removed obsolete HOL-Boogie session;
authorboehmes
Tue, 23 Jul 2013 18:36:23 +0200
changeset 52722 2c81f7baf8c4
parent 52721 6bafe21b13b2
child 52724 f547266a9338
removed obsolete HOL-Boogie session; keep examples that also test SMT solvers, using a minimal version of the old Boogie loader
src/HOL/Boogie/Boogie.thy
src/HOL/Boogie/Examples/Boogie_Dijkstra.b2i
src/HOL/Boogie/Examples/Boogie_Dijkstra.certs
src/HOL/Boogie/Examples/Boogie_Dijkstra.thy
src/HOL/Boogie/Examples/Boogie_Max.b2i
src/HOL/Boogie/Examples/Boogie_Max.certs
src/HOL/Boogie/Examples/Boogie_Max.thy
src/HOL/Boogie/Examples/Boogie_Max_Stepwise.thy
src/HOL/Boogie/Examples/VCC_Max.b2i
src/HOL/Boogie/Examples/VCC_Max.certs
src/HOL/Boogie/Examples/VCC_Max.thy
src/HOL/Boogie/Tools/boogie_commands.ML
src/HOL/Boogie/Tools/boogie_loader.ML
src/HOL/Boogie/Tools/boogie_tactics.ML
src/HOL/Boogie/Tools/boogie_vcs.ML
src/HOL/ROOT
src/HOL/SMT_Examples/Boogie.thy
src/HOL/SMT_Examples/Boogie_Dijkstra.b2i
src/HOL/SMT_Examples/Boogie_Dijkstra.certs
src/HOL/SMT_Examples/Boogie_Max.b2i
src/HOL/SMT_Examples/Boogie_Max.certs
src/HOL/SMT_Examples/VCC_Max.b2i
src/HOL/SMT_Examples/VCC_Max.certs
src/HOL/SMT_Examples/boogie.ML
--- a/src/HOL/Boogie/Boogie.thy	Tue Jul 23 13:14:14 2013 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,104 +0,0 @@
-(*  Title:      HOL/Boogie/Boogie.thy
-    Author:     Sascha Boehme, TU Muenchen
-*)
-
-header {* Integration of the Boogie program verifier *}
-
-theory Boogie
-imports Word
-keywords
-  "boogie_open" :: thy_load and
-  "boogie_end" :: thy_decl and
-  "boogie_vc" :: thy_goal and
-  "boogie_status" :: diag
-begin
-
-text {*
-HOL-Boogie and its applications are described in:
-\begin{itemize}
-
-\item Sascha B"ohme, K. Rustan M. Leino, and Burkhart Wolff.
-HOL-Boogie --- An Interactive Prover for the Boogie Program-Verifier.
-Theorem Proving in Higher Order Logics, 2008.
-
-\item Sascha B"ohme, Micha{\l} Moskal, Wolfram Schulte, and Burkhart Wolff.
-HOL-Boogie --- An Interactive Prover-Backend for the Verifying C Compiler.
-Journal of Automated Reasoning, 2009.
-
-\end{itemize}
-*}
-
-
-
-section {* Built-in types and functions of Boogie *}
-
-subsection {* Labels *}
-
-text {*
-See "Generating error traces from verification-condition counterexamples"
-by Leino e.a. (2004) for a description of Boogie's labelling mechanism and
-semantics.
-*}
-
-definition assert_at :: "bool \<Rightarrow> bool \<Rightarrow> bool" where "assert_at l P = P"
-definition block_at :: "bool \<Rightarrow> bool \<Rightarrow> bool" where "block_at l P = P"
-
-lemmas labels = assert_at_def block_at_def
-
-
-subsection {* Integer arithmetics *}
-
-text {*
-The operations @{text div} and @{text mod} are built-in in Boogie, but
-without a particular semantics due to different interpretations in
-programming languages. We assume that each application comes with a
-proper axiomatization.
-*}
-
-axiomatization
-  boogie_div :: "int \<Rightarrow> int \<Rightarrow> int" (infixl "div'_b" 70) and
-  boogie_mod :: "int \<Rightarrow> int \<Rightarrow> int" (infixl "mod'_b" 70)
-
-
-
-section {* Boogie environment *}
-
-text {*
-Proving Boogie-generated verification conditions happens inside
-a Boogie environment:
-
-  boogie_open "b2i file with extension"
-  boogie_vc "verification condition 1" ...
-  boogie_vc "verification condition 2" ...
-  boogie_vc "verification condition 3" ...
-  boogie_end
-
-See the Boogie examples for more details.
- 
-At most one Boogie environment should occur per theory,
-otherwise unexpected effects may arise.
-*}
-
-
-
-section {* Setup *}
-
-ML {*
-structure Boogie_Axioms = Named_Thms
-(
-  val name = @{binding boogie}
-  val description =
-    "Boogie background axioms loaded along with Boogie verification conditions"
-)
-*}
-setup Boogie_Axioms.setup
-
-ML_file "Tools/boogie_vcs.ML"
-ML_file "Tools/boogie_loader.ML"
-ML_file "Tools/boogie_tactics.ML"
-setup Boogie_Tactics.setup
-
-ML_file "Tools/boogie_commands.ML"
-setup Boogie_Commands.setup
-
-end
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.b2i	Tue Jul 23 13:14:14 2013 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,1879 +0,0 @@
-type-decl Vertex 0 0
-fun-decl G 1 0
-    array 3
-      type-con Vertex 0
-      type-con Vertex 0
-      int
-fun-decl Infinity 1 0
-    int
-fun-decl Source 1 0
-    type-con Vertex 0
-axiom 0
-    forall 2 0 3
-      var x
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.3:15
-      attribute uniqueId 1
-        string-attr 0
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    not
-    =
-    var x
-      type-con Vertex 0
-    var y
-      type-con Vertex 0
-    <
-    int-num 0
-    select 3
-    fun G 0
-    var x
-      type-con Vertex 0
-    var y
-      type-con Vertex 0
-axiom 0
-    forall 2 0 3
-      var x
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.4:15
-      attribute uniqueId 1
-        string-attr 1
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    =
-    var x
-      type-con Vertex 0
-    var y
-      type-con Vertex 0
-    =
-    select 3
-    fun G 0
-    var x
-      type-con Vertex 0
-    var y
-      type-con Vertex 0
-    int-num 0
-axiom 0
-    <
-    int-num 0
-    fun Infinity 0
-var-decl SP 0
-    array 2
-      type-con Vertex 0
-      int
-vc Dijkstra 1
-    implies
-    label pos 26 3
-    true
-    implies
-    true
-    implies
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.27:18
-      attribute uniqueId 1
-        string-attr 5
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    =
-    var x
-      type-con Vertex 0
-    fun Source 0
-    =
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    int-num 0
-    implies
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.28:18
-      attribute uniqueId 1
-        string-attr 6
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    not
-    =
-    var x
-      type-con Vertex 0
-    fun Source 0
-    =
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    fun Infinity 0
-    implies
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.31:18
-      attribute uniqueId 1
-        string-attr 7
-      attribute bvZ3Native 1
-        string-attr False
-    not
-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var x
-      type-con Vertex 0
-    implies
-    true
-    and 2
-    label neg 34 5
-    =
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    fun Source 0
-    int-num 0
-    implies
-    =
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    fun Source 0
-    int-num 0
-    and 2
-    label neg 35 5
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.35:23
-      attribute uniqueId 1
-        string-attr 9
-      attribute bvZ3Native 1
-        string-attr False
-    >=
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    int-num 0
-    implies
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.35:23
-      attribute uniqueId 1
-        string-attr 9
-      attribute bvZ3Native 1
-        string-attr False
-    >=
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    int-num 0
-    and 2
-    label neg 36 5
-    forall 2 0 3
-      var y
-        type-con Vertex 0
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.36:23
-      attribute uniqueId 1
-        string-attr 10
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <=
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    implies
-    forall 2 0 3
-      var y
-        type-con Vertex 0
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.36:23
-      attribute uniqueId 1
-        string-attr 10
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <=
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    and 2
-    label neg 38 5
-    forall 2 0 3
-      var z
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.38:23
-      attribute uniqueId 1
-        string-attr 11
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    <=
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    forall 2 0 3
-      var z
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.38:23
-      attribute uniqueId 1
-        string-attr 11
-      attribute bvZ3Native 1
-        string-attr False
-    implies
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-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    <=
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    and 2
-    label neg 40 5
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.40:23
-      attribute uniqueId 1
-        string-attr 13
-      attribute bvZ3Native 1
-        string-attr False
-    implies
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-    not
-    =
-    var z
-      type-con Vertex 0
-    fun Source 0
-    <
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    exists 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.41:15
-      attribute uniqueId 1
-        string-attr 12
-      attribute bvZ3Native 1
-        string-attr False
-    and 3
-    <
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    =
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.40:23
-      attribute uniqueId 1
-        string-attr 13
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    =
-    var z
-      type-con Vertex 0
-    fun Source 0
-    <
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    exists 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.41:15
-      attribute uniqueId 1
-        string-attr 12
-      attribute bvZ3Native 1
-        string-attr False
-    and 3
-    <
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@0
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    =
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@0
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    label pos 33 3
-    true
-    implies
-    true
-    implies
-    =
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    fun Source 0
-    int-num 0
-    implies
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.35:23
-      attribute uniqueId 1
-        string-attr 9
-      attribute bvZ3Native 1
-        string-attr False
-    >=
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    int-num 0
-    implies
-    forall 2 0 3
-      var y
-        type-con Vertex 0
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.36:23
-      attribute uniqueId 1
-        string-attr 10
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    select 2
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <=
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    implies
-    forall 2 0 3
-      var z
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.38:23
-      attribute uniqueId 1
-        string-attr 11
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    select 2
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    <=
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.40:23
-      attribute uniqueId 1
-        string-attr 13
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    =
-    var z
-      type-con Vertex 0
-    fun Source 0
-    <
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    exists 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.41:15
-      attribute uniqueId 1
-        string-attr 12
-      attribute bvZ3Native 1
-        string-attr False
-    and 3
-    <
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    =
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    true
-    and 2
-    implies
-    label pos 33 3
-    true
-    implies
-    true
-    implies
-    not
-    exists 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.33:18
-      attribute uniqueId 1
-        string-attr 8
-      attribute bvZ3Native 1
-        string-attr False
-    and 2
-    not
-    select 2
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var x
-      type-con Vertex 0
-    <
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    fun Infinity 0
-    implies
-    true
-    implies
-    label pos 0 0
-    true
-    implies
-    =
-    var Visited@3
-      array 2
-        type-con Vertex 0
-        bool
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    implies
-    =
-    var v@2
-      type-con Vertex 0
-    var v@0
-      type-con Vertex 0
-    implies
-    =
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    implies
-    =
-    var oldSP@1
-      array 2
-        type-con Vertex 0
-        int
-    var oldSP@0
-      array 2
-        type-con Vertex 0
-        int
-    implies
-    label pos 0 0
-    true
-    and 2
-    label neg 17 3
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.17:19
-      attribute uniqueId 1
-        string-attr 4
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    =
-    var z
-      type-con Vertex 0
-    fun Source 0
-    <
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    exists 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.18:13
-      attribute uniqueId 1
-        string-attr 3
-      attribute bvZ3Native 1
-        string-attr False
-    and 2
-    <
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    =
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.17:19
-      attribute uniqueId 1
-        string-attr 4
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    =
-    var z
-      type-con Vertex 0
-    fun Source 0
-    <
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    exists 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.18:13
-      attribute uniqueId 1
-        string-attr 3
-      attribute bvZ3Native 1
-        string-attr False
-    and 2
-    <
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    =
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    and 2
-    label neg 15 3
-    forall 2 0 3
-      var z
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.15:19
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    fun Infinity 0
-    <
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    <=
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    forall 2 0 3
-      var z
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.15:19
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    fun Infinity 0
-    <
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    <=
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    and 2
-    label neg 14 3
-    =
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    fun Source 0
-    int-num 0
-    implies
-    =
-    select 2
-    var SP@3
-      array 2
-        type-con Vertex 0
-        int
-    fun Source 0
-    int-num 0
-    true
-    implies
-    label pos 44 5
-    true
-    implies
-    true
-    implies
-    exists 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.33:18
-      attribute uniqueId 1
-        string-attr 8
-      attribute bvZ3Native 1
-        string-attr False
-    and 2
-    not
-    select 2
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var x
-      type-con Vertex 0
-    <
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    fun Infinity 0
-    implies
-    not
-    select 2
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var v@1
-      type-con Vertex 0
-    implies
-    <
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var v@1
-      type-con Vertex 0
-    fun Infinity 0
-    implies
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.47:20
-      attribute uniqueId 1
-        string-attr 14
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    not
-    select 2
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var x
-      type-con Vertex 0
-    <=
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var v@1
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    implies
-    =
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    store 3
-    var Visited@1
-      array 2
-        type-con Vertex 0
-        bool
-    var v@1
-      type-con Vertex 0
-    true
-    implies
-    forall 1 0 3
-      var u
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.53:20
-      attribute uniqueId 1
-        string-attr 15
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <
-    select 3
-    fun G 0
-    var v@1
-      type-con Vertex 0
-    var u
-      type-con Vertex 0
-    fun Infinity 0
-    <
-    +
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var v@1
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var v@1
-      type-con Vertex 0
-    var u
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var u
-      type-con Vertex 0
-    =
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var u
-      type-con Vertex 0
-    +
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var v@1
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var v@1
-      type-con Vertex 0
-    var u
-      type-con Vertex 0
-    implies
-    forall 1 0 3
-      var u
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.56:20
-      attribute uniqueId 1
-        string-attr 16
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    not
-    and 2
-    <
-    select 3
-    fun G 0
-    var v@1
-      type-con Vertex 0
-    var u
-      type-con Vertex 0
-    fun Infinity 0
-    <
-    +
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var v@1
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var v@1
-      type-con Vertex 0
-    var u
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var u
-      type-con Vertex 0
-    =
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var u
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var u
-      type-con Vertex 0
-    and 2
-    label neg 59 5
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.59:20
-      attribute uniqueId 1
-        string-attr 17
-      attribute bvZ3Native 1
-        string-attr False
-    <=
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    implies
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.59:20
-      attribute uniqueId 1
-        string-attr 17
-      attribute bvZ3Native 1
-        string-attr False
-    <=
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    and 2
-    label neg 60 5
-    forall 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.60:20
-      attribute uniqueId 1
-        string-attr 18
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    =
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    implies
-    forall 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.60:20
-      attribute uniqueId 1
-        string-attr 18
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    =
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@1
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    implies
-    true
-    implies
-    label pos 0 0
-    true
-    and 2
-    label neg 34 5
-    =
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    fun Source 0
-    int-num 0
-    implies
-    =
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    fun Source 0
-    int-num 0
-    and 2
-    label neg 35 5
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.35:23
-      attribute uniqueId 1
-        string-attr 9
-      attribute bvZ3Native 1
-        string-attr False
-    >=
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    int-num 0
-    implies
-    forall 1 0 3
-      var x
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.35:23
-      attribute uniqueId 1
-        string-attr 9
-      attribute bvZ3Native 1
-        string-attr False
-    >=
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var x
-      type-con Vertex 0
-    int-num 0
-    and 2
-    label neg 36 5
-    forall 2 0 3
-      var y
-        type-con Vertex 0
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.36:23
-      attribute uniqueId 1
-        string-attr 10
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <=
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    implies
-    forall 2 0 3
-      var y
-        type-con Vertex 0
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.36:23
-      attribute uniqueId 1
-        string-attr 10
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <=
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    and 2
-    label neg 38 5
-    forall 2 0 3
-      var z
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.38:23
-      attribute uniqueId 1
-        string-attr 11
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    <=
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    forall 2 0 3
-      var z
-        type-con Vertex 0
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.38:23
-      attribute uniqueId 1
-        string-attr 11
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    <
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    <=
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    and 2
-    label neg 40 5
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.40:23
-      attribute uniqueId 1
-        string-attr 13
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    =
-    var z
-      type-con Vertex 0
-    fun Source 0
-    <
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    exists 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.41:15
-      attribute uniqueId 1
-        string-attr 12
-      attribute bvZ3Native 1
-        string-attr False
-    and 3
-    <
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    =
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    forall 1 0 3
-      var z
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.40:23
-      attribute uniqueId 1
-        string-attr 13
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    not
-    =
-    var z
-      type-con Vertex 0
-    fun Source 0
-    <
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    fun Infinity 0
-    exists 1 0 3
-      var y
-        type-con Vertex 0
-      attribute qid 1
-        string-attr BoogieDi.41:15
-      attribute uniqueId 1
-        string-attr 12
-      attribute bvZ3Native 1
-        string-attr False
-    and 3
-    <
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    select 2
-    var Visited@2
-      array 2
-        type-con Vertex 0
-        bool
-    var y
-      type-con Vertex 0
-    =
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var z
-      type-con Vertex 0
-    +
-    select 2
-    var SP@2
-      array 2
-        type-con Vertex 0
-        int
-    var y
-      type-con Vertex 0
-    select 3
-    fun G 0
-    var y
-      type-con Vertex 0
-    var z
-      type-con Vertex 0
-    implies
-    false
-    true
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Tue Jul 23 13:14:14 2013 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,6048 +0,0 @@
-a549accb56a0340bea4e867d66fdfbbac187f40c 6047 0
-#2 := false
-#7 := 0::Int
-decl f30 :: (-> S2 Int)
-decl ?v1!7 :: (-> S2 S2)
-decl ?v0!20 :: S2
-#2034 := ?v0!20
-#5342 := (?v1!7 ?v0!20)
-#13325 := (f30 #5342)
-#923 := -1::Int
-#13327 := (* -1::Int #13325)
-decl f4 :: (-> S3 Int)
-decl f5 :: (-> S4 S2 S3)
-decl f6 :: (-> S5 S2 S4)
-decl f7 :: S5
-#13 := f7
-#5350 := (f6 f7 #5342)
-#5351 := (f5 #5350 ?v0!20)
-#5352 := (f4 #5351)
-#5353 := (* -1::Int #5352)
-#14209 := (+ #5353 #13327)
-#2037 := (f30 ?v0!20)
-#14210 := (+ #2037 #14209)
-#18243 := (>= #14210 0::Int)
-decl f19 :: (-> S11 S2 Int)
-decl f20 :: S11
-#109 := f20
-#5343 := (f19 f20 #5342)
-#5344 := (* -1::Int #5343)
-#5354 := (+ #5344 #5353)
-#5080 := (f19 f20 ?v0!20)
-#5355 := (+ #5080 #5354)
-#15530 := (>= #5355 0::Int)
-#5356 := (= #5355 0::Int)
-#5357 := (not #5356)
-decl f1 :: S1
-#3 := f1
-decl f11 :: (-> S7 S2 S1)
-decl f21 :: S7
-#115 := f21
-#5347 := (f11 f21 #5342)
-#5348 := (= #5347 f1)
-#5349 := (not #5348)
-#5345 := (+ #5080 #5344)
-#5346 := (<= #5345 0::Int)
-#5358 := (or #5346 #5349 #5357)
-#5359 := (not #5358)
-#5105 := (* -1::Int #5080)
-decl f3 :: Int
-#8 := f3
-#5340 := (+ f3 #5105)
-#5341 := (<= #5340 0::Int)
-#15968 := (not #5341)
-#5106 := (+ #2037 #5105)
-#12022 := (>= #5106 0::Int)
-#5087 := (= #2037 #5080)
-decl f28 :: S2
-#181 := f28
-#195 := (f6 f7 f28)
-#5121 := (f5 #195 ?v0!20)
-#5122 := (f4 #5121)
-#5139 := (+ #5105 #5122)
-#185 := (f19 f20 f28)
-#5140 := (+ #185 #5139)
-#5141 := (>= #5140 0::Int)
-#5123 := (* -1::Int #5122)
-#5124 := (+ f3 #5123)
-#5125 := (<= #5124 0::Int)
-#5146 := (or #5125 #5141)
-#2038 := (* -1::Int #2037)
-#5178 := (+ #2038 #5122)
-#5179 := (+ #185 #5178)
-#5182 := (= #5179 0::Int)
-#15374 := (not #5182)
-#12121 := (<= #5179 0::Int)
-#15379 := (not #12121)
-#4078 := (f30 f28)
-#4079 := (* -1::Int #4078)
-#5068 := (+ #2037 #4079)
-#5229 := (<= #5068 0::Int)
-#15402 := (not #5229)
-#15340 := (<= #5122 0::Int)
-#15358 := (not #15340)
-#15327 := (= f28 ?v0!20)
-#15368 := (not #15327)
-#9945 := (= ?v0!20 f28)
-#16393 := [hypothesis]: #15327
-#16394 := [symm #16393]: #9945
-#9687 := (not #9945)
-#5309 := (f11 f21 ?v0!20)
-#5310 := (= #5309 f1)
-#9951 := (or #9945 #5310)
-#9685 := (not #9951)
-decl f12 :: (-> S8 S1 S7)
-decl f13 :: (-> S9 S2 S8)
-decl f14 :: (-> S10 S7 S9)
-decl f15 :: S10
-#39 := f15
-#191 := (f14 f15 f21)
-#192 := (f13 #191 f28)
-#193 := (f12 #192 f1)
-#9943 := (f11 #193 ?v0!20)
-#9944 := (= #9943 f1)
-#9956 := (iff #9944 #9951)
-#11 := (:var 0 S2)
-#54 := (:var 1 S1)
-#52 := (:var 2 S2)
-#50 := (:var 3 S7)
-#51 := (f14 f15 #50)
-#53 := (f13 #51 #52)
-#55 := (f12 #53 #54)
-#56 := (f11 #55 #11)
-#3640 := (pattern #56)
-#60 := (f11 #50 #11)
-#61 := (= #60 f1)
-#59 := (= #54 f1)
-#58 := (= #11 #52)
-#62 := (if #58 #59 #61)
-#57 := (= #56 f1)
-#63 := (iff #57 #62)
-#3641 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #3640) #63)
-#64 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) #63)
-#3644 := (iff #64 #3641)
-#3642 := (iff #63 #63)
-#3643 := [refl]: #3642
-#3645 := [quant-intro #3643]: #3644
-#1496 := (~ #64 #64)
-#1524 := (~ #63 #63)
-#1525 := [refl]: #1524
-#1497 := [nnf-pos #1525]: #1496
-#342 := [asserted]: #64
-#1526 := [mp~ #342 #1497]: #64
-#3646 := [mp #1526 #3645]: #3641
-#7518 := (not #3641)
-#9763 := (or #7518 #9956)
-#4057 := (= f1 f1)
-#9946 := (if #9945 #4057 #5310)
-#9947 := (iff #9944 #9946)
-#9775 := (or #7518 #9947)
-#9715 := (iff #9775 #9763)
-#9722 := (iff #9763 #9763)
-#9724 := [rewrite]: #9722
-#9957 := (iff #9947 #9956)
-#9954 := (iff #9946 #9951)
-#1 := true
-#9948 := (if #9945 true #5310)
-#9952 := (iff #9948 #9951)
-#9953 := [rewrite]: #9952
-#9949 := (iff #9946 #9948)
-#4059 := (iff #4057 true)
-#4060 := [rewrite]: #4059
-#9950 := [monotonicity #4060]: #9949
-#9955 := [trans #9950 #9953]: #9954
-#9958 := [monotonicity #9955]: #9957
-#9706 := [monotonicity #9958]: #9715
-#9734 := [trans #9706 #9724]: #9715
-#9776 := [quant-inst #115 #181 #3 #2034]: #9775
-#9519 := [mp #9776 #9734]: #9763
-#16374 := [unit-resolution #9519 #3646]: #9956
-#9410 := (not #9944)
-decl f29 :: S7
-#190 := f29
-#4533 := (f11 f29 ?v0!20)
-#4534 := (= #4533 f1)
-#4541 := (not #4534)
-#16390 := (iff #4541 #9410)
-#16382 := (iff #4534 #9944)
-#16359 := (iff #9944 #4534)
-#16289 := (= #9943 #4533)
-#8145 := (= #193 f29)
-#194 := (= f29 #193)
-#91 := (f6 f7 #11)
-#3693 := (pattern #91)
-#212 := (f11 f29 #11)
-#3854 := (pattern #212)
-#202 := (f30 #11)
-#3829 := (pattern #202)
-#2047 := (f5 #91 ?v0!20)
-#2048 := (f4 #2047)
-#2383 := (+ #2038 #2048)
-#2384 := (+ #202 #2383)
-#2387 := (= #2384 0::Int)
-#2941 := (not #2387)
-#213 := (= #212 f1)
-#220 := (not #213)
-#2044 := (+ #202 #2038)
-#2045 := (>= #2044 0::Int)
-#2942 := (or #2045 #220 #2941)
-#3888 := (forall (vars (?v1 S2)) (:pat #3829 #3854 #3693) #2942)
-#3893 := (not #3888)
-#2039 := (+ f3 #2038)
-#2040 := (<= #2039 0::Int)
-decl f16 :: S2
-#65 := f16
-#2035 := (= ?v0!20 f16)
-#10 := (:var 1 S2)
-#92 := (f5 #91 #10)
-#3684 := (pattern #92)
-#224 := (f30 #10)
-#1186 := (* -1::Int #224)
-#1187 := (+ #202 #1186)
-#93 := (f4 #92)
-#1207 := (+ #93 #1187)
-#1205 := (>= #1207 0::Int)
-#938 := (* -1::Int #93)
-#939 := (+ f3 #938)
-#940 := (<= #939 0::Int)
-#2933 := (or #220 #940 #1205)
-#3880 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2933)
-#3885 := (not #3880)
-#3896 := (or #3885 #2035 #2040 #3893)
-#3899 := (not #3896)
-decl ?v0!19 :: S2
-#2003 := ?v0!19
-#2016 := (f30 ?v0!19)
-#2017 := (* -1::Int #2016)
-decl ?v1!18 :: S2
-#2002 := ?v1!18
-#2015 := (f30 ?v1!18)
-#2018 := (+ #2015 #2017)
-#2006 := (f6 f7 ?v1!18)
-#2007 := (f5 #2006 ?v0!19)
-#2008 := (f4 #2007)
-#2019 := (+ #2008 #2018)
-#2020 := (>= #2019 0::Int)
-#2009 := (* -1::Int #2008)
-#2010 := (+ f3 #2009)
-#2011 := (<= #2010 0::Int)
-#2004 := (f11 f29 ?v1!18)
-#2005 := (= #2004 f1)
-#2896 := (not #2005)
-#2911 := (or #2896 #2011 #2020)
-#2916 := (not #2911)
-#3902 := (or #2916 #3899)
-#3905 := (not #3902)
-#3871 := (pattern #202 #224)
-#1185 := (>= #1187 0::Int)
-#221 := (f11 f29 #10)
-#222 := (= #221 f1)
-#2873 := (not #222)
-#2888 := (or #213 #2873 #1185)
-#3872 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3871) #2888)
-#3877 := (not #3872)
-#3908 := (or #3877 #3905)
-#3911 := (not #3908)
-decl ?v0!17 :: S2
-#1976 := ?v0!17
-#1985 := (f30 ?v0!17)
-#1986 := (* -1::Int #1985)
-decl ?v1!16 :: S2
-#1975 := ?v1!16
-#1984 := (f30 ?v1!16)
-#1987 := (+ #1984 #1986)
-#1988 := (>= #1987 0::Int)
-#1980 := (f11 f29 ?v0!17)
-#1981 := (= #1980 f1)
-#2850 := (not #1981)
-#1977 := (f11 f29 ?v1!16)
-#1978 := (= #1977 f1)
-#2865 := (or #1978 #2850 #1988)
-#2870 := (not #2865)
-#3914 := (or #2870 #3911)
-#3917 := (not #3914)
-#1176 := (>= #202 0::Int)
-#3863 := (forall (vars (?v0 S2)) (:pat #3829) #1176)
-#3868 := (not #3863)
-#3920 := (or #3868 #3917)
-#3923 := (not #3920)
-decl ?v0!15 :: S2
-#1960 := ?v0!15
-#1961 := (f30 ?v0!15)
-#1962 := (>= #1961 0::Int)
-#1963 := (not #1962)
-#3926 := (or #1963 #3923)
-#3929 := (not #3926)
-#216 := (f30 f16)
-#217 := (= #216 0::Int)
-#661 := (not #217)
-#3932 := (or #661 #3929)
-#3935 := (not #3932)
-#3938 := (or #661 #3935)
-#3941 := (not #3938)
-#112 := (f19 f20 #11)
-#3716 := (pattern #112)
-#207 := (= #202 #112)
-#560 := (or #220 #207)
-#3855 := (forall (vars (?v0 S2)) (:pat #3854 #3829 #3716) #560)
-#3860 := (not #3855)
-#3944 := (or #3860 #3941)
-#3947 := (not #3944)
-decl ?v0!14 :: S2
-#1935 := ?v0!14
-#1940 := (f19 f20 ?v0!14)
-#1939 := (f30 ?v0!14)
-#1941 := (= #1939 #1940)
-#1936 := (f11 f29 ?v0!14)
-#1937 := (= #1936 f1)
-#1938 := (not #1937)
-#1942 := (or #1938 #1941)
-#1943 := (not #1942)
-#3950 := (or #1943 #3947)
-#3953 := (not #3950)
-#1166 := (* -1::Int #202)
-#1167 := (+ #112 #1166)
-#1165 := (>= #1167 0::Int)
-#3846 := (forall (vars (?v0 S2)) (:pat #3716 #3829) #1165)
-#3851 := (not #3846)
-#3956 := (or #3851 #3953)
-#3959 := (not #3956)
-decl ?v0!13 :: S2
-#1917 := ?v0!13
-#1919 := (f30 ?v0!13)
-#1920 := (* -1::Int #1919)
-#1918 := (f19 f20 ?v0!13)
-#1921 := (+ #1918 #1920)
-#1922 := (>= #1921 0::Int)
-#1923 := (not #1922)
-#3962 := (or #1923 #3959)
-#3965 := (not #3962)
-#196 := (f5 #195 #11)
-#3828 := (pattern #196)
-#197 := (f4 #196)
-#1140 := (* -1::Int #197)
-#1146 := (* -1::Int #185)
-#1147 := (+ #1146 #1140)
-#1148 := (+ #112 #1147)
-#1149 := (<= #1148 0::Int)
-#1141 := (+ f3 #1140)
-#1142 := (<= #1141 0::Int)
-#2822 := (or #1142 #1149)
-#2823 := (not #2822)
-#2844 := (or #2823 #207)
-#3838 := (forall (vars (?v0 S2)) (:pat #3828 #3716 #3829) #2844)
-#3843 := (not #3838)
-#1296 := (+ #197 #1166)
-#1297 := (+ #185 #1296)
-#1294 := (= #1297 0::Int)
-#2836 := (or #1142 #1149 #1294)
-#3830 := (forall (vars (?v0 S2)) (:pat #3828 #3716 #3829) #2836)
-#3835 := (not #3830)
-#715 := (not #194)
-#116 := (f11 f21 #11)
-#3750 := (pattern #116)
-#1309 := (+ #112 #1146)
-#1308 := (>= #1309 0::Int)
-#117 := (= #116 f1)
-#1312 := (or #117 #1308)
-#3820 := (forall (vars (?v0 S2)) (:pat #3750 #3716) #1312)
-#3825 := (not #3820)
-#1321 := (+ f3 #1146)
-#1322 := (<= #1321 0::Int)
-#182 := (f11 f21 f28)
-#183 := (= #182 f1)
-decl ?v0!12 :: S2
-#1872 := ?v0!12
-#1876 := (f19 f20 ?v0!12)
-#1877 := (* -1::Int #1876)
-#1878 := (+ f3 #1877)
-#1879 := (<= #1878 0::Int)
-#1873 := (f11 f21 ?v0!12)
-#1874 := (= #1873 f1)
-#3968 := (or #1874 #1879 #183 #1322 #3825 #715 #3835 #3843 #3965)
-#3971 := (not #3968)
-decl f25 :: S11
-#148 := f25
-#168 := (f19 f25 f16)
-#169 := (= #168 0::Int)
-#156 := (f19 f25 #10)
-#1060 := (* -1::Int #156)
-#153 := (f19 f25 #11)
-#1061 := (+ #153 #1060)
-#1067 := (+ #93 #1061)
-#1090 := (>= #1067 0::Int)
-#1047 := (* -1::Int #153)
-#1048 := (+ f3 #1047)
-#1049 := (<= #1048 0::Int)
-#2776 := (or #1049 #940 #1090)
-#3782 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2776)
-#3787 := (not #3782)
-#3790 := (or #3787 #169)
-#3793 := (not #3790)
-decl ?v0!11 :: S2
-#1816 := ?v0!11
-#1831 := (f19 f25 ?v0!11)
-#1832 := (* -1::Int #1831)
-decl ?v1!10 :: S2
-#1815 := ?v1!10
-#1822 := (f6 f7 ?v1!10)
-#1823 := (f5 #1822 ?v0!11)
-#1824 := (f4 #1823)
-#2352 := (+ #1824 #1832)
-#1817 := (f19 f25 ?v1!10)
-#2353 := (+ #1817 #2352)
-#2356 := (>= #2353 0::Int)
-#1825 := (* -1::Int #1824)
-#1826 := (+ f3 #1825)
-#1827 := (<= #1826 0::Int)
-#1818 := (* -1::Int #1817)
-#1819 := (+ f3 #1818)
-#1820 := (<= #1819 0::Int)
-#2754 := (or #1820 #1827 #2356)
-#2759 := (not #2754)
-#3796 := (or #2759 #3793)
-#3799 := (not #3796)
-#3759 := (pattern #153)
-decl ?v1!9 :: (-> S2 S2)
-#1791 := (?v1!9 #11)
-#1796 := (f6 f7 #1791)
-#1797 := (f5 #1796 #11)
-#1798 := (f4 #1797)
-#2335 := (* -1::Int #1798)
-#1792 := (f19 f25 #1791)
-#2318 := (* -1::Int #1792)
-#2336 := (+ #2318 #2335)
-#2337 := (+ #153 #2336)
-#2338 := (= #2337 0::Int)
-#2724 := (not #2338)
-#2319 := (+ #153 #2318)
-#2320 := (<= #2319 0::Int)
-#2725 := (or #2320 #2724)
-#2726 := (not #2725)
-#66 := (= #11 f16)
-#2732 := (or #66 #1049 #2726)
-#3774 := (forall (vars (?v0 S2)) (:pat #3759) #2732)
-#3779 := (not #3774)
-#3802 := (or #3779 #3799)
-#3805 := (not #3802)
-decl ?v0!8 :: S2
-#1751 := ?v0!8
-#1764 := (f5 #91 ?v0!8)
-#1765 := (f4 #1764)
-#1754 := (f19 f25 ?v0!8)
-#1755 := (* -1::Int #1754)
-#2288 := (+ #1755 #1765)
-#2289 := (+ #153 #2288)
-#2292 := (= #2289 0::Int)
-#2688 := (not #2292)
-#1761 := (+ #153 #1755)
-#1762 := (>= #1761 0::Int)
-#2689 := (or #1762 #2688)
-#3760 := (forall (vars (?v1 S2)) (:pat #3759 #3693) #2689)
-#3765 := (not #3760)
-#1756 := (+ f3 #1755)
-#1757 := (<= #1756 0::Int)
-#1752 := (= ?v0!8 f16)
-#3768 := (or #1752 #1757 #3765)
-#3771 := (not #3768)
-#3808 := (or #3771 #3805)
-#3811 := (not #3808)
-decl f27 :: S11
-#151 := f27
-decl f26 :: S11
-#150 := f26
-#152 := (= f26 f27)
-#494 := (not #152)
-#149 := (= f25 f20)
-#503 := (not #149)
-decl f24 :: S2
-#146 := f24
-decl f23 :: S2
-#145 := f23
-#147 := (= f23 f24)
-#512 := (not #147)
-decl f22 :: S7
-#143 := f22
-#144 := (= f22 f21)
-#521 := (not #144)
-#1002 := (* -1::Int #112)
-#1003 := (+ f3 #1002)
-#1004 := (<= #1003 0::Int)
-#2674 := (or #117 #1004)
-#3751 := (forall (vars (?v0 S2)) (:pat #3750 #3716) #2674)
-#3756 := (not #3751)
-#3814 := (or #3756 #521 #512 #503 #494 #3811)
-#3817 := (not #3814)
-#3974 := (or #3817 #3971)
-#3977 := (not #3974)
-#1707 := (?v1!7 #11)
-#1714 := (f6 f7 #1707)
-#1715 := (f5 #1714 #11)
-#1716 := (f4 #1715)
-#2261 := (* -1::Int #1716)
-#1708 := (f19 f20 #1707)
-#2244 := (* -1::Int #1708)
-#2262 := (+ #2244 #2261)
-#2263 := (+ #112 #2262)
-#2264 := (= #2263 0::Int)
-#2658 := (not #2264)
-#1712 := (f11 f21 #1707)
-#1713 := (= #1712 f1)
-#2657 := (not #1713)
-#2245 := (+ #112 #2244)
-#2246 := (<= #2245 0::Int)
-#2659 := (or #2246 #2657 #2658)
-#2660 := (not #2659)
-#2666 := (or #66 #1004 #2660)
-#3742 := (forall (vars (?v0 S2)) (:pat #3716) #2666)
-#3747 := (not #3742)
-#122 := (f19 f20 #10)
-#1016 := (* -1::Int #122)
-#1017 := (+ #112 #1016)
-#1018 := (+ #93 #1017)
-#1371 := (>= #1018 0::Int)
-#118 := (not #117)
-#2638 := (or #118 #940 #1371)
-#3734 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2638)
-#3739 := (not #3734)
-#119 := (f11 f21 #10)
-#3725 := (pattern #116 #119)
-#1020 := (>= #1017 0::Int)
-#120 := (= #119 f1)
-#2601 := (not #120)
-#2616 := (or #117 #2601 #1020)
-#3726 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3725) #2616)
-#3731 := (not #3726)
-#1394 := (>= #112 0::Int)
-#3717 := (forall (vars (?v0 S2)) (:pat #3716) #1394)
-#3722 := (not #3717)
-#110 := (f19 f20 f16)
-#111 := (= #110 0::Int)
-#804 := (not #111)
-decl f17 :: (-> S2 Int)
-#67 := (f17 #11)
-#3647 := (pattern #67)
-decl ?v1!6 :: (-> S2 S2)
-#1654 := (?v1!6 #11)
-#1661 := (f6 f7 #1654)
-#1662 := (f5 #1661 #11)
-#1663 := (f4 #1662)
-#2219 := (* -1::Int #1663)
-#1655 := (f17 #1654)
-#2202 := (* -1::Int #1655)
-#2220 := (+ #2202 #2219)
-#2221 := (+ #67 #2220)
-#2222 := (= #2221 0::Int)
-#2585 := (not #2222)
-decl f18 :: S7
-#75 := f18
-#1659 := (f11 f18 #1654)
-#1660 := (= #1659 f1)
-#2584 := (not #1660)
-#2203 := (+ #67 #2202)
-#2204 := (<= #2203 0::Int)
-#2586 := (or #2204 #2584 #2585)
-#2587 := (not #2586)
-#964 := (* -1::Int #67)
-#965 := (+ f3 #964)
-#966 := (<= #965 0::Int)
-#2593 := (or #66 #966 #2587)
-#3708 := (forall (vars (?v0 S2)) (:pat #3647) #2593)
-#3713 := (not #3708)
-#3980 := (or #3713 #804 #3722 #3731 #3739 #3747 #3977)
-#3983 := (not #3980)
-#76 := (f11 f18 #11)
-#3660 := (pattern #76)
-decl ?v0!5 :: S2
-#1613 := ?v0!5
-#1626 := (f5 #91 ?v0!5)
-#1627 := (f4 #1626)
-#1616 := (f17 ?v0!5)
-#1617 := (* -1::Int #1616)
-#1628 := (+ #1617 #1627)
-#1629 := (+ #67 #1628)
-#1630 := (= #1629 0::Int)
-#2548 := (not #1630)
-#77 := (= #76 f1)
-#78 := (not #77)
-#1623 := (+ #67 #1617)
-#1624 := (>= #1623 0::Int)
-#2549 := (or #1624 #78 #2548)
-#3694 := (forall (vars (?v1 S2)) (:pat #3647 #3660 #3693) #2549)
-#3699 := (not #3694)
-#1618 := (+ f3 #1617)
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-#1614 := (= ?v0!5 f16)
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-#6176 := (= f3 #1616)
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-#6629 := (iff #6574 #6176)
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-#1232 := (not #1185)
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-#1246 := (exists (vars (?v1 S2)) #1241)
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-#1357 := (or #1333 #183 #1322 #1318 #715 #1305 #1162 #1288)
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-#1059 := (>= #1061 0::Int)
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-#1072 := (exists (vars (?v1 S2)) #1069)
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-#1377 := (forall (vars (?v0 S2) (?v1 S2)) #1374)
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-#121 := (and #118 #120)
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-#87 := (f17 #10)
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-#925 := (>= #927 0::Int)
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-#920 := (not #917)
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-#80 := (f17 f16)
-#81 := (= #80 0::Int)
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-#68 := (= #67 0::Int)
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-#1465 := (or #898 #889 #880 #1453)
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-#229 := (+ #202 #93)
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-#237 := (and #213 #236)
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-#239 := (exists (vars (?v1 S2)) #238)
-#233 := (< #202 f3)
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-#1426 := [rewrite]: #1425
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-#1243 := [rewrite]: #1242
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-#1231 := [rewrite]: #1230
-#1237 := [monotonicity #1231]: #1236
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-#1245 := [trans #1240 #1243]: #1244
-#1248 := [quant-intro #1245]: #1247
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-#1221 := (iff #233 #1220)
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-#711 := [trans #705 #709]: #710
-#714 := [monotonicity #711]: #713
-#720 := [trans #714 #718]: #719
-#546 := (iff #189 #545)
-#543 := (iff #188 #542)
-#544 := [rewrite]: #543
-#547 := [quant-intro #544]: #546
-#723 := [monotonicity #547 #720]: #722
-#729 := [trans #723 #727]: #728
-#732 := [monotonicity #729]: #731
-#738 := [trans #732 #736]: #737
-#741 := [monotonicity #738]: #740
-#746 := [trans #741 #744]: #745
-#749 := [monotonicity #746]: #748
-#754 := [trans #749 #752]: #753
-#757 := [monotonicity #754]: #756
-#761 := [trans #757 #759]: #760
-#540 := (iff #180 #530)
-#535 := (implies true #530)
-#538 := (iff #535 #530)
-#539 := [rewrite]: #538
-#536 := (iff #180 #535)
-#533 := (iff #179 #530)
-#527 := (implies #142 #522)
-#531 := (iff #527 #530)
-#532 := [rewrite]: #531
-#528 := (iff #179 #527)
-#525 := (iff #178 #522)
-#518 := (implies #144 #513)
-#523 := (iff #518 #522)
-#524 := [rewrite]: #523
-#519 := (iff #178 #518)
-#516 := (iff #177 #513)
-#509 := (implies #147 #504)
-#514 := (iff #509 #513)
-#515 := [rewrite]: #514
-#510 := (iff #177 #509)
-#507 := (iff #176 #504)
-#500 := (implies #149 #495)
-#505 := (iff #500 #504)
-#506 := [rewrite]: #505
-#501 := (iff #176 #500)
-#498 := (iff #175 #495)
-#491 := (implies #152 #488)
-#496 := (iff #491 #495)
-#497 := [rewrite]: #496
-#492 := (iff #175 #491)
-#489 := (iff #174 #488)
-#486 := (iff #173 #483)
-#479 := (implies #447 #476)
-#484 := (iff #479 #483)
-#485 := [rewrite]: #484
-#480 := (iff #173 #479)
-#477 := (iff #172 #476)
-#474 := (iff #171 #471)
-#467 := (implies #462 #169)
-#472 := (iff #467 #471)
-#473 := [rewrite]: #472
-#468 := (iff #171 #467)
-#465 := (iff #170 #169)
-#466 := [rewrite]: #465
-#463 := (iff #167 #462)
-#460 := (iff #166 #457)
-#453 := (implies #164 #450)
-#458 := (iff #453 #457)
-#459 := [rewrite]: #458
-#454 := (iff #166 #453)
-#451 := (iff #165 #450)
-#427 := (= #158 #426)
-#428 := [rewrite]: #427
-#452 := [monotonicity #428]: #451
-#455 := [monotonicity #452]: #454
-#461 := [trans #455 #459]: #460
-#464 := [quant-intro #461]: #463
-#469 := [monotonicity #464 #466]: #468
-#475 := [trans #469 #473]: #474
-#478 := [monotonicity #464 #475]: #477
-#448 := (iff #163 #447)
-#445 := (iff #162 #442)
-#438 := (implies #155 #435)
-#443 := (iff #438 #442)
-#444 := [rewrite]: #443
-#439 := (iff #162 #438)
-#436 := (iff #161 #435)
-#433 := (iff #160 #432)
-#430 := (iff #159 #429)
-#431 := [monotonicity #428]: #430
-#434 := [monotonicity #431]: #433
-#437 := [quant-intro #434]: #436
-#440 := [monotonicity #437]: #439
-#446 := [trans #440 #444]: #445
-#449 := [quant-intro #446]: #448
-#481 := [monotonicity #449 #478]: #480
-#487 := [trans #481 #485]: #486
-#490 := [monotonicity #449 #487]: #489
-#493 := [monotonicity #490]: #492
-#499 := [trans #493 #497]: #498
-#502 := [monotonicity #499]: #501
-#508 := [trans #502 #506]: #507
-#511 := [monotonicity #508]: #510
-#517 := [trans #511 #515]: #516
-#520 := [monotonicity #517]: #519
-#526 := [trans #520 #524]: #525
-#529 := [monotonicity #526]: #528
-#534 := [trans #529 #532]: #533
-#537 := [monotonicity #534]: #536
-#541 := [trans #537 #539]: #540
-#764 := [monotonicity #541 #761]: #763
-#424 := (iff #139 #423)
-#421 := (iff #138 #418)
-#414 := (implies #132 #411)
-#419 := (iff #414 #418)
-#420 := [rewrite]: #419
-#415 := (iff #138 #414)
-#412 := (iff #137 #411)
-#409 := (iff #136 #408)
-#406 := (iff #135 #405)
-#403 := (iff #134 #402)
-#385 := (= #127 #384)
-#386 := [rewrite]: #385
-#404 := [monotonicity #386]: #403
-#407 := [monotonicity #404]: #406
-#410 := [monotonicity #407]: #409
-#413 := [quant-intro #410]: #412
-#416 := [monotonicity #413]: #415
-#422 := [trans #416 #420]: #421
-#425 := [quant-intro #422]: #424
-#767 := [monotonicity #425 #764]: #766
-#773 := [trans #767 #771]: #772
-#400 := (iff #130 #399)
-#397 := (iff #129 #394)
-#390 := (implies #126 #387)
-#395 := (iff #390 #394)
-#396 := [rewrite]: #395
-#391 := (iff #129 #390)
-#388 := (iff #128 #387)
-#389 := [monotonicity #386]: #388
-#392 := [monotonicity #389]: #391
-#398 := [trans #392 #396]: #397
-#401 := [quant-intro #398]: #400
-#776 := [monotonicity #401 #773]: #775
-#782 := [trans #776 #780]: #781
-#382 := (iff #125 #381)
-#379 := (iff #124 #378)
-#380 := [rewrite]: #379
-#383 := [quant-intro #380]: #382
-#785 := [monotonicity #383 #782]: #784
-#791 := [trans #785 #789]: #790
-#794 := [monotonicity #791]: #793
-#800 := [trans #794 #798]: #799
-#803 := [monotonicity #800]: #802
-#809 := [trans #803 #807]: #808
-#812 := [monotonicity #809]: #811
-#816 := [trans #812 #814]: #815
-#375 := (iff #108 #374)
-#372 := (iff #107 #371)
-#373 := [rewrite]: #372
-#376 := [quant-intro #373]: #375
-#819 := [monotonicity #376 #816]: #818
-#825 := [trans #819 #823]: #824
-#828 := [monotonicity #376 #825]: #827
-#368 := (iff #99 #367)
-#365 := (iff #98 #364)
-#366 := [rewrite]: #365
-#369 := [quant-intro #366]: #368
-#831 := [monotonicity #369 #828]: #830
-#837 := [trans #831 #835]: #836
-#840 := [monotonicity #369 #837]: #839
-#361 := (iff #90 #360)
-#358 := (iff #89 #357)
-#359 := [rewrite]: #358
-#362 := [quant-intro #359]: #361
-#843 := [monotonicity #362 #840]: #842
-#849 := [trans #843 #847]: #848
-#852 := [monotonicity #362 #849]: #851
-#855 := [monotonicity #852]: #854
-#861 := [trans #855 #859]: #860
-#864 := [monotonicity #861]: #863
-#867 := [monotonicity #864]: #866
-#873 := [trans #867 #871]: #872
-#876 := [monotonicity #873]: #875
-#879 := [monotonicity #876]: #878
-#885 := [trans #879 #883]: #884
-#354 := (iff #74 #353)
-#351 := (iff #73 #350)
-#352 := [rewrite]: #351
-#355 := [quant-intro #352]: #354
-#888 := [monotonicity #355 #885]: #887
-#894 := [trans #888 #892]: #893
-#348 := (iff #70 #347)
-#345 := (iff #69 #344)
-#346 := [rewrite]: #345
-#349 := [quant-intro #346]: #348
-#897 := [monotonicity #349 #894]: #896
-#903 := [trans #897 #901]: #902
-#906 := [monotonicity #903]: #905
-#910 := [trans #906 #908]: #909
-#913 := [monotonicity #910]: #912
-#1474 := [trans #913 #1472]: #1473
-#343 := [asserted]: #284
-#1475 := [mp #343 #1474]: #1470
-#1477 := [not-or-elim #1475]: #353
-#1532 := [mp~ #1477 #1501]: #353
-#3659 := [mp #1532 #3658]: #3654
-#3289 := (not #3654)
-#5853 := (or #3289 #1614 #6574)
-#6575 := (or #1614 #6574)
-#6155 := (or #3289 #6575)
-#6156 := (iff #6155 #5853)
-#6165 := [rewrite]: #6156
-#5702 := [quant-inst #1613]: #6155
-#6166 := [mp #5702 #6165]: #5853
-#6626 := [unit-resolution #6166 #3659 #6625]: #6574
-#6631 := [mp #6626 #6630]: #6176
-#6615 := (not #6176)
-#1620 := (not #1619)
-#3595 := (or #3702 #1620)
-#3596 := [def-axiom]: #3595
-#5852 := [unit-resolution #3596 #5790]: #1620
-#6616 := (or #6615 #1619)
-#6622 := [th-lemma arith triangle-eq]: #6616
-#6624 := [unit-resolution #6622 #5852]: #6615
-#6632 := [unit-resolution #6624 #6631]: false
-#6633 := [lemma #6632]: #3702
-#3986 := (or #3705 #3983)
-#3989 := (not #3986)
-#2540 := (or #78 #940 #951)
-#3685 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2540)
-#3690 := (not #3685)
-#3992 := (or #3690 #3989)
-#3995 := (not #3992)
-decl ?v0!4 :: S2
-#1582 := ?v0!4
-#1595 := (f17 ?v0!4)
-#1596 := (* -1::Int #1595)
-decl ?v1!3 :: S2
-#1581 := ?v1!3
-#1594 := (f17 ?v1!3)
-#2173 := (+ #1594 #1596)
-#1585 := (f6 f7 ?v1!3)
-#1586 := (f5 #1585 ?v0!4)
-#1587 := (f4 #1586)
-#2174 := (+ #1587 #2173)
-#2177 := (>= #2174 0::Int)
-#1588 := (* -1::Int #1587)
-#1589 := (+ f3 #1588)
-#1590 := (<= #1589 0::Int)
-#1583 := (f11 f18 ?v1!3)
-#1584 := (= #1583 f1)
-#2503 := (not #1584)
-#2518 := (or #2503 #1590 #2177)
-#2523 := (not #2518)
-#3998 := (or #2523 #3995)
-#4001 := (not #3998)
-#3675 := (pattern #67 #87)
-#1605 := (not #85)
-#2495 := (or #77 #1605 #925)
-#3676 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3675) #2495)
-#3681 := (not #3676)
-#4004 := (or #3681 #4001)
-#4007 := (not #4004)
-decl ?v0!2 :: S2
-#1555 := ?v0!2
-#1564 := (f17 ?v0!2)
-#1565 := (* -1::Int #1564)
-decl ?v1!1 :: S2
-#1554 := ?v1!1
-#1563 := (f17 ?v1!1)
-#1566 := (+ #1563 #1565)
-#1567 := (>= #1566 0::Int)
-#1559 := (f11 f18 ?v0!2)
-#1560 := (= #1559 f1)
-#1884 := (not #1560)
-#1556 := (f11 f18 ?v1!1)
-#1557 := (= #1556 f1)
-#1841 := (or #1557 #1884 #1567)
-#1946 := (not #1841)
-#4010 := (or #1946 #4007)
-#4013 := (not #4010)
-#3667 := (forall (vars (?v0 S2)) (:pat #3647) #916)
-#3672 := (not #3667)
-#4016 := (or #3672 #4013)
-#4019 := (not #4016)
-decl ?v0!0 :: S2
-#1539 := ?v0!0
-#1540 := (f17 ?v0!0)
-#1541 := (>= #1540 0::Int)
-#3259 := (= f3 #1540)
-#3321 := (= #1540 f3)
-#3223 := (iff #3321 #3259)
-#3224 := (iff #3259 #3321)
-#3227 := [commutativity]: #3224
-#3222 := [symm #3227]: #3223
-#3345 := (= ?v0!0 f16)
-#3353 := (not #3345)
-#3306 := (= #1540 0::Int)
-#3281 := (not #3306)
-#1542 := (not #1541)
-#3290 := [hypothesis]: #1542
-#3246 := (or #3281 #1541)
-#3244 := [th-lemma arith triangle-eq]: #3246
-#3247 := [unit-resolution #3244 #3290]: #3281
-#3648 := (forall (vars (?v0 S2)) (:pat #3647) #344)
-#3651 := (iff #347 #3648)
-#3649 := (iff #344 #344)
-#3650 := [refl]: #3649
-#3652 := [quant-intro #3650]: #3651
-#1498 := (~ #347 #347)
-#1527 := (~ #344 #344)
-#1528 := [refl]: #1527
-#1499 := [nnf-pos #1528]: #1498
-#1476 := [not-or-elim #1475]: #347
-#1529 := [mp~ #1476 #1499]: #347
-#3653 := [mp #1529 #3652]: #3648
-#3310 := (not #3648)
-#3309 := (or #3310 #3353 #3306)
-#3307 := (or #3353 #3306)
-#3303 := (or #3310 #3307)
-#3294 := (iff #3303 #3309)
-#3295 := [rewrite]: #3294
-#3304 := [quant-inst #1539]: #3303
-#3305 := [mp #3304 #3295]: #3309
-#3236 := [unit-resolution #3305 #3653 #3247]: #3353
-#3291 := (or #3289 #3345 #3321)
-#3308 := (or #3345 #3321)
-#3258 := (or #3289 #3308)
-#3268 := (iff #3258 #3291)
-#3269 := [rewrite]: #3268
-#3260 := [quant-inst #1539]: #3258
-#3267 := [mp #3260 #3269]: #3291
-#3248 := [unit-resolution #3267 #3659 #3236]: #3321
-#3228 := [mp #3248 #3222]: #3259
-#3316 := (* -1::Int #1540)
-#3270 := (+ f3 #3316)
-#3253 := (<= #3270 0::Int)
-#4045 := (not #3253)
-#307 := (<= f3 0::Int)
-#308 := (not #307)
-#9 := (< 0::Int f3)
-#309 := (iff #9 #308)
-#310 := [rewrite]: #309
-#304 := [asserted]: #9
-#311 := [mp #304 #310]: #308
-#3286 := (<= #1540 0::Int)
-#3203 := (or #3286 #1541)
-#3208 := [th-lemma arith farkas 1 1]: #3203
-#3213 := [unit-resolution #3208 #3290]: #3286
-#4046 := (not #3286)
-#4047 := (or #4045 #307 #4046)
-#4048 := [th-lemma arith assign-bounds 1 1]: #4047
-#4049 := [unit-resolution #4048 #3213 #311]: #4045
-#4044 := (not #3259)
-#4050 := (or #4044 #3253)
-#4051 := [th-lemma arith triangle-eq]: #4050
-#4052 := [unit-resolution #4051 #4049 #3228]: false
-#4053 := [lemma #4052]: #1541
-#4022 := (or #1542 #4019)
-#4025 := (not #4022)
-#4028 := (or #868 #4025)
-#4031 := (not #4028)
-#4121 := [hypothesis]: #868
-#4075 := (or #3310 #81)
-#6826 := (= f16 f16)
-#6905 := (not #6826)
-#4054 := (or #6905 #81)
-#4076 := (or #3310 #4054)
-#4084 := (iff #4076 #4075)
-#4117 := (iff #4075 #4075)
-#4118 := [rewrite]: #4117
-#4073 := (iff #4054 #81)
-#4068 := (or false #81)
-#4069 := (iff #4068 #81)
-#4072 := [rewrite]: #4069
-#4070 := (iff #4054 #4068)
-#6915 := (iff #6905 false)
-#6910 := (not true)
-#6913 := (iff #6910 false)
-#6914 := [rewrite]: #6913
-#6911 := (iff #6905 #6910)
-#6829 := (iff #6826 true)
-#6830 := [rewrite]: #6829
-#6912 := [monotonicity #6830]: #6911
-#6916 := [trans #6912 #6914]: #6915
-#4071 := [monotonicity #6916]: #4070
-#4074 := [trans #4071 #4072]: #4073
-#4085 := [monotonicity #4074]: #4084
-#4119 := [trans #4085 #4118]: #4084
-#4077 := [quant-inst #65]: #4076
-#4120 := [mp #4077 #4119]: #4075
-#4116 := [unit-resolution #4120 #3653 #4121]: false
-#4122 := [lemma #4116]: #81
-#4034 := (or #868 #4031)
-#2953 := (forall (vars (?v1 S2)) #2942)
-#2960 := (not #2953)
-#2938 := (forall (vars (?v0 S2) (?v1 S2)) #2933)
-#2959 := (not #2938)
-#2961 := (or #2959 #2035 #2040 #2960)
-#2962 := (not #2961)
-#2967 := (or #2916 #2962)
-#2974 := (not #2967)
-#2893 := (forall (vars (?v0 S2) (?v1 S2)) #2888)
-#2973 := (not #2893)
-#2975 := (or #2973 #2974)
-#2976 := (not #2975)
-#2981 := (or #2870 #2976)
-#2987 := (not #2981)
-#2988 := (or #1182 #2987)
-#2989 := (not #2988)
-#2994 := (or #1963 #2989)
-#3000 := (not #2994)
-#3001 := (or #661 #3000)
-#3002 := (not #3001)
-#3007 := (or #661 #3002)
-#3013 := (not #3007)
-#3014 := (or #673 #3013)
-#3015 := (not #3014)
-#3020 := (or #1943 #3015)
-#3026 := (not #3020)
-#3027 := (or #1173 #3026)
-#3028 := (not #3027)
-#3033 := (or #1923 #3028)
-#3041 := (not #3033)
-#2847 := (forall (vars (?v0 S2)) #2844)
-#3040 := (not #2847)
-#2841 := (forall (vars (?v0 S2)) #2836)
-#3039 := (not #2841)
-#3042 := (or #1874 #1879 #183 #1322 #1318 #715 #3039 #3040 #3041)
-#3043 := (not #3042)
-#2781 := (forall (vars (?v0 S2) (?v1 S2)) #2776)
-#2787 := (not #2781)
-#2788 := (or #2787 #169)
-#2789 := (not #2788)
-#2794 := (or #2759 #2789)
-#2801 := (not #2794)
-#2737 := (forall (vars (?v0 S2)) #2732)
-#2800 := (not #2737)
-#2802 := (or #2800 #2801)
-#2803 := (not #2802)
-#2700 := (forall (vars (?v1 S2)) #2689)
-#2706 := (not #2700)
-#2707 := (or #1752 #1757 #2706)
-#2708 := (not #2707)
-#2808 := (or #2708 #2803)
-#2815 := (not #2808)
-#2685 := (forall (vars (?v0 S2)) #2674)
-#2814 := (not #2685)
-#2816 := (or #2814 #521 #512 #503 #494 #2815)
-#2817 := (not #2816)
-#3048 := (or #2817 #3043)
-#3058 := (not #3048)
-#2671 := (forall (vars (?v0 S2)) #2666)
-#3057 := (not #2671)
-#2643 := (forall (vars (?v0 S2) (?v1 S2)) #2638)
-#3056 := (not #2643)
-#2621 := (forall (vars (?v0 S2) (?v1 S2)) #2616)
-#3055 := (not #2621)
-#2598 := (forall (vars (?v0 S2)) #2593)
-#3054 := (not #2598)
-#3059 := (or #3054 #804 #1400 #3055 #3056 #3057 #3058)
-#3060 := (not #3059)
-#2560 := (forall (vars (?v1 S2)) #2549)
-#2566 := (not #2560)
-#2567 := (or #1614 #1619 #2566)
-#2568 := (not #2567)
-#3065 := (or #2568 #3060)
-#3072 := (not #3065)
-#2545 := (forall (vars (?v0 S2) (?v1 S2)) #2540)
-#3071 := (not #2545)
-#3073 := (or #3071 #3072)
-#3074 := (not #3073)
-#3079 := (or #2523 #3074)
-#3086 := (not #3079)
-#2500 := (forall (vars (?v0 S2) (?v1 S2)) #2495)
-#3085 := (not #2500)
-#3087 := (or #3085 #3086)
-#3088 := (not #3087)
-#3093 := (or #1946 #3088)
-#3099 := (not #3093)
-#3100 := (or #920 #3099)
-#3101 := (not #3100)
-#3106 := (or #1542 #3101)
-#3112 := (not #3106)
-#3113 := (or #868 #3112)
-#3114 := (not #3113)
-#3119 := (or #868 #3114)
-#4035 := (iff #3119 #4034)
-#4032 := (iff #3114 #4031)
-#4029 := (iff #3113 #4028)
-#4026 := (iff #3112 #4025)
-#4023 := (iff #3106 #4022)
-#4020 := (iff #3101 #4019)
-#4017 := (iff #3100 #4016)
-#4014 := (iff #3099 #4013)
-#4011 := (iff #3093 #4010)
-#4008 := (iff #3088 #4007)
-#4005 := (iff #3087 #4004)
-#4002 := (iff #3086 #4001)
-#3999 := (iff #3079 #3998)
-#3996 := (iff #3074 #3995)
-#3993 := (iff #3073 #3992)
-#3990 := (iff #3072 #3989)
-#3987 := (iff #3065 #3986)
-#3984 := (iff #3060 #3983)
-#3981 := (iff #3059 #3980)
-#3978 := (iff #3058 #3977)
-#3975 := (iff #3048 #3974)
-#3972 := (iff #3043 #3971)
-#3969 := (iff #3042 #3968)
-#3966 := (iff #3041 #3965)
-#3963 := (iff #3033 #3962)
-#3960 := (iff #3028 #3959)
-#3957 := (iff #3027 #3956)
-#3954 := (iff #3026 #3953)
-#3951 := (iff #3020 #3950)
-#3948 := (iff #3015 #3947)
-#3945 := (iff #3014 #3944)
-#3942 := (iff #3013 #3941)
-#3939 := (iff #3007 #3938)
-#3936 := (iff #3002 #3935)
-#3933 := (iff #3001 #3932)
-#3930 := (iff #3000 #3929)
-#3927 := (iff #2994 #3926)
-#3924 := (iff #2989 #3923)
-#3921 := (iff #2988 #3920)
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-#2835 := [monotonicity #2832]: #2834
-#2840 := [trans #2835 #2838]: #2839
-#2843 := [quant-intro #2840]: #2842
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-#2790 := (iff #2784 #2789)
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-#2785 := (iff #1852 #2784)
-#2782 := (iff #1096 #2781)
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-#2753 := [monotonicity #2750]: #2752
-#2758 := [trans #2753 #2756]: #2757
-#2761 := [monotonicity #2758]: #2760
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-#2735 := (iff #2346 #2732)
-#2713 := (or #66 #1049)
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-#2733 := (iff #2729 #2732)
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-#2730 := (iff #2346 #2729)
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-#2721 := [rewrite]: #2720
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-#2719 := [monotonicity #2716]: #2718
-#2723 := [trans #2719 #2721]: #2722
-#2731 := [monotonicity #2723 #2728]: #2730
-#2736 := [trans #2731 #2734]: #2735
-#2739 := [quant-intro #2736]: #2738
-#2799 := [monotonicity #2739 #2796]: #2798
-#2807 := [trans #2799 #2805]: #2806
-#2711 := (iff #2307 #2708)
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-#2710 := [rewrite]: #2709
-#2704 := (iff #2307 #2703)
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-#2693 := (not #2690)
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-#2697 := [rewrite]: #2696
-#2694 := (iff #2298 #2693)
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-#2692 := [rewrite]: #2691
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-#2712 := [trans #2705 #2710]: #2711
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-#2683 := (iff #1733 #2674)
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-#2678 := (not #2675)
-#2681 := (iff #2678 #2674)
-#2682 := [rewrite]: #2681
-#2679 := (iff #1733 #2678)
-#2676 := (iff #1114 #2675)
-#2677 := [rewrite]: #2676
-#2680 := [monotonicity #2677]: #2679
-#2684 := [trans #2680 #2682]: #2683
-#2687 := [quant-intro #2684]: #2686
-#2813 := [monotonicity #2687 #2810]: #2812
-#2821 := [trans #2813 #2819]: #2820
-#3050 := [monotonicity #2821 #3047]: #3049
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-#2632 := [rewrite]: #2631
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-#2630 := [monotonicity #2627]: #2629
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-#2403 := (iff #2073 #2402)
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-#2385 := (= #2049 #2384)
-#2386 := [rewrite]: #2385
-#2389 := [monotonicity #2386]: #2388
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-#2398 := [quant-intro #2395]: #2397
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-#2401 := [monotonicity #2382 #2398]: #2400
-#2404 := [monotonicity #2401]: #2403
-#2409 := [trans #2404 #2407]: #2408
-#2412 := [monotonicity #2409]: #2411
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-#2421 := [monotonicity #2418]: #2420
-#2424 := [monotonicity #2421]: #2423
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-#2427 := [monotonicity #2380 #2424]: #2426
-#2430 := [monotonicity #2427]: #2429
-#2433 := [monotonicity #2430]: #2432
-#2436 := [monotonicity #2433]: #2435
-#2439 := [monotonicity #2436]: #2438
-#2442 := [monotonicity #2439]: #2441
-#2377 := (iff #1900 #194)
-#2378 := [rewrite]: #2377
-#2445 := [monotonicity #2378 #2442]: #2444
-#2450 := [trans #2445 #2448]: #2449
-#2375 := (iff #1868 #2374)
-#2372 := (iff #1864 #2371)
-#2369 := (iff #1860 #2368)
-#2366 := (iff #1856 #2365)
-#2363 := (iff #1837 #2362)
-#2360 := (iff #1836 #2359)
-#2357 := (iff #1835 #2356)
-#2354 := (= #1834 #2353)
-#2355 := [rewrite]: #2354
-#2358 := [monotonicity #2355]: #2357
-#2361 := [monotonicity #2358]: #2360
-#2364 := [monotonicity #2361]: #2363
-#2367 := [monotonicity #2364]: #2366
-#2350 := (iff #1809 #2349)
-#2347 := (iff #1806 #2346)
-#2344 := (iff #1801 #2343)
-#2341 := (iff #1800 #2338)
-#2328 := (+ #1792 #1798)
-#2329 := (+ #1047 #2328)
-#2332 := (= #2329 0::Int)
-#2339 := (iff #2332 #2338)
-#2340 := [rewrite]: #2339
-#2333 := (iff #1800 #2332)
-#2330 := (= #1799 #2329)
-#2331 := [rewrite]: #2330
-#2334 := [monotonicity #2331]: #2333
-#2342 := [trans #2334 #2340]: #2341
-#2326 := (iff #1795 #2325)
-#2323 := (iff #1794 #2320)
-#2312 := (+ #1047 #1792)
-#2315 := (>= #2312 0::Int)
-#2321 := (iff #2315 #2320)
-#2322 := [rewrite]: #2321
-#2316 := (iff #1794 #2315)
-#2313 := (= #1793 #2312)
-#2314 := [rewrite]: #2313
-#2317 := [monotonicity #2314]: #2316
-#2324 := [trans #2317 #2322]: #2323
-#2327 := [monotonicity #2324]: #2326
-#2345 := [monotonicity #2327 #2342]: #2344
-#2348 := [monotonicity #2345]: #2347
-#2351 := [quant-intro #2348]: #2350
-#2370 := [monotonicity #2351 #2367]: #2369
-#2310 := (iff #1784 #2307)
-#2304 := (and #1759 #2301)
-#2308 := (iff #2304 #2307)
-#2309 := [rewrite]: #2308
-#2305 := (iff #1784 #2304)
-#2302 := (iff #1780 #2301)
-#2299 := (iff #1777 #2298)
-#2296 := (iff #1768 #2295)
-#2293 := (iff #1767 #2292)
-#2290 := (= #1766 #2289)
-#2291 := [rewrite]: #2290
-#2294 := [monotonicity #2291]: #2293
-#2297 := [monotonicity #2294]: #2296
-#2300 := [monotonicity #2297]: #2299
-#2303 := [quant-intro #2300]: #2302
-#2286 := (iff #1774 #1759)
-#2287 := [rewrite]: #2286
-#2306 := [monotonicity #2287 #2303]: #2305
-#2311 := [trans #2306 #2309]: #2310
-#2373 := [monotonicity #2311 #2370]: #2372
-#2284 := (iff #1748 #152)
-#2285 := [rewrite]: #2284
-#2282 := (iff #1745 #149)
-#2283 := [rewrite]: #2282
-#2280 := (iff #1742 #147)
-#2281 := [rewrite]: #2280
-#2278 := (iff #1739 #144)
-#2279 := [rewrite]: #2278
-#2376 := [monotonicity #2279 #2281 #2283 #2285 #2373]: #2375
-#2453 := [monotonicity #2376 #2450]: #2452
-#2276 := (iff #1727 #2275)
-#2273 := (iff #1724 #2272)
-#2270 := (iff #1719 #2269)
-#2267 := (iff #1718 #2264)
-#2254 := (+ #1708 #1716)
-#2255 := (+ #1002 #2254)
-#2258 := (= #2255 0::Int)
-#2265 := (iff #2258 #2264)
-#2266 := [rewrite]: #2265
-#2259 := (iff #1718 #2258)
-#2256 := (= #1717 #2255)
-#2257 := [rewrite]: #2256
-#2260 := [monotonicity #2257]: #2259
-#2268 := [trans #2260 #2266]: #2267
-#2252 := (iff #1711 #2251)
-#2249 := (iff #1710 #2246)
-#2238 := (+ #1002 #1708)
-#2241 := (>= #2238 0::Int)
-#2247 := (iff #2241 #2246)
-#2248 := [rewrite]: #2247
-#2242 := (iff #1710 #2241)
-#2239 := (= #1709 #2238)
-#2240 := [rewrite]: #2239
-#2243 := [monotonicity #2240]: #2242
-#2250 := [trans #2243 #2248]: #2249
-#2253 := [monotonicity #2250]: #2252
-#2271 := [monotonicity #2253 #2268]: #2270
-#2274 := [monotonicity #2271]: #2273
-#2277 := [quant-intro #2274]: #2276
-#2236 := (iff #1681 #111)
-#2237 := [rewrite]: #2236
-#2234 := (iff #1675 #2233)
-#2231 := (iff #1672 #2230)
-#2228 := (iff #1667 #2227)
-#2225 := (iff #1666 #2222)
-#2212 := (+ #1655 #1663)
-#2213 := (+ #964 #2212)
-#2216 := (= #2213 0::Int)
-#2223 := (iff #2216 #2222)
-#2224 := [rewrite]: #2223
-#2217 := (iff #1666 #2216)
-#2214 := (= #1665 #2213)
-#2215 := [rewrite]: #2214
-#2218 := [monotonicity #2215]: #2217
-#2226 := [trans #2218 #2224]: #2225
-#2210 := (iff #1658 #2209)
-#2207 := (iff #1657 #2204)
-#2196 := (+ #964 #1655)
-#2199 := (>= #2196 0::Int)
-#2205 := (iff #2199 #2204)
-#2206 := [rewrite]: #2205
-#2200 := (iff #1657 #2199)
-#2197 := (= #1656 #2196)
-#2198 := [rewrite]: #2197
-#2201 := [monotonicity #2198]: #2200
-#2208 := [trans #2201 #2206]: #2207
-#2211 := [monotonicity #2208]: #2210
-#2229 := [monotonicity #2211 #2226]: #2228
-#2232 := [monotonicity #2229]: #2231
-#2235 := [quant-intro #2232]: #2234
-#2456 := [monotonicity #2235 #2237 #2277 #2453]: #2455
-#2194 := (iff #1647 #2191)
-#2188 := (and #1621 #1643)
-#2192 := (iff #2188 #2191)
-#2193 := [rewrite]: #2192
-#2189 := (iff #1647 #2188)
-#2186 := (iff #1637 #1621)
-#2187 := [rewrite]: #2186
-#2190 := [monotonicity #2187]: #2189
-#2195 := [trans #2190 #2193]: #2194
-#2459 := [monotonicity #2195 #2456]: #2458
-#2462 := [monotonicity #2459]: #2461
-#2184 := (iff #1601 #2183)
-#2181 := (iff #1600 #2180)
-#2178 := (iff #1599 #2177)
-#2175 := (= #1598 #2174)
-#2176 := [rewrite]: #2175
-#2179 := [monotonicity #2176]: #2178
-#2182 := [monotonicity #2179]: #2181
-#2185 := [monotonicity #2182]: #2184
-#2465 := [monotonicity #2185 #2462]: #2464
-#2468 := [monotonicity #2465]: #2467
-#2471 := [monotonicity #2468]: #2470
-#2474 := [monotonicity #2471]: #2473
-#2477 := [monotonicity #2474]: #2476
-#2171 := (iff #1504 #81)
-#2172 := [rewrite]: #2171
-#2480 := [monotonicity #2172 #2477]: #2479
-#2483 := [monotonicity #2480]: #2482
-#1479 := (not #1453)
-#2166 := (~ #1479 #2165)
-#2162 := (not #1450)
-#2163 := (~ #2162 #2161)
-#2158 := (not #1447)
-#2159 := (~ #2158 #2157)
-#2154 := (not #1444)
-#2155 := (~ #2154 #2153)
-#2150 := (not #1441)
-#2151 := (~ #2150 #2149)
-#2146 := (not #1438)
-#2147 := (~ #2146 #2145)
-#2142 := (not #1435)
-#2143 := (~ #2142 #2141)
-#2138 := (not #1432)
-#2139 := (~ #2138 #2137)
-#2134 := (not #1429)
-#2135 := (~ #2134 #2133)
-#2130 := (not #1424)
-#2131 := (~ #2130 #2129)
-#2126 := (not #1362)
-#2127 := (~ #2126 #2125)
-#2122 := (not #1357)
-#2123 := (~ #2122 #2121)
-#2118 := (not #1288)
-#2119 := (~ #2118 #2117)
-#2114 := (not #1285)
-#2115 := (~ #2114 #2113)
-#2110 := (not #1282)
-#2111 := (~ #2110 #2109)
-#2106 := (not #1279)
-#2107 := (~ #2106 #2105)
-#2102 := (not #1276)
-#2103 := (~ #2102 #2101)
-#2098 := (not #1273)
-#2099 := (~ #2098 #2097)
-#2094 := (not #1270)
-#2095 := (~ #2094 #2093)
-#2090 := (not #1267)
-#2091 := (~ #2090 #2089)
-#2086 := (not #1264)
-#2087 := (~ #2086 #2085)
-#2082 := (not #1261)
-#2083 := (~ #2082 #2081)
-#2078 := (not #1258)
-#2079 := (~ #2078 #2077)
-#2074 := (not #1255)
-#2075 := (~ #2074 #2073)
-#2055 := (not #1252)
-#2071 := (~ #2055 #2068)
-#2052 := (exists (vars (?v1 S2)) #2051)
-#2053 := (or #2043 #2052)
-#2054 := (not #2053)
-#2069 := (~ #2054 #2068)
-#2065 := (not #2052)
-#2066 := (~ #2065 #2064)
-#2062 := (~ #2061 #2061)
-#2063 := [refl]: #2062
-#2067 := [nnf-neg #2063]: #2066
-#2059 := (~ #2058 #2058)
-#2060 := [refl]: #2059
-#2070 := [nnf-neg #2060 #2067]: #2069
-#2056 := (~ #2055 #2054)
-#2057 := [sk]: #2056
-#2072 := [trans #2057 #2070]: #2071
-#2031 := (not #1215)
-#2032 := (~ #2031 #1212)
-#2029 := (~ #1212 #1212)
-#2027 := (~ #1209 #1209)
-#2028 := [refl]: #2027
-#2030 := [nnf-pos #2028]: #2029
-#2033 := [nnf-neg #2030]: #2032
-#2076 := [nnf-neg #2033 #2072]: #2075
-#2023 := (~ #1215 #2022)
-#2024 := [sk]: #2023
-#2080 := [nnf-neg #2024 #2076]: #2079
-#1999 := (not #1196)
-#2000 := (~ #1999 #1193)
-#1997 := (~ #1193 #1193)
-#1995 := (~ #1190 #1190)
-#1996 := [refl]: #1995
-#1998 := [nnf-pos #1996]: #1997
-#2001 := [nnf-neg #1998]: #2000
-#2084 := [nnf-neg #2001 #2080]: #2083
-#1991 := (~ #1196 #1990)
-#1992 := [sk]: #1991
-#2088 := [nnf-neg #1992 #2084]: #2087
-#1972 := (not #1182)
-#1973 := (~ #1972 #1179)
-#1970 := (~ #1179 #1179)
-#1968 := (~ #1176 #1176)
-#1969 := [refl]: #1968
-#1971 := [nnf-pos #1969]: #1970
-#1974 := [nnf-neg #1971]: #1973
-#2092 := [nnf-neg #1974 #2088]: #2091
-#1964 := (~ #1182 #1963)
-#1965 := [sk]: #1964
-#2096 := [nnf-neg #1965 #2092]: #2095
-#1958 := (~ #1957 #1957)
-#1959 := [refl]: #1958
-#2100 := [nnf-neg #1959 #2096]: #2099
-#1955 := (~ #661 #661)
-#1956 := [refl]: #1955
-#2104 := [nnf-neg #1956 #2100]: #2103
-#1952 := (not #673)
-#1953 := (~ #1952 #563)
-#1950 := (~ #563 #563)
-#1948 := (~ #560 #560)
-#1949 := [refl]: #1948
-#1951 := [nnf-pos #1949]: #1950
-#1954 := [nnf-neg #1951]: #1953
-#2108 := [nnf-neg #1954 #2104]: #2107
-#1944 := (~ #673 #1943)
-#1945 := [sk]: #1944
-#2112 := [nnf-neg #1945 #2108]: #2111
-#1932 := (not #1173)
-#1933 := (~ #1932 #1170)
-#1930 := (~ #1170 #1170)
-#1928 := (~ #1165 #1165)
-#1929 := [refl]: #1928
-#1931 := [nnf-pos #1929]: #1930
-#1934 := [nnf-neg #1931]: #1933
-#2116 := [nnf-neg #1934 #2112]: #2115
-#1924 := (~ #1173 #1923)
-#1925 := [sk]: #1924
-#2120 := [nnf-neg #1925 #2116]: #2119
-#1914 := (not #1162)
-#1915 := (~ #1914 #1159)
-#1912 := (~ #1159 #1159)
-#1910 := (~ #1156 #1156)
-#1911 := [refl]: #1910
-#1913 := [nnf-pos #1911]: #1912
-#1916 := [nnf-neg #1913]: #1915
-#1907 := (not #1305)
-#1908 := (~ #1907 #1302)
-#1905 := (~ #1302 #1302)
-#1903 := (~ #1299 #1299)
-#1904 := [refl]: #1903
-#1906 := [nnf-pos #1904]: #1905
-#1909 := [nnf-neg #1906]: #1908
-#1901 := (~ #1900 #1900)
-#1902 := [refl]: #1901
-#1897 := (not #1318)
-#1898 := (~ #1897 #1315)
-#1895 := (~ #1315 #1315)
-#1893 := (~ #1312 #1312)
-#1894 := [refl]: #1893
-#1896 := [nnf-pos #1894]: #1895
-#1899 := [nnf-neg #1896]: #1898
-#1891 := (~ #1323 #1323)
-#1892 := [refl]: #1891
-#1889 := (~ #184 #184)
-#1890 := [refl]: #1889
-#1886 := (not #1333)
-#1887 := (~ #1886 #1881)
-#1882 := (~ #1117 #1881)
-#1883 := [sk]: #1882
-#1888 := [nnf-neg #1883]: #1887
-#2124 := [nnf-neg #1888 #1890 #1892 #1899 #1902 #1909 #1916 #2120]: #2123
-#1869 := (not #1135)
-#1870 := (~ #1869 #1868)
-#1865 := (not #1111)
-#1866 := (~ #1865 #1864)
-#1861 := (not #1108)
-#1862 := (~ #1861 #1860)
-#1857 := (not #1105)
-#1858 := (~ #1857 #1856)
-#1853 := (not #1102)
-#1854 := (~ #1853 #1852)
-#1850 := (~ #1849 #1849)
-#1851 := [refl]: #1850
-#1846 := (not #1099)
-#1847 := (~ #1846 #1096)
-#1844 := (~ #1096 #1096)
-#1842 := (~ #1093 #1093)
-#1843 := [refl]: #1842
-#1845 := [nnf-pos #1843]: #1844
-#1848 := [nnf-neg #1845]: #1847
-#1855 := [nnf-neg #1848 #1851]: #1854
-#1838 := (~ #1099 #1837)
-#1839 := [sk]: #1838
-#1859 := [nnf-neg #1839 #1855]: #1858
-#1812 := (not #1081)
-#1813 := (~ #1812 #1809)
-#1810 := (~ #1078 #1809)
-#1807 := (~ #1075 #1806)
-#1802 := (~ #1072 #1801)
-#1803 := [sk]: #1802
-#1789 := (~ #1056 #1056)
-#1790 := [refl]: #1789
-#1808 := [monotonicity #1790 #1803]: #1807
-#1811 := [nnf-pos #1808]: #1810
-#1814 := [nnf-neg #1811]: #1813
-#1863 := [nnf-neg #1814 #1859]: #1862
-#1787 := (~ #1081 #1784)
-#1769 := (exists (vars (?v1 S2)) #1768)
-#1770 := (or #1760 #1769)
-#1771 := (not #1770)
-#1785 := (~ #1771 #1784)
-#1781 := (not #1769)
-#1782 := (~ #1781 #1780)
-#1778 := (~ #1777 #1777)
-#1779 := [refl]: #1778
-#1783 := [nnf-neg #1779]: #1782
-#1775 := (~ #1774 #1774)
-#1776 := [refl]: #1775
-#1786 := [nnf-neg #1776 #1783]: #1785
-#1772 := (~ #1081 #1771)
-#1773 := [sk]: #1772
-#1788 := [trans #1773 #1786]: #1787
-#1867 := [nnf-neg #1788 #1863]: #1866
-#1749 := (~ #1748 #1748)
-#1750 := [refl]: #1749
-#1746 := (~ #1745 #1745)
-#1747 := [refl]: #1746
-#1743 := (~ #1742 #1742)
-#1744 := [refl]: #1743
-#1740 := (~ #1739 #1739)
-#1741 := [refl]: #1740
-#1737 := (~ #1333 #1736)
-#1734 := (~ #1733 #1733)
-#1735 := [refl]: #1734
-#1738 := [nnf-neg #1735]: #1737
-#1871 := [nnf-neg #1738 #1741 #1744 #1747 #1750 #1867]: #1870
-#2128 := [nnf-neg #1871 #2124]: #2127
-#1730 := (not #1044)
-#1731 := (~ #1730 #1727)
-#1728 := (~ #1041 #1727)
-#1725 := (~ #1038 #1724)
-#1720 := (~ #1035 #1719)
-#1721 := [sk]: #1720
-#1705 := (~ #1011 #1011)
-#1706 := [refl]: #1705
-#1726 := [monotonicity #1706 #1721]: #1725
-#1729 := [nnf-pos #1726]: #1728
-#1732 := [nnf-neg #1729]: #1731
-#1702 := (not #1380)
-#1703 := (~ #1702 #1377)
-#1700 := (~ #1377 #1377)
-#1698 := (~ #1374 #1374)
-#1699 := [refl]: #1698
-#1701 := [nnf-pos #1699]: #1700
-#1704 := [nnf-neg #1701]: #1703
-#1695 := (not #1391)
-#1696 := (~ #1695 #1388)
-#1693 := (~ #1388 #1388)
-#1691 := (~ #1385 #1385)
-#1692 := [refl]: #1691
-#1694 := [nnf-pos #1692]: #1693
-#1697 := [nnf-neg #1694]: #1696
-#1688 := (not #1400)
-#1689 := (~ #1688 #1397)
-#1686 := (~ #1397 #1397)
-#1684 := (~ #1394 #1394)
-#1685 := [refl]: #1684
-#1687 := [nnf-pos #1685]: #1686
-#1690 := [nnf-neg #1687]: #1689
-#1682 := (~ #1681 #1681)
-#1683 := [refl]: #1682
-#1678 := (not #1403)
-#1679 := (~ #1678 #1675)
-#1676 := (~ #999 #1675)
-#1673 := (~ #996 #1672)
-#1668 := (~ #993 #1667)
-#1669 := [sk]: #1668
-#1652 := (~ #973 #973)
-#1653 := [refl]: #1652
-#1674 := [monotonicity #1653 #1669]: #1673
-#1677 := [nnf-pos #1674]: #1676
-#1680 := [nnf-neg #1677]: #1679
-#2132 := [nnf-neg #1680 #1683 #1690 #1697 #1704 #1732 #2128]: #2131
-#1650 := (~ #1403 #1647)
-#1632 := (exists (vars (?v1 S2)) #1631)
-#1633 := (or #1622 #1632)
-#1634 := (not #1633)
-#1648 := (~ #1634 #1647)
-#1644 := (not #1632)
-#1645 := (~ #1644 #1643)
-#1641 := (~ #1640 #1640)
-#1642 := [refl]: #1641
-#1646 := [nnf-neg #1642]: #1645
-#1638 := (~ #1637 #1637)
-#1639 := [refl]: #1638
-#1649 := [nnf-neg #1639 #1646]: #1648
-#1635 := (~ #1403 #1634)
-#1636 := [sk]: #1635
-#1651 := [trans #1636 #1649]: #1650
-#2136 := [nnf-neg #1651 #2132]: #2135
-#1610 := (not #961)
-#1611 := (~ #1610 #958)
-#1608 := (~ #958 #958)
-#1606 := (~ #955 #955)
-#1607 := [refl]: #1606
-#1609 := [nnf-pos #1607]: #1608
-#1612 := [nnf-neg #1609]: #1611
-#2140 := [nnf-neg #1612 #2136]: #2139
-#1602 := (~ #961 #1601)
-#1603 := [sk]: #1602
-#2144 := [nnf-neg #1603 #2140]: #2143
-#1578 := (not #935)
-#1579 := (~ #1578 #932)
-#1576 := (~ #932 #932)
-#1574 := (~ #929 #929)
-#1575 := [refl]: #1574
-#1577 := [nnf-pos #1575]: #1576
-#1580 := [nnf-neg #1577]: #1579
-#2148 := [nnf-neg #1580 #2144]: #2147
-#1570 := (~ #935 #1569)
-#1571 := [sk]: #1570
-#2152 := [nnf-neg #1571 #2148]: #2151
-#1551 := (not #920)
-#1552 := (~ #1551 #917)
-#1549 := (~ #917 #917)
-#1547 := (~ #916 #916)
-#1548 := [refl]: #1547
-#1550 := [nnf-pos #1548]: #1549
-#1553 := [nnf-neg #1550]: #1552
-#2156 := [nnf-neg #1553 #2152]: #2155
-#1543 := (~ #920 #1542)
-#1544 := [sk]: #1543
-#2160 := [nnf-neg #1544 #2156]: #2159
-#1505 := (~ #1504 #1504)
-#1538 := [refl]: #1505
-#2164 := [nnf-neg #1538 #2160]: #2163
-#1536 := (~ #868 #868)
-#1537 := [refl]: #1536
-#2167 := [nnf-neg #1537 #2164]: #2166
-#1480 := [not-or-elim #1475]: #1479
-#2168 := [mp~ #1480 #2167]: #2165
-#2169 := [mp #2168 #2483]: #2481
-#3122 := [mp #2169 #3121]: #3119
-#4037 := [mp #3122 #4036]: #4034
-#7144 := [unit-resolution #4037 #4122]: #4031
-#3361 := (or #4028 #4022)
-#3351 := [def-axiom]: #3361
-#7145 := [unit-resolution #3351 #7144]: #4022
-#3357 := (or #4025 #1542 #4019)
-#3359 := [def-axiom]: #3357
-#7146 := [unit-resolution #3359 #7145 #4053]: #4019
-#3355 := (or #4016 #4010)
-#3358 := [def-axiom]: #3355
-#7147 := [unit-resolution #3358 #7146]: #4010
-#4245 := [hypothesis]: #1560
-#3661 := (forall (vars (?v0 S2)) (:pat #3660) #78)
-#3664 := (iff #79 #3661)
-#3662 := (iff #78 #78)
-#3663 := [refl]: #3662
-#3665 := [quant-intro #3663]: #3664
-#1502 := (~ #79 #79)
-#1533 := (~ #78 #78)
-#1534 := [refl]: #1533
-#1503 := [nnf-pos #1534]: #1502
-#1478 := [not-or-elim #1475]: #79
-#1535 := [mp~ #1478 #1503]: #79
-#3666 := [mp #1535 #3665]: #3661
-#6940 := (not #3661)
-#4154 := (or #6940 #1884)
-#4155 := [quant-inst #1555]: #4154
-#4251 := [unit-resolution #4155 #3666 #4245]: false
-#4288 := [lemma #4251]: #1884
-#3186 := (or #1841 #1560)
-#3272 := [def-axiom]: #3186
-#7148 := [unit-resolution #3272 #4288]: #1841
-#3217 := (or #4013 #1946 #4007)
-#3375 := [def-axiom]: #3217
-#7149 := [unit-resolution #3375 #7148 #7147]: #4007
-#3397 := (or #4004 #3998)
-#3367 := [def-axiom]: #3397
-#7150 := [unit-resolution #3367 #7149]: #3998
-#6160 := [hypothesis]: #1584
-#6331 := (or #6940 #2503)
-#6332 := [quant-inst #1581]: #6331
-#6161 := [unit-resolution #6332 #3666 #6160]: false
-#6581 := [lemma #6161]: #2503
-#3277 := (or #2518 #1584)
-#3274 := [def-axiom]: #3277
-#7151 := [unit-resolution #3274 #6581]: #2518
-#3394 := (or #4001 #2523 #3995)
-#3395 := [def-axiom]: #3394
-#7152 := [unit-resolution #3395 #7151 #7150]: #3995
-#3378 := (or #3992 #3986)
-#3385 := [def-axiom]: #3378
-#7153 := [unit-resolution #3385 #7152]: #3986
-#3415 := (or #3989 #3705 #3983)
-#3400 := [def-axiom]: #3415
-#7154 := [unit-resolution #3400 #7153]: #3986
-#7155 := [unit-resolution #7154 #6633]: #3983
-#3407 := (or #3980 #3974)
-#3408 := [def-axiom]: #3407
-#7801 := [unit-resolution #3408 #7155]: #3974
-#6893 := [hypothesis]: #3817
-#3559 := (or #3814 #149)
-#3554 := [def-axiom]: #3559
-#6888 := [unit-resolution #3554 #6893]: #149
-#3555 := (or #3814 #3751)
-#3556 := [def-axiom]: #3555
-#6808 := [unit-resolution #3556 #6893]: #3751
-#3431 := (or #3980 #111)
-#3432 := [def-axiom]: #3431
-#6894 := [unit-resolution #3432 #7155]: #111
-#4278 := (or #503 #169 #804)
-#4273 := [hypothesis]: #111
-#4275 := (= #168 #110)
-#4274 := [hypothesis]: #149
-#4276 := [monotonicity #4274]: #4275
-#4271 := [trans #4276 #4273]: #169
-#4158 := [hypothesis]: #1849
-#4277 := [unit-resolution #4158 #4271]: false
-#4279 := [lemma #4277]: #4278
-#6895 := [unit-resolution #4279 #6888 #6894]: #169
-#3298 := (or #3790 #1849)
-#3299 := [def-axiom]: #3298
-#6896 := [unit-resolution #3299 #6895]: #3790
-#3402 := (or #3814 #3808)
-#3403 := [def-axiom]: #3402
-#6861 := [unit-resolution #3403 #6893]: #3808
-#7454 := (or #3768 #503)
-#6806 := (?v1!7 ?v0!8)
-#7010 := (f19 f25 #6806)
-#7056 := (* -1::Int #7010)
-#6807 := (f19 f20 #6806)
-#7278 := (+ #6807 #7056)
-#7328 := (>= #7278 0::Int)
-#7277 := (= #6807 #7010)
-#7409 := (= #7010 #6807)
-#7410 := [monotonicity #4274]: #7409
-#7411 := [symm #7410]: #7277
-#7412 := (not #7277)
-#7413 := (or #7412 #7328)
-#7414 := [th-lemma arith triangle-eq]: #7413
-#7415 := [unit-resolution #7414 #7411]: #7328
-#6897 := (* -1::Int #6807)
-#6741 := (f19 f20 ?v0!8)
-#6898 := (+ #6741 #6897)
-#6903 := (<= #6898 0::Int)
-#6821 := (not #6903)
-#6850 := (f6 f7 #6806)
-#6853 := (f5 #6850 ?v0!8)
-#6889 := (f4 #6853)
-#6890 := (* -1::Int #6889)
-#6908 := (+ #6897 #6890)
-#6925 := (+ #6741 #6908)
-#5298 := (= #6925 0::Int)
-#6077 := (not #5298)
-#6904 := (f11 f21 #6806)
-#6851 := (= #6904 f1)
-#6852 := (not #6851)
-#6078 := (or #6903 #6852 #6077)
-#6102 := (not #6078)
-#6742 := (* -1::Int #6741)
-#6772 := (+ f3 #6742)
-#6773 := (<= #6772 0::Int)
-#7378 := (not #6773)
-#7416 := [hypothesis]: #3771
-#3249 := (or #3768 #1758)
-#3591 := [def-axiom]: #3249
-#7417 := [unit-resolution #3591 #7416]: #1758
-#7026 := (+ #1754 #6742)
-#7012 := (>= #7026 0::Int)
-#7025 := (= #1754 #6741)
-#7418 := (= #6741 #1754)
-#6982 := (= f20 f25)
-#6983 := [symm #4274]: #6982
-#7419 := [monotonicity #6983]: #7418
-#7420 := [symm #7419]: #7025
-#7421 := (not #7025)
-#7422 := (or #7421 #7012)
-#7423 := [th-lemma arith triangle-eq]: #7422
-#7424 := [unit-resolution #7423 #7420]: #7012
-#7379 := (not #7012)
-#7380 := (or #7378 #7379 #1757)
-#7368 := [hypothesis]: #1758
-#7369 := [hypothesis]: #6773
-#7376 := [hypothesis]: #7012
-#7377 := [th-lemma arith farkas 1 -1 1 #7376 #7369 #7368]: false
-#7381 := [lemma #7377]: #7380
-#7425 := [unit-resolution #7381 #7424 #7417]: #7378
-#7428 := (or #6773 #6102)
-#3589 := (or #3768 #1753)
-#3254 := [def-axiom]: #3589
-#7426 := [unit-resolution #3254 #7416]: #1753
-#3405 := (or #3980 #3742)
-#3406 := [def-axiom]: #3405
-#7427 := [unit-resolution #3406 #7155]: #3742
-#6227 := (or #3747 #1752 #6773 #6102)
-#6103 := (or #1752 #6773 #6102)
-#6189 := (or #3747 #6103)
-#6704 := (iff #6189 #6227)
-#6805 := [rewrite]: #6704
-#6190 := [quant-inst #1751]: #6189
-#6797 := [mp #6190 #6805]: #6227
-#7429 := [unit-resolution #6797 #7427 #7426]: #7428
-#7430 := [unit-resolution #7429 #7425]: #6102
-#6854 := (or #6078 #6821)
-#6860 := [def-axiom]: #6854
-#7431 := [unit-resolution #6860 #7430]: #6821
-#7057 := (+ #1754 #7056)
-#7058 := (<= #7057 0::Int)
-#7101 := (+ #6890 #7056)
-#7102 := (+ #1754 #7101)
-#7105 := (= #7102 0::Int)
-#7195 := (<= #7102 0::Int)
-#7327 := (<= #7278 0::Int)
-#7432 := (or #7412 #7327)
-#7433 := [th-lemma arith triangle-eq]: #7432
-#7434 := [unit-resolution #7433 #7411]: #7327
-#6815 := (<= #6925 0::Int)
-#6862 := (or #6078 #5298)
-#6863 := [def-axiom]: #6862
-#7435 := [unit-resolution #6863 #7430]: #5298
-#7436 := (or #6077 #6815)
-#7437 := [th-lemma arith triangle-eq]: #7436
-#7438 := [unit-resolution #7437 #7435]: #6815
-#7011 := (<= #7026 0::Int)
-#7439 := (or #7421 #7011)
-#7440 := [th-lemma arith triangle-eq]: #7439
-#7441 := [unit-resolution #7440 #7420]: #7011
-#7390 := (not #7327)
-#7389 := (not #6815)
-#7388 := (not #7011)
-#7391 := (or #7195 #7388 #7389 #7390)
-#7375 := [hypothesis]: #7327
-#7128 := [hypothesis]: #6815
-#7384 := [hypothesis]: #7011
-#7385 := (not #7195)
-#7386 := [hypothesis]: #7385
-#7387 := [th-lemma arith farkas -1 1 1 1 #7386 #7384 #7128 #7375]: false
-#7392 := [lemma #7387]: #7391
-#7442 := [unit-resolution #7392 #7441 #7438 #7434]: #7195
-#7196 := (>= #7102 0::Int)
-#6820 := (>= #6925 0::Int)
-#7443 := (or #6077 #6820)
-#7444 := [th-lemma arith triangle-eq]: #7443
-#7445 := [unit-resolution #7444 #7435]: #6820
-#7406 := (not #7328)
-#7405 := (not #6820)
-#7407 := (or #7196 #7379 #7405 #7406)
-#7400 := [hypothesis]: #7328
-#7401 := [hypothesis]: #6820
-#7402 := (not #7196)
-#7403 := [hypothesis]: #7402
-#7404 := [th-lemma arith farkas -1 1 1 1 #7403 #7376 #7401 #7400]: false
-#7408 := [lemma #7404]: #7407
-#7446 := [unit-resolution #7408 #7424 #7445 #7415]: #7196
-#7447 := (or #7105 #7385 #7402)
-#7448 := [th-lemma arith triangle-eq]: #7447
-#7449 := [unit-resolution #7448 #7446 #7442]: #7105
-#7114 := (not #7105)
-#7122 := (or #7058 #7114)
-#3234 := (or #3768 #3760)
-#3575 := [def-axiom]: #3234
-#7450 := [unit-resolution #3575 #7416]: #3760
-#7125 := (or #3765 #7058 #7114)
-#7015 := (+ #1755 #6889)
-#7028 := (+ #7010 #7015)
-#7029 := (= #7028 0::Int)
-#7049 := (not #7029)
-#7013 := (+ #7010 #1755)
-#7014 := (>= #7013 0::Int)
-#7050 := (or #7014 #7049)
-#7126 := (or #3765 #7050)
-#7119 := (iff #7126 #7125)
-#6981 := (or #3765 #7122)
-#7017 := (iff #6981 #7125)
-#7118 := [rewrite]: #7017
-#7016 := (iff #7126 #6981)
-#7123 := (iff #7050 #7122)
-#7115 := (iff #7049 #7114)
-#7113 := (iff #7029 #7105)
-#7091 := (+ #6889 #7010)
-#7086 := (+ #1755 #7091)
-#7094 := (= #7086 0::Int)
-#7106 := (iff #7094 #7105)
-#7112 := [rewrite]: #7106
-#7095 := (iff #7029 #7094)
-#7092 := (= #7028 #7086)
-#7093 := [rewrite]: #7092
-#7096 := [monotonicity #7093]: #7095
-#7111 := [trans #7096 #7112]: #7113
-#7116 := [monotonicity #7111]: #7115
-#7089 := (iff #7014 #7058)
-#7051 := (+ #1755 #7010)
-#7048 := (>= #7051 0::Int)
-#7087 := (iff #7048 #7058)
-#7088 := [rewrite]: #7087
-#7054 := (iff #7014 #7048)
-#7052 := (= #7013 #7051)
-#7053 := [rewrite]: #7052
-#7055 := [monotonicity #7053]: #7054
-#7090 := [trans #7055 #7088]: #7089
-#7121 := [monotonicity #7090 #7116]: #7123
-#7124 := [monotonicity #7121]: #7016
-#7120 := [trans #7124 #7118]: #7119
-#6980 := [quant-inst #6806]: #7126
-#7127 := [mp #6980 #7120]: #7125
-#7451 := [unit-resolution #7127 #7450]: #7122
-#7452 := [unit-resolution #7451 #7449]: #7058
-#7453 := [th-lemma arith farkas 1 -1 1 1 #7424 #7452 #7431 #7415]: false
-#7455 := [lemma #7453]: #7454
-#6859 := [unit-resolution #7455 #6888]: #3768
-#3562 := (or #3811 #3771 #3805)
-#3566 := [def-axiom]: #3562
-#6864 := [unit-resolution #3566 #6859 #6861]: #3805
-#3283 := (or #3802 #3796)
-#3284 := [def-axiom]: #3283
-#6869 := [unit-resolution #3284 #6864]: #3796
-#3571 := (or #3799 #2759 #3793)
-#3568 := [def-axiom]: #3571
-#6935 := [unit-resolution #3568 #6869 #6896]: #2759
-#3225 := (or #2754 #1828)
-#3226 := [def-axiom]: #3225
-#6870 := [unit-resolution #3226 #6935]: #1828
-#6589 := (f19 f20 ?v1!10)
-#6584 := (* -1::Int #6589)
-#6868 := (+ #1817 #6584)
-#6946 := (>= #6868 0::Int)
-#4646 := (or #6946 #503)
-#6329 := (= #1817 #6589)
-#6605 := (= #6589 #1817)
-#6606 := [monotonicity #6983]: #6605
-#6585 := [symm #6606]: #6329
-#7134 := (not #6946)
-#6586 := [hypothesis]: #7134
-#6330 := (not #6329)
-#6322 := (or #6330 #6946)
-#6328 := [th-lemma arith triangle-eq]: #6322
-#6580 := [unit-resolution #6328 #6586 #6585]: false
-#4567 := [lemma #6580]: #4646
-#6867 := [unit-resolution #4567 #6888]: #6946
-#3583 := (or #2754 #1821)
-#3585 := [def-axiom]: #3583
-#6945 := [unit-resolution #3585 #6935]: #1821
-#3586 := (not #2356)
-#3584 := (or #2754 #3586)
-#3587 := [def-axiom]: #3584
-#6866 := [unit-resolution #3587 #6935]: #3586
-#7019 := (or #7134 #3756 #1827 #2356 #1820 #503)
-#6765 := (f19 f20 ?v0!11)
-#6766 := (* -1::Int #6765)
-#6948 := (+ #1831 #6766)
-#6949 := (<= #6948 0::Int)
-#6947 := (= #1831 #6765)
-#6984 := (= #6765 #1831)
-#6985 := [monotonicity #6983]: #6984
-#6986 := [symm #6985]: #6947
-#6987 := (not #6947)
-#6988 := (or #6987 #6949)
-#6975 := [th-lemma arith triangle-eq]: #6988
-#6976 := [unit-resolution #6975 #6986]: #6949
-#7130 := [hypothesis]: #3586
-#7143 := [hypothesis]: #1828
-#7140 := [hypothesis]: #3751
-#7131 := [hypothesis]: #6946
-#6572 := (+ f3 #6584)
-#6576 := (<= #6572 0::Int)
-#7138 := (not #6576)
-#6974 := [hypothesis]: #1821
-#6977 := (or #7138 #1820 #7134)
-#6978 := [th-lemma arith assign-bounds -1 -1]: #6977
-#6979 := [unit-resolution #6978 #7131 #6974]: #7138
-#7133 := (not #6949)
-#7160 := (or #6576 #1827 #3756 #7134 #2356 #7133)
-#6907 := (+ #6589 #6766)
-#6926 := (+ #1824 #6907)
-#6924 := (>= #6926 0::Int)
-#7132 := (not #6924)
-#7129 := [hypothesis]: #6949
-#7135 := (or #7132 #7133 #2356 #7134)
-#7136 := [th-lemma arith assign-bounds -1 -1 1]: #7135
-#7137 := [unit-resolution #7136 #7131 #7130 #7129]: #7132
-#6587 := (f11 f21 ?v1!10)
-#6588 := (= #6587 f1)
-#7139 := [hypothesis]: #7138
-#5703 := (or #6588 #6576)
-#6635 := (or #3756 #6588 #6576)
-#6636 := (or #3756 #5703)
-#6638 := (iff #6636 #6635)
-#6211 := [rewrite]: #6638
-#6637 := [quant-inst #1815]: #6636
-#6252 := [mp #6637 #6211]: #6635
-#7141 := [unit-resolution #6252 #7140]: #5703
-#7142 := [unit-resolution #7141 #7139]: #6588
-#6849 := (not #6588)
-#7157 := (or #6849 #6924)
-#3399 := (or #3980 #3734)
-#3404 := [def-axiom]: #3399
-#7156 := [unit-resolution #3404 #7155]: #3734
-#6930 := (or #3739 #6849 #1827 #6924)
-#6927 := (or #6849 #1827 #6924)
-#6931 := (or #3739 #6927)
-#3348 := (iff #6931 #6930)
-#3221 := [rewrite]: #3348
-#6932 := [quant-inst #1816 #1815]: #6931
-#4127 := [mp #6932 #3221]: #6930
-#7158 := [unit-resolution #4127 #7156 #7143]: #7157
-#7159 := [unit-resolution #7158 #7142 #7137]: false
-#7161 := [lemma #7159]: #7160
-#7018 := [unit-resolution #7161 #6979 #7131 #7140 #7143 #7130 #6976]: false
-#7020 := [lemma #7018]: #7019
-#6950 := [unit-resolution #7020 #6866 #6945 #6867 #6870 #6808 #6888]: false
-#7021 := [lemma #6950]: #3814
-#3419 := (or #3977 #3817 #3971)
-#3421 := [def-axiom]: #3419
-#7802 := [unit-resolution #3421 #7021 #7801]: #3971
-#3459 := (or #3968 #194)
-#3464 := [def-axiom]: #3459
-#8144 := [unit-resolution #3464 #7802]: #194
-#8146 := [symm #8144]: #8145
-#16380 := [monotonicity #8146]: #16289
-#16388 := [monotonicity #16380]: #16359
-#16389 := [symm #16388]: #16382
-#16391 := [monotonicity #16389]: #16390
-#19086 := [hypothesis]: #4534
-#5090 := (or #4541 #5087)
-#8395 := [hypothesis]: #1943
-#3547 := (or #1942 #1937)
-#3543 := [def-axiom]: #3547
-#8389 := [unit-resolution #3543 #8395]: #1937
-#3548 := (not #1941)
-#3542 := (or #1942 #3548)
-#3549 := [def-axiom]: #3542
-#8396 := [unit-resolution #3549 #8395]: #3548
-#5879 := (* -1::Int #1940)
-#5980 := (+ #185 #5879)
-#7760 := (>= #5980 0::Int)
-#4329 := (f11 f21 ?v0!14)
-#4316 := (= #4329 f1)
-#4315 := (= ?v0!14 f28)
-#4345 := (or #4315 #4316)
-#4328 := (f11 #193 ?v0!14)
-#4330 := (= #4328 f1)
-#4348 := (iff #4330 #4345)
-#8073 := (or #7518 #4348)
-#4314 := (if #4315 #4057 #4316)
-#4317 := (iff #4330 #4314)
-#8074 := (or #7518 #4317)
-#8078 := (iff #8074 #8073)
-#8080 := (iff #8073 #8073)
-#8081 := [rewrite]: #8080
-#4337 := (iff #4317 #4348)
-#4344 := (iff #4314 #4345)
-#4318 := (if #4315 true #4316)
-#4346 := (iff #4318 #4345)
-#4338 := [rewrite]: #4346
-#4319 := (iff #4314 #4318)
-#4332 := [monotonicity #4060]: #4319
-#4347 := [trans #4332 #4338]: #4344
-#4349 := [monotonicity #4347]: #4337
-#8079 := [monotonicity #4349]: #8078
-#8082 := [trans #8079 #8081]: #8078
-#8077 := [quant-inst #115 #181 #3 #1935]: #8074
-#8083 := [mp #8077 #8082]: #8073
-#8113 := [unit-resolution #8083 #3646]: #4348
-#8114 := [hypothesis]: #1937
-#8147 := (= #4328 #1936)
-#8148 := [monotonicity #8146]: #8147
-#8149 := [trans #8148 #8114]: #4330
-#8094 := (not #4330)
-#8091 := (not #4348)
-#8095 := (or #8091 #8094 #4345)
-#8096 := [def-axiom]: #8095
-#8150 := [unit-resolution #8096 #8149 #8113]: #4345
-#8088 := (not #4345)
-#8152 := (or #8088 #4316)
-#7690 := (not #4315)
-#7795 := [hypothesis]: #3548
-#7815 := (or #7690 #1941)
-#7809 := (= #185 #1940)
-#7807 := (= #1940 #185)
-#7796 := [hypothesis]: #4315
-#7808 := [monotonicity #7796]: #7807
-#7810 := [symm #7808]: #7809
-#7811 := (= #1939 #185)
-#4131 := (= #4078 #185)
-#4082 := (f5 #195 f28)
-#4083 := (f4 #4082)
-#4101 := (>= #4083 0::Int)
-#4086 := (* -1::Int #4083)
-#4087 := (+ f3 #4086)
-#4088 := (<= #4087 0::Int)
-#4133 := (or #4088 #4101)
-#6365 := (= #4083 0::Int)
-#6474 := (not #6365)
-#6475 := [hypothesis]: #6474
-#14 := (f6 f7 #10)
-#15 := (f5 #14 #11)
-#3600 := (pattern #15)
-#16 := (f4 #15)
-#17 := (= #16 0::Int)
-#12 := (= #10 #11)
-#20 := (not #12)
-#306 := (or #20 #17)
-#3601 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3600) #306)
-#314 := (forall (vars (?v0 S2) (?v1 S2)) #306)
-#3604 := (iff #314 #3601)
-#3602 := (iff #306 #306)
-#3603 := [refl]: #3602
-#3605 := [quant-intro #3603]: #3604
-#1510 := (~ #314 #314)
-#1508 := (~ #306 #306)
-#1509 := [refl]: #1508
-#1511 := [nnf-pos #1509]: #1510
-#18 := (implies #12 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
-#315 := (iff #19 #314)
-#312 := (iff #18 #306)
-#313 := [rewrite]: #312
-#316 := [quant-intro #313]: #315
-#305 := [asserted]: #19
-#319 := [mp #305 #316]: #314
-#1484 := [mp~ #319 #1511]: #314
-#3606 := [mp #1484 #3605]: #3601
-#6226 := (not #3601)
-#6401 := (or #6226 #6365)
-#4403 := (= f28 f28)
-#6358 := (not #4403)
-#6369 := (or #6358 #6365)
-#6400 := (or #6226 #6369)
-#6403 := (iff #6400 #6401)
-#6471 := (iff #6401 #6401)
-#6466 := [rewrite]: #6471
-#6387 := (iff #6369 #6365)
-#6377 := (or false #6365)
-#6382 := (iff #6377 #6365)
-#6386 := [rewrite]: #6382
-#6383 := (iff #6369 #6377)
-#6378 := (iff #6358 false)
-#6370 := (iff #6358 #6910)
-#4406 := (iff #4403 true)
-#4407 := [rewrite]: #4406
-#6375 := [monotonicity #4407]: #6370
-#6379 := [trans #6375 #6914]: #6378
-#6384 := [monotonicity #6379]: #6383
-#6398 := [trans #6384 #6386]: #6387
-#6439 := [monotonicity #6398]: #6403
-#6470 := [trans #6439 #6466]: #6403
-#6402 := [quant-inst #181 #181]: #6400
-#6472 := [mp #6402 #6470]: #6401
-#6476 := [unit-resolution #6472 #3606 #6475]: false
-#6482 := [lemma #6476]: #6365
-#7797 := (or #6474 #4101)
-#7798 := [th-lemma arith triangle-eq]: #7797
-#7799 := [unit-resolution #7798 #6482]: #4101
-#7285 := (not #4101)
-#7283 := (or #4133 #7285)
-#7286 := [def-axiom]: #7283
-#7800 := [unit-resolution #7286 #7799]: #4133
-#3445 := (or #3968 #3838)
-#3426 := [def-axiom]: #3445
-#7803 := [unit-resolution #3426 #7802]: #3838
-#4136 := (not #4133)
-#7259 := (or #3843 #4136 #4131)
-#4089 := (+ #1146 #4086)
-#4090 := (+ #185 #4089)
-#4091 := (<= #4090 0::Int)
-#4129 := (or #4088 #4091)
-#4130 := (not #4129)
-#4132 := (or #4130 #4131)
-#7260 := (or #3843 #4132)
-#7266 := (iff #7260 #7259)
-#4139 := (or #4136 #4131)
-#7262 := (or #3843 #4139)
-#7265 := (iff #7262 #7259)
-#7261 := [rewrite]: #7265
-#7263 := (iff #7260 #7262)
-#4140 := (iff #4132 #4139)
-#4137 := (iff #4130 #4136)
-#4134 := (iff #4129 #4133)
-#4104 := (iff #4091 #4101)
-#4098 := (<= #4086 0::Int)
-#4102 := (iff #4098 #4101)
-#4103 := [rewrite]: #4102
-#4099 := (iff #4091 #4098)
-#4096 := (= #4090 #4086)
-#4097 := [rewrite]: #4096
-#4100 := [monotonicity #4097]: #4099
-#4105 := [trans #4100 #4103]: #4104
-#4135 := [monotonicity #4105]: #4134
-#4138 := [monotonicity #4135]: #4137
-#4141 := [monotonicity #4138]: #4140
-#7264 := [monotonicity #4141]: #7263
-#7271 := [trans #7264 #7261]: #7266
-#7256 := [quant-inst #181]: #7260
-#7272 := [mp #7256 #7271]: #7259
-#7804 := [unit-resolution #7272 #7803 #7800]: #4131
-#7805 := (= #1939 #4078)
-#7806 := [monotonicity #7796]: #7805
-#7812 := [trans #7806 #7804]: #7811
-#7813 := [trans #7812 #7810]: #1941
-#7814 := [unit-resolution #7795 #7813]: false
-#7816 := [lemma #7814]: #7815
-#8151 := [unit-resolution #7816 #7795]: #7690
-#8089 := (or #8088 #4315 #4316)
-#8090 := [def-axiom]: #8089
-#8153 := [unit-resolution #8090 #8151]: #8152
-#8154 := [unit-resolution #8153 #8150]: #4316
-#3456 := (or #3968 #184)
-#3457 := [def-axiom]: #3456
-#8155 := [unit-resolution #3457 #7802]: #184
-#3443 := (or #3980 #3726)
-#3398 := [def-axiom]: #3443
-#8156 := [unit-resolution #3398 #7155]: #3726
-#7693 := (not #4316)
-#8138 := (or #3731 #183 #7693 #7760)
-#7761 := (or #183 #7693 #7760)
-#8139 := (or #3731 #7761)
-#8141 := (iff #8139 #8138)
-#8142 := [rewrite]: #8141
-#8140 := [quant-inst #1935 #181]: #8139
-#8143 := [mp #8140 #8142]: #8138
-#8157 := [unit-resolution #8143 #8156 #8155 #8154]: #7760
-#6005 := (f5 #195 ?v0!14)
-#6011 := (f4 #6005)
-#6036 := (+ #5879 #6011)
-#6037 := (+ #185 #6036)
-#6038 := (>= #6037 0::Int)
-#8046 := (not #6038)
-#6012 := (* -1::Int #6011)
-#6010 := (+ f3 #6012)
-#6014 := (<= #6010 0::Int)
-#6049 := (or #6014 #6038)
-#6056 := (not #6049)
-#8032 := (or #3843 #6056 #1941)
-#6015 := (+ #1146 #6012)
-#6013 := (+ #1940 #6015)
-#6017 := (<= #6013 0::Int)
-#6051 := (or #6014 #6017)
-#6052 := (not #6051)
-#6054 := (or #6052 #1941)
-#8033 := (or #3843 #6054)
-#8040 := (iff #8033 #8032)
-#6067 := (or #6056 #1941)
-#8035 := (or #3843 #6067)
-#8038 := (iff #8035 #8032)
-#8039 := [rewrite]: #8038
-#8036 := (iff #8033 #8035)
-#6068 := (iff #6054 #6067)
-#6057 := (iff #6052 #6056)
-#6055 := (iff #6051 #6049)
-#6043 := (iff #6017 #6038)
-#6027 := (+ #1940 #6012)
-#6030 := (+ #1146 #6027)
-#6034 := (<= #6030 0::Int)
-#6039 := (iff #6034 #6038)
-#6040 := [rewrite]: #6039
-#6035 := (iff #6017 #6034)
-#6031 := (= #6013 #6030)
-#6032 := [rewrite]: #6031
-#6033 := [monotonicity #6032]: #6035
-#6044 := [trans #6033 #6040]: #6043
-#6053 := [monotonicity #6044]: #6055
-#6058 := [monotonicity #6053]: #6057
-#6045 := [monotonicity #6058]: #6068
-#8037 := [monotonicity #6045]: #8036
-#8041 := [trans #8037 #8039]: #8040
-#8034 := [quant-inst #1935]: #8033
-#8042 := [mp #8034 #8041]: #8032
-#8158 := [unit-resolution #8042 #7803 #7795]: #6056
-#8047 := (or #6049 #8046)
-#8048 := [def-axiom]: #8047
-#8159 := [unit-resolution #8048 #8158]: #8046
-#8125 := (>= #6011 0::Int)
-#6251 := (<= #6011 0::Int)
-#6224 := (not #6251)
-#6208 := (= f28 ?v0!14)
-#6209 := (not #6208)
-#8164 := (iff #7690 #6209)
-#8162 := (iff #4315 #6208)
-#8160 := (iff #6208 #4315)
-#8161 := [commutativity]: #8160
-#8163 := [symm #8161]: #8162
-#8165 := [monotonicity #8163]: #8164
-#8166 := [mp #8151 #8165]: #6209
-#6225 := (or #6208 #6224)
-#325 := (<= #16 0::Int)
-#326 := (not #325)
-#329 := (or #12 #326)
-#3607 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3600) #329)
-#332 := (forall (vars (?v0 S2) (?v1 S2)) #329)
-#3610 := (iff #332 #3607)
-#3608 := (iff #329 #329)
-#3609 := [refl]: #3608
-#3611 := [quant-intro #3609]: #3610
-#1486 := (~ #332 #332)
-#1485 := (~ #329 #329)
-#1482 := [refl]: #1485
-#1487 := [nnf-pos #1482]: #1486
-#21 := (< 0::Int #16)
-#22 := (implies #20 #21)
-#23 := (forall (vars (?v0 S2) (?v1 S2)) #22)
-#335 := (iff #23 #332)
-#318 := (or #12 #21)
-#322 := (forall (vars (?v0 S2) (?v1 S2)) #318)
-#333 := (iff #322 #332)
-#330 := (iff #318 #329)
-#327 := (iff #21 #326)
-#328 := [rewrite]: #327
-#331 := [monotonicity #328]: #330
-#334 := [quant-intro #331]: #333
-#323 := (iff #23 #322)
-#320 := (iff #22 #318)
-#321 := [rewrite]: #320
-#324 := [quant-intro #321]: #323
-#336 := [trans #324 #334]: #335
-#317 := [asserted]: #23
-#337 := [mp #317 #336]: #332
-#1483 := [mp~ #337 #1487]: #332
-#3612 := [mp #1483 #3611]: #3607
-#7600 := (not #3607)
-#8126 := (or #7600 #6208 #6224)
-#8127 := (or #7600 #6225)
-#8129 := (iff #8127 #8126)
-#8130 := [rewrite]: #8129
-#8128 := [quant-inst #181 #1935]: #8127
-#8131 := [mp #8128 #8130]: #8126
-#8167 := [unit-resolution #8131 #3612]: #6225
-#8168 := [unit-resolution #8167 #8166]: #6224
-#8169 := (or #8125 #6251)
-#8170 := [th-lemma arith farkas 1 1]: #8169
-#8171 := [unit-resolution #8170 #8168]: #8125
-#8172 := [th-lemma arith farkas 1 -1 1 #8171 #8159 #8157]: false
-#8173 := [lemma #8172]: #1942
-#8376 := [unit-resolution #8173 #8396 #8389]: false
-#8397 := [lemma #8376]: #1942
-#3450 := (or #3968 #3962)
-#3451 := [def-axiom]: #3450
-#7966 := [unit-resolution #3451 #7802]: #3962
-#3444 := (or #3968 #3830)
-#3390 := [def-axiom]: #3444
-#7967 := [unit-resolution #3390 #7802]: #3830
-#5748 := (or #1922 #3835 #3843)
-#4760 := (f5 #195 ?v0!13)
-#4761 := (f4 #4760)
-#4791 := (+ #1920 #4761)
-#4792 := (+ #185 #4791)
-#4951 := (>= #4792 0::Int)
-#4794 := (= #4792 0::Int)
-#4766 := (* -1::Int #4761)
-#4767 := (+ f3 #4766)
-#4768 := (<= #4767 0::Int)
-#5036 := (not #4768)
-#4703 := (* -1::Int #1918)
-#4881 := (+ #4703 #4761)
-#4879 := (+ #185 #4881)
-#4882 := (>= #4879 0::Int)
-#4975 := (or #4768 #4882)
-#4979 := (not #4975)
-#4945 := (= #1919 #1918)
-#5470 := (not #4945)
-#5031 := (= #1918 #1919)
-#5429 := (not #5031)
-#5471 := (iff #5429 #5470)
-#5469 := (iff #5031 #4945)
-#5468 := [commutativity]: #5469
-#5472 := [monotonicity #5468]: #5471
-#5428 := [hypothesis]: #1923
-#5431 := (or #5429 #1922)
-#5467 := [th-lemma arith triangle-eq]: #5431
-#5466 := [unit-resolution #5467 #5428]: #5429
-#5474 := [mp #5466 #5472]: #5470
-#4981 := (or #4979 #4945)
-#5494 := [hypothesis]: #3838
-#4983 := (or #3843 #4979 #4945)
-#4769 := (+ #1146 #4766)
-#4770 := (+ #1918 #4769)
-#4798 := (<= #4770 0::Int)
-#4954 := (or #4768 #4798)
-#4955 := (not #4954)
-#4974 := (or #4955 #4945)
-#5002 := (or #3843 #4974)
-#5074 := (iff #5002 #4983)
-#5004 := (or #3843 #4981)
-#5066 := (iff #5004 #4983)
-#5067 := [rewrite]: #5066
-#5064 := (iff #5002 #5004)
-#4977 := (iff #4974 #4981)
-#4980 := (iff #4955 #4979)
-#4976 := (iff #4954 #4975)
-#4889 := (iff #4798 #4882)
-#4871 := (+ #1918 #4766)
-#4872 := (+ #1146 #4871)
-#4874 := (<= #4872 0::Int)
-#4883 := (iff #4874 #4882)
-#4884 := [rewrite]: #4883
-#4875 := (iff #4798 #4874)
-#4870 := (= #4770 #4872)
-#4873 := [rewrite]: #4870
-#4880 := [monotonicity #4873]: #4875
-#4890 := [trans #4880 #4884]: #4889
-#4978 := [monotonicity #4890]: #4976
-#4973 := [monotonicity #4978]: #4980
-#4982 := [monotonicity #4973]: #4977
-#5065 := [monotonicity #4982]: #5064
-#5075 := [trans #5065 #5067]: #5074
-#5003 := [quant-inst #1917]: #5002
-#5035 := [mp #5003 #5075]: #4983
-#5473 := [unit-resolution #5035 #5494]: #4981
-#5495 := [unit-resolution #5473 #5474]: #4979
-#5008 := (or #4975 #5036)
-#5009 := [def-axiom]: #5008
-#5496 := [unit-resolution #5009 #5495]: #5036
-#5005 := (not #4882)
-#5010 := (or #4975 #5005)
-#5011 := [def-axiom]: #5010
-#5497 := [unit-resolution #5011 #5495]: #5005
-#4796 := (or #4768 #4882 #4794)
-#5498 := [hypothesis]: #3830
-#4854 := (or #3835 #4768 #4882 #4794)
-#4799 := (+ #4761 #1920)
-#4864 := (+ #185 #4799)
-#4865 := (= #4864 0::Int)
-#4866 := (or #4768 #4798 #4865)
-#4852 := (or #3835 #4866)
-#4863 := (iff #4852 #4854)
-#4855 := (or #3835 #4796)
-#4857 := (iff #4855 #4854)
-#4862 := [rewrite]: #4857
-#4888 := (iff #4852 #4855)
-#4797 := (iff #4866 #4796)
-#4789 := (iff #4865 #4794)
-#4790 := (= #4864 #4792)
-#4793 := [rewrite]: #4790
-#4795 := [monotonicity #4793]: #4789
-#4891 := [monotonicity #4890 #4795]: #4797
-#4856 := [monotonicity #4891]: #4888
-#4861 := [trans #4856 #4862]: #4863
-#4853 := [quant-inst #1917]: #4852
-#4952 := [mp #4853 #4861]: #4854
-#5493 := [unit-resolution #4952 #5498]: #4796
-#5450 := [unit-resolution #5493 #5497 #5496]: #4794
-#5424 := (not #4794)
-#5366 := (or #5424 #4951)
-#5425 := [th-lemma arith triangle-eq]: #5366
-#5423 := [unit-resolution #5425 #5450]: #4951
-#5032 := (<= #1921 0::Int)
-#5426 := (or #5032 #1922)
-#5743 := [th-lemma arith farkas 1 1]: #5426
-#5746 := [unit-resolution #5743 #5428]: #5032
-#5747 := [th-lemma arith farkas 1 -1 1 #5746 #5497 #5423]: false
-#5749 := [lemma #5747]: #5748
-#7968 := [unit-resolution #5749 #7803 #7967]: #1922
-#3449 := (or #3965 #1923 #3959)
-#3342 := [def-axiom]: #3449
-#7969 := [unit-resolution #3342 #7968 #7966]: #3959
-#3470 := (or #3956 #3950)
-#3471 := [def-axiom]: #3470
-#10050 := [unit-resolution #3471 #7969]: #3950
-#3469 := (or #3953 #1943 #3947)
-#3465 := [def-axiom]: #3469
-#10051 := [unit-resolution #3465 #10050]: #3950
-#10052 := [unit-resolution #10051 #8397]: #3947
-#3497 := (or #3944 #3855)
-#3475 := [def-axiom]: #3497
-#10053 := [unit-resolution #3475 #10052]: #3855
-#10974 := (or #3860 #4541 #5087)
-#11004 := (or #3860 #5090)
-#10996 := (iff #11004 #10974)
-#11018 := [rewrite]: #10996
-#10999 := [quant-inst #2034]: #11004
-#11019 := [mp #10999 #11018]: #10974
-#19095 := [unit-resolution #11019 #10053]: #5090
-#19096 := [unit-resolution #19095 #19086]: #5087
-#11867 := (not #5087)
-#11974 := (or #11867 #12022)
-#12636 := [th-lemma arith triangle-eq]: #11974
-#19097 := [unit-resolution #12636 #19096]: #12022
-#13344 := (+ #5343 #13327)
-#13366 := (>= #13344 0::Int)
-#3466 := (or #3956 #3846)
-#3467 := [def-axiom]: #3466
-#7970 := [unit-resolution #3467 #7969]: #3846
-#18080 := (or #3851 #13366)
-#18086 := [quant-inst #5342]: #18080
-#19087 := [unit-resolution #18086 #7970]: #13366
-#15969 := (not #12022)
-#19098 := (or #15968 #15969)
-#3538 := (not #1988)
-#5971 := [hypothesis]: #2870
-#3541 := (or #2865 #3538)
-#3425 := [def-axiom]: #3541
-#5972 := [unit-resolution #3425 #5971]: #3538
-#3536 := (or #2865 #1979)
-#3539 := [def-axiom]: #3536
-#5974 := [unit-resolution #3539 #5971]: #1979
-#3537 := (or #2865 #1981)
-#3540 := [def-axiom]: #3537
-#5973 := [unit-resolution #3540 #5971]: #1981
-#10629 := (or #2850 #1988 #1978)
-#5727 := (= ?v1!16 f28)
-#9301 := (= f28 ?v1!16)
-#5888 := (f5 #195 ?v1!16)
-#5889 := (f4 #5888)
-#9302 := (<= #5889 0::Int)
-#9711 := [hypothesis]: #3538
-#5985 := (+ #1985 #4079)
-#9236 := (<= #5985 0::Int)
-#5682 := (f11 f21 ?v0!17)
-#5683 := (= #5682 f1)
-#5681 := (= ?v0!17 f28)
-#5689 := (or #5681 #5683)
-#5671 := (f11 #193 ?v0!17)
-#5672 := (= #5671 f1)
-#5694 := (iff #5672 #5689)
-#9981 := (or #7518 #5694)
-#5684 := (if #5681 #4057 #5683)
-#5685 := (iff #5672 #5684)
-#9982 := (or #7518 #5685)
-#9550 := (iff #9982 #9981)
-#9683 := (iff #9981 #9981)
-#9737 := [rewrite]: #9683
-#5695 := (iff #5685 #5694)
-#5692 := (iff #5684 #5689)
-#5686 := (if #5681 true #5683)
-#5690 := (iff #5686 #5689)
-#5691 := [rewrite]: #5690
-#5687 := (iff #5684 #5686)
-#5688 := [monotonicity #4060]: #5687
-#5693 := [trans #5688 #5691]: #5692
-#5696 := [monotonicity #5693]: #5695
-#9267 := [monotonicity #5696]: #9550
-#9960 := [trans #9267 #9737]: #9550
-#9682 := [quant-inst #115 #181 #3 #1976]: #9982
-#9972 := [mp #9682 #9960]: #9981
-#10602 := [unit-resolution #9972 #3646]: #5694
-#10603 := [hypothesis]: #1981
-#10604 := (= #5671 #1980)
-#10599 := [monotonicity #8146]: #10604
-#10571 := [trans #10599 #10603]: #5672
-#9787 := (not #5672)
-#9971 := (not #5694)
-#9963 := (or #9971 #9787 #5689)
-#9964 := [def-axiom]: #9963
-#10605 := [unit-resolution #9964 #10571 #10602]: #5689
-#8065 := (not #5689)
-#10754 := (or #9236 #8065)
-#9774 := (not #9236)
-#10735 := [hypothesis]: #9774
-#5652 := (f19 f20 ?v0!17)
-#5545 := (* -1::Int #5652)
-#5605 := (+ #1985 #5545)
-#5610 := (<= #5605 0::Int)
-#8385 := (or #3851 #5610)
-#5582 := (+ #5652 #1986)
-#5595 := (>= #5582 0::Int)
-#8384 := (or #3851 #5595)
-#7710 := (iff #8384 #8385)
-#7667 := (iff #8385 #8385)
-#8392 := [rewrite]: #7667
-#5612 := (iff #5595 #5610)
-#5596 := (+ #1986 #5652)
-#5600 := (>= #5596 0::Int)
-#5611 := (iff #5600 #5610)
-#5609 := [rewrite]: #5611
-#5603 := (iff #5595 #5600)
-#5601 := (= #5582 #5596)
-#5602 := [rewrite]: #5601
-#5604 := [monotonicity #5602]: #5603
-#5613 := [trans #5604 #5609]: #5612
-#7791 := [monotonicity #5613]: #7710
-#7912 := [trans #7791 #8392]: #7710
-#8393 := [quant-inst #1976]: #8384
-#8060 := [mp #8393 #7912]: #8385
-#9712 := [unit-resolution #8060 #7970]: #5610
-#5540 := (+ #185 #5545)
-#9420 := (>= #5540 0::Int)
-#9400 := [hypothesis]: #5689
-#8193 := (not #5681)
-#9234 := (= #1985 #4078)
-#9689 := (not #9234)
-#9518 := (or #9689 #9236)
-#9690 := [th-lemma arith triangle-eq]: #9518
-#10715 := [unit-resolution #9690 #10735]: #9689
-#10725 := (or #8193 #9234)
-#9309 := [hypothesis]: #5681
-#10737 := [monotonicity #9309]: #9234
-#10736 := [hypothesis]: #9689
-#10724 := [unit-resolution #10736 #10737]: false
-#10726 := [lemma #10724]: #10725
-#10727 := [unit-resolution #10726 #10715]: #8193
-#8066 := (or #8065 #5681 #5683)
-#8067 := [def-axiom]: #8066
-#10723 := [unit-resolution #8067 #10727 #9400]: #5683
-#8196 := (not #5683)
-#9377 := (or #8196 #9420)
-#9723 := (not #9420)
-#9387 := [hypothesis]: #9723
-#9362 := [hypothesis]: #5683
-#9219 := (or #3731 #183 #8196 #9420)
-#9438 := (or #183 #8196 #9420)
-#9235 := (or #3731 #9438)
-#9246 := (iff #9235 #9219)
-#9220 := [rewrite]: #9246
-#9237 := [quant-inst #1976 #181]: #9235
-#8778 := [mp #9237 #9220]: #9219
-#9376 := [unit-resolution #8778 #8156 #8155 #9362 #9387]: false
-#9457 := [lemma #9376]: #9377
-#10721 := [unit-resolution #9457 #10723]: #9420
-#4080 := (+ #185 #4079)
-#4439 := (<= #4080 0::Int)
-#7295 := (= #185 #4078)
-#10741 := (iff #4131 #7295)
-#10728 := (iff #7295 #4131)
-#10729 := [commutativity]: #10728
-#10742 := [symm #10729]: #10741
-#10743 := [mp #7804 #10742]: #7295
-#10747 := (not #7295)
-#10748 := (or #10747 #4439)
-#10750 := [th-lemma arith triangle-eq]: #10748
-#10752 := [unit-resolution #10750 #10743]: #4439
-#10753 := [th-lemma arith farkas -1 1 -1 1 #10752 #10721 #9712 #10735]: false
-#10749 := [lemma #10753]: #10754
-#10606 := [unit-resolution #10749 #10605]: #9236
-#4081 := (>= #4080 0::Int)
-#7188 := (or #3851 #4081)
-#7230 := [quant-inst #181]: #7188
-#9459 := [unit-resolution #7230 #7970]: #4081
-#4492 := (* -1::Int #1984)
-#5947 := (+ #4492 #5889)
-#5948 := (+ #185 #5947)
-#7908 := (<= #5948 0::Int)
-#5951 := (= #5948 0::Int)
-#5855 := (f19 f20 ?v1!16)
-#5872 := (* -1::Int #5855)
-#5907 := (+ #5872 #5889)
-#5908 := (+ #185 #5907)
-#5909 := (>= #5908 0::Int)
-#5890 := (* -1::Int #5889)
-#5891 := (+ f3 #5890)
-#5892 := (<= #5891 0::Int)
-#5914 := (or #5892 #5909)
-#5917 := (not #5914)
-#5898 := (= #1984 #5855)
-#10613 := (not #5898)
-#5873 := (+ #1984 #5872)
-#8314 := (>= #5873 0::Int)
-#9718 := (not #8314)
-#4924 := (+ #185 #5872)
-#4925 := (<= #4924 0::Int)
-#5728 := (f11 f21 ?v1!16)
-#5729 := (= #5728 f1)
-#9937 := (not #5729)
-#5735 := (or #5727 #5729)
-#9563 := (not #5735)
-#5725 := (f11 #193 ?v1!16)
-#5726 := (= #5725 f1)
-#5740 := (iff #5726 #5735)
-#9884 := (or #7518 #5740)
-#5730 := (if #5727 #4057 #5729)
-#5731 := (iff #5726 #5730)
-#9851 := (or #7518 #5731)
-#9678 := (iff #9851 #9884)
-#9677 := (iff #9884 #9884)
-#9566 := [rewrite]: #9677
-#5741 := (iff #5731 #5740)
-#5738 := (iff #5730 #5735)
-#5732 := (if #5727 true #5729)
-#5736 := (iff #5732 #5735)
-#5737 := [rewrite]: #5736
-#5733 := (iff #5730 #5732)
-#5734 := [monotonicity #4060]: #5733
-#5739 := [trans #5734 #5737]: #5738
-#5742 := [monotonicity #5739]: #5741
-#9679 := [monotonicity #5742]: #9678
-#8478 := [trans #9679 #9566]: #9678
-#9932 := [quant-inst #115 #181 #3 #1975]: #9851
-#7394 := [mp #9932 #8478]: #9884
-#10476 := [unit-resolution #7394 #3646]: #5740
-#8333 := (not #5726)
-#10578 := (iff #1979 #8333)
-#10579 := (iff #1978 #5726)
-#10551 := (iff #5726 #1978)
-#10541 := (= #5725 #1977)
-#10544 := [monotonicity #8146]: #10541
-#10552 := [monotonicity #10544]: #10551
-#10580 := [symm #10552]: #10579
-#10581 := [monotonicity #10580]: #10578
-#10477 := [hypothesis]: #1979
-#10600 := [mp #10477 #10581]: #8333
-#8954 := (not #5740)
-#9175 := (or #8954 #5726 #9563)
-#7890 := [def-axiom]: #9175
-#10601 := [unit-resolution #7890 #10600 #10476]: #9563
-#8489 := (or #5735 #9937)
-#9914 := [def-axiom]: #8489
-#10607 := [unit-resolution #9914 #10601]: #9937
-#4948 := (or #5729 #4925)
-#3462 := (or #3968 #3820)
-#3463 := [def-axiom]: #3462
-#9789 := [unit-resolution #3463 #7802]: #3820
-#9716 := (or #3825 #5729 #4925)
-#4892 := (+ #5855 #1146)
-#4893 := (>= #4892 0::Int)
-#4918 := (or #5729 #4893)
-#9628 := (or #3825 #4918)
-#10139 := (iff #9628 #9716)
-#10115 := (or #3825 #4948)
-#10118 := (iff #10115 #9716)
-#10138 := [rewrite]: #10118
-#10117 := (iff #9628 #10115)
-#4949 := (iff #4918 #4948)
-#4946 := (iff #4893 #4925)
-#4919 := (+ #1146 #5855)
-#4922 := (>= #4919 0::Int)
-#4926 := (iff #4922 #4925)
-#4927 := [rewrite]: #4926
-#4917 := (iff #4893 #4922)
-#4920 := (= #4892 #4919)
-#4921 := [rewrite]: #4920
-#4923 := [monotonicity #4921]: #4917
-#4947 := [trans #4923 #4927]: #4946
-#4950 := [monotonicity #4947]: #4949
-#10112 := [monotonicity #4950]: #10117
-#10140 := [trans #10112 #10138]: #10139
-#10116 := [quant-inst #1975]: #9628
-#10141 := [mp #10116 #10140]: #9716
-#10608 := [unit-resolution #10141 #9789]: #4948
-#10609 := [unit-resolution #10608 #10607]: #4925
-#11010 := (not #4925)
-#11011 := (or #9774 #9718 #1988 #11010)
-#11006 := [hypothesis]: #4925
-#9759 := [hypothesis]: #9236
-#9707 := [hypothesis]: #8314
-#11009 := [th-lemma arith farkas -1 1 1 -1 1 #9707 #9759 #9711 #9459 #11006]: false
-#11012 := [lemma #11009]: #11011
-#10612 := [unit-resolution #11012 #10606 #9711 #10609]: #9718
-#10614 := (or #10613 #8314)
-#10615 := [th-lemma arith triangle-eq]: #10614
-#10610 := [unit-resolution #10615 #10612]: #10613
-#5920 := (or #5917 #5898)
-#10033 := (or #3843 #5917 #5898)
-#5893 := (+ #1146 #5890)
-#5894 := (+ #5855 #5893)
-#5895 := (<= #5894 0::Int)
-#5896 := (or #5892 #5895)
-#5897 := (not #5896)
-#5899 := (or #5897 #5898)
-#10016 := (or #3843 #5899)
-#9991 := (iff #10016 #10033)
-#10017 := (or #3843 #5920)
-#10008 := (iff #10017 #10033)
-#10004 := [rewrite]: #10008
-#9989 := (iff #10016 #10017)
-#5921 := (iff #5899 #5920)
-#5918 := (iff #5897 #5917)
-#5915 := (iff #5896 #5914)
-#5912 := (iff #5895 #5909)
-#5900 := (+ #5855 #5890)
-#5901 := (+ #1146 #5900)
-#5904 := (<= #5901 0::Int)
-#5910 := (iff #5904 #5909)
-#5911 := [rewrite]: #5910
-#5905 := (iff #5895 #5904)
-#5902 := (= #5894 #5901)
-#5903 := [rewrite]: #5902
-#5906 := [monotonicity #5903]: #5905
-#5913 := [trans #5906 #5911]: #5912
-#5916 := [monotonicity #5913]: #5915
-#5919 := [monotonicity #5916]: #5918
-#5922 := [monotonicity #5919]: #5921
-#10005 := [monotonicity #5922]: #9989
-#10002 := [trans #10005 #10004]: #9991
-#9962 := [quant-inst #1975]: #10016
-#10010 := [mp #9962 #10002]: #10033
-#10611 := [unit-resolution #10010 #7803]: #5920
-#10616 := [unit-resolution #10611 #10610]: #5917
-#9749 := (or #5914 #5951)
-#9732 := (not #5951)
-#9742 := [hypothesis]: #9732
-#8264 := (not #5892)
-#9745 := [hypothesis]: #5917
-#8000 := (or #5914 #8264)
-#8092 := [def-axiom]: #8000
-#9727 := [unit-resolution #8092 #9745]: #8264
-#8284 := (not #5909)
-#8311 := (or #5914 #8284)
-#8280 := [def-axiom]: #8311
-#9746 := [unit-resolution #8280 #9745]: #8284
-#5954 := (or #5892 #5909 #5951)
-#8310 := (or #3835 #5892 #5909 #5951)
-#5943 := (+ #5889 #4492)
-#5944 := (+ #185 #5943)
-#5945 := (= #5944 0::Int)
-#5946 := (or #5892 #5895 #5945)
-#8334 := (or #3835 #5946)
-#8377 := (iff #8334 #8310)
-#8335 := (or #3835 #5954)
-#8378 := (iff #8335 #8310)
-#8379 := [rewrite]: #8378
-#8336 := (iff #8334 #8335)
-#5955 := (iff #5946 #5954)
-#5952 := (iff #5945 #5951)
-#5949 := (= #5944 #5948)
-#5950 := [rewrite]: #5949
-#5953 := [monotonicity #5950]: #5952
-#5956 := [monotonicity #5913 #5953]: #5955
-#8337 := [monotonicity #5956]: #8336
-#8371 := [trans #8337 #8379]: #8377
-#8279 := [quant-inst #1975]: #8334
-#8381 := [mp #8279 #8371]: #8310
-#9747 := [unit-resolution #8381 #7967]: #5954
-#9748 := [unit-resolution #9747 #9746 #9727 #9742]: false
-#9750 := [lemma #9748]: #9749
-#10617 := [unit-resolution #9750 #10616]: #5951
-#10618 := (or #9732 #7908)
-#10619 := [th-lemma arith triangle-eq]: #10618
-#10620 := [unit-resolution #10619 #10617]: #7908
-#10624 := (not #4081)
-#10623 := (not #7908)
-#10625 := (or #9302 #10623 #1988 #9774 #10624)
-#10626 := [th-lemma arith assign-bounds 1 1 1 1]: #10625
-#10621 := [unit-resolution #10626 #10620 #9459 #10606 #9711]: #9302
-#9349 := (not #9302)
-#10411 := (or #7600 #9301 #9349)
-#9385 := (or #9301 #9349)
-#10539 := (or #7600 #9385)
-#10540 := (iff #10539 #10411)
-#10542 := [rewrite]: #10540
-#10381 := [quant-inst #181 #1975]: #10539
-#10543 := [mp #10381 #10542]: #10411
-#10622 := [unit-resolution #10543 #3612 #10621]: #9301
-#10627 := [symm #10622]: #5727
-#7819 := (not #5727)
-#9916 := (or #5735 #7819)
-#9935 := [def-axiom]: #9916
-#10577 := [unit-resolution #9935 #10601]: #7819
-#10628 := [unit-resolution #10577 #10627]: false
-#10630 := [lemma #10628]: #10629
-#9889 := [unit-resolution #10630 #5973 #5974 #5972]: false
-#9891 := [lemma #9889]: #2865
-#8784 := (or #1962 #3860)
-#4183 := (>= #185 0::Int)
-#3442 := (or #3980 #3717)
-#3422 := [def-axiom]: #3442
-#7614 := [unit-resolution #3422 #7155]: #3717
-#7345 := (or #3722 #4183)
-#7351 := [quant-inst #181]: #7345
-#7620 := [unit-resolution #7351 #7614]: #4183
-#6537 := (f5 #195 ?v0!15)
-#6538 := (f4 #6537)
-#4488 := (* -1::Int #1961)
-#6594 := (+ #4488 #6538)
-#6595 := (+ #185 #6594)
-#8465 := (<= #6595 0::Int)
-#6598 := (= #6595 0::Int)
-#6496 := (f19 f20 ?v0!15)
-#6521 := (* -1::Int #6496)
-#6555 := (+ #6521 #6538)
-#6556 := (+ #185 #6555)
-#6557 := (>= #6556 0::Int)
-#6539 := (* -1::Int #6538)
-#6540 := (+ f3 #6539)
-#6541 := (<= #6540 0::Int)
-#6562 := (or #6541 #6557)
-#6565 := (not #6562)
-#6497 := (= #1961 #6496)
-#9674 := (not #6497)
-#6522 := (+ #1961 #6521)
-#9653 := (>= #6522 0::Int)
-#9661 := (not #9653)
-#6618 := [hypothesis]: #1963
-#9453 := (or #9661 #1962)
-#8190 := (>= #6496 0::Int)
-#8498 := (or #3722 #8190)
-#8474 := [quant-inst #1960]: #8498
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-#9654 := [hypothesis]: #9653
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-#9454 := [lemma #9452]: #9453
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-#9675 := (or #9674 #9653)
-#8499 := [hypothesis]: #9661
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-#8503 := [unit-resolution #9676 #8502 #8499]: false
-#8506 := [lemma #8503]: #9675
-#8735 := [unit-resolution #8506 #8733]: #9674
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-#6544 := (<= #6543 0::Int)
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-#6546 := (not #6545)
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-#8449 := (iff #8446 #8443)
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-#6552 := (<= #6549 0::Int)
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-#6559 := [rewrite]: #6558
-#6553 := (iff #6544 #6552)
-#6550 := (= #6543 #6549)
-#6551 := [rewrite]: #6550
-#6554 := [monotonicity #6551]: #6553
-#6561 := [trans #6554 #6559]: #6560
-#6564 := [monotonicity #6561]: #6563
-#6567 := [monotonicity #6564]: #6566
-#6570 := [monotonicity #6567]: #6569
-#8448 := [monotonicity #6570]: #8447
-#8434 := [trans #8448 #8432]: #8433
-#8445 := [quant-inst #1960]: #8444
-#8435 := [mp #8445 #8434]: #8443
-#9672 := [unit-resolution #8435 #7803]: #6568
-#8736 := [unit-resolution #9672 #8735]: #6565
-#9651 := (or #6562 #6598)
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-#8438 := (not #6557)
-#8439 := (or #6562 #8438)
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-#6590 := (+ #6538 #4488)
-#6591 := (+ #185 #6590)
-#6592 := (= #6591 0::Int)
-#6593 := (or #6541 #6544 #6592)
-#8453 := (or #3835 #6593)
-#8459 := (iff #8453 #8452)
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-#8457 := (iff #8455 #8452)
-#8458 := [rewrite]: #8457
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-#6596 := (= #6591 #6595)
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-#6600 := [monotonicity #6597]: #6599
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-#8460 := [trans #8456 #8458]: #8459
-#8454 := [quant-inst #1960]: #8453
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-#9564 := (= f28 ?v0!15)
-#9601 := (not #9564)
-#9422 := (= ?v0!15 f28)
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-#9602 := (iff #9445 #9601)
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-#9571 := (iff #9564 #9422)
-#9624 := [commutativity]: #9571
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-#9603 := [monotonicity #9626]: #9602
-#8093 := (f11 f21 ?v0!15)
-#8097 := (= #8093 f1)
-#9428 := (or #9422 #8097)
-#9451 := (not #9428)
-#9414 := (f11 #193 ?v0!15)
-#9415 := (= #9414 f1)
-#9433 := (iff #9415 #9428)
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-#9423 := (if #9422 #4057 #8097)
-#9424 := (iff #9415 #9423)
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-#8514 := [rewrite]: #8510
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-#9425 := (if #9422 true #8097)
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-#9430 := [rewrite]: #9429
-#9426 := (iff #9423 #9425)
-#9427 := [monotonicity #4060]: #9426
-#9432 := [trans #9427 #9430]: #9431
-#9435 := [monotonicity #9432]: #9434
-#8512 := [monotonicity #9435]: #8511
-#8515 := [trans #8512 #8514]: #8511
-#8507 := [quant-inst #115 #181 #3 #1960]: #8509
-#8513 := [mp #8507 #8515]: #8508
-#8738 := [unit-resolution #8513 #3646]: #9433
-#8520 := (not #9415)
-#4485 := (f11 f29 ?v0!15)
-#4486 := (= #4485 f1)
-#4487 := (not #4486)
-#8754 := (iff #4487 #8520)
-#8755 := (iff #4486 #9415)
-#8702 := (iff #9415 #4486)
-#8748 := (= #9414 #4485)
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-#8703 := [monotonicity #8749]: #8702
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-#8757 := [monotonicity #8756]: #8754
-#6506 := (or #4487 #6497)
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-#8421 := (or #3860 #4487 #6497)
-#8422 := (or #3860 #6506)
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-#8424 := [rewrite]: #8406
-#8423 := [quant-inst #1960]: #8422
-#8405 := [mp #8423 #8424]: #8421
-#8744 := [unit-resolution #8405 #8739]: #6506
-#8745 := [unit-resolution #8744 #8735]: #4487
-#8758 := [mp #8745 #8757]: #8520
-#8518 := (not #9433)
-#8519 := (or #8518 #9415 #9451)
-#8517 := [def-axiom]: #8519
-#8767 := [unit-resolution #8517 #8758 #8738]: #9451
-#9446 := (or #9428 #9445)
-#9447 := [def-axiom]: #9446
-#8768 := [unit-resolution #9447 #8767]: #9445
-#8774 := [mp #8768 #9603]: #9601
-#9572 := (or #9564 #9568)
-#9574 := (or #7600 #9564 #9568)
-#9575 := (or #7600 #9572)
-#9579 := (iff #9575 #9574)
-#9580 := [rewrite]: #9579
-#9576 := [quant-inst #181 #1960]: #9575
-#9578 := [mp #9576 #9580]: #9574
-#9605 := [unit-resolution #9578 #3612]: #9572
-#8775 := [unit-resolution #9605 #8774]: #9568
-#8773 := (or #8633 #9565)
-#8776 := [th-lemma arith farkas 1 1]: #8773
-#8769 := [unit-resolution #8776 #8775]: #8633
-#8777 := [th-lemma arith farkas 1 1 -1 1 #6618 #8769 #8737 #7620]: false
-#8782 := [lemma #8777]: #8784
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-#4342 := (f5 #195 f16)
-#4343 := (f4 #4342)
-#7596 := (<= #4343 0::Int)
-#7588 := (not #7596)
-#4163 := (= f28 f16)
-#7583 := (not #4163)
-#7834 := [hypothesis]: #661
-#7847 := (or #7583 #217)
-#4358 := (= #216 #110)
-#7840 := (= #185 #110)
-#7835 := [hypothesis]: #4163
-#7841 := [monotonicity #7835]: #7840
-#7842 := (= #216 #185)
-#7838 := (= #216 #4078)
-#7836 := (= f16 f28)
-#7837 := [symm #7835]: #7836
-#7839 := [monotonicity #7837]: #7838
-#7843 := [trans #7839 #7804]: #7842
-#7844 := [trans #7843 #7841]: #4358
-#7845 := [trans #7844 #6894]: #217
-#7846 := [unit-resolution #7834 #7845]: false
-#7848 := [lemma #7846]: #7847
-#7599 := [unit-resolution #7848 #7834]: #7583
-#7589 := (or #4163 #7588)
-#7601 := (or #7600 #4163 #7588)
-#7602 := (or #7600 #7589)
-#7604 := (iff #7602 #7601)
-#7605 := [rewrite]: #7604
-#7603 := [quant-inst #181 #65]: #7602
-#7606 := [mp #7603 #7605]: #7601
-#7607 := [unit-resolution #7606 #3612]: #7589
-#7598 := [unit-resolution #7607 #7599]: #7588
-#4350 := (* -1::Int #4343)
-#4353 := (+ #1146 #4350)
-#4354 := (+ #110 #4353)
-#4355 := (<= #4354 0::Int)
-#7500 := (not #4355)
-#4351 := (+ f3 #4350)
-#4352 := (<= #4351 0::Int)
-#4356 := (or #4352 #4355)
-#4357 := (not #4356)
-#7612 := (not #4358)
-#7613 := (iff #661 #7612)
-#7610 := (iff #217 #4358)
-#7608 := (iff #4358 #217)
-#7609 := [monotonicity #6894]: #7608
-#7611 := [symm #7609]: #7610
-#7615 := [monotonicity #7611]: #7613
-#7616 := [mp #7834 #7615]: #7612
-#4359 := (or #4357 #4358)
-#7491 := (or #3843 #4357 #4358)
-#7492 := (or #3843 #4359)
-#7494 := (iff #7492 #7491)
-#7495 := [rewrite]: #7494
-#7493 := [quant-inst #65]: #7492
-#7496 := [mp #7493 #7495]: #7491
-#7617 := [unit-resolution #7496 #7803]: #4359
-#7618 := [unit-resolution #7617 #7616]: #4357
-#7501 := (or #4356 #7500)
-#7502 := [def-axiom]: #7501
-#7619 := [unit-resolution #7502 #7618]: #7500
-#4504 := (<= #110 0::Int)
-#7621 := (or #804 #4504)
-#7622 := [th-lemma arith triangle-eq]: #7621
-#7623 := [unit-resolution #7622 #6894]: #4504
-#7624 := [th-lemma arith farkas 1 1 1 1 #7623 #7620 #7619 #7598]: false
-#7626 := [lemma #7624]: #217
-#3476 := (or #3944 #3938)
-#3478 := [def-axiom]: #3476
-#10055 := [unit-resolution #3478 #10052]: #3938
-#3496 := (or #3941 #661 #3935)
-#3486 := [def-axiom]: #3496
-#10056 := [unit-resolution #3486 #10055 #7626]: #3935
-#3488 := (or #3932 #3926)
-#3489 := [def-axiom]: #3488
-#10057 := [unit-resolution #3489 #10056]: #3926
-#3504 := (or #3929 #1963 #3923)
-#3484 := [def-axiom]: #3504
-#10058 := [unit-resolution #3484 #10057 #10054]: #3923
-#3507 := (or #3920 #3914)
-#3512 := [def-axiom]: #3507
-#18172 := [unit-resolution #3512 #10058]: #3914
-#3508 := (or #3917 #2870 #3911)
-#3509 := [def-axiom]: #3508
-#18183 := [unit-resolution #3509 #18172]: #3914
-#18184 := [unit-resolution #18183 #9891]: #3911
-#3517 := (or #3908 #3902)
-#3518 := [def-axiom]: #3517
-#18185 := [unit-resolution #3518 #18184]: #3902
-#18186 := (or #3905 #3899)
-#15845 := [hypothesis]: #2916
-#3530 := (or #2911 #2012)
-#3533 := [def-axiom]: #3530
-#15846 := [unit-resolution #3533 #15845]: #2012
-#6483 := (f5 #195 ?v0!19)
-#6481 := (f4 #6483)
-#6484 := (* -1::Int #6481)
-#15446 := (+ #2008 #6484)
-#15535 := (>= #15446 0::Int)
-#15445 := (= #2008 #6481)
-#15962 := (= #2007 #6483)
-#15956 := (= #2006 #195)
-#5407 := (= ?v1!18 f28)
-#5408 := (f11 f21 ?v1!18)
-#5409 := (= #5408 f1)
-#5415 := (or #5407 #5409)
-#5397 := (f11 #193 ?v1!18)
-#5398 := (= #5397 f1)
-#5420 := (iff #5398 #5415)
-#14616 := (or #7518 #5420)
-#5410 := (if #5407 #4057 #5409)
-#5411 := (iff #5398 #5410)
-#14606 := (or #7518 #5411)
-#14610 := (iff #14606 #14616)
-#14613 := (iff #14616 #14616)
-#14619 := [rewrite]: #14613
-#5421 := (iff #5411 #5420)
-#5418 := (iff #5410 #5415)
-#5412 := (if #5407 true #5409)
-#5416 := (iff #5412 #5415)
-#5417 := [rewrite]: #5416
-#5413 := (iff #5410 #5412)
-#5414 := [monotonicity #4060]: #5413
-#5419 := [trans #5414 #5417]: #5418
-#5422 := [monotonicity #5419]: #5421
-#14620 := [monotonicity #5422]: #14610
-#14630 := [trans #14620 #14619]: #14610
-#14618 := [quant-inst #115 #181 #3 #2002]: #14606
-#14662 := [mp #14618 #14630]: #14616
-#15893 := [unit-resolution #14662 #3646]: #5420
-#3434 := (or #2911 #2005)
-#3529 := [def-axiom]: #3434
-#15907 := [unit-resolution #3529 #15845]: #2005
-#15926 := (= #5397 #2004)
-#15928 := [monotonicity #8146]: #15926
-#15908 := [trans #15928 #15907]: #5398
-#11373 := (not #5398)
-#15102 := (not #5420)
-#15199 := (or #15102 #11373 #5415)
-#15197 := [def-axiom]: #15199
-#15929 := [unit-resolution #15197 #15908 #15893]: #5415
-#6623 := (not #5409)
-#6374 := (f19 f20 ?v0!19)
-#6445 := (* -1::Int #6374)
-#5362 := (f19 f20 ?v1!18)
-#6639 := (+ #5362 #6445)
-#6640 := (+ #2008 #6639)
-#6641 := (>= #6640 0::Int)
-#15933 := (not #6641)
-#3418 := (not #2020)
-#3433 := (or #2911 #3418)
-#3435 := [def-axiom]: #3433
-#15930 := [unit-resolution #3435 #15845]: #3418
-#6446 := (+ #2016 #6445)
-#6447 := (<= #6446 0::Int)
-#12992 := (not #6447)
-#12993 := [hypothesis]: #12992
-#12524 := (or #3851 #6447)
-#6389 := (+ #6374 #2017)
-#6399 := (>= #6389 0::Int)
-#12525 := (or #3851 #6399)
-#12527 := (iff #12525 #12524)
-#12530 := (iff #12524 #12524)
-#12531 := [rewrite]: #12530
-#6468 := (iff #6399 #6447)
-#6440 := (+ #2017 #6374)
-#6443 := (>= #6440 0::Int)
-#6448 := (iff #6443 #6447)
-#6467 := [rewrite]: #6448
-#6438 := (iff #6399 #6443)
-#6441 := (= #6389 #6440)
-#6442 := [rewrite]: #6441
-#6444 := [monotonicity #6442]: #6438
-#6469 := [trans #6444 #6467]: #6468
-#12529 := [monotonicity #6469]: #12527
-#12532 := [trans #12529 #12531]: #12527
-#12526 := [quant-inst #2003]: #12525
-#12533 := [mp #12526 #12532]: #12524
-#12610 := [unit-resolution #12533 #7970 #12993]: false
-#12611 := [lemma #12610]: #6447
-#5459 := (* -1::Int #5362)
-#5460 := (+ #2015 #5459)
-#12226 := (>= #5460 0::Int)
-#5380 := (= #2015 #5362)
-#12307 := (or #3860 #2896 #5380)
-#5383 := (or #2896 #5380)
-#12303 := (or #3860 #5383)
-#12279 := (iff #12303 #12307)
-#12410 := [rewrite]: #12279
-#12304 := [quant-inst #2002]: #12303
-#12398 := [mp #12304 #12410]: #12307
-#15925 := [unit-resolution #12398 #10053 #15907]: #5380
-#15889 := (not #5380)
-#15931 := (or #15889 #12226)
-#15927 := [th-lemma arith triangle-eq]: #15931
-#15932 := [unit-resolution #15927 #15925]: #12226
-#15883 := (not #12226)
-#15934 := (or #15933 #15883 #12992 #2020)
-#15935 := [th-lemma arith assign-bounds 1 -1 -1]: #15934
-#15955 := [unit-resolution #15935 #15932 #12611 #15930]: #15933
-#15957 := (or #6623 #6641)
-#15290 := (or #3739 #6623 #2011 #6641)
-#6642 := (or #6623 #2011 #6641)
-#15291 := (or #3739 #6642)
-#15288 := (iff #15291 #15290)
-#15308 := [rewrite]: #15288
-#15270 := [quant-inst #2003 #2002]: #15291
-#15282 := [mp #15270 #15308]: #15290
-#15958 := [unit-resolution #15282 #7156 #15846]: #15957
-#15954 := [unit-resolution #15958 #15955]: #6623
-#15090 := (not #5415)
-#15098 := (or #15090 #5407 #5409)
-#15091 := [def-axiom]: #15098
-#15960 := [unit-resolution #15091 #15954 #15929]: #5407
-#15961 := [monotonicity #15960]: #15956
-#15959 := [monotonicity #15961]: #15962
-#15963 := [monotonicity #15959]: #15445
-#15964 := (not #15445)
-#13461 := (or #15964 #15535)
-#11575 := [th-lemma arith triangle-eq]: #13461
-#14042 := [unit-resolution #11575 #15963]: #15535
-#6485 := (+ f3 #6484)
-#6486 := (<= #6485 0::Int)
-#6610 := (+ #2017 #6481)
-#6611 := (+ #185 #6610)
-#6614 := (= #6611 0::Int)
-#15542 := (not #6614)
-#14614 := (>= #6611 0::Int)
-#13597 := (not #14614)
-#6363 := (+ #2015 #4079)
-#6364 := (>= #6363 0::Int)
-#7961 := (= #2015 #4078)
-#14062 := [monotonicity #15960]: #7961
-#15213 := (not #7961)
-#15268 := (or #15213 #6364)
-#15479 := [th-lemma arith triangle-eq]: #15268
-#15484 := [unit-resolution #15479 #14062]: #6364
-#12694 := (not #15535)
-#14493 := (not #4439)
-#15269 := (not #6364)
-#12544 := (or #13597 #2020 #15269 #14493 #12694)
-#14974 := [th-lemma arith assign-bounds -1 1 -1 1]: #12544
-#15581 := [unit-resolution #14974 #15930 #10752 #15484 #14042]: #13597
-#15702 := (or #15542 #14614)
-#15714 := [th-lemma arith triangle-eq]: #15702
-#15715 := [unit-resolution #15714 #15581]: #15542
-#6511 := (+ #6445 #6481)
-#6509 := (+ #185 #6511)
-#6512 := (>= #6509 0::Int)
-#13034 := (not #6512)
-#15736 := (or #13034 #12992 #2020 #15269 #14493 #12694)
-#15582 := [th-lemma arith assign-bounds -1 -1 1 -1 1]: #15736
-#15841 := [unit-resolution #15582 #15930 #12611 #10752 #15484 #14042]: #13034
-#5073 := (or #6486 #6512 #6614)
-#14397 := (or #3835 #6486 #6512 #6614)
-#6607 := (+ #6481 #2017)
-#6608 := (+ #185 #6607)
-#6609 := (= #6608 0::Int)
-#6491 := (+ #1146 #6484)
-#6492 := (+ #6374 #6491)
-#6490 := (<= #6492 0::Int)
-#6604 := (or #6486 #6490 #6609)
-#12671 := (or #3835 #6604)
-#14485 := (iff #12671 #14397)
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-#14478 := (iff #14423 #14397)
-#14483 := [rewrite]: #14478
-#14389 := (iff #12671 #14423)
-#5263 := (iff #6604 #5073)
-#5033 := (iff #6609 #6614)
-#6612 := (= #6608 #6611)
-#6613 := [rewrite]: #6612
-#5034 := [monotonicity #6613]: #5033
-#6529 := (iff #6490 #6512)
-#6499 := (+ #6374 #6484)
-#6500 := (+ #1146 #6499)
-#6502 := (<= #6500 0::Int)
-#6513 := (iff #6502 #6512)
-#6514 := [rewrite]: #6513
-#6503 := (iff #6490 #6502)
-#6498 := (= #6492 #6500)
-#6501 := [rewrite]: #6498
-#6510 := [monotonicity #6501]: #6503
-#6530 := [trans #6510 #6514]: #6529
-#5264 := [monotonicity #6530 #5034]: #5263
-#14396 := [monotonicity #5264]: #14389
-#14472 := [trans #14396 #14483]: #14485
-#14422 := [quant-inst #2003]: #12671
-#14486 := [mp #14422 #14472]: #14397
-#15735 := [unit-resolution #14486 #7967]: #5073
-#15853 := [unit-resolution #15735 #15841 #15715]: #6486
-#15854 := [th-lemma arith farkas -1 1 1 #15853 #14042 #15846]: false
-#15894 := [lemma #15854]: #2911
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-#18188 := [unit-resolution #18187 #18185]: #3899
-#3441 := (or #3896 #2041)
-#3534 := [def-axiom]: #3441
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-#15966 := [hypothesis]: #5341
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-#19100 := [unit-resolution #19099 #19097]: #15968
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-#5360 := (or #2035 #5341 #5359)
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-#12251 := (iff #12245 #12207)
-#12352 := [rewrite]: #12251
-#12240 := [quant-inst #2034]: #12245
-#12292 := [mp #12240 #12352]: #12207
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-#15554 := [def-axiom]: #15553
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-#18355 := (or #5357 #15530)
-#18361 := [th-lemma arith triangle-eq]: #18355
-#18362 := [unit-resolution #18361 #18351]: #15530
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-#18367 := [unit-resolution #18365 #18362 #19087 #19097]: #18243
-#14134 := (<= #14210 0::Int)
-#14035 := (+ f3 #5353)
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-#18369 := (not #14131)
-#13911 := (>= #5343 0::Int)
-#18177 := (or #3722 #13911)
-#18180 := [quant-inst #5342]: #18177
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-#18363 := (not #13911)
-#18372 := (or #18369 #18363 #18364 #15969)
-#18371 := (or #18369 #18363 #18364 #2040 #15969)
-#18366 := [th-lemma arith assign-bounds -1 -1 -1 -1]: #18371
-#18373 := [unit-resolution #18366 #18189]: #18372
-#18378 := [unit-resolution #18373 #18368 #18362 #19097]: #18369
-#13322 := (f11 f29 #5342)
-#13321 := (= #13322 f1)
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-#19105 := (not #15217)
-#12311 := (not #5346)
-#12351 := (or #5358 #12311)
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-#19107 := (or #19105 #5346 #15969 #19106)
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-#19109 := [unit-resolution #19108 #19104 #19097 #19087]: #19105
-#15548 := (or #13321 #4541 #15217)
-#3523 := (or #3908 #3872)
-#3528 := [def-axiom]: #3523
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-#10669 := (or #3877 #13321 #4541 #15217)
-#14133 := (+ #13325 #2038)
-#15115 := (>= #14133 0::Int)
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-#15255 := (>= #15259 0::Int)
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-#15216 := [monotonicity #15258]: #15208
-#15202 := [trans #15216 #15261]: #15222
-#15555 := [monotonicity #15202]: #15557
-#10681 := [monotonicity #15555]: #10679
-#10677 := [trans #10681 #10672]: #10689
-#10676 := [quant-inst #2034 #5342]: #10675
-#10678 := [mp #10676 #10677]: #10669
-#19114 := [unit-resolution #10678 #18201]: #15548
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-#13323 := (not #13321)
-#11985 := (or #13323 #14131 #14134)
-#3437 := (or #3896 #3880)
-#3438 := [def-axiom]: #3437
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-#14205 := (+ #5352 #14133)
-#12308 := (>= #14205 0::Int)
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-#11853 := (+ #5352 #13325)
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-#14211 := [rewrite]: #8205
-#14206 := (iff #12308 #14155)
-#12309 := (= #14205 #14129)
-#12299 := [rewrite]: #12309
-#14118 := [monotonicity #12299]: #14206
-#14132 := [trans #14118 #14211]: #14226
-#11847 := [monotonicity #14132]: #12007
-#17095 := [monotonicity #11847]: #18182
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-#15298 := (= #14210 0::Int)
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-#15303 := (or #15217 #13323 #15302)
-#3531 := (or #3896 #3888)
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-#15198 := (+ #2038 #5352)
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-#15204 := (= #15203 0::Int)
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-#15285 := (= #14129 0::Int)
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-#15297 := [rewrite]: #15299
-#15279 := (iff #15204 #15285)
-#15264 := (= #15203 #14129)
-#15254 := [rewrite]: #15264
-#15284 := [monotonicity #15254]: #15279
-#15300 := [trans #15284 #15297]: #15275
-#15289 := [monotonicity #15300]: #15304
-#15301 := [monotonicity #15202 #15289]: #15292
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-#18236 := [trans #18254 #18238]: #18239
-#18252 := [quant-inst #5342]: #18220
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-#18381 := [unit-resolution #18242 #18380]: #15303
-#18382 := [unit-resolution #18381 #18370 #19109]: #15302
-#18393 := (not #18243)
-#18392 := (not #14134)
-#18388 := (or #15298 #18392 #18393)
-#18394 := [th-lemma arith triangle-eq]: #18388
-#18396 := [unit-resolution #18394 #18382 #18376 #18367]: false
-#18397 := [lemma #18396]: #4541
-#16386 := [mp #18397 #16391]: #9410
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-#9346 := (or #9307 #9944 #9685)
-#9347 := [def-axiom]: #9346
-#16392 := [unit-resolution #9347 #16386 #16374]: #9685
-#9688 := (or #9951 #9687)
-#9684 := [def-axiom]: #9688
-#16383 := [unit-resolution #9684 #16392]: #9687
-#16395 := [unit-resolution #16383 #16394]: false
-#16405 := [lemma #16395]: #15368
-#16379 := [hypothesis]: #15340
-#15365 := (or #7600 #15327 #15358)
-#15362 := (or #15327 #15358)
-#15360 := (or #7600 #15362)
-#15351 := (iff #15360 #15365)
-#15352 := [rewrite]: #15351
-#15364 := [quant-inst #181 #2034]: #15360
-#15353 := [mp #15364 #15352]: #15365
-#16275 := [unit-resolution #15353 #3612 #16379 #16405]: false
-#16404 := [lemma #16275]: #15358
-#16322 := [hypothesis]: #12121
-#16307 := (or #15340 #15379 #15402)
-#15400 := (or #15340 #15379 #15402 #10624)
-#15403 := [th-lemma arith assign-bounds -1 -1 1]: #15400
-#16283 := [unit-resolution #15403 #9459]: #16307
-#16319 := [unit-resolution #16283 #16322 #16404]: #15402
-#5241 := (+ #4079 #5123)
-#5242 := (+ #2037 #5241)
-#5243 := (= #5242 0::Int)
-#12167 := (>= #5242 0::Int)
-#16360 := (or #12167 #15379)
-#15382 := (or #12167 #10624 #15379)
-#14315 := [th-lemma arith assign-bounds -1 1]: #15382
-#16376 := [unit-resolution #14315 #9459]: #16360
-#16377 := [unit-resolution #16376 #16322]: #12167
-#15390 := (not #12167)
-#16258 := (or #5243 #15390)
-#12074 := (<= #5242 0::Int)
-#4339 := (+ #110 #1146)
-#7776 := (<= #4339 0::Int)
-#4340 := (>= #4339 0::Int)
-#9693 := (not #4340)
-#4164 := (?v1!7 f28)
-#4165 := (f19 f20 #4164)
-#4166 := (* -1::Int #4165)
-#4167 := (+ #185 #4166)
-#4168 := (<= #4167 0::Int)
-#7320 := (not #4168)
-#4172 := (f6 f7 #4164)
-#4173 := (f5 #4172 f28)
-#4174 := (f4 #4173)
-#4175 := (* -1::Int #4174)
-#4176 := (+ #4166 #4175)
-#4177 := (+ #185 #4176)
-#4178 := (= #4177 0::Int)
-#4179 := (not #4178)
-#4169 := (f11 f21 #4164)
-#4170 := (= #4169 f1)
-#4171 := (not #4170)
-#4180 := (or #4168 #4171 #4179)
-#4181 := (not #4180)
-#4335 := (f11 f21 f16)
-#4336 := (= #4335 f1)
-#13038 := (or #3896 #2040 #4336)
-#12906 := [hypothesis]: #3899
-#12800 := [unit-resolution #3535 #12906]: #3888
-#7302 := (not #4336)
-#15705 := [hypothesis]: #7302
-#4341 := (or #4336 #4340)
-#7485 := (or #3825 #4336 #4340)
-#7486 := (or #3825 #4341)
-#7488 := (iff #7486 #7485)
-#7489 := [rewrite]: #7488
-#7487 := [quant-inst #65]: #7486
-#7490 := [mp #7487 #7489]: #7485
-#15712 := [unit-resolution #7490 #9789]: #4341
-#15713 := [unit-resolution #15712 #15705]: #4340
-#15716 := (or #9693 #4168)
-#7756 := (>= #4165 0::Int)
-#7707 := (not #7756)
-#7708 := [hypothesis]: #7707
-#7822 := (or #3722 #7756)
-#7824 := [quant-inst #4164]: #7822
-#7859 := [unit-resolution #7824 #7614 #7708]: false
-#7860 := [lemma #7859]: #7756
-#15719 := (or #9693 #7707 #4168)
-#7972 := (not #4504)
-#15717 := (or #9693 #7972 #7707 #4168)
-#15718 := [th-lemma arith assign-bounds -1 1 1]: #15717
-#15721 := [unit-resolution #15718 #7623]: #15719
-#15722 := [unit-resolution #15721 #7860]: #15716
-#15723 := [unit-resolution #15722 #15713]: #4168
-#7326 := (or #4180 #7320)
-#7330 := [def-axiom]: #7326
-#15728 := [unit-resolution #7330 #15723]: #4180
-#7978 := (or #4163 #4181)
-#3458 := (or #3968 #1323)
-#3461 := [def-axiom]: #3458
-#7977 := [unit-resolution #3461 #7802]: #1323
-#7294 := (or #3747 #4163 #1322 #4181)
-#4182 := (or #4163 #1322 #4181)
-#7297 := (or #3747 #4182)
-#7321 := (iff #7297 #7294)
-#7323 := [rewrite]: #7321
-#7298 := [quant-inst #181]: #7297
-#7324 := [mp #7298 #7323]: #7294
-#7979 := [unit-resolution #7324 #7427 #7977]: #7978
-#15748 := [unit-resolution #7979 #15728]: #4163
-#11585 := [unit-resolution #3440 #12906]: #2036
-#15405 := (or #15374 #2035 #7583 #3893)
-#15369 := (iff #2036 #15368)
-#15350 := (iff #2035 #15327)
-#15367 := (iff #15327 #2035)
-#12076 := (= f16 ?v0!20)
-#15366 := (iff #12076 #2035)
-#15354 := [commutativity]: #15366
-#15357 := (iff #15327 #12076)
-#15317 := [monotonicity #7835]: #15357
-#15318 := [trans #15317 #15354]: #15367
-#15336 := [symm #15318]: #15350
-#15370 := [monotonicity #15336]: #15369
-#15363 := [hypothesis]: #2036
-#15373 := [mp #15363 #15370]: #15368
-#15335 := [hypothesis]: #5182
-#15375 := (or #15374 #12121)
-#15376 := [th-lemma arith triangle-eq]: #15375
-#15378 := [unit-resolution #15376 #15335]: #12121
-#15381 := [unit-resolution #14315 #15378 #9459]: #12167
-#12123 := (>= #5179 0::Int)
-#14322 := (or #15374 #12123)
-#11027 := [th-lemma arith triangle-eq]: #14322
-#15349 := [unit-resolution #11027 #15335]: #12123
-#15265 := (not #12123)
-#14563 := (or #12074 #14493 #15265)
-#15266 := [th-lemma arith assign-bounds -1 1]: #14563
-#15286 := [unit-resolution #15266 #15349 #10752]: #12074
-#14562 := (not #12074)
-#15295 := (or #5243 #14562 #15390)
-#15391 := [th-lemma arith triangle-eq]: #15295
-#15392 := [unit-resolution #15391 #15286 #15381]: #5243
-#5248 := (not #5243)
-#15394 := (or #5229 #5248)
-#4429 := (f11 f29 f28)
-#4430 := (= #4429 f1)
-#4055 := (f11 #193 f28)
-#4056 := (= #4055 f1)
-#43 := (:var 0 S1)
-#40 := (:var 2 S7)
-#41 := (f14 f15 #40)
-#42 := (f13 #41 #10)
-#44 := (f12 #42 #43)
-#3633 := (pattern #44)
-#47 := (= #43 f1)
-#45 := (f11 #44 #10)
-#46 := (= #45 f1)
-#48 := (iff #46 #47)
-#3634 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) (:pat #3633) #48)
-#49 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) #48)
-#3637 := (iff #49 #3634)
-#3635 := (iff #48 #48)
-#3636 := [refl]: #3635
-#3638 := [quant-intro #3636]: #3637
-#1494 := (~ #49 #49)
-#1521 := (~ #48 #48)
-#1522 := [refl]: #1521
-#1495 := [nnf-pos #1522]: #1494
-#341 := [asserted]: #49
-#1523 := [mp~ #341 #1495]: #49
-#3639 := [mp #1523 #3638]: #3634
-#7192 := (not #3634)
-#7205 := (or #7192 #4056)
-#4058 := (iff #4056 #4057)
-#7206 := (or #7192 #4058)
-#7227 := (iff #7206 #7205)
-#7229 := (iff #7205 #7205)
-#7200 := [rewrite]: #7229
-#4066 := (iff #4058 #4056)
-#4061 := (iff #4056 true)
-#4064 := (iff #4061 #4056)
-#4065 := [rewrite]: #4064
-#4062 := (iff #4058 #4061)
-#4063 := [monotonicity #4060]: #4062
-#4067 := [trans #4063 #4065]: #4066
-#7228 := [monotonicity #4067]: #7227
-#7201 := [trans #7228 #7200]: #7227
-#7226 := [quant-inst #115 #181 #3]: #7206
-#7199 := [mp #7226 #7201]: #7205
-#15296 := [unit-resolution #7199 #3639]: #4056
-#14014 := (= #4429 #4055)
-#15393 := [monotonicity #8144]: #14014
-#15395 := [trans #15393 #15296]: #4430
-#15396 := [hypothesis]: #3888
-#4431 := (not #4430)
-#12122 := (or #3893 #5229 #4431 #5248)
-#5219 := (+ #4078 #5178)
-#5220 := (= #5219 0::Int)
-#5221 := (not #5220)
-#5209 := (+ #4078 #2038)
-#5210 := (>= #5209 0::Int)
-#5222 := (or #5210 #4431 #5221)
-#12125 := (or #3893 #5222)
-#12149 := (iff #12125 #12122)
-#5251 := (or #5229 #4431 #5248)
-#12146 := (or #3893 #5251)
-#12083 := (iff #12146 #12122)
-#12143 := [rewrite]: #12083
-#12131 := (iff #12125 #12146)
-#5252 := (iff #5222 #5251)
-#5249 := (iff #5221 #5248)
-#5246 := (iff #5220 #5243)
-#5234 := (+ #4078 #5122)
-#5235 := (+ #2038 #5234)
-#5238 := (= #5235 0::Int)
-#5244 := (iff #5238 #5243)
-#5245 := [rewrite]: #5244
-#5239 := (iff #5220 #5238)
-#5236 := (= #5219 #5235)
-#5237 := [rewrite]: #5236
-#5240 := [monotonicity #5237]: #5239
-#5247 := [trans #5240 #5245]: #5246
-#5250 := [monotonicity #5247]: #5249
-#5232 := (iff #5210 #5229)
-#5223 := (+ #2038 #4078)
-#5226 := (>= #5223 0::Int)
-#5230 := (iff #5226 #5229)
-#5231 := [rewrite]: #5230
-#5227 := (iff #5210 #5226)
-#5224 := (= #5209 #5223)
-#5225 := [rewrite]: #5224
-#5228 := [monotonicity #5225]: #5227
-#5233 := [trans #5228 #5231]: #5232
-#5253 := [monotonicity #5233 #5250]: #5252
-#12082 := [monotonicity #5253]: #12131
-#12147 := [trans #12082 #12143]: #12149
-#12075 := [quant-inst #181]: #12125
-#12124 := [mp #12075 #12147]: #12122
-#15399 := [unit-resolution #12124 #15396 #15395]: #15394
-#15401 := [unit-resolution #15399 #15392]: #5229
-#15397 := [unit-resolution #15403 #15378 #15401 #9459]: #15340
-#15398 := [unit-resolution #15353 #3612]: #15362
-#15404 := [unit-resolution #15398 #15397 #15373]: false
-#15406 := [lemma #15404]: #15405
-#11721 := [unit-resolution #15406 #11585 #15748 #12800]: #15374
-#12105 := (not #5125)
-#5149 := (not #5146)
-#15784 := (or #15969 #4336 #2040 #2035)
-#15708 := [unit-resolution #15971 #15965 #13634]: #15968
-#15709 := [unit-resolution #12292 #7427 #15363]: #15703
-#15710 := [unit-resolution #15709 #15708]: #5359
-#12264 := (or #5358 #5348)
-#12306 := [def-axiom]: #12264
-#15453 := [unit-resolution #12306 #15710]: #5348
-#15775 := (= #4335 #5347)
-#15780 := (= #182 #5347)
-#15777 := (= f28 #5342)
-#15752 := (= f16 #5342)
-#13856 := (= #5342 f16)
-#13857 := (?v1!7 #5342)
-#13952 := (f6 f7 #13857)
-#13906 := (f5 #13952 #5342)
-#13881 := (f4 #13906)
-#13913 := (* -1::Int #13881)
-#13835 := (f19 f20 #13857)
-#13871 := (* -1::Int #13835)
-#13806 := (+ #13871 #13913)
-#11518 := (+ #5343 #13806)
-#11879 := (= #11518 0::Int)
-#13861 := (not #11879)
-#13937 := (f11 f21 #13857)
-#13943 := (= #13937 f1)
-#13938 := (not #13943)
-#13870 := (+ #5343 #13871)
-#13936 := (<= #13870 0::Int)
-#11576 := (or #13936 #13938 #13861)
-#12649 := (+ #185 #5344)
-#12802 := (>= #12649 0::Int)
-#11633 := (or #3731 #183 #5349 #12802)
-#11028 := (or #183 #5349 #12802)
-#12259 := (or #3731 #11028)
-#11754 := (iff #12259 #11633)
-#12879 := [rewrite]: #11754
-#12287 := [quant-inst #5342 #181]: #12259
-#12883 := [mp #12287 #12879]: #11633
-#15747 := [unit-resolution #12883 #8156 #8155 #15453]: #12802
-#17243 := (not #12802)
-#17244 := (or #13936 #9693 #17243)
-#17239 := [hypothesis]: #12802
-#14038 := (not #13936)
-#17240 := [hypothesis]: #14038
-#17043 := (>= #13835 0::Int)
-#17063 := (or #3722 #17043)
-#17064 := [quant-inst #13857]: #17063
-#17241 := [unit-resolution #17064 #7614]: #17043
-#9714 := [hypothesis]: #4340
-#17242 := [th-lemma arith farkas -1 1 1 1 1 #7623 #9714 #17241 #17240 #17239]: false
-#17245 := [lemma #17242]: #17244
-#15749 := [unit-resolution #17245 #15747 #15713]: #13936
-#14010 := (or #11576 #14038)
-#14095 := [def-axiom]: #14010
-#15750 := [unit-resolution #14095 #15749]: #11576
-#13847 := (+ f3 #5344)
-#13841 := (<= #13847 0::Int)
-#16579 := (not #13841)
-#15746 := [unit-resolution #12297 #15710]: #12311
-#16524 := (or #16579 #2040 #15969 #5346)
-#16576 := [hypothesis]: #13841
-#16577 := [hypothesis]: #12311
-#16578 := [th-lemma arith farkas 1 1 1 1 #13634 #15965 #16577 #16576]: false
-#16580 := [lemma #16578]: #16524
-#15711 := [unit-resolution #16580 #15965 #13634 #15746]: #16579
-#13912 := (not #11576)
-#13915 := (or #13856 #13841 #13912)
-#14033 := (or #3747 #13856 #13841 #13912)
-#14036 := (or #3747 #13915)
-#14009 := (iff #14036 #14033)
-#14008 := [rewrite]: #14009
-#14011 := [quant-inst #5342]: #14036
-#14037 := [mp #14011 #14008]: #14033
-#15720 := [unit-resolution #14037 #7427]: #13915
-#15751 := [unit-resolution #15720 #15711 #15750]: #13856
-#15753 := [symm #15751]: #15752
-#15778 := [trans #15748 #15753]: #15777
-#15754 := [monotonicity #15778]: #15780
-#15776 := (= #4335 #182)
-#15727 := [symm #15748]: #7836
-#15779 := [monotonicity #15727]: #15776
-#15782 := [trans #15779 #15754]: #15775
-#15783 := [trans #15782 #15453]: #4336
-#15781 := [unit-resolution #15705 #15783]: false
-#15786 := [lemma #15781]: #15784
-#12801 := [unit-resolution #15786 #11585 #13634 #15705]: #15969
-#12564 := [unit-resolution #12636 #12801]: #11867
-#5152 := (or #5149 #5087)
-#11970 := (or #3843 #5149 #5087)
-#5126 := (+ #1146 #5123)
-#5127 := (+ #5080 #5126)
-#5128 := (<= #5127 0::Int)
-#5129 := (or #5125 #5128)
-#5130 := (not #5129)
-#5131 := (or #5130 #5087)
-#12023 := (or #3843 #5131)
-#12067 := (iff #12023 #11970)
-#12068 := (or #3843 #5152)
-#12042 := (iff #12068 #11970)
-#12107 := [rewrite]: #12042
-#12058 := (iff #12023 #12068)
-#5153 := (iff #5131 #5152)
-#5150 := (iff #5130 #5149)
-#5147 := (iff #5129 #5146)
-#5144 := (iff #5128 #5141)
-#5132 := (+ #5080 #5123)
-#5133 := (+ #1146 #5132)
-#5136 := (<= #5133 0::Int)
-#5142 := (iff #5136 #5141)
-#5143 := [rewrite]: #5142
-#5137 := (iff #5128 #5136)
-#5134 := (= #5127 #5133)
-#5135 := [rewrite]: #5134
-#5138 := [monotonicity #5135]: #5137
-#5145 := [trans #5138 #5143]: #5144
-#5148 := [monotonicity #5145]: #5147
-#5151 := [monotonicity #5148]: #5150
-#5154 := [monotonicity #5151]: #5153
-#12062 := [monotonicity #5154]: #12058
-#12070 := [trans #12062 #12107]: #12067
-#12017 := [quant-inst #2034]: #12023
-#12084 := [mp #12017 #12070]: #11970
-#9728 := [unit-resolution #12084 #7803]: #5152
-#12860 := [unit-resolution #9728 #12564]: #5149
-#12072 := (or #5146 #12105)
-#12071 := [def-axiom]: #12072
-#13044 := [unit-resolution #12071 #12860]: #12105
-#12081 := (not #5141)
-#12073 := (or #5146 #12081)
-#12118 := [def-axiom]: #12073
-#13025 := [unit-resolution #12118 #12860]: #12081
-#5185 := (or #5125 #5141 #5182)
-#12077 := (or #3835 #5125 #5141 #5182)
-#5174 := (+ #5122 #2038)
-#5175 := (+ #185 #5174)
-#5176 := (= #5175 0::Int)
-#5177 := (or #5125 #5128 #5176)
-#12079 := (or #3835 #5177)
-#12130 := (iff #12079 #12077)
-#12113 := (or #3835 #5185)
-#12114 := (iff #12113 #12077)
-#12129 := [rewrite]: #12114
-#12117 := (iff #12079 #12113)
-#5186 := (iff #5177 #5185)
-#5183 := (iff #5176 #5182)
-#5180 := (= #5175 #5179)
-#5181 := [rewrite]: #5180
-#5184 := [monotonicity #5181]: #5183
-#5187 := [monotonicity #5145 #5184]: #5186
-#12115 := [monotonicity #5187]: #12117
-#12109 := [trans #12115 #12129]: #12130
-#12120 := [quant-inst #2034]: #12079
-#12128 := [mp #12120 #12109]: #12077
-#11095 := [unit-resolution #12128 #7967]: #5185
-#13026 := [unit-resolution #11095 #13025 #13044 #11721]: false
-#11841 := [lemma #13026]: #13038
-#18190 := [unit-resolution #11841 #18188 #18189]: #4336
-#9665 := (or #7583 #7302)
-#8260 := [hypothesis]: #4336
-#9629 := (= #182 #4335)
-#9567 := [monotonicity #7835]: #9629
-#7820 := [trans #9567 #8260]: #183
-#7888 := [unit-resolution #8155 #7820]: false
-#7765 := [lemma #7888]: #9665
-#18191 := [unit-resolution #7765 #18190]: #7583
-#18192 := [unit-resolution #7979 #18191]: #4181
-#18193 := [unit-resolution #7330 #18192]: #7320
-#16378 := [unit-resolution #15722 #18193]: #9693
-#16277 := (or #7776 #4340)
-#16270 := [th-lemma arith farkas 1 1]: #16277
-#16406 := [unit-resolution #16270 #16378]: #7776
-#9345 := (not #7776)
-#12779 := (or #12074 #9345 #2040 #3885)
-#12732 := [hypothesis]: #14562
-#12904 := (or #5125 #12074)
-#12870 := [hypothesis]: #3880
-#12757 := (or #3885 #4431 #5125 #12074)
-#15309 := (+ #5122 #5209)
-#15305 := (>= #15309 0::Int)
-#15310 := (or #4431 #5125 #15305)
-#12733 := (or #3885 #15310)
-#12657 := (iff #12733 #12757)
-#15344 := (or #4431 #5125 #12074)
-#12731 := (or #3885 #15344)
-#12778 := (iff #12731 #12757)
-#12664 := [rewrite]: #12778
-#12760 := (iff #12733 #12731)
-#15345 := (iff #15310 #15344)
-#15319 := (iff #15305 #12074)
-#15287 := (>= #5235 0::Int)
-#15315 := (iff #15287 #12074)
-#15321 := [rewrite]: #15315
-#15312 := (iff #15305 #15287)
-#15307 := (= #15309 #5235)
-#15311 := [rewrite]: #15307
-#15313 := [monotonicity #15311]: #15312
-#15342 := [trans #15313 #15321]: #15319
-#15343 := [monotonicity #15342]: #15345
-#12770 := [monotonicity #15343]: #12760
-#12730 := [trans #12770 #12664]: #12657
-#12432 := [quant-inst #2034 #181]: #12733
-#12772 := [mp #12432 #12730]: #12757
-#12909 := [unit-resolution #12772 #12870 #15395]: #12904
-#12907 := [unit-resolution #12909 #12732]: #5125
-#12775 := (or #12167 #12074)
-#12881 := [th-lemma arith farkas 1 1]: #12775
-#12865 := [unit-resolution #12881 #12732]: #12167
-#9736 := [hypothesis]: #7776
-#3233 := (>= #110 0::Int)
-#4506 := (or #3722 #3233)
-#4549 := [quant-inst #65]: #4506
-#9790 := [unit-resolution #4549 #7614]: #3233
-#12861 := [th-lemma arith farkas 1 1 1 1 -1 1 #10752 #9790 #9736 #12865 #12907 #13634]: false
-#12858 := [lemma #12861]: #12779
-#16384 := [unit-resolution #12858 #16406 #18189 #18542]: #12074
-#16235 := [unit-resolution #15391 #16384]: #16258
-#16285 := [unit-resolution #16235 #16377]: #5243
-#16416 := [unit-resolution #12124 #18380]: #5251
-#16417 := [unit-resolution #16416 #15395]: #15394
-#16408 := [unit-resolution #16417 #16285 #16319]: false
-#16407 := [lemma #16408]: #15379
-#16321 := [unit-resolution #15376 #16407]: #15374
-#16309 := [hypothesis]: #5149
-#16410 := [unit-resolution #12071 #16309]: #12105
-#16431 := [unit-resolution #12118 #16309]: #12081
-#16434 := [unit-resolution #11095 #16431 #16410 #16321]: false
-#16432 := [lemma #16434]: #5146
-#16614 := [unit-resolution #9728 #16432]: #5087
-#16615 := [unit-resolution #12636 #16614]: #12022
-#16603 := [unit-resolution #19099 #16615]: #15968
-#16597 := [unit-resolution #19102 #16603]: #5359
-#16549 := [unit-resolution #15554 #16597]: #5356
-#16573 := [unit-resolution #18361 #16549]: #15530
-#16590 := [unit-resolution #18365 #19087 #16615 #16573]: #18243
-#16554 := [unit-resolution #18373 #18368 #16573 #16615]: #18369
-#16552 := (f11 #193 #5342)
-#16553 := (= #16552 f1)
-#16559 := (= #5342 f28)
-#16561 := (or #16559 #5348)
-#16545 := (iff #16553 #16561)
-#16568 := (or #7518 #16545)
-#16522 := (if #16559 #4057 #5348)
-#16560 := (iff #16553 #16522)
-#16569 := (or #7518 #16560)
-#16571 := (iff #16569 #16568)
-#16563 := (iff #16568 #16568)
-#16588 := [rewrite]: #16563
-#16567 := (iff #16560 #16545)
-#16564 := (iff #16522 #16561)
-#16557 := (if #16559 true #5348)
-#16565 := (iff #16557 #16561)
-#16547 := [rewrite]: #16565
-#16562 := (iff #16522 #16557)
-#16548 := [monotonicity #4060]: #16562
-#16566 := [trans #16548 #16547]: #16564
-#16546 := [monotonicity #16566]: #16567
-#16574 := [monotonicity #16546]: #16571
-#16586 := [trans #16574 #16588]: #16571
-#16572 := [quant-inst #115 #181 #3 #5342]: #16569
-#16589 := [mp #16572 #16586]: #16568
-#16611 := [unit-resolution #16589 #3646]: #16545
-#16373 := (not #16545)
-#16635 := (or #16373 #16553)
-#16598 := [unit-resolution #12306 #16597]: #5348
-#15874 := (or #16561 #5349)
-#16585 := [def-axiom]: #15874
-#16596 := [unit-resolution #16585 #16598]: #16561
-#15886 := (not #16561)
-#16515 := (or #16373 #16553 #15886)
-#16581 := [def-axiom]: #16515
-#16599 := [unit-resolution #16581 #16596]: #16635
-#16620 := [unit-resolution #16599 #16611]: #16553
-#16621 := (= #13322 #16552)
-#16619 := [monotonicity #8144]: #16621
-#16595 := [trans #16619 #16620]: #13321
-#16610 := [hypothesis]: #13323
-#16622 := [unit-resolution #16610 #16595]: false
-#16600 := [lemma #16622]: #13321
-#16372 := [unit-resolution #18379 #16600 #16554]: #14134
-#16550 := [unit-resolution #12297 #16597]: #12311
-#16043 := [unit-resolution #19108 #19087 #16615 #16550]: #19105
-#16044 := [unit-resolution #18381 #16600 #16043]: #15302
-[unit-resolution #18394 #16044 #16372 #16590]: false
-unsat
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.thy	Tue Jul 23 13:14:14 2013 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,93 +0,0 @@
-(*  Title:      HOL/Boogie/Examples/Boogie_Dijkstra.thy
-    Author:     Sascha Boehme, TU Muenchen
-*)
-
-header {* Boogie example: Dijkstra's algorithm *}
-
-theory Boogie_Dijkstra
-imports Boogie
-begin
-
-text {*
-We prove correct the verification condition generated from the following
-Boogie code:
-
-\begin{verbatim}
-type Vertex;
-const G: [Vertex, Vertex] int;
-axiom (forall x: Vertex, y: Vertex ::  x != y ==> 0 < G[x,y]);
-axiom (forall x: Vertex, y: Vertex ::  x == y ==> G[x,y] == 0);
-
-const Infinity: int;
-axiom 0 < Infinity;
-
-const Source: Vertex;
-var SP: [Vertex] int;
-
-procedure Dijkstra();
-  modifies SP;
-  ensures (SP[Source] == 0);
-  ensures (forall z: Vertex, y: Vertex ::
-    SP[y] < Infinity && G[y,z] < Infinity ==> SP[z] <= SP[y] + G[y,z]);
-  ensures (forall z: Vertex :: z != Source && SP[z] < Infinity ==>
-    (exists y: Vertex :: SP[y] < SP[z] && SP[z] == SP[y] + G[y,z]));
-
-implementation Dijkstra()
-{
-  var v: Vertex;
-  var Visited: [Vertex] bool;
-  var oldSP: [Vertex] int;
-
-  havoc SP;
-  assume (forall x: Vertex :: x == Source ==> SP[x] == 0);
-  assume (forall x: Vertex :: x != Source ==> SP[x] == Infinity);
-
-  havoc Visited;
-  assume (forall x: Vertex :: !Visited[x]);
-
-  while ((exists x: Vertex :: !Visited[x] && SP[x] < Infinity))
-    invariant (SP[Source] == 0);
-    invariant (forall x: Vertex :: SP[x] >= 0);
-    invariant (forall y: Vertex, z: Vertex :: 
-      !Visited[z] && Visited[y] ==> SP[y] <= SP[z]);
-    invariant (forall z: Vertex, y: Vertex ::
-      Visited[y] && G[y,z] < Infinity ==> SP[z] <= SP[y] + G[y,z]);
-    invariant (forall z: Vertex :: z != Source && SP[z] < Infinity ==>
-      (exists y: Vertex :: SP[y] < SP[z] && Visited[y] && 
-        SP[z] == SP[y] + G[y,z]));
-  {
-    havoc v;
-    assume (!Visited[v]);
-    assume (SP[v] < Infinity); 
-    assume (forall x: Vertex :: !Visited[x] ==> SP[v] <= SP[x]);
-
-    Visited[v] := true;
-
-    oldSP := SP;
-    havoc SP;
-    assume (forall u: Vertex :: 
-      G[v,u] < Infinity && oldSP[v] + G[v,u] < oldSP[u] ==> 
-        SP[u] == oldSP[v] + G[v,u]);
-    assume (forall u: Vertex :: 
-      !(G[v,u] < Infinity && oldSP[v] + G[v,u] < oldSP[u]) ==> 
-        SP[u] == oldSP[u]);
-    assert (forall z: Vertex:: SP[z] <= oldSP[z]);
-    assert (forall y: Vertex:: Visited[y] ==> SP[y] == oldSP[y]);
-  }
-}
-\end{verbatim}
-*}
-
-
-boogie_open "Boogie_Dijkstra.b2i"
-
-declare [[smt_oracle = false]]
-declare [[smt_certificates = "Boogie_Dijkstra.certs"]]
-declare [[smt_read_only_certificates = true]]
-
-boogie_vc Dijkstra
-  by boogie
-
-boogie_end
-
-end
--- a/src/HOL/Boogie/Examples/Boogie_Max.b2i	Tue Jul 23 13:14:14 2013 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,748 +0,0 @@
-vc max 1
-    implies
-    label pos 10 7
-    true
-    implies
-    <
-    int-num 0
-    var length
-      int
-    implies
-    true
-    implies
-    =
-    var max@0
-      int
-    select 2
-    var array
-      array 2
-        int
-        int
-    int-num 0
-    implies
-    and 4
-    <=
-    int-num 0
-    int-num 0
-    <=
-    int-num 0
-    int-num 0
-    <=
-    int-num 1
-    int-num 1
-    <=
-    int-num 1
-    int-num 1
-    and 2
-    label neg 14 5
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.14:23
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    int-num 1
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@0
-      int
-    implies
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.14:23
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    int-num 1
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@0
-      int
-    and 2
-    label neg 15 5
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    int-num 0
-    var max@0
-      int
-    implies
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    int-num 0
-    var max@0
-      int
-    implies
-    label pos 13 3
-    true
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.14:23
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var p@0
-      int
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@1
-      int
-    implies
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    var k@0
-      int
-    var max@1
-      int
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    and 2
-    implies
-    label pos 13 3
-    true
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    >=
-    var p@0
-      int
-    var length
-      int
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    label pos 0 0
-    true
-    implies
-    =
-    var k@2
-      int
-    var k@0
-      int
-    implies
-    =
-    var max@4
-      int
-    var max@1
-      int
-    implies
-    =
-    var p@2
-      int
-    var p@0
-      int
-    implies
-    label pos 0 0
-    true
-    and 2
-    label neg 5 3
-    exists 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.5:19
-      attribute uniqueId 1
-        string-attr 1
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var length
-      int
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@4
-      int
-    implies
-    exists 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.5:19
-      attribute uniqueId 1
-        string-attr 1
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var length
-      int
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@4
-      int
-    and 2
-    label neg 4 3
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.4:19
-      attribute uniqueId 1
-        string-attr 0
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var length
-      int
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@4
-      int
-    implies
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.4:19
-      attribute uniqueId 1
-        string-attr 0
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var length
-      int
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@4
-      int
-    true
-    implies
-    label pos 17 5
-    true
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    <
-    var p@0
-      int
-    var length
-      int
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    and 2
-    implies
-    label pos 17 31
-    true
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    >
-    select 2
-    var array
-      array 2
-        int
-        int
-    var p@0
-      int
-    var max@1
-      int
-    implies
-    =
-    var max@2
-      int
-    select 2
-    var array
-      array 2
-        int
-        int
-    var p@0
-      int
-    implies
-    and 2
-    <=
-    int-num 1
-    var p@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    label pos 0 0
-    true
-    implies
-    =
-    var k@1
-      int
-    var p@0
-      int
-    implies
-    =
-    var max@3
-      int
-    var max@2
-      int
-    implies
-    label pos 18 7
-    true
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@1
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    =
-    var p@1
-      int
-    +
-    var p@0
-      int
-    int-num 1
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@1
-      int
-    <=
-    int-num 2
-    var p@1
-      int
-    implies
-    label pos 0 0
-    true
-    and 2
-    label neg 14 5
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.14:23
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var p@1
-      int
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@3
-      int
-    implies
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.14:23
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var p@1
-      int
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@3
-      int
-    and 2
-    label neg 15 5
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    var k@1
-      int
-    var max@3
-      int
-    implies
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    var k@1
-      int
-    var max@3
-      int
-    implies
-    false
-    true
-    implies
-    label pos 17 5
-    true
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var p@0
-      int
-    var max@1
-      int
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@0
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    label pos 0 0
-    true
-    implies
-    =
-    var k@1
-      int
-    var k@0
-      int
-    implies
-    =
-    var max@3
-      int
-    var max@1
-      int
-    implies
-    label pos 18 7
-    true
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@1
-      int
-    <=
-    int-num 1
-    var p@0
-      int
-    implies
-    =
-    var p@1
-      int
-    +
-    var p@0
-      int
-    int-num 1
-    implies
-    and 2
-    <=
-    int-num 0
-    var k@1
-      int
-    <=
-    int-num 2
-    var p@1
-      int
-    implies
-    label pos 0 0
-    true
-    and 2
-    label neg 14 5
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.14:23
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var p@1
-      int
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@3
-      int
-    implies
-    forall 1 0 3
-      var i
-        int
-      attribute qid 1
-        string-attr BoogieMa.14:23
-      attribute uniqueId 1
-        string-attr 2
-      attribute bvZ3Native 1
-        string-attr False
-    implies
-    and 2
-    <=
-    int-num 0
-    var i
-      int
-    <
-    var i
-      int
-    var p@1
-      int
-    <=
-    select 2
-    var array
-      array 2
-        int
-        int
-    var i
-      int
-    var max@3
-      int
-    and 2
-    label neg 15 5
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    var k@1
-      int
-    var max@3
-      int
-    implies
-    =
-    select 2
-    var array
-      array 2
-        int
-        int
-    var k@1
-      int
-    var max@3
-      int
-    implies
-    false
-    true
--- a/src/HOL/Boogie/Examples/Boogie_Max.certs	Tue Jul 23 13:14:14 2013 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,2079 +0,0 @@
-43f8affa0232e904defc8acf7ee4c00d186b27a1 2078 0
-#2 := false
-#7 := 0::Int
-decl ?v0!3 :: Int
-#1093 := ?v0!3
-#616 := -1::Int
-#1238 := (* -1::Int ?v0!3)
-decl f8 :: Int
-#31 := f8
-#2314 := (+ f8 #1238)
-#2315 := (<= #2314 0::Int)
-#2420 := (not #2315)
-#2347 := (>= #2314 0::Int)
-decl f16 :: Int
-#79 := f16
-#725 := (* -1::Int f16)
-#757 := (+ f8 #725)
-#1758 := (>= #757 -1::Int)
-#756 := (= #757 -1::Int)
-decl f15 :: Int
-#75 := f15
-decl f5 :: (-> S2 Int Int)
-decl f14 :: Int
-#73 := f14
-decl f6 :: S2
-#11 := f6
-#90 := (f5 f6 f14)
-#91 := (= #90 f15)
-#20 := (:var 0 Int)
-#24 := (f5 f6 #20)
-#2076 := (pattern #24)
-#736 := (* -1::Int f15)
-#737 := (+ #24 #736)
-#738 := (<= #737 0::Int)
-#726 := (+ #20 #725)
-#724 := (>= #726 0::Int)
-#605 := (>= #20 0::Int)
-#1341 := (not #605)
-#1515 := (or #1341 #724 #738)
-#2110 := (forall (vars (?v0 Int)) (:pat #2076) #1515)
-#2115 := (not #2110)
-#2118 := (or #2115 #91)
-#2121 := (not #2118)
-#1100 := (f5 f6 ?v0!3)
-#1260 := (* -1::Int #1100)
-#1261 := (+ f15 #1260)
-#1262 := (>= #1261 0::Int)
-#1239 := (+ f16 #1238)
-#1240 := (<= #1239 0::Int)
-#1094 := (>= ?v0!3 0::Int)
-#1478 := (not #1094)
-#1493 := (or #1478 #1240 #1262)
-#1498 := (not #1493)
-#2124 := (or #1498 #2121)
-#2127 := (not #2124)
-#82 := 2::Int
-#716 := (>= f16 2::Int)
-#1540 := (not #716)
-#713 := (>= f14 0::Int)
-#1539 := (not #713)
-#760 := (not #756)
-#15 := 1::Int
-#635 := (>= f8 1::Int)
-#769 := (not #635)
-decl f9 :: Int
-#36 := f9
-#108 := (= f15 f9)
-#395 := (not #108)
-decl f7 :: Int
-#29 := f7
-#107 := (= f14 f7)
-#404 := (not #107)
-#68 := (f5 f6 f8)
-#774 := (* -1::Int #68)
-#775 := (+ f9 #774)
-#773 := (>= #775 0::Int)
-#772 := (not #773)
-#632 := (>= f7 0::Int)
-#1470 := (not #632)
-#2136 := (or #1470 #772 #404 #395 #769 #760 #1539 #1540 #2127)
-#2139 := (not #2136)
-decl f13 :: Int
-#70 := f13
-#76 := (= f15 f13)
-#335 := (not #76)
-#74 := (= f14 f8)
-#344 := (not #74)
-#71 := (= f13 #68)
-#362 := (not #71)
-#2130 := (or #1470 #773 #362 #344 #335 #769 #760 #1539 #1540 #2127)
-#2133 := (not #2130)
-#2142 := (or #2133 #2139)
-#2145 := (not #2142)
-#681 := (* -1::Int f8)
-decl f3 :: Int
-#8 := f3
-#682 := (+ f3 #681)
-#683 := (<= #682 0::Int)
-#2148 := (or #1470 #769 #683 #2145)
-#2151 := (not #2148)
-decl ?v0!2 :: Int
-#1038 := ?v0!2
-#1046 := (f5 f6 ?v0!2)
-#1191 := (* -1::Int #1046)
-decl f11 :: Int
-#45 := f11
-#1192 := (+ f11 #1191)
-#1193 := (>= #1192 0::Int)
-#1040 := (* -1::Int ?v0!2)
-#1041 := (+ f3 #1040)
-#1042 := (<= #1041 0::Int)
-#1039 := (>= ?v0!2 0::Int)
-#1431 := (not #1039)
-decl ?v0!1 :: Int
-#1020 := ?v0!1
-#1028 := (f5 f6 ?v0!1)
-#1029 := (= #1028 f11)
-#1022 := (* -1::Int ?v0!1)
-#1023 := (+ f3 #1022)
-#1024 := (<= #1023 0::Int)
-#1021 := (>= ?v0!1 0::Int)
-#1411 := (not #1021)
-#1426 := (or #1411 #1024 #1029)
-#1457 := (not #1426)
-#1458 := (or #1457 #1431 #1042 #1193)
-#1459 := (not #1458)
-#51 := (= #24 f11)
-#643 := (* -1::Int #20)
-#644 := (+ f3 #643)
-#645 := (<= #644 0::Int)
-#1400 := (or #1341 #645 #51)
-#1405 := (not #1400)
-#2093 := (forall (vars (?v0 Int)) (:pat #2076) #1405)
-#2098 := (or #2093 #1459)
-#2101 := (not #2098)
-decl f12 :: Int
-#47 := f12
-#48 := (= f12 f8)
-#212 := (not #48)
-#46 := (= f11 f9)
-#221 := (not #46)
-decl f10 :: Int
-#43 := f10
-#44 := (= f10 f7)
-#230 := (not #44)
-#686 := (not #683)
-#2104 := (or #1470 #769 #686 #230 #221 #212 #2101)
-#2107 := (not #2104)
-#2154 := (or #2107 #2151)
-#2157 := (not #2154)
-#40 := (f5 f6 f7)
-#41 := (= #40 f9)
-#491 := (not #41)
-#881 := (* -1::Int f9)
-#882 := (+ #24 #881)
-#883 := (<= #882 0::Int)
-#871 := (+ #20 #681)
-#870 := (>= #871 0::Int)
-#1378 := (or #1341 #870 #883)
-#2085 := (forall (vars (?v0 Int)) (:pat #2076) #1378)
-#2090 := (not #2085)
-decl f4 :: Int
-#10 := f4
-#12 := (f5 f6 0::Int)
-#28 := (= #12 f4)
-#524 := (not #28)
-#2160 := (or #524 #1470 #769 #2090 #491 #2157)
-#2163 := (not #2160)
-#2166 := (or #524 #2163)
-#2169 := (not #2166)
-#619 := (* -1::Int #24)
-#620 := (+ f4 #619)
-#618 := (>= #620 0::Int)
-#608 := (>= #20 1::Int)
-#1356 := (or #1341 #608 #618)
-#2077 := (forall (vars (?v0 Int)) (:pat #2076) #1356)
-#2082 := (not #2077)
-#2172 := (or #2082 #2169)
-#2175 := (not #2172)
-decl ?v0!0 :: Int
-#968 := ?v0!0
-#962 := (f5 f6 ?v0!0)
-#963 := (* -1::Int #962)
-#960 := (+ f4 #963)
-#961 := (>= #960 0::Int)
-#970 := (>= ?v0!0 1::Int)
-#969 := (>= ?v0!0 0::Int)
-#1033 := (not #969)
-#1333 := (or #1033 #970 #961)
-#1927 := (= f4 #962)
-#1853 := (= #12 #962)
-#1893 := (= #962 #12)
-#1903 := (= ?v0!0 0::Int)
-#971 := (not #970)
-#1338 := (not #1333)
-#1926 := [hypothesis]: #1338
-#1663 := (or #1333 #971)
-#1748 := [def-axiom]: #1663
-#1928 := [unit-resolution #1748 #1926]: #971
-#1662 := (or #1333 #969)
-#1747 := [def-axiom]: #1662
-#1896 := [unit-resolution #1747 #1926]: #969
-#1862 := [th-lemma arith eq-propagate 0 0 #1896 #1928]: #1903
-#1895 := [monotonicity #1862]: #1893
-#1854 := [symm #1895]: #1853
-#13 := (= f4 #12)
-#727 := (not #724)
-#730 := (and #605 #727)
-#733 := (not #730)
-#741 := (or #733 #738)
-#744 := (forall (vars (?v0 Int)) #741)
-#747 := (not #744)
-#750 := (or #747 #91)
-#753 := (and #744 #750)
-#718 := (and #713 #716)
-#721 := (not #718)
-#763 := (and #713 #635)
-#766 := (not #763)
-#637 := (and #632 #635)
-#640 := (not #637)
-#836 := (or #640 #772 #404 #395 #766 #760 #721 #753)
-#812 := (or #640 #773 #362 #769 #344 #335 #766 #760 #721 #753)
-#841 := (and #812 #836)
-#862 := (or #640 #683 #841)
-#664 := (* -1::Int f11)
-#665 := (+ #24 #664)
-#666 := (<= #665 0::Int)
-#646 := (not #645)
-#649 := (and #605 #646)
-#652 := (not #649)
-#669 := (or #652 #666)
-#672 := (forall (vars (?v0 Int)) #669)
-#655 := (or #652 #51)
-#658 := (exists (vars (?v0 Int)) #655)
-#661 := (not #658)
-#675 := (or #661 #672)
-#678 := (and #658 #675)
-#707 := (or #640 #686 #230 #221 #212 #678)
-#867 := (and #707 #862)
-#872 := (not #870)
-#875 := (and #605 #872)
-#878 := (not #875)
-#886 := (or #878 #883)
-#889 := (forall (vars (?v0 Int)) #886)
-#892 := (not #889)
-#910 := (or #524 #640 #892 #491 #867)
-#915 := (and #28 #910)
-#606 := (not #608)
-#610 := (and #605 #606)
-#613 := (not #610)
-#622 := (or #613 #618)
-#625 := (forall (vars (?v0 Int)) #622)
-#628 := (not #625)
-#918 := (or #628 #915)
-#921 := (and #625 #918)
-#557 := (not #13)
-#924 := (<= f3 0::Int)
-#944 := (or #924 #557 #921)
-#949 := (not #944)
-#1 := true
-#92 := (and #91 true)
-#87 := (<= #24 f15)
-#85 := (< #20 f16)
-#21 := (<= 0::Int #20)
-#86 := (and #21 #85)
-#88 := (implies #86 #87)
-#89 := (forall (vars (?v0 Int)) #88)
-#93 := (implies #89 #92)
-#94 := (and #89 #93)
-#83 := (<= 2::Int f16)
-#77 := (<= 0::Int f14)
-#84 := (and #77 #83)
-#95 := (implies #84 #94)
-#80 := (+ f8 1::Int)
-#81 := (= f16 #80)
-#96 := (implies #81 #95)
-#32 := (<= 1::Int f8)
-#78 := (and #77 #32)
-#97 := (implies #78 #96)
-#98 := (implies true #97)
-#109 := (implies #108 #98)
-#110 := (implies #107 #109)
-#30 := (<= 0::Int f7)
-#33 := (and #30 #32)
-#111 := (implies #33 #110)
-#106 := (<= #68 f9)
-#112 := (implies #106 #111)
-#113 := (implies #33 #112)
-#114 := (implies true #113)
-#99 := (implies #76 #98)
-#100 := (implies #74 #99)
-#72 := (and #32 #32)
-#101 := (implies #72 #100)
-#102 := (implies #71 #101)
-#69 := (< f9 #68)
-#103 := (implies #69 #102)
-#104 := (implies #33 #103)
-#105 := (implies true #104)
-#115 := (and #105 #114)
-#116 := (implies #33 #115)
-#67 := (< f8 f3)
-#117 := (implies #67 #116)
-#118 := (implies #33 #117)
-#119 := (implies true #118)
-#54 := (<= #24 f11)
-#49 := (< #20 f3)
-#50 := (and #21 #49)
-#55 := (implies #50 #54)
-#56 := (forall (vars (?v0 Int)) #55)
-#57 := (and #56 true)
-#52 := (implies #50 #51)
-#53 := (exists (vars (?v0 Int)) #52)
-#58 := (implies #53 #57)
-#59 := (and #53 #58)
-#60 := (implies #48 #59)
-#61 := (implies #46 #60)
-#62 := (implies #44 #61)
-#63 := (implies #33 #62)
-#42 := (<= f3 f8)
-#64 := (implies #42 #63)
-#65 := (implies #33 #64)
-#66 := (implies true #65)
-#120 := (and #66 #119)
-#121 := (implies #33 #120)
-#122 := (implies #41 #121)
-#37 := (<= #24 f9)
-#34 := (< #20 f8)
-#35 := (and #21 #34)
-#38 := (implies #35 #37)
-#39 := (forall (vars (?v0 Int)) #38)
-#123 := (implies #39 #122)
-#124 := (implies #33 #123)
-#125 := (implies true #124)
-#126 := (implies #28 #125)
-#127 := (and #28 #126)
-#25 := (<= #24 f4)
-#22 := (< #20 1::Int)
-#23 := (and #21 #22)
-#26 := (implies #23 #25)
-#27 := (forall (vars (?v0 Int)) #26)
-#128 := (implies #27 #127)
-#129 := (and #27 #128)
-#16 := (<= 1::Int 1::Int)
-#17 := (and #16 #16)
-#14 := (<= 0::Int 0::Int)
-#18 := (and #14 #17)
-#19 := (and #14 #18)
-#130 := (implies #19 #129)
-#131 := (implies #13 #130)
-#9 := (< 0::Int f3)
-#132 := (implies #9 #131)
-#133 := (implies true #132)
-#134 := (not #133)
-#952 := (iff #134 #949)
-#277 := (not #86)
-#278 := (or #277 #87)
-#281 := (forall (vars (?v0 Int)) #278)
-#289 := (not #281)
-#290 := (or #289 #91)
-#295 := (and #281 #290)
-#301 := (not #84)
-#302 := (or #301 #295)
-#271 := (+ 1::Int f8)
-#274 := (= f16 #271)
-#310 := (not #274)
-#311 := (or #310 #302)
-#319 := (not #78)
-#320 := (or #319 #311)
-#396 := (or #395 #320)
-#405 := (or #404 #396)
-#239 := (not #33)
-#413 := (or #239 #405)
-#421 := (not #106)
-#422 := (or #421 #413)
-#430 := (or #239 #422)
-#336 := (or #335 #320)
-#345 := (or #344 #336)
-#353 := (not #32)
-#354 := (or #353 #345)
-#363 := (or #362 #354)
-#371 := (not #69)
-#372 := (or #371 #363)
-#380 := (or #239 #372)
-#442 := (and #380 #430)
-#448 := (or #239 #442)
-#456 := (not #67)
-#457 := (or #456 #448)
-#465 := (or #239 #457)
-#177 := (not #50)
-#184 := (or #177 #54)
-#187 := (forall (vars (?v0 Int)) #184)
-#178 := (or #177 #51)
-#181 := (exists (vars (?v0 Int)) #178)
-#200 := (not #181)
-#201 := (or #200 #187)
-#206 := (and #181 #201)
-#213 := (or #212 #206)
-#222 := (or #221 #213)
-#231 := (or #230 #222)
-#240 := (or #239 #231)
-#248 := (not #42)
-#249 := (or #248 #240)
-#257 := (or #239 #249)
-#477 := (and #257 #465)
-#483 := (or #239 #477)
-#492 := (or #491 #483)
-#170 := (not #35)
-#171 := (or #170 #37)
-#174 := (forall (vars (?v0 Int)) #171)
-#500 := (not #174)
-#501 := (or #500 #492)
-#509 := (or #239 #501)
-#525 := (or #524 #509)
-#530 := (and #28 #525)
-#163 := (not #23)
-#164 := (or #163 #25)
-#167 := (forall (vars (?v0 Int)) #164)
-#536 := (not #167)
-#537 := (or #536 #530)
-#542 := (and #167 #537)
-#157 := (and #14 #16)
-#160 := (and #14 #157)
-#548 := (not #160)
-#549 := (or #548 #542)
-#558 := (or #557 #549)
-#566 := (not #9)
-#567 := (or #566 #558)
-#579 := (not #567)
-#950 := (iff #579 #949)
-#947 := (iff #567 #944)
-#935 := (or false #921)
-#938 := (or #557 #935)
-#941 := (or #924 #938)
-#945 := (iff #941 #944)
-#946 := [rewrite]: #945
-#942 := (iff #567 #941)
-#939 := (iff #558 #938)
-#936 := (iff #549 #935)
-#922 := (iff #542 #921)
-#919 := (iff #537 #918)
-#916 := (iff #530 #915)
-#913 := (iff #525 #910)
-#895 := (or #640 #867)
-#898 := (or #491 #895)
-#901 := (or #892 #898)
-#904 := (or #640 #901)
-#907 := (or #524 #904)
-#911 := (iff #907 #910)
-#912 := [rewrite]: #911
-#908 := (iff #525 #907)
-#905 := (iff #509 #904)
-#902 := (iff #501 #901)
-#899 := (iff #492 #898)
-#896 := (iff #483 #895)
-#868 := (iff #477 #867)
-#865 := (iff #465 #862)
-#853 := (or #640 #841)
-#856 := (or #683 #853)
-#859 := (or #640 #856)
-#863 := (iff #859 #862)
-#864 := [rewrite]: #863
-#860 := (iff #465 #859)
-#857 := (iff #457 #856)
-#854 := (iff #448 #853)
-#842 := (iff #442 #841)
-#839 := (iff #430 #836)
-#785 := (or #721 #753)
-#788 := (or #760 #785)
-#791 := (or #766 #788)
-#821 := (or #395 #791)
-#824 := (or #404 #821)
-#827 := (or #640 #824)
-#830 := (or #772 #827)
-#833 := (or #640 #830)
-#837 := (iff #833 #836)
-#838 := [rewrite]: #837
-#834 := (iff #430 #833)
-#831 := (iff #422 #830)
-#828 := (iff #413 #827)
-#825 := (iff #405 #824)
-#822 := (iff #396 #821)
-#792 := (iff #320 #791)
-#789 := (iff #311 #788)
-#786 := (iff #302 #785)
-#754 := (iff #295 #753)
-#751 := (iff #290 #750)
-#748 := (iff #289 #747)
-#745 := (iff #281 #744)
-#742 := (iff #278 #741)
-#739 := (iff #87 #738)
-#740 := [rewrite]: #739
-#734 := (iff #277 #733)
-#731 := (iff #86 #730)
-#728 := (iff #85 #727)
-#729 := [rewrite]: #728
-#603 := (iff #21 #605)
-#604 := [rewrite]: #603
-#732 := [monotonicity #604 #729]: #731
-#735 := [monotonicity #732]: #734
-#743 := [monotonicity #735 #740]: #742
-#746 := [quant-intro #743]: #745
-#749 := [monotonicity #746]: #748
-#752 := [monotonicity #749]: #751
-#755 := [monotonicity #746 #752]: #754
-#722 := (iff #301 #721)
-#719 := (iff #84 #718)
-#715 := (iff #83 #716)
-#717 := [rewrite]: #715
-#712 := (iff #77 #713)
-#714 := [rewrite]: #712
-#720 := [monotonicity #714 #717]: #719
-#723 := [monotonicity #720]: #722
-#787 := [monotonicity #723 #755]: #786
-#761 := (iff #310 #760)
-#758 := (iff #274 #756)
-#759 := [rewrite]: #758
-#762 := [monotonicity #759]: #761
-#790 := [monotonicity #762 #787]: #789
-#767 := (iff #319 #766)
-#764 := (iff #78 #763)
-#634 := (iff #32 #635)
-#636 := [rewrite]: #634
-#765 := [monotonicity #714 #636]: #764
-#768 := [monotonicity #765]: #767
-#793 := [monotonicity #768 #790]: #792
-#823 := [monotonicity #793]: #822
-#826 := [monotonicity #823]: #825
-#641 := (iff #239 #640)
-#638 := (iff #33 #637)
-#631 := (iff #30 #632)
-#633 := [rewrite]: #631
-#639 := [monotonicity #633 #636]: #638
-#642 := [monotonicity #639]: #641
-#829 := [monotonicity #642 #826]: #828
-#819 := (iff #421 #772)
-#817 := (iff #106 #773)
-#818 := [rewrite]: #817
-#820 := [monotonicity #818]: #819
-#832 := [monotonicity #820 #829]: #831
-#835 := [monotonicity #642 #832]: #834
-#840 := [trans #835 #838]: #839
-#815 := (iff #380 #812)
-#794 := (or #335 #791)
-#797 := (or #344 #794)
-#800 := (or #769 #797)
-#803 := (or #362 #800)
-#806 := (or #773 #803)
-#809 := (or #640 #806)
-#813 := (iff #809 #812)
-#814 := [rewrite]: #813
-#810 := (iff #380 #809)
-#807 := (iff #372 #806)
-#804 := (iff #363 #803)
-#801 := (iff #354 #800)
-#798 := (iff #345 #797)
-#795 := (iff #336 #794)
-#796 := [monotonicity #793]: #795
-#799 := [monotonicity #796]: #798
-#770 := (iff #353 #769)
-#771 := [monotonicity #636]: #770
-#802 := [monotonicity #771 #799]: #801
-#805 := [monotonicity #802]: #804
-#783 := (iff #371 #773)
-#778 := (not #772)
-#781 := (iff #778 #773)
-#782 := [rewrite]: #781
-#779 := (iff #371 #778)
-#776 := (iff #69 #772)
-#777 := [rewrite]: #776
-#780 := [monotonicity #777]: #779
-#784 := [trans #780 #782]: #783
-#808 := [monotonicity #784 #805]: #807
-#811 := [monotonicity #642 #808]: #810
-#816 := [trans #811 #814]: #815
-#843 := [monotonicity #816 #840]: #842
-#855 := [monotonicity #642 #843]: #854
-#851 := (iff #456 #683)
-#846 := (not #686)
-#849 := (iff #846 #683)
-#850 := [rewrite]: #849
-#847 := (iff #456 #846)
-#844 := (iff #67 #686)
-#845 := [rewrite]: #844
-#848 := [monotonicity #845]: #847
-#852 := [trans #848 #850]: #851
-#858 := [monotonicity #852 #855]: #857
-#861 := [monotonicity #642 #858]: #860
-#866 := [trans #861 #864]: #865
-#710 := (iff #257 #707)
-#689 := (or #212 #678)
-#692 := (or #221 #689)
-#695 := (or #230 #692)
-#698 := (or #640 #695)
-#701 := (or #686 #698)
-#704 := (or #640 #701)
-#708 := (iff #704 #707)
-#709 := [rewrite]: #708
-#705 := (iff #257 #704)
-#702 := (iff #249 #701)
-#699 := (iff #240 #698)
-#696 := (iff #231 #695)
-#693 := (iff #222 #692)
-#690 := (iff #213 #689)
-#679 := (iff #206 #678)
-#676 := (iff #201 #675)
-#673 := (iff #187 #672)
-#670 := (iff #184 #669)
-#667 := (iff #54 #666)
-#668 := [rewrite]: #667
-#653 := (iff #177 #652)
-#650 := (iff #50 #649)
-#647 := (iff #49 #646)
-#648 := [rewrite]: #647
-#651 := [monotonicity #604 #648]: #650
-#654 := [monotonicity #651]: #653
-#671 := [monotonicity #654 #668]: #670
-#674 := [quant-intro #671]: #673
-#662 := (iff #200 #661)
-#659 := (iff #181 #658)
-#656 := (iff #178 #655)
-#657 := [monotonicity #654]: #656
-#660 := [quant-intro #657]: #659
-#663 := [monotonicity #660]: #662
-#677 := [monotonicity #663 #674]: #676
-#680 := [monotonicity #660 #677]: #679
-#691 := [monotonicity #680]: #690
-#694 := [monotonicity #691]: #693
-#697 := [monotonicity #694]: #696
-#700 := [monotonicity #642 #697]: #699
-#687 := (iff #248 #686)
-#684 := (iff #42 #683)
-#685 := [rewrite]: #684
-#688 := [monotonicity #685]: #687
-#703 := [monotonicity #688 #700]: #702
-#706 := [monotonicity #642 #703]: #705
-#711 := [trans #706 #709]: #710
-#869 := [monotonicity #711 #866]: #868
-#897 := [monotonicity #642 #869]: #896
-#900 := [monotonicity #897]: #899
-#893 := (iff #500 #892)
-#890 := (iff #174 #889)
-#887 := (iff #171 #886)
-#884 := (iff #37 #883)
-#885 := [rewrite]: #884
-#879 := (iff #170 #878)
-#876 := (iff #35 #875)
-#873 := (iff #34 #872)
-#874 := [rewrite]: #873
-#877 := [monotonicity #604 #874]: #876
-#880 := [monotonicity #877]: #879
-#888 := [monotonicity #880 #885]: #887
-#891 := [quant-intro #888]: #890
-#894 := [monotonicity #891]: #893
-#903 := [monotonicity #894 #900]: #902
-#906 := [monotonicity #642 #903]: #905
-#909 := [monotonicity #906]: #908
-#914 := [trans #909 #912]: #913
-#917 := [monotonicity #914]: #916
-#629 := (iff #536 #628)
-#626 := (iff #167 #625)
-#623 := (iff #164 #622)
-#617 := (iff #25 #618)
-#621 := [rewrite]: #617
-#614 := (iff #163 #613)
-#611 := (iff #23 #610)
-#607 := (iff #22 #606)
-#609 := [rewrite]: #607
-#612 := [monotonicity #604 #609]: #611
-#615 := [monotonicity #612]: #614
-#624 := [monotonicity #615 #621]: #623
-#627 := [quant-intro #624]: #626
-#630 := [monotonicity #627]: #629
-#920 := [monotonicity #630 #917]: #919
-#923 := [monotonicity #627 #920]: #922
-#601 := (iff #548 false)
-#596 := (not true)
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-#1505 := (not #1502)
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-#1504 := [rewrite]: #1503
-#1507 := [monotonicity #1504]: #1506
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-#1514 := [monotonicity #1511]: #1513
-#1519 := [trans #1514 #1517]: #1518
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-#1490 := (or #1479 #1262)
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-#1432 := (or #1431 #1042)
-#1443 := (or #1432 #1193)
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-#1444 := (iff #1198 #1443)
-#1441 := (iff #1045 #1432)
-#1433 := (not #1432)
-#1436 := (not #1433)
-#1439 := (iff #1436 #1432)
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-#1445 := [monotonicity #1442]: #1444
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-#1389 := [rewrite]: #1388
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-#1130 := [nnf-neg #992 #1071 #1074 #1077 #1080 #1083 #1086 #1089 #1092 #1126]: #1129
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-#1059 := [nnf-neg #1037 #1053]: #1058
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-#1063 := [nnf-neg #1019 #1059]: #1062
-#1012 := (~ #1011 #1011)
-#1013 := [refl]: #1012
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-#1154 := [nnf-neg #1067 #1150]: #1153
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-#989 := [refl]: #988
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-#986 := [refl]: #985
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-#981 := [nnf-pos #979]: #980
-#984 := [nnf-neg #981]: #983
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-#974 := (~ #628 #973)
-#975 := [sk]: #974
-#1169 := [nnf-neg #975 #1166]: #1168
-#958 := [not-or-elim #954]: #957
-#1170 := [mp~ #958 #1169]: #1167
-#1171 := [mp #1170 #1326]: #1324
-#1601 := [mp #1171 #1600]: #1598
-#2181 := [mp #1601 #2180]: #2178
-#1676 := [unit-resolution #2181 #1868]: #2175
-#1946 := (or #2172 #2166)
-#1947 := [def-axiom]: #1946
-#1672 := [unit-resolution #1947 #1676]: #2166
-#1668 := (or #2169 #2163)
-#1666 := (iff #13 #28)
-#1677 := (iff #28 #13)
-#1664 := [commutativity]: #1677
-#1667 := [symm #1664]: #1666