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362 lines
8.4 KiB
Common Lisp
362 lines
8.4 KiB
Common Lisp
;;; -*- Mode: Lisp; Syntax: Common-Lisp; Package: snark-user -*-
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;;; File: coder-examples.lisp
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;;; The contents of this file are subject to the Mozilla Public License
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;;; Version 1.1 (the "License"); you may not use this file except in
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;;; compliance with the License. You may obtain a copy of the License at
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;;; http://www.mozilla.org/MPL/
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;;;
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;;; Software distributed under the License is distributed on an "AS IS"
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;;; basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the
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;;; License for the specific language governing rights and limitations
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;;; under the License.
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;;;
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;;; The Original Code is SNARK.
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;;; The Initial Developer of the Original Code is SRI International.
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;;; Portions created by the Initial Developer are Copyright (C) 1981-2004.
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;;; All Rights Reserved.
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;;;
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;;; Contributor(s): Mark E. Stickel <stickel@ai.sri.com>.
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(in-package :snark-user)
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(defun coder-test ()
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(time (coder-overbeek6))
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(time (coder-ycl-rst))
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(time (coder-ycl-rst-together))
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(time (coder-veroff-5-2))
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(time (coder-veroff-4-1 :all-proofs t))
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(time (coder-ex7b))
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(time (coder-ex9 :max-syms 18 :max-vars 2))
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nil)
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(defun coder-xcb-reflex (&rest options)
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;; 10-step proof
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;; 11-step proof by (coder-xcb-reflex :max-syms 35)
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;; 13-step proof by (coder-xcb-reflex :max-syms 31)
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(apply
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'coder
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'((e ?x (e (e (e ?x ?y) (e ?z ?y)) ?z)))
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'(e a a)
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options))
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(defun coder-overbeek6 (&rest options)
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;; 5-step proof
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(apply
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'coder
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'("i(a,i(b,a))" ;Prolog style with declared variables
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"i(i(X,Y),i(i(Y,?z),i(X,?z)))" ;Prolog style with explicit variables (capitalized-or ?-prefix)
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(i (i (i a b) b) (i (i b a) a)) ;Lisp style with declared variables
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(i (i (n ?x) (n ?y)) (i ?y ?x))) ;Lisp style with explicit variables
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"i(i(a,b),i(i(c,a),i(c,b)))" ;variable declarations don't apply to target
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:variables '(a b c)
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options))
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(defun coder-overbeek4 (&rest options)
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;; 10-step proof
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(apply
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'coder
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'((e ?x (e (e ?y (e ?z ?x)) (e ?z ?y))))
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'(e (e (e a (e b c)) c) (e b a))
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options))
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(defun coder-ycl-rst (&rest options)
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;; prove reflexivity (4-step proof),
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;; symmetry (5-step proof),
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;; and transitivity (6-step proof) from ycl
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;; coder searches until all have been found
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(apply
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'coder
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'((e (e ?x ?y) (e (e ?z ?y) (e ?x ?z))))
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'(and
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(e a a)
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(e (e a b) (e b a))
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(e (e a b) (e (e b c) (e a c))))
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options))
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(defun coder-ycl-rst-together (&rest options)
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;; prove reflexivity, symmetry, and transitivity from ycl in a single derivation
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;; 9-step proof
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(apply
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'coder
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'((e (e ?x ?y) (e (e ?z ?y) (e ?x ?z))))
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'(together
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(e a a)
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(e (e a b) (e b a))
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(e (e a b) (e (e b c) (e a c))))
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options))
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(defun coder-veroff-5-2 (&rest options)
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;; problem from
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;; Robert Veroff, "Finding Shortest Proofs: An Application of Linked Inference Rules",
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;; JAR 27,2 (August 2001), 123-129
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;; 8-step proof
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(apply
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'coder
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'((i ?x (i ?y ?x))
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(i (i ?x (i ?y ?z)) (i (i ?x ?y) (i ?x ?z))))
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'(i (i a (i b c)) (i b (i a c)))
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options))
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(defun coder-veroff-4-1 (&rest options)
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;; converse (because there's a typo) of problem from
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;; Robert Veroff, "Finding Shortest Proofs: An Application of Linked Inference Rules",
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;; JAR 27,2 (August 2001), 123-129
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;; 7 6-step proofs, just like Veroff reported
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(apply
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'coder
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'((i (i (i ?v1 ?v2) ?v3) (i (i ?v2 (i ?v3 ?v5)) (i ?v4 (i ?v2 ?v5)))))
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'(i (i v2 (i v3 v5)) (i (i (i v1 v2) v3) (i v4 (i v2 v5))))
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options))
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(defun ii-schema ()
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'(i ?x (i ?y ?x)))
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(defun id-schema ()
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'(i (i ?x (i ?y ?z)) (i (i ?x ?y) (i ?x ?z))))
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(defun cr-schema1 ()
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'(i (i ?x (n ?y)) (i (i ?x ?y) (n ?x))))
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(defun cr-schema2 ()
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'(i (i (n ?x) (n ?y)) (i (i (n ?x) ?y) ?x)))
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(defun eq-schema1 ()
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'(i (e ?x ?y) (i ?x ?y)))
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(defun eq-schema2 ()
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'(i (e ?x ?y) (i ?y ?x)))
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(defun eq-schema3 ()
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'(i (i ?x ?y) (i (i ?y ?x) (e ?y ?x))))
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(defun or-schema ()
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'(e (o ?x ?y) (i (n ?x) ?y)))
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(defun and-schema ()
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'(e (a ?x ?y) (n (o (n ?x) (n ?y)))))
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(defun alt-and-schema ()
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'(e (a ?x ?y) (n (i ?x (n ?y)))))
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(defun coder-ex1 (&rest options)
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;; from Genesereth chapter 4
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;; 3-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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'(i p q)
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'(i q r))
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'(i p r)
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options))
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(defun coder-ex2 (&rest options)
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;; from Genesereth chapter 4 exercise
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;; 6-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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'(i p q)
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'(i q r))
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'(i (i p (n r)) (n p))
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options))
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(defun coder-ex3 (&rest options)
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;; from Genesereth chapter 4 exercise
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;; 5-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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'(n (n p)))
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'p
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options))
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(defun coder-ex4 (&rest options)
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;; 5-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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'p)
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'(n (n p))
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options))
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(defun coder-ex5 (&rest options)
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;; 4-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3))
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'(e p p)
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options))
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(defun coder-ex6 (&rest options)
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;; 4-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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'(e p q))
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'(e q p)
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options))
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(defun coder-ex6a (&rest options)
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;; 5-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3))
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'(i (e p q) (e q p))
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options))
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(defun coder-ex6b (&rest options)
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;; 7-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3))
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'(e (e p q) (e q p))
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options))
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(defun coder-ex7a ()
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;; 5-step proof, 5-step proof, 2-step proof
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(coder (list (ii-schema)
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(id-schema)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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'(e p q)
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'(e q r))
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'(i p r)
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:must-use '(6 7))
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(coder (list (ii-schema)
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(id-schema)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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'(e p q)
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'(e q r))
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'(i r p)
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:must-use '(6 7))
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(coder (list (ii-schema)
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(id-schema)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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'(i p r)
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'(i r p))
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'(e p r)
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:must-use '(6 7)))
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(defun coder-ex7b ()
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;; 12-step proof
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(coder (list (ii-schema)
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(id-schema)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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'(e p q)
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'(e q r))
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'(together (e p r) (i p q) (i q r) (i p r) (i r q) (i q p) (i r p))
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:must-use t
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:max-syms 7))
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(defun coder-ex8 (&rest options)
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;; 3-step proof
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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(or-schema)
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'q)
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'(o p q)
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options))
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(defun coder-ex9 (&rest options)
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;; no 1,...,8-step proof
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;; 9-step proof by (coder-ex9 :max-syms 18 :max-vars 2)
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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(or-schema)
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'p)
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'(o p q)
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options))
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(defun coder-ex10 (&rest options)
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;; no 1,...,8-step proof
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;; 13-step proof by (coder-ex10 :max-syms 18 :max-vars 2 :must-use '(1 2 3 4 5 6 8 9 10 11))
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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(or-schema)
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(and-schema)
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'p
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'q)
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'(a p q)
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options))
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(defun coder-ex11 (&rest options)
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;; no 1,...,8-step proof
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;; 9-step proof by (coder-ex11 :max-syms 16 :max-vars 2)
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(apply
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'coder
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(list (ii-schema)
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(id-schema)
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(cr-schema1)
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(cr-schema2)
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(eq-schema1)
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(eq-schema2)
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(eq-schema3)
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(alt-and-schema)
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'p
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'q)
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'(a p q)
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options))
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;;; coder-examples.lisp EOF
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