,5 +0,0 @@
-WARNING: invalid function application, sort mismatch on argument at position 1
-WARNING: (define iff Bool Bool Bool) applied to: 
-x of sort Int
-y of sort Bool
-

src/api/ml/test_capi.regress.out

@@ -1,386 +0,0 @@
-Z3 4.2.0.0
-
-simple_example
-CONTEXT:
-(solver)END OF CONTEXT
-
-DeMorgan
-DeMorgan is valid
-
-find_model_example1
-model for: x xor y
-sat
-y -> false
-x -> true
-
-
-find_model_example2
-model for: x < y + 1, x > 2
-sat
-y -> 3
-x -> 3
-
-model for: x < y + 1, x > 2, not(x = y)
-sat
-y -> 4
-x -> 3
-
-
-prove_example1
-prove: x = y implies g(x) = g(y)
-valid
-disprove: x = y implies g(g(x)) = g(y)
-invalid
-counterexample:
-y -> U!val!0
-x -> U!val!0
-g -> {
-  U!val!0 -> U!val!1
-  U!val!1 -> U!val!2
-  else -> U!val!1
-}
-
-
-prove_example2
-prove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < 0
-valid
-disprove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < -1
-invalid
-counterexample:
-z -> (- 1)
-y -> (- 7719)
-x -> (- 7719)
-g -> {
-  (- 7719) -> 0
-  0 -> 2
-  (- 1) -> 3
-  else -> 0
-}
-
-
-push_pop_example1
-assert: x >= 'big number'
-push
-number of scopes: 1
-assert: x <= 3
-unsat
-pop
-number of scopes: 0
-sat
-x = 1000000000000000000000000000000000000000000000000000000:int
-function interpretations:
-assert: y > x
-sat
-y = 1000000000000000000000000000000000000000000000000000001:int
-x = 1000000000000000000000000000000000000000000000000000000:int
-function interpretations:
-
-quantifier_example1
-pattern: {(f #0 #1)}
-
-assert axiom:
-(forall (k!0 Int) (k!1 Int) (= (inv!0 (f k!1 k!0)) k!0) :pat {(f k!1 k!0)})
-prove: f(x, y) = f(w, v) implies y = v
-valid
-disprove: f(x, y) = f(w, v) implies x = w
-that is: not(f(x, y) = f(w, v) implies x = w) is satisfiable
-unknown
-potential model:
-w = 2:int
-v = 1:int
-y = 1:int
-x = 0:int
-function interpretations:
-f = {(else|->(define f!52 Int Int Int)[(define k!50 Int Int)[#unknown], (define k!51 Int Int)[#unknown]])}
-#51 = {(2:int|->2:int), (1:int|->1:int), (15:int|->15:int), (11:int|->11:int), (0:int|->0:int), (19:int|->19:int), (else|->2:int)}
-f!52 = {(0:int, 1:int|->3:int), (2:int, 1:int|->3:int), (0:int, 0:int|->4:int), (2:int, 0:int|->5:int), (6:int, 2:int|->7:int), (2:int, 2:int|->8:int), (0:int, 2:int|->9:int), (6:int, 0:int|->10:int), (0:int, 11:int|->12:int), (2:int, 11:int|->13:int), (6:int, 11:int|->14:int), (0:int, 15:int|->16:int), (2:int, 15:int|->17:int), (6:int, 15:int|->18:int), (0:int, 19:int|->20:int), (6:int, 19:int|->21:int), (2:int, 19:int|->22:int), (else|->3:int)}
-inv!0 = {(3:int|->1:int), (4:int|->0:int), (5:int|->0:int), (7:int|->2:int), (8:int|->2:int), (9:int|->2:int), (10:int|->0:int), (12:int|->11:int), (13:int|->11:int), (14:int|->11:int), (16:int|->15:int), (17:int|->15:int), (18:int|->15:int), (20:int|->19:int), (21:int|->19:int), (22:int|->19:int), (else|->2:int)}
-#50 = {(2:int|->2:int), (6:int|->6:int), (0:int|->0:int), (else|->2:int)}
-reason for last failure: 7 (7 = quantifiers)
-
-array_example1
-prove: store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3))
-(=> (= (store a1 i1 v1) (store a2 i2 v2))
-    (or (= i1 i3) (= i2 i3) (= (select a1 i3) (select a2 i3))))
-valid
-
-array_example2
-n = 2
-(distinct k!0 k!1)
-sat
-#0 = (define as-array[k!0] (Array Bool Bool))
-#1 = (define as-array[k!1] (Array Bool Bool))
-function interpretations:
-#0 = {((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
-#1 = {((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
-n = 3
-(distinct k!0 k!1 k!2)
-sat
-#0 = (define as-array[k!0] (Array Bool Bool))
-#1 = (define as-array[k!1] (Array Bool Bool))
-#2 = (define as-array[k!2] (Array Bool Bool))
-function interpretations:
-#0 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define false Bool)), (else|->(define true Bool))}
-#1 = {((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
-#2 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
-n = 4
-(distinct k!0 k!1 k!2 k!3)
-sat
-#0 = (define as-array[k!0] (Array Bool Bool))
-#1 = (define as-array[k!1] (Array Bool Bool))
-#2 = (define as-array[k!2] (Array Bool Bool))
-#3 = (define as-array[k!3] (Array Bool Bool))
-function interpretations:
-#0 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define true Bool)), (else|->(define false Bool))}
-#1 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define false Bool)), (else|->(define true Bool))}
-#2 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
-#3 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
-n = 5
-(distinct k!0 k!1 k!2 k!3 k!4)
-unsat
-
-array_example3
-domain: int
-range:  bool
-
-tuple_example1
-tuple_sort: (real, real)
-prove: get_x(mk_pair(x, y)) = 1 implies x = 1
-valid
-disprove: get_x(mk_pair(x, y)) = 1 implies y = 1
-invalid
-counterexample:
-y -> 0
-x -> 1
-
-prove: get_x(p1) = get_x(p2) and get_y(p1) = get_y(p2) implies p1 = p2
-valid
-disprove: get_x(p1) = get_x(p2) implies p1 = p2
-invalid
-counterexample:
-p1 -> (mk_pair 1 0)
-p2 -> (mk_pair 1 2)
-
-prove: p2 = update(p1, 0, 10) implies get_x(p2) = 10
-valid
-disprove: p2 = update(p1, 0, 10) implies get_y(p2) = 10
-invalid
-counterexample:
-p2 -> (mk_pair 10 1)
-p1 -> (mk_pair 0 1)
-
-
-bitvector_example1
-disprove: x - 10 <= 0 IFF x <= 10 for (32-bit) machine integers
-invalid
-counterexample:
-x -> bv2147483656[32]
-
-
-bitvector_example2
-find values of x and y, such that x ^ y - 103 == x * y
-sat
-y -> bv3905735879[32]
-x -> bv3787456528[32]
-
-
-eval_example1
-MODEL:
-y -> 4
-x -> 3
-
-evaluating x+y
-result = 7:int
-
-two_contexts_example1
-k!0
-
-error_code_example1
-last call succeeded.
-last call failed.
-
-error_code_example2
-before Z3_mk_iff
-Z3 error: type error.
-
-parser_example1
-formula 0: (> x y)
-formula 1: (> x 0)
-sat
-y -> 0
-x -> 1
-
-
-parser_example2
-formula: (> x y)
-sat
-y -> (- 1)
-x -> 0
-
-
-parser_example3
-assert axiom:
-(forall (x Int) (y Int) (= (g x y) (g y x)) :qid {k!1})
-formula: (forall (x Int) (y Int) (=> (= x y) (= (g x 0) (g 0 y))) :qid {k!1})
-valid
-
-parser_example4
-declaration 0: (define y Int)
-declaration 1: (define sk_hack Bool Bool)
-declaration 2: (define x Int)
-assumption 0: (= x 20)
-formula 0: (> x y)
-formula 1: (> x 0)
-
-parser_example5
-Z3 error: parser error.
-Error message: 'ERROR: line 1 column 41: could not find sort symbol 'y'.
-'.
-
-numeral_example
-Numerals n1:1/2 n2:1/2
-valid
-Numerals n1:(- 1/3) n2:(- 33333333333333333333333333333333333333333333333333/100000000000000000000000000000000000000000000000000)
-valid
-
-ite_example
-term: (if false 1 0)
-
-list_example
-valid
-valid
-valid
-valid
-valid
-valid
-valid
-Formula (=> (is_cons u) (= u (cons (head u) (tail u))))
-valid
-invalid
-counterexample:
-u -> nil
-
-
-tree_example
-valid
-valid
-valid
-valid
-valid
-Formula (=> (is_cons u) (= u (cons (car u) (cdr u))))
-valid
-invalid
-counterexample:
-u -> nil
-
-
-forest_example
-valid
-valid
-valid
-valid
-valid
-valid
-
-binary_tree_example
-valid
-valid
-valid
-valid
-valid
-
-enum_example
-(define apple[fruit:0] fruit)
-(define banana[fruit:1] fruit)
-(define orange[fruit:2] fruit)
-(define is_apple[fruit:0] fruit Bool)
-(define is_banana[fruit:1] fruit Bool)
-(define is_orange[fruit:2] fruit Bool)
-valid
-valid
-invalid
-counterexample:
-
-valid
-valid
-
-unsat_core_and_proof_example
-unsat
-proof: [unit-resolution
-  [def-axiom (or (or (not PredA) PredB (not PredC)) (not PredB))]
-  [unit-resolution
-    [def-axiom (or (or (not PredA) (not PredB) (not PredC)) PredB)]
-    [unit-resolution
-      [mp
-        [asserted (or (and PredA PredB PredC) P1)]
-        [monotonicity
-          [rewrite
-            (iff (and PredA PredB PredC)
-                 (not (or (not PredA) (not PredB) (not PredC))))]
-          (iff (or (and PredA PredB PredC) P1)
-               (or (not (or (not PredA) (not PredB) (not PredC))) P1))]
-        (or (not (or (not PredA) (not PredB) (not PredC))) P1)]
-      [asserted (not P1)]
-      (not (or (not PredA) (not PredB) (not PredC)))]
-    PredB]
-  [unit-resolution
-    [mp
-      [asserted (or (and PredA (not PredB) PredC) P2)]
-      [monotonicity
-        [rewrite
-          (iff (and PredA (not PredB) PredC)
-               (not (or (not PredA) PredB (not PredC))))]
-        (iff (or (and PredA (not PredB) PredC) P2)
-             (or (not (or (not PredA) PredB (not PredC))) P2))]
-      (or (not (or (not PredA) PredB (not PredC))) P2)]
-    [asserted (not P2)]
-    (not (or (not PredA) PredB (not PredC)))]
-  false]
-
-core:
-(not P1)
-(not P2)
-
-
-get_implied_equalities example
-Class a |-> 0
-Class b |-> 0
-Class c |-> 0
-Class d |-> 3
-Class (f a) |-> 0
-Class (f b) |-> 0
-Class (f c) |-> 0
-asserting f(a) <= b
-Class a |-> 0
-Class b |-> 0
-Class c |-> 0
-Class d |-> 3
-Class (f a) |-> 0
-Class (f b) |-> 0
-Class (f c) |-> 0
-
-incremental_example1
-unsat core: 0 2 3 
-unsat
-sat
-unsat core: 0 2 3 
-unsat
-unsat core: 0 2 3 
-unsat
-sat
-
-reference_counter_example
-model for: x xor y
-sat
-y -> false
-x -> true
-
-
-smt2parser_example
-formulas: (and (bvuge a bv16[8]) (bvule a bv240[8]))
-
-substitute_example
-substitution result: (f (f a 0) 1)
-
-substitute_vars_example
-substitution result: (f (f a (g b)) a)

src/api/ml/test_mlapi.regress.out

@@ -1,32 +0,0 @@
-datatype created:
-sort: tree
-constructor: (define leaf[tree:0] Int tree) recognizer: (define is_leaf[tree:0] tree Bool) accessors: (define data[tree:0:0] tree Int)
-constructor: (define node[tree:1] forest tree) recognizer: (define is_node[tree:1] tree Bool) accessors: (define children[tree:1:0] tree forest)
-sort: forest
-constructor: (define nil[forest:0] forest) recognizer: (define is_nil[forest:0] forest Bool) accessors:
-constructor: (define cons[forest:1] tree forest forest) recognizer: (define is_cons[forest:1] forest Bool) accessors: (define hd[forest:1:0] forest tree) (define tl[forest:1:1] forest forest)
-
-t1: (node (cons (leaf 1) (cons (leaf 2) nil)))
-t2: (node (cons (node (cons (leaf 1) (cons (leaf 2) nil))) (cons (leaf 3) nil)))
-t3: (node (cons (node (cons (leaf 1) (cons (leaf 2) nil)))
-            (cons (node (cons (leaf 1) (cons (leaf 2) nil))) nil)))
-t4: (node (cons (leaf 4) (cons (node (cons (leaf 1) (cons (leaf 2) nil))) nil)))
-f1: (cons (leaf 0) nil)
-f2: (cons (node (cons (leaf 1) (cons (leaf 2) nil))) nil)
-f3: (cons (node (cons (leaf 1) (cons (leaf 2) nil))) (cons (leaf 0) nil))
-t1: (node (cons (leaf 1) (cons (leaf 2) nil)))
-t2: (node (cons (node (cons (leaf 1) (cons (leaf 2) nil))) (cons (leaf 3) nil)))
-t3: (node (cons (node (cons (leaf 1) (cons (leaf 2) nil)))
-            (cons (node (cons (leaf 1) (cons (leaf 2) nil))) nil)))
-t4: (node (cons (leaf 4) (cons (node (cons (leaf 1) (cons (leaf 2) nil))) nil)))
-f1: (cons (leaf 0) nil)
-f2: (cons (node (cons (leaf 1) (cons (leaf 2) nil))) nil)
-f3: (cons (node (cons (leaf 1) (cons (leaf 2) nil))) (cons (leaf 0) nil))
-valid
-valid
-l1: (cons x u)
-l2: (cons y v)
-valid
-valid
-valid
-valid

src/api/ml/test_mlapiV3.regress.err

@@ -1,5 +0,0 @@
-WARNING: invalid function application, sort mismatch on argument at position 1
-WARNING: (define iff Bool Bool Bool) applied to: 
-x of sort Int
-y of sort Bool
-

src/api/ml/test_mlapiV3.regress.out

@@ -1,315 +0,0 @@
-Z3 4.2.0.0
-
-simple_example
-CONTEXT:
-(solver)END OF CONTEXT
-
-DeMorgan
-DeMorgan is valid
-
-find_model_example1
-model for: x xor y
-sat
-y -> false
-x -> true
-
-
-find_model_example2
-model for: x < y + 1, x > 2
-sat
-y -> 3
-x -> 3
-
-model for: x < y + 1, x > 2, not(x = y)
-sat
-y -> 4
-x -> 3
-
-
-prove_example1
-prove: x = y implies g(x) = g(y)
-valid
-disprove: x = y implies g(g(x)) = g(y)
-invalid
-counterexample:
-y -> U!val!0
-x -> U!val!0
-g -> {
-  U!val!0 -> U!val!1
-  U!val!1 -> U!val!2
-  else -> U!val!1
-}
-
-
-prove_example2
-prove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < 0
-valid
-disprove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < -1
-invalid
-counterexample:
-z -> (- 1)
-y -> (- 7719)
-x -> (- 7719)
-g -> {
-  (- 7719) -> 0
-  0 -> 2
-  (- 1) -> 3
-  else -> 0
-}
-
-
-push_pop_example1
-assert: x >= 'big number'
-push
-number of scopes: 1
-assert: x <= 3
-unsat
-pop
-number of scopes: 0
-sat
-x = 1000000000000000000000000000000000000000000000000000000:int
-function interpretations:
-assert: y > x
-sat
-y = 1000000000000000000000000000000000000000000000000000001:int
-x = 1000000000000000000000000000000000000000000000000000000:int
-function interpretations:
-
-quantifier_example1
-pattern: {(f #0 #1)}
-
-assert axiom:
-(forall (k!0 Int) (k!1 Int) (= (inv!0 (f k!1 k!0)) k!0) :pat {(f k!1 k!0)})
-prove: f(x, y) = f(w, v) implies y = v
-valid
-disprove: f(x, y) = f(w, v) implies x = w
-that is: not(f(x, y) = f(w, v) implies x = w) is satisfiable
-unknown
-potential model:
-w = 2:int
-v = 1:int
-y = 1:int
-x = 0:int
-function interpretations:
-f = {(else|->(define f!52 Int Int Int)[(define k!50 Int Int)[#unknown], (define k!51 Int Int)[#unknown]])}
-#51 = {(2:int|->2:int), (1:int|->1:int), (15:int|->15:int), (11:int|->11:int), (0:int|->0:int), (19:int|->19:int), (else|->2:int)}
-f!52 = {(0:int, 1:int|->3:int), (2:int, 1:int|->3:int), (0:int, 0:int|->4:int), (2:int, 0:int|->5:int), (6:int, 2:int|->7:int), (2:int, 2:int|->8:int), (0:int, 2:int|->9:int), (6:int, 0:int|->10:int), (0:int, 11:int|->12:int), (2:int, 11:int|->13:int), (6:int, 11:int|->14:int), (0:int, 15:int|->16:int), (2:int, 15:int|->17:int), (6:int, 15:int|->18:int), (0:int, 19:int|->20:int), (6:int, 19:int|->21:int), (2:int, 19:int|->22:int), (else|->3:int)}
-inv!0 = {(3:int|->1:int), (4:int|->0:int), (5:int|->0:int), (7:int|->2:int), (8:int|->2:int), (9:int|->2:int), (10:int|->0:int), (12:int|->11:int), (13:int|->11:int), (14:int|->11:int), (16:int|->15:int), (17:int|->15:int), (18:int|->15:int), (20:int|->19:int), (21:int|->19:int), (22:int|->19:int), (else|->2:int)}
-#50 = {(2:int|->2:int), (6:int|->6:int), (0:int|->0:int), (else|->2:int)}
-reason for last failure: 7 (7 = quantifiers)
-
-array_example1
-prove: store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3))
-(=> (= (store a1 i1 v1) (store a2 i2 v2))
-    (or (= i1 i3) (= i2 i3) (= (select a1 i3) (select a2 i3))))
-valid
-
-array_example2
-n = 2
-(distinct k!0 k!1)
-sat
-#0 = (define as-array[k!0] (Array Bool Bool))
-#1 = (define as-array[k!1] (Array Bool Bool))
-function interpretations:
-#0 = {((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
-#1 = {((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
-n = 3
-(distinct k!0 k!1 k!2)
-sat
-#0 = (define as-array[k!0] (Array Bool Bool))
-#1 = (define as-array[k!1] (Array Bool Bool))
-#2 = (define as-array[k!2] (Array Bool Bool))
-function interpretations:
-#0 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define false Bool)), (else|->(define true Bool))}
-#1 = {((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
-#2 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
-n = 4
-(distinct k!0 k!1 k!2 k!3)
-sat
-#0 = (define as-array[k!0] (Array Bool Bool))
-#1 = (define as-array[k!1] (Array Bool Bool))
-#2 = (define as-array[k!2] (Array Bool Bool))
-#3 = (define as-array[k!3] (Array Bool Bool))
-function interpretations:
-#0 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define true Bool)), (else|->(define false Bool))}
-#1 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define false Bool)), (else|->(define true Bool))}
-#2 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
-#3 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
-n = 5
-(distinct k!0 k!1 k!2 k!3 k!4)
-unsat
-
-array_example3
-domain: int
-range:  bool
-
-tuple_example1
-tuple_sort: (real, real)
-prove: get_x(mk_pair(x, y)) = 1 implies x = 1
-valid
-disprove: get_x(mk_pair(x, y)) = 1 implies y = 1
-invalid
-counterexample:
-y -> 0
-x -> 1
-
-prove: get_x(p1) = get_x(p2) and get_y(p1) = get_y(p2) implies p1 = p2
-valid
-disprove: get_x(p1) = get_x(p2) implies p1 = p2
-invalid
-counterexample:
-p1 -> (mk_pair 1 0)
-p2 -> (mk_pair 1 2)
-
-prove: p2 = update(p1, 0, 10) implies get_x(p2) = 10
-valid
-disprove: p2 = update(p1, 0, 10) implies get_y(p2) = 10
-invalid
-counterexample:
-p2 -> (mk_pair 10 1)
-p1 -> (mk_pair 0 1)
-
-
-bitvector_example1
-disprove: x - 10 <= 0 IFF x <= 10 for (32-bit) machine integers
-invalid
-counterexample:
-x -> bv2147483656[32]
-
-
-bitvector_example2
-find values of x and y, such that x ^ y - 103 == x * y
-sat
-y -> bv3905735879[32]
-x -> bv3787456528[32]
-
-
-eval_example1
-MODEL:
-y -> 4
-x -> 3
-
-evaluating x+y
-result = 7:int
-
-two_contexts_example1
-k!0
-
-error_code_example1
-last call succeeded.
-last call failed.
-
-error_code_example2
-before Z3_mk_iff
-Z3 error: type error.
-
-parser_example1
-formula 0: (> x y)
-formula 1: (> x 0)
-sat
-y -> 0
-x -> 1
-
-
-parser_example2
-formula: (> x y)
-sat
-y -> (- 1)
-x -> 0
-
-
-parser_example3
-assert axiom:
-(forall (x Int) (y Int) (= (g x y) (g y x)) :qid {k!1})
-formula: (forall (x Int) (y Int) (=> (= x y) (= (g x 0) (g 0 y))) :qid {k!1})
-valid
-
-parser_example4
-declaration 0: (define y Int)
-declaration 1: (define sk_hack Bool Bool)
-declaration 2: (define x Int)
-assumption 0: (= x 20)
-formula 0: (> x y)
-formula 1: (> x 0)
-
-parser_example5
-Z3 error: parser error.
-Error message: 'ERROR: line 1 column 41: could not find sort symbol 'y'.
-'.
-
-ite_example
-term: (if false 1 0)
-
-enum_example
-(define apple[fruit:0] fruit)
-(define banana[fruit:1] fruit)
-(define orange[fruit:2] fruit)
-(define is_apple[fruit:0] fruit Bool)
-(define is_banana[fruit:1] fruit Bool)
-(define is_orange[fruit:2] fruit Bool)
-valid
-valid
-invalid
-counterexample:
-
-valid
-valid
-
-unsat_core_and_proof_example
-unsat
-proof: [unit-resolution
-  [def-axiom (or (or (not PredA) PredC (not PredB)) (not PredC))]
-  [unit-resolution
-    [def-axiom (or (or (not PredA) (not PredB) (not PredC)) PredC)]
-    [unit-resolution
-      [mp
-        [asserted (or (and PredA PredB PredC) P1)]
-        [monotonicity
-          [rewrite
-            (iff (and PredA PredB PredC)
-                 (not (or (not PredA) (not PredB) (not PredC))))]
-          (iff (or (and PredA PredB PredC) P1)
-               (or (not (or (not PredA) (not PredB) (not PredC))) P1))]
-        (or (not (or (not PredA) (not PredB) (not PredC))) P1)]
-      [asserted (not P1)]
-      (not (or (not PredA) (not PredB) (not PredC)))]
-    PredC]
-  [unit-resolution
-    [mp
-      [asserted (or (and PredA (not PredC) PredB) P2)]
-      [monotonicity
-        [rewrite
-          (iff (and PredA (not PredC) PredB)
-               (not (or (not PredA) PredC (not PredB))))]
-        (iff (or (and PredA (not PredC) PredB) P2)
-             (or (not (or (not PredA) PredC (not PredB))) P2))]
-      (or (not (or (not PredA) PredC (not PredB))) P2)]
-    [asserted (not P2)]
-    (not (or (not PredA) PredC (not PredB)))]
-  false]
-
-core:
-(not P2)
-(not P1)
-
-
-abstract_example
-formula: (> x y)
-abstracted formula: (> #0 y)
-
-get_implied_equalities example
-Class a |-> 0
-Class b |-> 0
-Class c |-> 0
-Class d |-> 3
-Class (f a) |-> 0
-Class (f b) |-> 0
-Class (f c) |-> 0
-asserting f(a) <= b
-Class a |-> 0
-Class b |-> 0
-Class c |-> 0
-Class d |-> 3
-Class (f a) |-> 0
-Class (f b) |-> 0
-Class (f c) |-> 0