removed obsolete HOL-Boogie session;
authorboehmes
Tue Jul 23 18:36:23 2013 +0200 (2013-07-23)
changeset 527222c81f7baf8c4
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
     1.1 --- a/src/HOL/Boogie/Boogie.thy	Tue Jul 23 13:14:14 2013 +0200
     1.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.3 @@ -1,104 +0,0 @@
     1.4 -(*  Title:      HOL/Boogie/Boogie.thy
     1.5 -    Author:     Sascha Boehme, TU Muenchen
     1.6 -*)
     1.7 -
     1.8 -header {* Integration of the Boogie program verifier *}
     1.9 -
    1.10 -theory Boogie
    1.11 -imports Word
    1.12 -keywords
    1.13 -  "boogie_open" :: thy_load and
    1.14 -  "boogie_end" :: thy_decl and
    1.15 -  "boogie_vc" :: thy_goal and
    1.16 -  "boogie_status" :: diag
    1.17 -begin
    1.18 -
    1.19 -text {*
    1.20 -HOL-Boogie and its applications are described in:
    1.21 -\begin{itemize}
    1.22 -
    1.23 -\item Sascha B"ohme, K. Rustan M. Leino, and Burkhart Wolff.
    1.24 -HOL-Boogie --- An Interactive Prover for the Boogie Program-Verifier.
    1.25 -Theorem Proving in Higher Order Logics, 2008.
    1.26 -
    1.27 -\item Sascha B"ohme, Micha{\l} Moskal, Wolfram Schulte, and Burkhart Wolff.
    1.28 -HOL-Boogie --- An Interactive Prover-Backend for the Verifying C Compiler.
    1.29 -Journal of Automated Reasoning, 2009.
    1.30 -
    1.31 -\end{itemize}
    1.32 -*}
    1.33 -
    1.34 -
    1.35 -
    1.36 -section {* Built-in types and functions of Boogie *}
    1.37 -
    1.38 -subsection {* Labels *}
    1.39 -
    1.40 -text {*
    1.41 -See "Generating error traces from verification-condition counterexamples"
    1.42 -by Leino e.a. (2004) for a description of Boogie's labelling mechanism and
    1.43 -semantics.
    1.44 -*}
    1.45 -
    1.46 -definition assert_at :: "bool \<Rightarrow> bool \<Rightarrow> bool" where "assert_at l P = P"
    1.47 -definition block_at :: "bool \<Rightarrow> bool \<Rightarrow> bool" where "block_at l P = P"
    1.48 -
    1.49 -lemmas labels = assert_at_def block_at_def
    1.50 -
    1.51 -
    1.52 -subsection {* Integer arithmetics *}
    1.53 -
    1.54 -text {*
    1.55 -The operations @{text div} and @{text mod} are built-in in Boogie, but
    1.56 -without a particular semantics due to different interpretations in
    1.57 -programming languages. We assume that each application comes with a
    1.58 -proper axiomatization.
    1.59 -*}
    1.60 -
    1.61 -axiomatization
    1.62 -  boogie_div :: "int \<Rightarrow> int \<Rightarrow> int" (infixl "div'_b" 70) and
    1.63 -  boogie_mod :: "int \<Rightarrow> int \<Rightarrow> int" (infixl "mod'_b" 70)
    1.64 -
    1.65 -
    1.66 -
    1.67 -section {* Boogie environment *}
    1.68 -
    1.69 -text {*
    1.70 -Proving Boogie-generated verification conditions happens inside
    1.71 -a Boogie environment:
    1.72 -
    1.73 -  boogie_open "b2i file with extension"
    1.74 -  boogie_vc "verification condition 1" ...
    1.75 -  boogie_vc "verification condition 2" ...
    1.76 -  boogie_vc "verification condition 3" ...
    1.77 -  boogie_end
    1.78 -
    1.79 -See the Boogie examples for more details.
    1.80 - 
    1.81 -At most one Boogie environment should occur per theory,
    1.82 -otherwise unexpected effects may arise.
    1.83 -*}
    1.84 -
    1.85 -
    1.86 -
    1.87 -section {* Setup *}
    1.88 -
    1.89 -ML {*
    1.90 -structure Boogie_Axioms = Named_Thms
    1.91 -(
    1.92 -  val name = @{binding boogie}
    1.93 -  val description =
    1.94 -    "Boogie background axioms loaded along with Boogie verification conditions"
    1.95 -)
    1.96 -*}
    1.97 -setup Boogie_Axioms.setup
    1.98 -
    1.99 -ML_file "Tools/boogie_vcs.ML"
   1.100 -ML_file "Tools/boogie_loader.ML"
   1.101 -ML_file "Tools/boogie_tactics.ML"
   1.102 -setup Boogie_Tactics.setup
   1.103 -
   1.104 -ML_file "Tools/boogie_commands.ML"
   1.105 -setup Boogie_Commands.setup
   1.106 -
   1.107 -end
     2.1 --- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.b2i	Tue Jul 23 13:14:14 2013 +0200
     2.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     2.3 @@ -1,1879 +0,0 @@
     2.4 -type-decl Vertex 0 0
     2.5 -fun-decl G 1 0
     2.6 -    array 3
     2.7 -      type-con Vertex 0
     2.8 -      type-con Vertex 0
     2.9 -      int
    2.10 -fun-decl Infinity 1 0
    2.11 -    int
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    2.14 -axiom 0
    2.15 -    forall 2 0 3
    2.16 -      var x
    2.17 -        type-con Vertex 0
    2.18 -      var y
    2.19 -        type-con Vertex 0
    2.20 -      attribute qid 1
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    2.24 -      attribute bvZ3Native 1
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    2.26 -    implies
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    2.33 -    <
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    2.41 -axiom 0
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    2.45 -      var y
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    2.48 -        string-attr BoogieDi.4:15
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    2.59 -    =
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    2.70 -    fun Infinity 0
    2.71 -var-decl SP 0
    2.72 -    array 2
    2.73 -      type-con Vertex 0
    2.74 -      int
    2.75 -vc Dijkstra 1
    2.76 -    implies
    2.77 -    label pos 26 3
    2.78 -    true
    2.79 -    implies
    2.80 -    true
    2.81 -    implies
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    2.83 -      var x
    2.84 -        type-con Vertex 0
    2.85 -      attribute qid 1
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    2.90 -        string-attr False
    2.91 -    implies
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    2.94 -      type-con Vertex 0
    2.95 -    fun Source 0
    2.96 -    =
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   2.100 -        type-con Vertex 0
   2.101 -        int
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   2.109 -      attribute qid 1
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   2.115 -    implies
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   2.151 -    label neg 34 5
   2.152 -    =
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   2.233 -      array 2
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   2.235 -        bool
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   2.238 -    <=
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   2.250 -        int
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   2.258 -        type-con Vertex 0
   2.259 -      attribute qid 1
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   2.265 -    implies
   2.266 -    and 2
   2.267 -    not
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   2.270 -      array 2
   2.271 -        type-con Vertex 0
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   2.281 -      type-con Vertex 0
   2.282 -    <=
   2.283 -    select 2
   2.284 -    var SP@0
   2.285 -      array 2
   2.286 -        type-con Vertex 0
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   2.293 -        type-con Vertex 0
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   2.304 -      attribute qid 1
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   2.314 -      array 2
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   2.316 -        bool
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   2.318 -      type-con Vertex 0
   2.319 -    <
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   2.330 -      array 2
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   2.370 -    <
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   2.377 -    fun Infinity 0
   2.378 -    <=
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   2.381 -      array 2
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   2.418 -    <
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   2.449 -        int
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   2.456 -        bool
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   2.459 -    =
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   2.464 -        int
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   2.510 -      attribute qid 1
   2.511 -        string-attr BoogieDi.41:15
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  2.1095 -        int
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  2.1106 -    =
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  2.1110 -        type-con Vertex 0
  2.1111 -        int
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  2.1114 -    implies
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  2.1120 -        int
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  2.1123 -    true
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  2.1125 -    label pos 44 5
  2.1126 -    true
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  2.1128 -    true
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  2.1137 -      attribute bvZ3Native 1
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  2.1139 -    and 2
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  2.1153 -        int
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  2.1168 -    select 2
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  2.1178 -      var x
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  2.1200 -        int
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  2.1226 -      var u
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  2.1228 -      attribute qid 1
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  2.1234 -    implies
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  2.1236 -    <
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  2.1250 -        int
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  2.1638 -    <
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  2.1680 -    implies
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  2.1702 -        int
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  2.1841 -        int
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  2.1852 -    var Visited@2
  2.1853 -      array 2
  2.1854 -        type-con Vertex 0
  2.1855 -        bool
  2.1856 -    var y
  2.1857 -      type-con Vertex 0
  2.1858 -    =
  2.1859 -    select 2
  2.1860 -    var SP@2
  2.1861 -      array 2
  2.1862 -        type-con Vertex 0
  2.1863 -        int
  2.1864 -    var z
  2.1865 -      type-con Vertex 0
  2.1866 -    +
  2.1867 -    select 2
  2.1868 -    var SP@2
  2.1869 -      array 2
  2.1870 -        type-con Vertex 0
  2.1871 -        int
  2.1872 -    var y
  2.1873 -      type-con Vertex 0
  2.1874 -    select 3
  2.1875 -    fun G 0
  2.1876 -    var y
  2.1877 -      type-con Vertex 0
  2.1878 -    var z
  2.1879 -      type-con Vertex 0
  2.1880 -    implies
  2.1881 -    false
  2.1882 -    true
     3.1 --- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Tue Jul 23 13:14:14 2013 +0200
     3.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     3.3 @@ -1,6048 +0,0 @@
     3.4 -a549accb56a0340bea4e867d66fdfbbac187f40c 6047 0
     3.5 -#2 := false
     3.6 -#7 := 0::Int
     3.7 -decl f30 :: (-> S2 Int)
     3.8 -decl ?v1!7 :: (-> S2 S2)
     3.9 -decl ?v0!20 :: S2
    3.10 -#2034 := ?v0!20
    3.11 -#5342 := (?v1!7 ?v0!20)
    3.12 -#13325 := (f30 #5342)
    3.13 -#923 := -1::Int
    3.14 -#13327 := (* -1::Int #13325)
    3.15 -decl f4 :: (-> S3 Int)
    3.16 -decl f5 :: (-> S4 S2 S3)
    3.17 -decl f6 :: (-> S5 S2 S4)
    3.18 -decl f7 :: S5
    3.19 -#13 := f7
    3.20 -#5350 := (f6 f7 #5342)
    3.21 -#5351 := (f5 #5350 ?v0!20)
    3.22 -#5352 := (f4 #5351)
    3.23 -#5353 := (* -1::Int #5352)
    3.24 -#14209 := (+ #5353 #13327)
    3.25 -#2037 := (f30 ?v0!20)
    3.26 -#14210 := (+ #2037 #14209)
    3.27 -#18243 := (>= #14210 0::Int)
    3.28 -decl f19 :: (-> S11 S2 Int)
    3.29 -decl f20 :: S11
    3.30 -#109 := f20
    3.31 -#5343 := (f19 f20 #5342)
    3.32 -#5344 := (* -1::Int #5343)
    3.33 -#5354 := (+ #5344 #5353)
    3.34 -#5080 := (f19 f20 ?v0!20)
    3.35 -#5355 := (+ #5080 #5354)
    3.36 -#15530 := (>= #5355 0::Int)
    3.37 -#5356 := (= #5355 0::Int)
    3.38 -#5357 := (not #5356)
    3.39 -decl f1 :: S1
    3.40 -#3 := f1
    3.41 -decl f11 :: (-> S7 S2 S1)
    3.42 -decl f21 :: S7
    3.43 -#115 := f21
    3.44 -#5347 := (f11 f21 #5342)
    3.45 -#5348 := (= #5347 f1)
    3.46 -#5349 := (not #5348)
    3.47 -#5345 := (+ #5080 #5344)
    3.48 -#5346 := (<= #5345 0::Int)
    3.49 -#5358 := (or #5346 #5349 #5357)
    3.50 -#5359 := (not #5358)
    3.51 -#5105 := (* -1::Int #5080)
    3.52 -decl f3 :: Int
    3.53 -#8 := f3
    3.54 -#5340 := (+ f3 #5105)
    3.55 -#5341 := (<= #5340 0::Int)
    3.56 -#15968 := (not #5341)
    3.57 -#5106 := (+ #2037 #5105)
    3.58 -#12022 := (>= #5106 0::Int)
    3.59 -#5087 := (= #2037 #5080)
    3.60 -decl f28 :: S2
    3.61 -#181 := f28
    3.62 -#195 := (f6 f7 f28)
    3.63 -#5121 := (f5 #195 ?v0!20)
    3.64 -#5122 := (f4 #5121)
    3.65 -#5139 := (+ #5105 #5122)
    3.66 -#185 := (f19 f20 f28)
    3.67 -#5140 := (+ #185 #5139)
    3.68 -#5141 := (>= #5140 0::Int)
    3.69 -#5123 := (* -1::Int #5122)
    3.70 -#5124 := (+ f3 #5123)
    3.71 -#5125 := (<= #5124 0::Int)
    3.72 -#5146 := (or #5125 #5141)
    3.73 -#2038 := (* -1::Int #2037)
    3.74 -#5178 := (+ #2038 #5122)
    3.75 -#5179 := (+ #185 #5178)
    3.76 -#5182 := (= #5179 0::Int)
    3.77 -#15374 := (not #5182)
    3.78 -#12121 := (<= #5179 0::Int)
    3.79 -#15379 := (not #12121)
    3.80 -#4078 := (f30 f28)
    3.81 -#4079 := (* -1::Int #4078)
    3.82 -#5068 := (+ #2037 #4079)
    3.83 -#5229 := (<= #5068 0::Int)
    3.84 -#15402 := (not #5229)
    3.85 -#15340 := (<= #5122 0::Int)
    3.86 -#15358 := (not #15340)
    3.87 -#15327 := (= f28 ?v0!20)
    3.88 -#15368 := (not #15327)
    3.89 -#9945 := (= ?v0!20 f28)
    3.90 -#16393 := [hypothesis]: #15327
    3.91 -#16394 := [symm #16393]: #9945
    3.92 -#9687 := (not #9945)
    3.93 -#5309 := (f11 f21 ?v0!20)
    3.94 -#5310 := (= #5309 f1)
    3.95 -#9951 := (or #9945 #5310)
    3.96 -#9685 := (not #9951)
    3.97 -decl f12 :: (-> S8 S1 S7)
    3.98 -decl f13 :: (-> S9 S2 S8)
    3.99 -decl f14 :: (-> S10 S7 S9)
   3.100 -decl f15 :: S10
   3.101 -#39 := f15
   3.102 -#191 := (f14 f15 f21)
   3.103 -#192 := (f13 #191 f28)
   3.104 -#193 := (f12 #192 f1)
   3.105 -#9943 := (f11 #193 ?v0!20)
   3.106 -#9944 := (= #9943 f1)
   3.107 -#9956 := (iff #9944 #9951)
   3.108 -#11 := (:var 0 S2)
   3.109 -#54 := (:var 1 S1)
   3.110 -#52 := (:var 2 S2)
   3.111 -#50 := (:var 3 S7)
   3.112 -#51 := (f14 f15 #50)
   3.113 -#53 := (f13 #51 #52)
   3.114 -#55 := (f12 #53 #54)
   3.115 -#56 := (f11 #55 #11)
   3.116 -#3640 := (pattern #56)
   3.117 -#60 := (f11 #50 #11)
   3.118 -#61 := (= #60 f1)
   3.119 -#59 := (= #54 f1)
   3.120 -#58 := (= #11 #52)
   3.121 -#62 := (if #58 #59 #61)
   3.122 -#57 := (= #56 f1)
   3.123 -#63 := (iff #57 #62)
   3.124 -#3641 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #3640) #63)
   3.125 -#64 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) #63)
   3.126 -#3644 := (iff #64 #3641)
   3.127 -#3642 := (iff #63 #63)
   3.128 -#3643 := [refl]: #3642
   3.129 -#3645 := [quant-intro #3643]: #3644
   3.130 -#1496 := (~ #64 #64)
   3.131 -#1524 := (~ #63 #63)
   3.132 -#1525 := [refl]: #1524
   3.133 -#1497 := [nnf-pos #1525]: #1496
   3.134 -#342 := [asserted]: #64
   3.135 -#1526 := [mp~ #342 #1497]: #64
   3.136 -#3646 := [mp #1526 #3645]: #3641
   3.137 -#7518 := (not #3641)
   3.138 -#9763 := (or #7518 #9956)
   3.139 -#4057 := (= f1 f1)
   3.140 -#9946 := (if #9945 #4057 #5310)
   3.141 -#9947 := (iff #9944 #9946)
   3.142 -#9775 := (or #7518 #9947)
   3.143 -#9715 := (iff #9775 #9763)
   3.144 -#9722 := (iff #9763 #9763)
   3.145 -#9724 := [rewrite]: #9722
   3.146 -#9957 := (iff #9947 #9956)
   3.147 -#9954 := (iff #9946 #9951)
   3.148 -#1 := true
   3.149 -#9948 := (if #9945 true #5310)
   3.150 -#9952 := (iff #9948 #9951)
   3.151 -#9953 := [rewrite]: #9952
   3.152 -#9949 := (iff #9946 #9948)
   3.153 -#4059 := (iff #4057 true)
   3.154 -#4060 := [rewrite]: #4059
   3.155 -#9950 := [monotonicity #4060]: #9949
   3.156 -#9955 := [trans #9950 #9953]: #9954
   3.157 -#9958 := [monotonicity #9955]: #9957
   3.158 -#9706 := [monotonicity #9958]: #9715
   3.159 -#9734 := [trans #9706 #9724]: #9715
   3.160 -#9776 := [quant-inst #115 #181 #3 #2034]: #9775
   3.161 -#9519 := [mp #9776 #9734]: #9763
   3.162 -#16374 := [unit-resolution #9519 #3646]: #9956
   3.163 -#9410 := (not #9944)
   3.164 -decl f29 :: S7
   3.165 -#190 := f29
   3.166 -#4533 := (f11 f29 ?v0!20)
   3.167 -#4534 := (= #4533 f1)
   3.168 -#4541 := (not #4534)
   3.169 -#16390 := (iff #4541 #9410)
   3.170 -#16382 := (iff #4534 #9944)
   3.171 -#16359 := (iff #9944 #4534)
   3.172 -#16289 := (= #9943 #4533)
   3.173 -#8145 := (= #193 f29)
   3.174 -#194 := (= f29 #193)
   3.175 -#91 := (f6 f7 #11)
   3.176 -#3693 := (pattern #91)
   3.177 -#212 := (f11 f29 #11)
   3.178 -#3854 := (pattern #212)
   3.179 -#202 := (f30 #11)
   3.180 -#3829 := (pattern #202)
   3.181 -#2047 := (f5 #91 ?v0!20)
   3.182 -#2048 := (f4 #2047)
   3.183 -#2383 := (+ #2038 #2048)
   3.184 -#2384 := (+ #202 #2383)
   3.185 -#2387 := (= #2384 0::Int)
   3.186 -#2941 := (not #2387)
   3.187 -#213 := (= #212 f1)
   3.188 -#220 := (not #213)
   3.189 -#2044 := (+ #202 #2038)
   3.190 -#2045 := (>= #2044 0::Int)
   3.191 -#2942 := (or #2045 #220 #2941)
   3.192 -#3888 := (forall (vars (?v1 S2)) (:pat #3829 #3854 #3693) #2942)
   3.193 -#3893 := (not #3888)
   3.194 -#2039 := (+ f3 #2038)
   3.195 -#2040 := (<= #2039 0::Int)
   3.196 -decl f16 :: S2
   3.197 -#65 := f16
   3.198 -#2035 := (= ?v0!20 f16)
   3.199 -#10 := (:var 1 S2)
   3.200 -#92 := (f5 #91 #10)
   3.201 -#3684 := (pattern #92)
   3.202 -#224 := (f30 #10)
   3.203 -#1186 := (* -1::Int #224)
   3.204 -#1187 := (+ #202 #1186)
   3.205 -#93 := (f4 #92)
   3.206 -#1207 := (+ #93 #1187)
   3.207 -#1205 := (>= #1207 0::Int)
   3.208 -#938 := (* -1::Int #93)
   3.209 -#939 := (+ f3 #938)
   3.210 -#940 := (<= #939 0::Int)
   3.211 -#2933 := (or #220 #940 #1205)
   3.212 -#3880 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2933)
   3.213 -#3885 := (not #3880)
   3.214 -#3896 := (or #3885 #2035 #2040 #3893)
   3.215 -#3899 := (not #3896)
   3.216 -decl ?v0!19 :: S2
   3.217 -#2003 := ?v0!19
   3.218 -#2016 := (f30 ?v0!19)
   3.219 -#2017 := (* -1::Int #2016)
   3.220 -decl ?v1!18 :: S2
   3.221 -#2002 := ?v1!18
   3.222 -#2015 := (f30 ?v1!18)
   3.223 -#2018 := (+ #2015 #2017)
   3.224 -#2006 := (f6 f7 ?v1!18)
   3.225 -#2007 := (f5 #2006 ?v0!19)
   3.226 -#2008 := (f4 #2007)
   3.227 -#2019 := (+ #2008 #2018)
   3.228 -#2020 := (>= #2019 0::Int)
   3.229 -#2009 := (* -1::Int #2008)
   3.230 -#2010 := (+ f3 #2009)
   3.231 -#2011 := (<= #2010 0::Int)
   3.232 -#2004 := (f11 f29 ?v1!18)
   3.233 -#2005 := (= #2004 f1)
   3.234 -#2896 := (not #2005)
   3.235 -#2911 := (or #2896 #2011 #2020)
   3.236 -#2916 := (not #2911)
   3.237 -#3902 := (or #2916 #3899)
   3.238 -#3905 := (not #3902)
   3.239 -#3871 := (pattern #202 #224)
   3.240 -#1185 := (>= #1187 0::Int)
   3.241 -#221 := (f11 f29 #10)
   3.242 -#222 := (= #221 f1)
   3.243 -#2873 := (not #222)
   3.244 -#2888 := (or #213 #2873 #1185)
   3.245 -#3872 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3871) #2888)
   3.246 -#3877 := (not #3872)
   3.247 -#3908 := (or #3877 #3905)
   3.248 -#3911 := (not #3908)
   3.249 -decl ?v0!17 :: S2
   3.250 -#1976 := ?v0!17
   3.251 -#1985 := (f30 ?v0!17)
   3.252 -#1986 := (* -1::Int #1985)
   3.253 -decl ?v1!16 :: S2
   3.254 -#1975 := ?v1!16
   3.255 -#1984 := (f30 ?v1!16)
   3.256 -#1987 := (+ #1984 #1986)
   3.257 -#1988 := (>= #1987 0::Int)
   3.258 -#1980 := (f11 f29 ?v0!17)
   3.259 -#1981 := (= #1980 f1)
   3.260 -#2850 := (not #1981)
   3.261 -#1977 := (f11 f29 ?v1!16)
   3.262 -#1978 := (= #1977 f1)
   3.263 -#2865 := (or #1978 #2850 #1988)
   3.264 -#2870 := (not #2865)
   3.265 -#3914 := (or #2870 #3911)
   3.266 -#3917 := (not #3914)
   3.267 -#1176 := (>= #202 0::Int)
   3.268 -#3863 := (forall (vars (?v0 S2)) (:pat #3829) #1176)
   3.269 -#3868 := (not #3863)
   3.270 -#3920 := (or #3868 #3917)
   3.271 -#3923 := (not #3920)
   3.272 -decl ?v0!15 :: S2
   3.273 -#1960 := ?v0!15
   3.274 -#1961 := (f30 ?v0!15)
   3.275 -#1962 := (>= #1961 0::Int)
   3.276 -#1963 := (not #1962)
   3.277 -#3926 := (or #1963 #3923)
   3.278 -#3929 := (not #3926)
   3.279 -#216 := (f30 f16)
   3.280 -#217 := (= #216 0::Int)
   3.281 -#661 := (not #217)
   3.282 -#3932 := (or #661 #3929)
   3.283 -#3935 := (not #3932)
   3.284 -#3938 := (or #661 #3935)
   3.285 -#3941 := (not #3938)
   3.286 -#112 := (f19 f20 #11)
   3.287 -#3716 := (pattern #112)
   3.288 -#207 := (= #202 #112)
   3.289 -#560 := (or #220 #207)
   3.290 -#3855 := (forall (vars (?v0 S2)) (:pat #3854 #3829 #3716) #560)
   3.291 -#3860 := (not #3855)
   3.292 -#3944 := (or #3860 #3941)
   3.293 -#3947 := (not #3944)
   3.294 -decl ?v0!14 :: S2
   3.295 -#1935 := ?v0!14
   3.296 -#1940 := (f19 f20 ?v0!14)
   3.297 -#1939 := (f30 ?v0!14)
   3.298 -#1941 := (= #1939 #1940)
   3.299 -#1936 := (f11 f29 ?v0!14)
   3.300 -#1937 := (= #1936 f1)
   3.301 -#1938 := (not #1937)
   3.302 -#1942 := (or #1938 #1941)
   3.303 -#1943 := (not #1942)
   3.304 -#3950 := (or #1943 #3947)
   3.305 -#3953 := (not #3950)
   3.306 -#1166 := (* -1::Int #202)
   3.307 -#1167 := (+ #112 #1166)
   3.308 -#1165 := (>= #1167 0::Int)
   3.309 -#3846 := (forall (vars (?v0 S2)) (:pat #3716 #3829) #1165)
   3.310 -#3851 := (not #3846)
   3.311 -#3956 := (or #3851 #3953)
   3.312 -#3959 := (not #3956)
   3.313 -decl ?v0!13 :: S2
   3.314 -#1917 := ?v0!13
   3.315 -#1919 := (f30 ?v0!13)
   3.316 -#1920 := (* -1::Int #1919)
   3.317 -#1918 := (f19 f20 ?v0!13)
   3.318 -#1921 := (+ #1918 #1920)
   3.319 -#1922 := (>= #1921 0::Int)
   3.320 -#1923 := (not #1922)
   3.321 -#3962 := (or #1923 #3959)
   3.322 -#3965 := (not #3962)
   3.323 -#196 := (f5 #195 #11)
   3.324 -#3828 := (pattern #196)
   3.325 -#197 := (f4 #196)
   3.326 -#1140 := (* -1::Int #197)
   3.327 -#1146 := (* -1::Int #185)
   3.328 -#1147 := (+ #1146 #1140)
   3.329 -#1148 := (+ #112 #1147)
   3.330 -#1149 := (<= #1148 0::Int)
   3.331 -#1141 := (+ f3 #1140)
   3.332 -#1142 := (<= #1141 0::Int)
   3.333 -#2822 := (or #1142 #1149)
   3.334 -#2823 := (not #2822)
   3.335 -#2844 := (or #2823 #207)
   3.336 -#3838 := (forall (vars (?v0 S2)) (:pat #3828 #3716 #3829) #2844)
   3.337 -#3843 := (not #3838)
   3.338 -#1296 := (+ #197 #1166)
   3.339 -#1297 := (+ #185 #1296)
   3.340 -#1294 := (= #1297 0::Int)
   3.341 -#2836 := (or #1142 #1149 #1294)
   3.342 -#3830 := (forall (vars (?v0 S2)) (:pat #3828 #3716 #3829) #2836)
   3.343 -#3835 := (not #3830)
   3.344 -#715 := (not #194)
   3.345 -#116 := (f11 f21 #11)
   3.346 -#3750 := (pattern #116)
   3.347 -#1309 := (+ #112 #1146)
   3.348 -#1308 := (>= #1309 0::Int)
   3.349 -#117 := (= #116 f1)
   3.350 -#1312 := (or #117 #1308)
   3.351 -#3820 := (forall (vars (?v0 S2)) (:pat #3750 #3716) #1312)
   3.352 -#3825 := (not #3820)
   3.353 -#1321 := (+ f3 #1146)
   3.354 -#1322 := (<= #1321 0::Int)
   3.355 -#182 := (f11 f21 f28)
   3.356 -#183 := (= #182 f1)
   3.357 -decl ?v0!12 :: S2
   3.358 -#1872 := ?v0!12
   3.359 -#1876 := (f19 f20 ?v0!12)
   3.360 -#1877 := (* -1::Int #1876)
   3.361 -#1878 := (+ f3 #1877)
   3.362 -#1879 := (<= #1878 0::Int)
   3.363 -#1873 := (f11 f21 ?v0!12)
   3.364 -#1874 := (= #1873 f1)
   3.365 -#3968 := (or #1874 #1879 #183 #1322 #3825 #715 #3835 #3843 #3965)
   3.366 -#3971 := (not #3968)
   3.367 -decl f25 :: S11
   3.368 -#148 := f25
   3.369 -#168 := (f19 f25 f16)
   3.370 -#169 := (= #168 0::Int)
   3.371 -#156 := (f19 f25 #10)
   3.372 -#1060 := (* -1::Int #156)
   3.373 -#153 := (f19 f25 #11)
   3.374 -#1061 := (+ #153 #1060)
   3.375 -#1067 := (+ #93 #1061)
   3.376 -#1090 := (>= #1067 0::Int)
   3.377 -#1047 := (* -1::Int #153)
   3.378 -#1048 := (+ f3 #1047)
   3.379 -#1049 := (<= #1048 0::Int)
   3.380 -#2776 := (or #1049 #940 #1090)
   3.381 -#3782 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2776)
   3.382 -#3787 := (not #3782)
   3.383 -#3790 := (or #3787 #169)
   3.384 -#3793 := (not #3790)
   3.385 -decl ?v0!11 :: S2
   3.386 -#1816 := ?v0!11
   3.387 -#1831 := (f19 f25 ?v0!11)
   3.388 -#1832 := (* -1::Int #1831)
   3.389 -decl ?v1!10 :: S2
   3.390 -#1815 := ?v1!10
   3.391 -#1822 := (f6 f7 ?v1!10)
   3.392 -#1823 := (f5 #1822 ?v0!11)
   3.393 -#1824 := (f4 #1823)
   3.394 -#2352 := (+ #1824 #1832)
   3.395 -#1817 := (f19 f25 ?v1!10)
   3.396 -#2353 := (+ #1817 #2352)
   3.397 -#2356 := (>= #2353 0::Int)
   3.398 -#1825 := (* -1::Int #1824)
   3.399 -#1826 := (+ f3 #1825)
   3.400 -#1827 := (<= #1826 0::Int)
   3.401 -#1818 := (* -1::Int #1817)
   3.402 -#1819 := (+ f3 #1818)
   3.403 -#1820 := (<= #1819 0::Int)
   3.404 -#2754 := (or #1820 #1827 #2356)
   3.405 -#2759 := (not #2754)
   3.406 -#3796 := (or #2759 #3793)
   3.407 -#3799 := (not #3796)
   3.408 -#3759 := (pattern #153)
   3.409 -decl ?v1!9 :: (-> S2 S2)
   3.410 -#1791 := (?v1!9 #11)
   3.411 -#1796 := (f6 f7 #1791)
   3.412 -#1797 := (f5 #1796 #11)
   3.413 -#1798 := (f4 #1797)
   3.414 -#2335 := (* -1::Int #1798)
   3.415 -#1792 := (f19 f25 #1791)
   3.416 -#2318 := (* -1::Int #1792)
   3.417 -#2336 := (+ #2318 #2335)
   3.418 -#2337 := (+ #153 #2336)
   3.419 -#2338 := (= #2337 0::Int)
   3.420 -#2724 := (not #2338)
   3.421 -#2319 := (+ #153 #2318)
   3.422 -#2320 := (<= #2319 0::Int)
   3.423 -#2725 := (or #2320 #2724)
   3.424 -#2726 := (not #2725)
   3.425 -#66 := (= #11 f16)
   3.426 -#2732 := (or #66 #1049 #2726)
   3.427 -#3774 := (forall (vars (?v0 S2)) (:pat #3759) #2732)
   3.428 -#3779 := (not #3774)
   3.429 -#3802 := (or #3779 #3799)
   3.430 -#3805 := (not #3802)
   3.431 -decl ?v0!8 :: S2
   3.432 -#1751 := ?v0!8
   3.433 -#1764 := (f5 #91 ?v0!8)
   3.434 -#1765 := (f4 #1764)
   3.435 -#1754 := (f19 f25 ?v0!8)
   3.436 -#1755 := (* -1::Int #1754)
   3.437 -#2288 := (+ #1755 #1765)
   3.438 -#2289 := (+ #153 #2288)
   3.439 -#2292 := (= #2289 0::Int)
   3.440 -#2688 := (not #2292)
   3.441 -#1761 := (+ #153 #1755)
   3.442 -#1762 := (>= #1761 0::Int)
   3.443 -#2689 := (or #1762 #2688)
   3.444 -#3760 := (forall (vars (?v1 S2)) (:pat #3759 #3693) #2689)
   3.445 -#3765 := (not #3760)
   3.446 -#1756 := (+ f3 #1755)
   3.447 -#1757 := (<= #1756 0::Int)
   3.448 -#1752 := (= ?v0!8 f16)
   3.449 -#3768 := (or #1752 #1757 #3765)
   3.450 -#3771 := (not #3768)
   3.451 -#3808 := (or #3771 #3805)
   3.452 -#3811 := (not #3808)
   3.453 -decl f27 :: S11
   3.454 -#151 := f27
   3.455 -decl f26 :: S11
   3.456 -#150 := f26
   3.457 -#152 := (= f26 f27)
   3.458 -#494 := (not #152)
   3.459 -#149 := (= f25 f20)
   3.460 -#503 := (not #149)
   3.461 -decl f24 :: S2
   3.462 -#146 := f24
   3.463 -decl f23 :: S2
   3.464 -#145 := f23
   3.465 -#147 := (= f23 f24)
   3.466 -#512 := (not #147)
   3.467 -decl f22 :: S7
   3.468 -#143 := f22
   3.469 -#144 := (= f22 f21)
   3.470 -#521 := (not #144)
   3.471 -#1002 := (* -1::Int #112)
   3.472 -#1003 := (+ f3 #1002)
   3.473 -#1004 := (<= #1003 0::Int)
   3.474 -#2674 := (or #117 #1004)
   3.475 -#3751 := (forall (vars (?v0 S2)) (:pat #3750 #3716) #2674)
   3.476 -#3756 := (not #3751)
   3.477 -#3814 := (or #3756 #521 #512 #503 #494 #3811)
   3.478 -#3817 := (not #3814)
   3.479 -#3974 := (or #3817 #3971)
   3.480 -#3977 := (not #3974)
   3.481 -#1707 := (?v1!7 #11)
   3.482 -#1714 := (f6 f7 #1707)
   3.483 -#1715 := (f5 #1714 #11)
   3.484 -#1716 := (f4 #1715)
   3.485 -#2261 := (* -1::Int #1716)
   3.486 -#1708 := (f19 f20 #1707)
   3.487 -#2244 := (* -1::Int #1708)
   3.488 -#2262 := (+ #2244 #2261)
   3.489 -#2263 := (+ #112 #2262)
   3.490 -#2264 := (= #2263 0::Int)
   3.491 -#2658 := (not #2264)
   3.492 -#1712 := (f11 f21 #1707)
   3.493 -#1713 := (= #1712 f1)
   3.494 -#2657 := (not #1713)
   3.495 -#2245 := (+ #112 #2244)
   3.496 -#2246 := (<= #2245 0::Int)
   3.497 -#2659 := (or #2246 #2657 #2658)
   3.498 -#2660 := (not #2659)
   3.499 -#2666 := (or #66 #1004 #2660)
   3.500 -#3742 := (forall (vars (?v0 S2)) (:pat #3716) #2666)
   3.501 -#3747 := (not #3742)
   3.502 -#122 := (f19 f20 #10)
   3.503 -#1016 := (* -1::Int #122)
   3.504 -#1017 := (+ #112 #1016)
   3.505 -#1018 := (+ #93 #1017)
   3.506 -#1371 := (>= #1018 0::Int)
   3.507 -#118 := (not #117)
   3.508 -#2638 := (or #118 #940 #1371)
   3.509 -#3734 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2638)
   3.510 -#3739 := (not #3734)
   3.511 -#119 := (f11 f21 #10)
   3.512 -#3725 := (pattern #116 #119)
   3.513 -#1020 := (>= #1017 0::Int)
   3.514 -#120 := (= #119 f1)
   3.515 -#2601 := (not #120)
   3.516 -#2616 := (or #117 #2601 #1020)
   3.517 -#3726 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3725) #2616)
   3.518 -#3731 := (not #3726)
   3.519 -#1394 := (>= #112 0::Int)
   3.520 -#3717 := (forall (vars (?v0 S2)) (:pat #3716) #1394)
   3.521 -#3722 := (not #3717)
   3.522 -#110 := (f19 f20 f16)
   3.523 -#111 := (= #110 0::Int)
   3.524 -#804 := (not #111)
   3.525 -decl f17 :: (-> S2 Int)
   3.526 -#67 := (f17 #11)
   3.527 -#3647 := (pattern #67)
   3.528 -decl ?v1!6 :: (-> S2 S2)
   3.529 -#1654 := (?v1!6 #11)
   3.530 -#1661 := (f6 f7 #1654)
   3.531 -#1662 := (f5 #1661 #11)
   3.532 -#1663 := (f4 #1662)
   3.533 -#2219 := (* -1::Int #1663)
   3.534 -#1655 := (f17 #1654)
   3.535 -#2202 := (* -1::Int #1655)
   3.536 -#2220 := (+ #2202 #2219)
   3.537 -#2221 := (+ #67 #2220)
   3.538 -#2222 := (= #2221 0::Int)
   3.539 -#2585 := (not #2222)
   3.540 -decl f18 :: S7
   3.541 -#75 := f18
   3.542 -#1659 := (f11 f18 #1654)
   3.543 -#1660 := (= #1659 f1)
   3.544 -#2584 := (not #1660)
   3.545 -#2203 := (+ #67 #2202)
   3.546 -#2204 := (<= #2203 0::Int)
   3.547 -#2586 := (or #2204 #2584 #2585)
   3.548 -#2587 := (not #2586)
   3.549 -#964 := (* -1::Int #67)
   3.550 -#965 := (+ f3 #964)
   3.551 -#966 := (<= #965 0::Int)
   3.552 -#2593 := (or #66 #966 #2587)
   3.553 -#3708 := (forall (vars (?v0 S2)) (:pat #3647) #2593)
   3.554 -#3713 := (not #3708)
   3.555 -#3980 := (or #3713 #804 #3722 #3731 #3739 #3747 #3977)
   3.556 -#3983 := (not #3980)
   3.557 -#76 := (f11 f18 #11)
   3.558 -#3660 := (pattern #76)
   3.559 -decl ?v0!5 :: S2
   3.560 -#1613 := ?v0!5
   3.561 -#1626 := (f5 #91 ?v0!5)
   3.562 -#1627 := (f4 #1626)
   3.563 -#1616 := (f17 ?v0!5)
   3.564 -#1617 := (* -1::Int #1616)
   3.565 -#1628 := (+ #1617 #1627)
   3.566 -#1629 := (+ #67 #1628)
   3.567 -#1630 := (= #1629 0::Int)
   3.568 -#2548 := (not #1630)
   3.569 -#77 := (= #76 f1)
   3.570 -#78 := (not #77)
   3.571 -#1623 := (+ #67 #1617)
   3.572 -#1624 := (>= #1623 0::Int)
   3.573 -#2549 := (or #1624 #78 #2548)
   3.574 -#3694 := (forall (vars (?v1 S2)) (:pat #3647 #3660 #3693) #2549)
   3.575 -#3699 := (not #3694)
   3.576 -#1618 := (+ f3 #1617)
   3.577 -#1619 := (<= #1618 0::Int)
   3.578 -#1614 := (= ?v0!5 f16)
   3.579 -#3702 := (or #1614 #1619 #3699)
   3.580 -#6176 := (= f3 #1616)
   3.581 -#6574 := (= #1616 f3)
   3.582 -#6629 := (iff #6574 #6176)
   3.583 -#6627 := (iff #6176 #6574)
   3.584 -#6628 := [commutativity]: #6627
   3.585 -#6630 := [symm #6628]: #6629
   3.586 -#1615 := (not #1614)
   3.587 -#3705 := (not #3702)
   3.588 -#5790 := [hypothesis]: #3705
   3.589 -#3262 := (or #3702 #1615)
   3.590 -#3263 := [def-axiom]: #3262
   3.591 -#6625 := [unit-resolution #3263 #5790]: #1615
   3.592 -#72 := (= #67 f3)
   3.593 -#350 := (or #66 #72)
   3.594 -#3654 := (forall (vars (?v0 S2)) (:pat #3647) #350)
   3.595 -#353 := (forall (vars (?v0 S2)) #350)
   3.596 -#3657 := (iff #353 #3654)
   3.597 -#3655 := (iff #350 #350)
   3.598 -#3656 := [refl]: #3655
   3.599 -#3658 := [quant-intro #3656]: #3657
   3.600 -#1500 := (~ #353 #353)
   3.601 -#1530 := (~ #350 #350)
   3.602 -#1531 := [refl]: #1530
   3.603 -#1501 := [nnf-pos #1531]: #1500
   3.604 -#1229 := (= #1207 0::Int)
   3.605 -#1232 := (not #1185)
   3.606 -#1241 := (and #1232 #213 #1229)
   3.607 -#1246 := (exists (vars (?v1 S2)) #1241)
   3.608 -#1218 := (+ f3 #1166)
   3.609 -#1219 := (<= #1218 0::Int)
   3.610 -#1220 := (not #1219)
   3.611 -#71 := (not #66)
   3.612 -#1223 := (and #71 #1220)
   3.613 -#1226 := (not #1223)
   3.614 -#1249 := (or #1226 #1246)
   3.615 -#1252 := (forall (vars (?v0 S2)) #1249)
   3.616 -#941 := (not #940)
   3.617 -#1199 := (and #213 #941)
   3.618 -#1202 := (not #1199)
   3.619 -#1209 := (or #1202 #1205)
   3.620 -#1212 := (forall (vars (?v0 S2) (?v1 S2)) #1209)
   3.621 -#1215 := (not #1212)
   3.622 -#1255 := (or #1215 #1252)
   3.623 -#1258 := (and #1212 #1255)
   3.624 -#223 := (and #220 #222)
   3.625 -#566 := (not #223)
   3.626 -#1190 := (or #566 #1185)
   3.627 -#1193 := (forall (vars (?v0 S2) (?v1 S2)) #1190)
   3.628 -#1196 := (not #1193)
   3.629 -#1261 := (or #1196 #1258)
   3.630 -#1264 := (and #1193 #1261)
   3.631 -#1179 := (forall (vars (?v0 S2)) #1176)
   3.632 -#1182 := (not #1179)
   3.633 -#1267 := (or #1182 #1264)
   3.634 -#1270 := (and #1179 #1267)
   3.635 -#1273 := (or #661 #1270)
   3.636 -#1276 := (and #217 #1273)
   3.637 -#563 := (forall (vars (?v0 S2)) #560)
   3.638 -#673 := (not #563)
   3.639 -#1279 := (or #673 #1276)
   3.640 -#1282 := (and #563 #1279)
   3.641 -#1170 := (forall (vars (?v0 S2)) #1165)
   3.642 -#1173 := (not #1170)
   3.643 -#1285 := (or #1173 #1282)
   3.644 -#1288 := (and #1170 #1285)
   3.645 -#1150 := (not #1149)
   3.646 -#1143 := (not #1142)
   3.647 -#1153 := (and #1143 #1150)
   3.648 -#1156 := (or #1153 #207)
   3.649 -#1159 := (forall (vars (?v0 S2)) #1156)
   3.650 -#1162 := (not #1159)
   3.651 -#1291 := (not #1153)
   3.652 -#1299 := (or #1291 #1294)
   3.653 -#1302 := (forall (vars (?v0 S2)) #1299)
   3.654 -#1305 := (not #1302)
   3.655 -#1315 := (forall (vars (?v0 S2)) #1312)
   3.656 -#1318 := (not #1315)
   3.657 -#1005 := (not #1004)
   3.658 -#1114 := (and #118 #1005)
   3.659 -#1117 := (exists (vars (?v0 S2)) #1114)
   3.660 -#1333 := (not #1117)
   3.661 -#1357 := (or #1333 #183 #1322 #1318 #715 #1305 #1162 #1288)
   3.662 -#1050 := (not #1049)
   3.663 -#1084 := (and #1050 #941)
   3.664 -#1087 := (not #1084)
   3.665 -#1093 := (or #1087 #1090)
   3.666 -#1096 := (forall (vars (?v0 S2) (?v1 S2)) #1093)
   3.667 -#1099 := (not #1096)
   3.668 -#1102 := (or #1099 #169)
   3.669 -#1105 := (and #1096 #1102)
   3.670 -#1065 := (= #1067 0::Int)
   3.671 -#1059 := (>= #1061 0::Int)
   3.672 -#1062 := (not #1059)
   3.673 -#1069 := (and #1062 #1065)
   3.674 -#1072 := (exists (vars (?v1 S2)) #1069)
   3.675 -#1053 := (and #71 #1050)
   3.676 -#1056 := (not #1053)
   3.677 -#1075 := (or #1056 #1072)
   3.678 -#1078 := (forall (vars (?v0 S2)) #1075)
   3.679 -#1081 := (not #1078)
   3.680 -#1108 := (or #1081 #1105)
   3.681 -#1111 := (and #1078 #1108)
   3.682 -#1135 := (or #1117 #521 #512 #503 #494 #1111)
   3.683 -#1362 := (and #1135 #1357)
   3.684 -#1014 := (= #1018 0::Int)
   3.685 -#1021 := (not #1020)
   3.686 -#1030 := (and #1021 #117 #1014)
   3.687 -#1035 := (exists (vars (?v1 S2)) #1030)
   3.688 -#1008 := (and #71 #1005)
   3.689 -#1011 := (not #1008)
   3.690 -#1038 := (or #1011 #1035)
   3.691 -#1041 := (forall (vars (?v0 S2)) #1038)
   3.692 -#1044 := (not #1041)
   3.693 -#1365 := (and #117 #941)
   3.694 -#1368 := (not #1365)
   3.695 -#1374 := (or #1368 #1371)
   3.696 -#1377 := (forall (vars (?v0 S2) (?v1 S2)) #1374)
   3.697 -#1380 := (not #1377)
   3.698 -#121 := (and #118 #120)
   3.699 -#377 := (not #121)
   3.700 -#1385 := (or #377 #1020)
   3.701 -#1388 := (forall (vars (?v0 S2) (?v1 S2)) #1385)
   3.702 -#1391 := (not #1388)
   3.703 -#1397 := (forall (vars (?v0 S2)) #1394)
   3.704 -#1400 := (not #1397)
   3.705 -#87 := (f17 #10)
   3.706 -#926 := (* -1::Int #87)
   3.707 -#953 := (+ #926 #93)
   3.708 -#954 := (+ #67 #953)
   3.709 -#976 := (= #954 0::Int)
   3.710 -#927 := (+ #67 #926)
   3.711 -#925 := (>= #927 0::Int)
   3.712 -#979 := (not #925)
   3.713 -#988 := (and #979 #77 #976)
   3.714 -#993 := (exists (vars (?v1 S2)) #988)
   3.715 -#967 := (not #966)
   3.716 -#970 := (and #71 #967)
   3.717 -#973 := (not #970)
   3.718 -#996 := (or #973 #993)
   3.719 -#999 := (forall (vars (?v0 S2)) #996)
   3.720 -#1403 := (not #999)
   3.721 -#1424 := (or #1403 #804 #1400 #1391 #1380 #1044 #1362)
   3.722 -#1429 := (and #999 #1424)
   3.723 -#951 := (>= #954 0::Int)
   3.724 -#944 := (and #77 #941)
   3.725 -#947 := (not #944)
   3.726 -#955 := (or #947 #951)
   3.727 -#958 := (forall (vars (?v0 S2) (?v1 S2)) #955)
   3.728 -#961 := (not #958)
   3.729 -#1432 := (or #961 #1429)
   3.730 -#1435 := (and #958 #1432)
   3.731 -#84 := (f11 f18 #10)
   3.732 -#85 := (= #84 f1)
   3.733 -#86 := (and #78 #85)
   3.734 -#356 := (not #86)
   3.735 -#929 := (or #356 #925)
   3.736 -#932 := (forall (vars (?v0 S2) (?v1 S2)) #929)
   3.737 -#935 := (not #932)
   3.738 -#1438 := (or #935 #1435)
   3.739 -#1441 := (and #932 #1438)
   3.740 -#916 := (>= #67 0::Int)
   3.741 -#917 := (forall (vars (?v0 S2)) #916)
   3.742 -#920 := (not #917)
   3.743 -#1444 := (or #920 #1441)
   3.744 -#1447 := (and #917 #1444)
   3.745 -#80 := (f17 f16)
   3.746 -#81 := (= #80 0::Int)
   3.747 -#868 := (not #81)
   3.748 -#1450 := (or #868 #1447)
   3.749 -#1453 := (and #81 #1450)
   3.750 -#79 := (forall (vars (?v0 S2)) #78)
   3.751 -#880 := (not #79)
   3.752 -#889 := (not #353)
   3.753 -#68 := (= #67 0::Int)
   3.754 -#344 := (or #71 #68)
   3.755 -#347 := (forall (vars (?v0 S2)) #344)
   3.756 -#898 := (not #347)
   3.757 -#1465 := (or #898 #889 #880 #1453)
   3.758 -#1470 := (not #1465)
   3.759 -#229 := (+ #202 #93)
   3.760 -#236 := (= #224 #229)
   3.761 -#237 := (and #213 #236)
   3.762 -#235 := (< #202 #224)
   3.763 -#238 := (and #235 #237)
   3.764 -#239 := (exists (vars (?v1 S2)) #238)
   3.765 -#233 := (< #202 f3)
   3.766 -#234 := (and #71 #233)
   3.767 -#240 := (implies #234 #239)
   3.768 -#241 := (forall (vars (?v0 S2)) #240)
   3.769 -#242 := (and #241 true)
   3.770 -#230 := (<= #224 #229)
   3.771 -#94 := (< #93 f3)
   3.772 -#228 := (and #213 #94)
   3.773 -#231 := (implies #228 #230)
   3.774 -#232 := (forall (vars (?v0 S2) (?v1 S2)) #231)
   3.775 -#243 := (implies #232 #242)
   3.776 -#244 := (and #232 #243)
   3.777 -#225 := (<= #224 #202)
   3.778 -#226 := (implies #223 #225)
   3.779 -#227 := (forall (vars (?v0 S2) (?v1 S2)) #226)
   3.780 -#245 := (implies #227 #244)
   3.781 -#246 := (and #227 #245)
   3.782 -#218 := (<= 0::Int #202)
   3.783 -#219 := (forall (vars (?v0 S2)) #218)
   3.784 -#247 := (implies #219 #246)
   3.785 -#248 := (and #219 #247)
   3.786 -#249 := (implies #217 #248)
   3.787 -#250 := (and #217 #249)
   3.788 -#214 := (implies #213 #207)
   3.789 -#215 := (forall (vars (?v0 S2)) #214)
   3.790 -#251 := (implies #215 #250)
   3.791 -#252 := (and #215 #251)
   3.792 -#210 := (<= #202 #112)
   3.793 -#211 := (forall (vars (?v0 S2)) #210)
   3.794 -#253 := (implies #211 #252)
   3.795 -#254 := (and #211 #253)
   3.796 -#199 := (+ #185 #197)
   3.797 -#200 := (< #199 #112)
   3.798 -#198 := (< #197 f3)
   3.799 -#201 := (and #198 #200)
   3.800 -#206 := (not #201)
   3.801 -#208 := (implies #206 #207)
   3.802 -#209 := (forall (vars (?v0 S2)) #208)
   3.803 -#255 := (implies #209 #254)
   3.804 -#203 := (= #202 #199)
   3.805 -#204 := (implies #201 #203)
   3.806 -#205 := (forall (vars (?v0 S2)) #204)
   3.807 -#256 := (implies #205 #255)
   3.808 -#257 := (implies #194 #256)
   3.809 -#187 := (<= #185 #112)
   3.810 -#188 := (implies #118 #187)
   3.811 -#189 := (forall (vars (?v0 S2)) #188)
   3.812 -#258 := (implies #189 #257)
   3.813 -#186 := (< #185 f3)
   3.814 -#259 := (implies #186 #258)
   3.815 -#184 := (not #183)
   3.816 -#260 := (implies #184 #259)
   3.817 -#131 := (< #112 f3)
   3.818 -#140 := (and #118 #131)
   3.819 -#141 := (exists (vars (?v0 S2)) #140)
   3.820 -#261 := (implies #141 #260)
   3.821 -#262 := (implies true #261)
   3.822 -#170 := (and #169 true)
   3.823 -#158 := (+ #153 #93)
   3.824 -#165 := (<= #156 #158)
   3.825 -#154 := (< #153 f3)
   3.826 -#164 := (and #154 #94)
   3.827 -#166 := (implies #164 #165)
   3.828 -#167 := (forall (vars (?v0 S2) (?v1 S2)) #166)
   3.829 -#171 := (implies #167 #170)
   3.830 -#172 := (and #167 #171)
   3.831 -#159 := (= #156 #158)
   3.832 -#157 := (< #153 #156)
   3.833 -#160 := (and #157 #159)
   3.834 -#161 := (exists (vars (?v1 S2)) #160)
   3.835 -#155 := (and #71 #154)
   3.836 -#162 := (implies #155 #161)
   3.837 -#163 := (forall (vars (?v0 S2)) #162)
   3.838 -#173 := (implies #163 #172)
   3.839 -#174 := (and #163 #173)
   3.840 -#175 := (implies #152 #174)
   3.841 -#176 := (implies #149 #175)
   3.842 -#177 := (implies #147 #176)
   3.843 -#178 := (implies #144 #177)
   3.844 -#142 := (not #141)
   3.845 -#179 := (implies #142 #178)
   3.846 -#180 := (implies true #179)
   3.847 -#263 := (and #180 #262)
   3.848 -#127 := (+ #112 #93)
   3.849 -#134 := (= #122 #127)
   3.850 -#135 := (and #117 #134)
   3.851 -#133 := (< #112 #122)
   3.852 -#136 := (and #133 #135)
   3.853 -#137 := (exists (vars (?v1 S2)) #136)
   3.854 -#132 := (and #71 #131)
   3.855 -#138 := (implies #132 #137)
   3.856 -#139 := (forall (vars (?v0 S2)) #138)
   3.857 -#264 := (implies #139 #263)
   3.858 -#128 := (<= #122 #127)
   3.859 -#126 := (and #117 #94)
   3.860 -#129 := (implies #126 #128)
   3.861 -#130 := (forall (vars (?v0 S2) (?v1 S2)) #129)
   3.862 -#265 := (implies #130 #264)
   3.863 -#123 := (<= #122 #112)
   3.864 -#124 := (implies #121 #123)
   3.865 -#125 := (forall (vars (?v0 S2) (?v1 S2)) #124)
   3.866 -#266 := (implies #125 #265)
   3.867 -#113 := (<= 0::Int #112)
   3.868 -#114 := (forall (vars (?v0 S2)) #113)
   3.869 -#267 := (implies #114 #266)
   3.870 -#268 := (implies #111 #267)
   3.871 -#269 := (implies true #268)
   3.872 -#96 := (+ #67 #93)
   3.873 -#103 := (= #87 #96)
   3.874 -#104 := (and #77 #103)
   3.875 -#102 := (< #67 #87)
   3.876 -#105 := (and #102 #104)
   3.877 -#106 := (exists (vars (?v1 S2)) #105)
   3.878 -#100 := (< #67 f3)
   3.879 -#101 := (and #71 #100)
   3.880 -#107 := (implies #101 #106)
   3.881 -#108 := (forall (vars (?v0 S2)) #107)
   3.882 -#270 := (implies #108 #269)
   3.883 -#271 := (and #108 #270)
   3.884 -#97 := (<= #87 #96)
   3.885 -#95 := (and #77 #94)
   3.886 -#98 := (implies #95 #97)
   3.887 -#99 := (forall (vars (?v0 S2) (?v1 S2)) #98)
   3.888 -#272 := (implies #99 #271)
   3.889 -#273 := (and #99 #272)
   3.890 -#88 := (<= #87 #67)
   3.891 -#89 := (implies #86 #88)
   3.892 -#90 := (forall (vars (?v0 S2) (?v1 S2)) #89)
   3.893 -#274 := (implies #90 #273)
   3.894 -#275 := (and #90 #274)
   3.895 -#82 := (<= 0::Int #67)
   3.896 -#83 := (forall (vars (?v0 S2)) #82)
   3.897 -#276 := (implies #83 #275)
   3.898 -#277 := (and #83 #276)
   3.899 -#278 := (implies #81 #277)
   3.900 -#279 := (and #81 #278)
   3.901 -#280 := (implies #79 #279)
   3.902 -#73 := (implies #71 #72)
   3.903 -#74 := (forall (vars (?v0 S2)) #73)
   3.904 -#281 := (implies #74 #280)
   3.905 -#69 := (implies #66 #68)
   3.906 -#70 := (forall (vars (?v0 S2)) #69)
   3.907 -#282 := (implies #70 #281)
   3.908 -#283 := (implies true #282)
   3.909 -#284 := (not #283)
   3.910 -#1473 := (iff #284 #1470)
   3.911 -#573 := (+ #93 #202)
   3.912 -#591 := (= #224 #573)
   3.913 -#594 := (and #213 #591)
   3.914 -#597 := (and #235 #594)
   3.915 -#600 := (exists (vars (?v1 S2)) #597)
   3.916 -#606 := (not #234)
   3.917 -#607 := (or #606 #600)
   3.918 -#612 := (forall (vars (?v0 S2)) #607)
   3.919 -#576 := (<= #224 #573)
   3.920 -#582 := (not #228)
   3.921 -#583 := (or #582 #576)
   3.922 -#588 := (forall (vars (?v0 S2) (?v1 S2)) #583)
   3.923 -#625 := (not #588)
   3.924 -#626 := (or #625 #612)
   3.925 -#631 := (and #588 #626)
   3.926 -#567 := (or #566 #225)
   3.927 -#570 := (forall (vars (?v0 S2) (?v1 S2)) #567)
   3.928 -#637 := (not #570)
   3.929 -#638 := (or #637 #631)
   3.930 -#643 := (and #570 #638)
   3.931 -#649 := (not #219)
   3.932 -#650 := (or #649 #643)
   3.933 -#655 := (and #219 #650)
   3.934 -#662 := (or #661 #655)
   3.935 -#667 := (and #217 #662)
   3.936 -#674 := (or #673 #667)
   3.937 -#679 := (and #563 #674)
   3.938 -#685 := (not #211)
   3.939 -#686 := (or #685 #679)
   3.940 -#691 := (and #211 #686)
   3.941 -#554 := (or #201 #207)
   3.942 -#557 := (forall (vars (?v0 S2)) #554)
   3.943 -#697 := (not #557)
   3.944 -#698 := (or #697 #691)
   3.945 -#548 := (or #206 #203)
   3.946 -#551 := (forall (vars (?v0 S2)) #548)
   3.947 -#706 := (not #551)
   3.948 -#707 := (or #706 #698)
   3.949 -#716 := (or #715 #707)
   3.950 -#542 := (or #117 #187)
   3.951 -#545 := (forall (vars (?v0 S2)) #542)
   3.952 -#724 := (not #545)
   3.953 -#725 := (or #724 #716)
   3.954 -#733 := (not #186)
   3.955 -#734 := (or #733 #725)
   3.956 -#742 := (or #183 #734)
   3.957 -#750 := (or #142 #742)
   3.958 -#426 := (+ #93 #153)
   3.959 -#450 := (<= #156 #426)
   3.960 -#456 := (not #164)
   3.961 -#457 := (or #456 #450)
   3.962 -#462 := (forall (vars (?v0 S2) (?v1 S2)) #457)
   3.963 -#470 := (not #462)
   3.964 -#471 := (or #470 #169)
   3.965 -#476 := (and #462 #471)
   3.966 -#429 := (= #156 #426)
   3.967 -#432 := (and #157 #429)
   3.968 -#435 := (exists (vars (?v1 S2)) #432)
   3.969 -#441 := (not #155)
   3.970 -#442 := (or #441 #435)
   3.971 -#447 := (forall (vars (?v0 S2)) #442)
   3.972 -#482 := (not #447)
   3.973 -#483 := (or #482 #476)
   3.974 -#488 := (and #447 #483)
   3.975 -#495 := (or #494 #488)
   3.976 -#504 := (or #503 #495)
   3.977 -#513 := (or #512 #504)
   3.978 -#522 := (or #521 #513)
   3.979 -#530 := (or #141 #522)
   3.980 -#762 := (and #530 #750)
   3.981 -#384 := (+ #93 #112)
   3.982 -#402 := (= #122 #384)
   3.983 -#405 := (and #117 #402)
   3.984 -#408 := (and #133 #405)
   3.985 -#411 := (exists (vars (?v1 S2)) #408)
   3.986 -#417 := (not #132)
   3.987 -#418 := (or #417 #411)
   3.988 -#423 := (forall (vars (?v0 S2)) #418)
   3.989 -#768 := (not #423)
   3.990 -#769 := (or #768 #762)
   3.991 -#387 := (<= #122 #384)
   3.992 -#393 := (not #126)
   3.993 -#394 := (or #393 #387)
   3.994 -#399 := (forall (vars (?v0 S2) (?v1 S2)) #394)
   3.995 -#777 := (not #399)
   3.996 -#778 := (or #777 #769)
   3.997 -#378 := (or #377 #123)
   3.998 -#381 := (forall (vars (?v0 S2) (?v1 S2)) #378)
   3.999 -#786 := (not #381)
  3.1000 -#787 := (or #786 #778)
  3.1001 -#795 := (not #114)
  3.1002 -#796 := (or #795 #787)
  3.1003 -#805 := (or #804 #796)
  3.1004 -#370 := (not #101)
  3.1005 -#371 := (or #370 #106)
  3.1006 -#374 := (forall (vars (?v0 S2)) #371)
  3.1007 -#820 := (not #374)
  3.1008 -#821 := (or #820 #805)
  3.1009 -#826 := (and #374 #821)
  3.1010 -#363 := (not #95)
  3.1011 -#364 := (or #363 #97)
  3.1012 -#367 := (forall (vars (?v0 S2) (?v1 S2)) #364)
  3.1013 -#832 := (not #367)
  3.1014 -#833 := (or #832 #826)
  3.1015 -#838 := (and #367 #833)
  3.1016 -#357 := (or #356 #88)
  3.1017 -#360 := (forall (vars (?v0 S2) (?v1 S2)) #357)
  3.1018 -#844 := (not #360)
  3.1019 -#845 := (or #844 #838)
  3.1020 -#850 := (and #360 #845)
  3.1021 -#856 := (not #83)
  3.1022 -#857 := (or #856 #850)
  3.1023 -#862 := (and #83 #857)
  3.1024 -#869 := (or #868 #862)
  3.1025 -#874 := (and #81 #869)
  3.1026 -#881 := (or #880 #874)
  3.1027 -#890 := (or #889 #881)
  3.1028 -#899 := (or #898 #890)
  3.1029 -#911 := (not #899)
  3.1030 -#1471 := (iff #911 #1470)
  3.1031 -#1468 := (iff #899 #1465)
  3.1032 -#1456 := (or #880 #1453)
  3.1033 -#1459 := (or #889 #1456)
  3.1034 -#1462 := (or #898 #1459)
  3.1035 -#1466 := (iff #1462 #1465)
  3.1036 -#1467 := [rewrite]: #1466
  3.1037 -#1463 := (iff #899 #1462)
  3.1038 -#1460 := (iff #890 #1459)
  3.1039 -#1457 := (iff #881 #1456)
  3.1040 -#1454 := (iff #874 #1453)
  3.1041 -#1451 := (iff #869 #1450)
  3.1042 -#1448 := (iff #862 #1447)
  3.1043 -#1445 := (iff #857 #1444)
  3.1044 -#1442 := (iff #850 #1441)
  3.1045 -#1439 := (iff #845 #1438)
  3.1046 -#1436 := (iff #838 #1435)
  3.1047 -#1433 := (iff #833 #1432)
  3.1048 -#1430 := (iff #826 #1429)
  3.1049 -#1427 := (iff #821 #1424)
  3.1050 -#1406 := (or #1044 #1362)
  3.1051 -#1409 := (or #1380 #1406)
  3.1052 -#1412 := (or #1391 #1409)
  3.1053 -#1415 := (or #1400 #1412)
  3.1054 -#1418 := (or #804 #1415)
  3.1055 -#1421 := (or #1403 #1418)
  3.1056 -#1425 := (iff #1421 #1424)
  3.1057 -#1426 := [rewrite]: #1425
  3.1058 -#1422 := (iff #821 #1421)
  3.1059 -#1419 := (iff #805 #1418)
  3.1060 -#1416 := (iff #796 #1415)
  3.1061 -#1413 := (iff #787 #1412)
  3.1062 -#1410 := (iff #778 #1409)
  3.1063 -#1407 := (iff #769 #1406)
  3.1064 -#1363 := (iff #762 #1362)
  3.1065 -#1360 := (iff #750 #1357)
  3.1066 -#1336 := (or #1162 #1288)
  3.1067 -#1339 := (or #1305 #1336)
  3.1068 -#1342 := (or #715 #1339)
  3.1069 -#1345 := (or #1318 #1342)
  3.1070 -#1348 := (or #1322 #1345)
  3.1071 -#1351 := (or #183 #1348)
  3.1072 -#1354 := (or #1333 #1351)
  3.1073 -#1358 := (iff #1354 #1357)
  3.1074 -#1359 := [rewrite]: #1358
  3.1075 -#1355 := (iff #750 #1354)
  3.1076 -#1352 := (iff #742 #1351)
  3.1077 -#1349 := (iff #734 #1348)
  3.1078 -#1346 := (iff #725 #1345)
  3.1079 -#1343 := (iff #716 #1342)
  3.1080 -#1340 := (iff #707 #1339)
  3.1081 -#1337 := (iff #698 #1336)
  3.1082 -#1289 := (iff #691 #1288)
  3.1083 -#1286 := (iff #686 #1285)
  3.1084 -#1283 := (iff #679 #1282)
  3.1085 -#1280 := (iff #674 #1279)
  3.1086 -#1277 := (iff #667 #1276)
  3.1087 -#1274 := (iff #662 #1273)
  3.1088 -#1271 := (iff #655 #1270)
  3.1089 -#1268 := (iff #650 #1267)
  3.1090 -#1265 := (iff #643 #1264)
  3.1091 -#1262 := (iff #638 #1261)
  3.1092 -#1259 := (iff #631 #1258)
  3.1093 -#1256 := (iff #626 #1255)
  3.1094 -#1253 := (iff #612 #1252)
  3.1095 -#1250 := (iff #607 #1249)
  3.1096 -#1247 := (iff #600 #1246)
  3.1097 -#1244 := (iff #597 #1241)
  3.1098 -#1235 := (and #213 #1229)
  3.1099 -#1238 := (and #1232 #1235)
  3.1100 -#1242 := (iff #1238 #1241)
  3.1101 -#1243 := [rewrite]: #1242
  3.1102 -#1239 := (iff #597 #1238)
  3.1103 -#1236 := (iff #594 #1235)
  3.1104 -#1230 := (iff #591 #1229)
  3.1105 -#1231 := [rewrite]: #1230
  3.1106 -#1237 := [monotonicity #1231]: #1236
  3.1107 -#1233 := (iff #235 #1232)
  3.1108 -#1234 := [rewrite]: #1233
  3.1109 -#1240 := [monotonicity #1234 #1237]: #1239
  3.1110 -#1245 := [trans #1240 #1243]: #1244
  3.1111 -#1248 := [quant-intro #1245]: #1247
  3.1112 -#1227 := (iff #606 #1226)
  3.1113 -#1224 := (iff #234 #1223)
  3.1114 -#1221 := (iff #233 #1220)
  3.1115 -#1222 := [rewrite]: #1221
  3.1116 -#1225 := [monotonicity #1222]: #1224
  3.1117 -#1228 := [monotonicity #1225]: #1227
  3.1118 -#1251 := [monotonicity #1228 #1248]: #1250
  3.1119 -#1254 := [quant-intro #1251]: #1253
  3.1120 -#1216 := (iff #625 #1215)
  3.1121 -#1213 := (iff #588 #1212)
  3.1122 -#1210 := (iff #583 #1209)
  3.1123 -#1206 := (iff #576 #1205)
  3.1124 -#1208 := [rewrite]: #1206
  3.1125 -#1203 := (iff #582 #1202)
  3.1126 -#1200 := (iff #228 #1199)
  3.1127 -#942 := (iff #94 #941)
  3.1128 -#943 := [rewrite]: #942
  3.1129 -#1201 := [monotonicity #943]: #1200
  3.1130 -#1204 := [monotonicity #1201]: #1203
  3.1131 -#1211 := [monotonicity #1204 #1208]: #1210
  3.1132 -#1214 := [quant-intro #1211]: #1213
  3.1133 -#1217 := [monotonicity #1214]: #1216
  3.1134 -#1257 := [monotonicity #1217 #1254]: #1256
  3.1135 -#1260 := [monotonicity #1214 #1257]: #1259
  3.1136 -#1197 := (iff #637 #1196)
  3.1137 -#1194 := (iff #570 #1193)
  3.1138 -#1191 := (iff #567 #1190)
  3.1139 -#1188 := (iff #225 #1185)
  3.1140 -#1189 := [rewrite]: #1188
  3.1141 -#1192 := [monotonicity #1189]: #1191
  3.1142 -#1195 := [quant-intro #1192]: #1194
  3.1143 -#1198 := [monotonicity #1195]: #1197
  3.1144 -#1263 := [monotonicity #1198 #1260]: #1262
  3.1145 -#1266 := [monotonicity #1195 #1263]: #1265
  3.1146 -#1183 := (iff #649 #1182)
  3.1147 -#1180 := (iff #219 #1179)
  3.1148 -#1177 := (iff #218 #1176)
  3.1149 -#1178 := [rewrite]: #1177
  3.1150 -#1181 := [quant-intro #1178]: #1180
  3.1151 -#1184 := [monotonicity #1181]: #1183
  3.1152 -#1269 := [monotonicity #1184 #1266]: #1268
  3.1153 -#1272 := [monotonicity #1181 #1269]: #1271
  3.1154 -#1275 := [monotonicity #1272]: #1274
  3.1155 -#1278 := [monotonicity #1275]: #1277
  3.1156 -#1281 := [monotonicity #1278]: #1280
  3.1157 -#1284 := [monotonicity #1281]: #1283
  3.1158 -#1174 := (iff #685 #1173)
  3.1159 -#1171 := (iff #211 #1170)
  3.1160 -#1168 := (iff #210 #1165)
  3.1161 -#1169 := [rewrite]: #1168
  3.1162 -#1172 := [quant-intro #1169]: #1171
  3.1163 -#1175 := [monotonicity #1172]: #1174
  3.1164 -#1287 := [monotonicity #1175 #1284]: #1286
  3.1165 -#1290 := [monotonicity #1172 #1287]: #1289
  3.1166 -#1163 := (iff #697 #1162)
  3.1167 -#1160 := (iff #557 #1159)
  3.1168 -#1157 := (iff #554 #1156)
  3.1169 -#1154 := (iff #201 #1153)
  3.1170 -#1151 := (iff #200 #1150)
  3.1171 -#1152 := [rewrite]: #1151
  3.1172 -#1144 := (iff #198 #1143)
  3.1173 -#1145 := [rewrite]: #1144
  3.1174 -#1155 := [monotonicity #1145 #1152]: #1154
  3.1175 -#1158 := [monotonicity #1155]: #1157
  3.1176 -#1161 := [quant-intro #1158]: #1160
  3.1177 -#1164 := [monotonicity #1161]: #1163
  3.1178 -#1338 := [monotonicity #1164 #1290]: #1337
  3.1179 -#1306 := (iff #706 #1305)
  3.1180 -#1303 := (iff #551 #1302)
  3.1181 -#1300 := (iff #548 #1299)
  3.1182 -#1295 := (iff #203 #1294)
  3.1183 -#1298 := [rewrite]: #1295
  3.1184 -#1292 := (iff #206 #1291)
  3.1185 -#1293 := [monotonicity #1155]: #1292
  3.1186 -#1301 := [monotonicity #1293 #1298]: #1300
  3.1187 -#1304 := [quant-intro #1301]: #1303
  3.1188 -#1307 := [monotonicity #1304]: #1306
  3.1189 -#1341 := [monotonicity #1307 #1338]: #1340
  3.1190 -#1344 := [monotonicity #1341]: #1343
  3.1191 -#1319 := (iff #724 #1318)
  3.1192 -#1316 := (iff #545 #1315)
  3.1193 -#1313 := (iff #542 #1312)
  3.1194 -#1310 := (iff #187 #1308)
  3.1195 -#1311 := [rewrite]: #1310
  3.1196 -#1314 := [monotonicity #1311]: #1313
  3.1197 -#1317 := [quant-intro #1314]: #1316
  3.1198 -#1320 := [monotonicity #1317]: #1319
  3.1199 -#1347 := [monotonicity #1320 #1344]: #1346
  3.1200 -#1331 := (iff #733 #1322)
  3.1201 -#1323 := (not #1322)
  3.1202 -#1326 := (not #1323)
  3.1203 -#1329 := (iff #1326 #1322)
  3.1204 -#1330 := [rewrite]: #1329
  3.1205 -#1327 := (iff #733 #1326)
  3.1206 -#1324 := (iff #186 #1323)
  3.1207 -#1325 := [rewrite]: #1324
  3.1208 -#1328 := [monotonicity #1325]: #1327
  3.1209 -#1332 := [trans #1328 #1330]: #1331
  3.1210 -#1350 := [monotonicity #1332 #1347]: #1349
  3.1211 -#1353 := [monotonicity #1350]: #1352
  3.1212 -#1334 := (iff #142 #1333)
  3.1213 -#1118 := (iff #141 #1117)
  3.1214 -#1115 := (iff #140 #1114)
  3.1215 -#1006 := (iff #131 #1005)
  3.1216 -#1007 := [rewrite]: #1006
  3.1217 -#1116 := [monotonicity #1007]: #1115
  3.1218 -#1119 := [quant-intro #1116]: #1118
  3.1219 -#1335 := [monotonicity #1119]: #1334
  3.1220 -#1356 := [monotonicity #1335 #1353]: #1355
  3.1221 -#1361 := [trans #1356 #1359]: #1360
  3.1222 -#1138 := (iff #530 #1135)
  3.1223 -#1120 := (or #494 #1111)
  3.1224 -#1123 := (or #503 #1120)
  3.1225 -#1126 := (or #512 #1123)
  3.1226 -#1129 := (or #521 #1126)
  3.1227 -#1132 := (or #1117 #1129)
  3.1228 -#1136 := (iff #1132 #1135)
  3.1229 -#1137 := [rewrite]: #1136
  3.1230 -#1133 := (iff #530 #1132)
  3.1231 -#1130 := (iff #522 #1129)
  3.1232 -#1127 := (iff #513 #1126)
  3.1233 -#1124 := (iff #504 #1123)
  3.1234 -#1121 := (iff #495 #1120)
  3.1235 -#1112 := (iff #488 #1111)
  3.1236 -#1109 := (iff #483 #1108)
  3.1237 -#1106 := (iff #476 #1105)
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  3.1267 -#1054 := (iff #155 #1053)
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  3.1271 -#1080 := [quant-intro #1077]: #1079
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  3.1274 -#1113 := [monotonicity #1080 #1110]: #1112
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  3.1283 -#1042 := (iff #423 #1041)
  3.1284 -#1039 := (iff #418 #1038)
  3.1285 -#1036 := (iff #411 #1035)
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  3.1292 -#1025 := (iff #405 #1024)
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  3.1297 -#1023 := [rewrite]: #1022
  3.1298 -#1029 := [monotonicity #1023 #1026]: #1028
  3.1299 -#1034 := [trans #1029 #1032]: #1033
  3.1300 -#1037 := [quant-intro #1034]: #1036
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  3.1302 -#1009 := (iff #132 #1008)
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  3.1304 -#1013 := [monotonicity #1010]: #1012
  3.1305 -#1040 := [monotonicity #1013 #1037]: #1039
  3.1306 -#1043 := [quant-intro #1040]: #1042
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  3.1308 -#1408 := [monotonicity #1046 #1364]: #1407
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  3.1310 -#1378 := (iff #399 #1377)
  3.1311 -#1375 := (iff #394 #1374)
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  3.1315 -#1366 := (iff #126 #1365)
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  3.1317 -#1370 := [monotonicity #1367]: #1369
  3.1318 -#1376 := [monotonicity #1370 #1373]: #1375
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  3.1321 -#1411 := [monotonicity #1382 #1408]: #1410
  3.1322 -#1392 := (iff #786 #1391)
  3.1323 -#1389 := (iff #381 #1388)
  3.1324 -#1386 := (iff #378 #1385)
  3.1325 -#1383 := (iff #123 #1020)
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  3.1330 -#1414 := [monotonicity #1393 #1411]: #1413
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  3.1485 -#772 := (iff #264 #769)
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  3.1573 -#610 := (iff #240 #607)
  3.1574 -#603 := (implies #234 #600)
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  3.1578 -#601 := (iff #239 #600)
  3.1579 -#598 := (iff #238 #597)
  3.1580 -#595 := (iff #237 #594)
  3.1581 -#592 := (iff #236 #591)
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  3.1595 -#579 := (implies #228 #576)
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  3.1604 -#624 := [monotonicity #590 #621]: #623
  3.1605 -#630 := [trans #624 #628]: #629
  3.1606 -#633 := [monotonicity #590 #630]: #632
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  3.1612 -#642 := [trans #636 #640]: #641
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  3.1626 -#681 := [monotonicity #565 #678]: #680
  3.1627 -#684 := [monotonicity #681]: #683
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  3.1634 -#696 := [monotonicity #559 #693]: #695
  3.1635 -#702 := [trans #696 #700]: #701
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  3.1640 -#705 := [monotonicity #553 #702]: #704
  3.1641 -#711 := [trans #705 #709]: #710
  3.1642 -#714 := [monotonicity #711]: #713
  3.1643 -#720 := [trans #714 #718]: #719
  3.1644 -#546 := (iff #189 #545)
  3.1645 -#543 := (iff #188 #542)
  3.1646 -#544 := [rewrite]: #543
  3.1647 -#547 := [quant-intro #544]: #546
  3.1648 -#723 := [monotonicity #547 #720]: #722
  3.1649 -#729 := [trans #723 #727]: #728
  3.1650 -#732 := [monotonicity #729]: #731
  3.1651 -#738 := [trans #732 #736]: #737
  3.1652 -#741 := [monotonicity #738]: #740
  3.1653 -#746 := [trans #741 #744]: #745
  3.1654 -#749 := [monotonicity #746]: #748
  3.1655 -#754 := [trans #749 #752]: #753
  3.1656 -#757 := [monotonicity #754]: #756
  3.1657 -#761 := [trans #757 #759]: #760
  3.1658 -#540 := (iff #180 #530)
  3.1659 -#535 := (implies true #530)
  3.1660 -#538 := (iff #535 #530)
  3.1661 -#539 := [rewrite]: #538
  3.1662 -#536 := (iff #180 #535)
  3.1663 -#533 := (iff #179 #530)
  3.1664 -#527 := (implies #142 #522)
  3.1665 -#531 := (iff #527 #530)
  3.1666 -#532 := [rewrite]: #531
  3.1667 -#528 := (iff #179 #527)
  3.1668 -#525 := (iff #178 #522)
  3.1669 -#518 := (implies #144 #513)
  3.1670 -#523 := (iff #518 #522)
  3.1671 -#524 := [rewrite]: #523
  3.1672 -#519 := (iff #178 #518)
  3.1673 -#516 := (iff #177 #513)
  3.1674 -#509 := (implies #147 #504)
  3.1675 -#514 := (iff #509 #513)
  3.1676 -#515 := [rewrite]: #514
  3.1677 -#510 := (iff #177 #509)
  3.1678 -#507 := (iff #176 #504)
  3.1679 -#500 := (implies #149 #495)
  3.1680 -#505 := (iff #500 #504)
  3.1681 -#506 := [rewrite]: #505
  3.1682 -#501 := (iff #176 #500)
  3.1683 -#498 := (iff #175 #495)
  3.1684 -#491 := (implies #152 #488)
  3.1685 -#496 := (iff #491 #495)
  3.1686 -#497 := [rewrite]: #496
  3.1687 -#492 := (iff #175 #491)
  3.1688 -#489 := (iff #174 #488)
  3.1689 -#486 := (iff #173 #483)
  3.1690 -#479 := (implies #447 #476)
  3.1691 -#484 := (iff #479 #483)
  3.1692 -#485 := [rewrite]: #484
  3.1693 -#480 := (iff #173 #479)
  3.1694 -#477 := (iff #172 #476)
  3.1695 -#474 := (iff #171 #471)
  3.1696 -#467 := (implies #462 #169)
  3.1697 -#472 := (iff #467 #471)
  3.1698 -#473 := [rewrite]: #472
  3.1699 -#468 := (iff #171 #467)
  3.1700 -#465 := (iff #170 #169)
  3.1701 -#466 := [rewrite]: #465
  3.1702 -#463 := (iff #167 #462)
  3.1703 -#460 := (iff #166 #457)
  3.1704 -#453 := (implies #164 #450)
  3.1705 -#458 := (iff #453 #457)
  3.1706 -#459 := [rewrite]: #458
  3.1707 -#454 := (iff #166 #453)
  3.1708 -#451 := (iff #165 #450)
  3.1709 -#427 := (= #158 #426)
  3.1710 -#428 := [rewrite]: #427
  3.1711 -#452 := [monotonicity #428]: #451
  3.1712 -#455 := [monotonicity #452]: #454
  3.1713 -#461 := [trans #455 #459]: #460
  3.1714 -#464 := [quant-intro #461]: #463
  3.1715 -#469 := [monotonicity #464 #466]: #468
  3.1716 -#475 := [trans #469 #473]: #474
  3.1717 -#478 := [monotonicity #464 #475]: #477
  3.1718 -#448 := (iff #163 #447)
  3.1719 -#445 := (iff #162 #442)
  3.1720 -#438 := (implies #155 #435)
  3.1721 -#443 := (iff #438 #442)
  3.1722 -#444 := [rewrite]: #443
  3.1723 -#439 := (iff #162 #438)
  3.1724 -#436 := (iff #161 #435)
  3.1725 -#433 := (iff #160 #432)
  3.1726 -#430 := (iff #159 #429)
  3.1727 -#431 := [monotonicity #428]: #430
  3.1728 -#434 := [monotonicity #431]: #433
  3.1729 -#437 := [quant-intro #434]: #436
  3.1730 -#440 := [monotonicity #437]: #439
  3.1731 -#446 := [trans #440 #444]: #445
  3.1732 -#449 := [quant-intro #446]: #448
  3.1733 -#481 := [monotonicity #449 #478]: #480
  3.1734 -#487 := [trans #481 #485]: #486
  3.1735 -#490 := [monotonicity #449 #487]: #489
  3.1736 -#493 := [monotonicity #490]: #492
  3.1737 -#499 := [trans #493 #497]: #498
  3.1738 -#502 := [monotonicity #499]: #501
  3.1739 -#508 := [trans #502 #506]: #507
  3.1740 -#511 := [monotonicity #508]: #510
  3.1741 -#517 := [trans #511 #515]: #516
  3.1742 -#520 := [monotonicity #517]: #519
  3.1743 -#526 := [trans #520 #524]: #525
  3.1744 -#529 := [monotonicity #526]: #528
  3.1745 -#534 := [trans #529 #532]: #533
  3.1746 -#537 := [monotonicity #534]: #536
  3.1747 -#541 := [trans #537 #539]: #540
  3.1748 -#764 := [monotonicity #541 #761]: #763
  3.1749 -#424 := (iff #139 #423)
  3.1750 -#421 := (iff #138 #418)
  3.1751 -#414 := (implies #132 #411)
  3.1752 -#419 := (iff #414 #418)
  3.1753 -#420 := [rewrite]: #419
  3.1754 -#415 := (iff #138 #414)
  3.1755 -#412 := (iff #137 #411)
  3.1756 -#409 := (iff #136 #408)
  3.1757 -#406 := (iff #135 #405)
  3.1758 -#403 := (iff #134 #402)
  3.1759 -#385 := (= #127 #384)
  3.1760 -#386 := [rewrite]: #385
  3.1761 -#404 := [monotonicity #386]: #403
  3.1762 -#407 := [monotonicity #404]: #406
  3.1763 -#410 := [monotonicity #407]: #409
  3.1764 -#413 := [quant-intro #410]: #412
  3.1765 -#416 := [monotonicity #413]: #415
  3.1766 -#422 := [trans #416 #420]: #421
  3.1767 -#425 := [quant-intro #422]: #424
  3.1768 -#767 := [monotonicity #425 #764]: #766
  3.1769 -#773 := [trans #767 #771]: #772
  3.1770 -#400 := (iff #130 #399)
  3.1771 -#397 := (iff #129 #394)
  3.1772 -#390 := (implies #126 #387)
  3.1773 -#395 := (iff #390 #394)
  3.1774 -#396 := [rewrite]: #395
  3.1775 -#391 := (iff #129 #390)
  3.1776 -#388 := (iff #128 #387)
  3.1777 -#389 := [monotonicity #386]: #388
  3.1778 -#392 := [monotonicity #389]: #391
  3.1779 -#398 := [trans #392 #396]: #397
  3.1780 -#401 := [quant-intro #398]: #400
  3.1781 -#776 := [monotonicity #401 #773]: #775
  3.1782 -#782 := [trans #776 #780]: #781
  3.1783 -#382 := (iff #125 #381)
  3.1784 -#379 := (iff #124 #378)
  3.1785 -#380 := [rewrite]: #379
  3.1786 -#383 := [quant-intro #380]: #382
  3.1787 -#785 := [monotonicity #383 #782]: #784
  3.1788 -#791 := [trans #785 #789]: #790
  3.1789 -#794 := [monotonicity #791]: #793
  3.1790 -#800 := [trans #794 #798]: #799
  3.1791 -#803 := [monotonicity #800]: #802
  3.1792 -#809 := [trans #803 #807]: #808
  3.1793 -#812 := [monotonicity #809]: #811
  3.1794 -#816 := [trans #812 #814]: #815
  3.1795 -#375 := (iff #108 #374)
  3.1796 -#372 := (iff #107 #371)
  3.1797 -#373 := [rewrite]: #372
  3.1798 -#376 := [quant-intro #373]: #375
  3.1799 -#819 := [monotonicity #376 #816]: #818
  3.1800 -#825 := [trans #819 #823]: #824
  3.1801 -#828 := [monotonicity #376 #825]: #827
  3.1802 -#368 := (iff #99 #367)
  3.1803 -#365 := (iff #98 #364)
  3.1804 -#366 := [rewrite]: #365
  3.1805 -#369 := [quant-intro #366]: #368
  3.1806 -#831 := [monotonicity #369 #828]: #830
  3.1807 -#837 := [trans #831 #835]: #836
  3.1808 -#840 := [monotonicity #369 #837]: #839
  3.1809 -#361 := (iff #90 #360)
  3.1810 -#358 := (iff #89 #357)
  3.1811 -#359 := [rewrite]: #358
  3.1812 -#362 := [quant-intro #359]: #361
  3.1813 -#843 := [monotonicity #362 #840]: #842
  3.1814 -#849 := [trans #843 #847]: #848
  3.1815 -#852 := [monotonicity #362 #849]: #851
  3.1816 -#855 := [monotonicity #852]: #854
  3.1817 -#861 := [trans #855 #859]: #860
  3.1818 -#864 := [monotonicity #861]: #863
  3.1819 -#867 := [monotonicity #864]: #866
  3.1820 -#873 := [trans #867 #871]: #872
  3.1821 -#876 := [monotonicity #873]: #875
  3.1822 -#879 := [monotonicity #876]: #878
  3.1823 -#885 := [trans #879 #883]: #884
  3.1824 -#354 := (iff #74 #353)
  3.1825 -#351 := (iff #73 #350)
  3.1826 -#352 := [rewrite]: #351
  3.1827 -#355 := [quant-intro #352]: #354
  3.1828 -#888 := [monotonicity #355 #885]: #887
  3.1829 -#894 := [trans #888 #892]: #893
  3.1830 -#348 := (iff #70 #347)
  3.1831 -#345 := (iff #69 #344)
  3.1832 -#346 := [rewrite]: #345
  3.1833 -#349 := [quant-intro #346]: #348
  3.1834 -#897 := [monotonicity #349 #894]: #896
  3.1835 -#903 := [trans #897 #901]: #902
  3.1836 -#906 := [monotonicity #903]: #905
  3.1837 -#910 := [trans #906 #908]: #909
  3.1838 -#913 := [monotonicity #910]: #912
  3.1839 -#1474 := [trans #913 #1472]: #1473
  3.1840 -#343 := [asserted]: #284
  3.1841 -#1475 := [mp #343 #1474]: #1470
  3.1842 -#1477 := [not-or-elim #1475]: #353
  3.1843 -#1532 := [mp~ #1477 #1501]: #353
  3.1844 -#3659 := [mp #1532 #3658]: #3654
  3.1845 -#3289 := (not #3654)
  3.1846 -#5853 := (or #3289 #1614 #6574)
  3.1847 -#6575 := (or #1614 #6574)
  3.1848 -#6155 := (or #3289 #6575)
  3.1849 -#6156 := (iff #6155 #5853)
  3.1850 -#6165 := [rewrite]: #6156
  3.1851 -#5702 := [quant-inst #1613]: #6155
  3.1852 -#6166 := [mp #5702 #6165]: #5853
  3.1853 -#6626 := [unit-resolution #6166 #3659 #6625]: #6574
  3.1854 -#6631 := [mp #6626 #6630]: #6176
  3.1855 -#6615 := (not #6176)
  3.1856 -#1620 := (not #1619)
  3.1857 -#3595 := (or #3702 #1620)
  3.1858 -#3596 := [def-axiom]: #3595
  3.1859 -#5852 := [unit-resolution #3596 #5790]: #1620
  3.1860 -#6616 := (or #6615 #1619)
  3.1861 -#6622 := [th-lemma arith triangle-eq]: #6616
  3.1862 -#6624 := [unit-resolution #6622 #5852]: #6615
  3.1863 -#6632 := [unit-resolution #6624 #6631]: false
  3.1864 -#6633 := [lemma #6632]: #3702
  3.1865 -#3986 := (or #3705 #3983)
  3.1866 -#3989 := (not #3986)
  3.1867 -#2540 := (or #78 #940 #951)
  3.1868 -#3685 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3684) #2540)
  3.1869 -#3690 := (not #3685)
  3.1870 -#3992 := (or #3690 #3989)
  3.1871 -#3995 := (not #3992)
  3.1872 -decl ?v0!4 :: S2
  3.1873 -#1582 := ?v0!4
  3.1874 -#1595 := (f17 ?v0!4)
  3.1875 -#1596 := (* -1::Int #1595)
  3.1876 -decl ?v1!3 :: S2
  3.1877 -#1581 := ?v1!3
  3.1878 -#1594 := (f17 ?v1!3)
  3.1879 -#2173 := (+ #1594 #1596)
  3.1880 -#1585 := (f6 f7 ?v1!3)
  3.1881 -#1586 := (f5 #1585 ?v0!4)
  3.1882 -#1587 := (f4 #1586)
  3.1883 -#2174 := (+ #1587 #2173)
  3.1884 -#2177 := (>= #2174 0::Int)
  3.1885 -#1588 := (* -1::Int #1587)
  3.1886 -#1589 := (+ f3 #1588)
  3.1887 -#1590 := (<= #1589 0::Int)
  3.1888 -#1583 := (f11 f18 ?v1!3)
  3.1889 -#1584 := (= #1583 f1)
  3.1890 -#2503 := (not #1584)
  3.1891 -#2518 := (or #2503 #1590 #2177)
  3.1892 -#2523 := (not #2518)
  3.1893 -#3998 := (or #2523 #3995)
  3.1894 -#4001 := (not #3998)
  3.1895 -#3675 := (pattern #67 #87)
  3.1896 -#1605 := (not #85)
  3.1897 -#2495 := (or #77 #1605 #925)
  3.1898 -#3676 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3675) #2495)
  3.1899 -#3681 := (not #3676)
  3.1900 -#4004 := (or #3681 #4001)
  3.1901 -#4007 := (not #4004)
  3.1902 -decl ?v0!2 :: S2
  3.1903 -#1555 := ?v0!2
  3.1904 -#1564 := (f17 ?v0!2)
  3.1905 -#1565 := (* -1::Int #1564)
  3.1906 -decl ?v1!1 :: S2
  3.1907 -#1554 := ?v1!1
  3.1908 -#1563 := (f17 ?v1!1)
  3.1909 -#1566 := (+ #1563 #1565)
  3.1910 -#1567 := (>= #1566 0::Int)
  3.1911 -#1559 := (f11 f18 ?v0!2)
  3.1912 -#1560 := (= #1559 f1)
  3.1913 -#1884 := (not #1560)
  3.1914 -#1556 := (f11 f18 ?v1!1)
  3.1915 -#1557 := (= #1556 f1)
  3.1916 -#1841 := (or #1557 #1884 #1567)
  3.1917 -#1946 := (not #1841)
  3.1918 -#4010 := (or #1946 #4007)
  3.1919 -#4013 := (not #4010)
  3.1920 -#3667 := (forall (vars (?v0 S2)) (:pat #3647) #916)
  3.1921 -#3672 := (not #3667)
  3.1922 -#4016 := (or #3672 #4013)
  3.1923 -#4019 := (not #4016)
  3.1924 -decl ?v0!0 :: S2
  3.1925 -#1539 := ?v0!0
  3.1926 -#1540 := (f17 ?v0!0)
  3.1927 -#1541 := (>= #1540 0::Int)
  3.1928 -#3259 := (= f3 #1540)
  3.1929 -#3321 := (= #1540 f3)
  3.1930 -#3223 := (iff #3321 #3259)
  3.1931 -#3224 := (iff #3259 #3321)
  3.1932 -#3227 := [commutativity]: #3224
  3.1933 -#3222 := [symm #3227]: #3223
  3.1934 -#3345 := (= ?v0!0 f16)
  3.1935 -#3353 := (not #3345)
  3.1936 -#3306 := (= #1540 0::Int)
  3.1937 -#3281 := (not #3306)
  3.1938 -#1542 := (not #1541)
  3.1939 -#3290 := [hypothesis]: #1542
  3.1940 -#3246 := (or #3281 #1541)
  3.1941 -#3244 := [th-lemma arith triangle-eq]: #3246
  3.1942 -#3247 := [unit-resolution #3244 #3290]: #3281
  3.1943 -#3648 := (forall (vars (?v0 S2)) (:pat #3647) #344)
  3.1944 -#3651 := (iff #347 #3648)
  3.1945 -#3649 := (iff #344 #344)
  3.1946 -#3650 := [refl]: #3649
  3.1947 -#3652 := [quant-intro #3650]: #3651
  3.1948 -#1498 := (~ #347 #347)
  3.1949 -#1527 := (~ #344 #344)
  3.1950 -#1528 := [refl]: #1527
  3.1951 -#1499 := [nnf-pos #1528]: #1498
  3.1952 -#1476 := [not-or-elim #1475]: #347
  3.1953 -#1529 := [mp~ #1476 #1499]: #347
  3.1954 -#3653 := [mp #1529 #3652]: #3648
  3.1955 -#3310 := (not #3648)
  3.1956 -#3309 := (or #3310 #3353 #3306)
  3.1957 -#3307 := (or #3353 #3306)
  3.1958 -#3303 := (or #3310 #3307)
  3.1959 -#3294 := (iff #3303 #3309)
  3.1960 -#3295 := [rewrite]: #3294
  3.1961 -#3304 := [quant-inst #1539]: #3303
  3.1962 -#3305 := [mp #3304 #3295]: #3309
  3.1963 -#3236 := [unit-resolution #3305 #3653 #3247]: #3353
  3.1964 -#3291 := (or #3289 #3345 #3321)
  3.1965 -#3308 := (or #3345 #3321)
  3.1966 -#3258 := (or #3289 #3308)
  3.1967 -#3268 := (iff #3258 #3291)
  3.1968 -#3269 := [rewrite]: #3268
  3.1969 -#3260 := [quant-inst #1539]: #3258
  3.1970 -#3267 := [mp #3260 #3269]: #3291
  3.1971 -#3248 := [unit-resolution #3267 #3659 #3236]: #3321
  3.1972 -#3228 := [mp #3248 #3222]: #3259
  3.1973 -#3316 := (* -1::Int #1540)
  3.1974 -#3270 := (+ f3 #3316)
  3.1975 -#3253 := (<= #3270 0::Int)
  3.1976 -#4045 := (not #3253)
  3.1977 -#307 := (<= f3 0::Int)
  3.1978 -#308 := (not #307)
  3.1979 -#9 := (< 0::Int f3)
  3.1980 -#309 := (iff #9 #308)
  3.1981 -#310 := [rewrite]: #309
  3.1982 -#304 := [asserted]: #9
  3.1983 -#311 := [mp #304 #310]: #308
  3.1984 -#3286 := (<= #1540 0::Int)
  3.1985 -#3203 := (or #3286 #1541)
  3.1986 -#3208 := [th-lemma arith farkas 1 1]: #3203
  3.1987 -#3213 := [unit-resolution #3208 #3290]: #3286
  3.1988 -#4046 := (not #3286)
  3.1989 -#4047 := (or #4045 #307 #4046)
  3.1990 -#4048 := [th-lemma arith assign-bounds 1 1]: #4047
  3.1991 -#4049 := [unit-resolution #4048 #3213 #311]: #4045
  3.1992 -#4044 := (not #3259)
  3.1993 -#4050 := (or #4044 #3253)
  3.1994 -#4051 := [th-lemma arith triangle-eq]: #4050
  3.1995 -#4052 := [unit-resolution #4051 #4049 #3228]: false
  3.1996 -#4053 := [lemma #4052]: #1541
  3.1997 -#4022 := (or #1542 #4019)
  3.1998 -#4025 := (not #4022)
  3.1999 -#4028 := (or #868 #4025)
  3.2000 -#4031 := (not #4028)
  3.2001 -#4121 := [hypothesis]: #868
  3.2002 -#4075 := (or #3310 #81)
  3.2003 -#6826 := (= f16 f16)
  3.2004 -#6905 := (not #6826)
  3.2005 -#4054 := (or #6905 #81)
  3.2006 -#4076 := (or #3310 #4054)
  3.2007 -#4084 := (iff #4076 #4075)
  3.2008 -#4117 := (iff #4075 #4075)
  3.2009 -#4118 := [rewrite]: #4117
  3.2010 -#4073 := (iff #4054 #81)
  3.2011 -#4068 := (or false #81)
  3.2012 -#4069 := (iff #4068 #81)
  3.2013 -#4072 := [rewrite]: #4069
  3.2014 -#4070 := (iff #4054 #4068)
  3.2015 -#6915 := (iff #6905 false)
  3.2016 -#6910 := (not true)
  3.2017 -#6913 := (iff #6910 false)
  3.2018 -#6914 := [rewrite]: #6913
  3.2019 -#6911 := (iff #6905 #6910)
  3.2020 -#6829 := (iff #6826 true)
  3.2021 -#6830 := [rewrite]: #6829
  3.2022 -#6912 := [monotonicity #6830]: #6911
  3.2023 -#6916 := [trans #6912 #6914]: #6915
  3.2024 -#4071 := [monotonicity #6916]: #4070
  3.2025 -#4074 := [trans #4071 #4072]: #4073
  3.2026 -#4085 := [monotonicity #4074]: #4084
  3.2027 -#4119 := [trans #4085 #4118]: #4084
  3.2028 -#4077 := [quant-inst #65]: #4076
  3.2029 -#4120 := [mp #4077 #4119]: #4075
  3.2030 -#4116 := [unit-resolution #4120 #3653 #4121]: false
  3.2031 -#4122 := [lemma #4116]: #81
  3.2032 -#4034 := (or #868 #4031)
  3.2033 -#2953 := (forall (vars (?v1 S2)) #2942)
  3.2034 -#2960 := (not #2953)
  3.2035 -#2938 := (forall (vars (?v0 S2) (?v1 S2)) #2933)
  3.2036 -#2959 := (not #2938)
  3.2037 -#2961 := (or #2959 #2035 #2040 #2960)
  3.2038 -#2962 := (not #2961)
  3.2039 -#2967 := (or #2916 #2962)
  3.2040 -#2974 := (not #2967)
  3.2041 -#2893 := (forall (vars (?v0 S2) (?v1 S2)) #2888)
  3.2042 -#2973 := (not #2893)
  3.2043 -#2975 := (or #2973 #2974)
  3.2044 -#2976 := (not #2975)
  3.2045 -#2981 := (or #2870 #2976)
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  3.2141 -#3990 := (iff #3072 #3989)
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  3.2187 -#3904 := [monotonicity #3901]: #3903
  3.2188 -#3907 := [monotonicity #3904]: #3906
  3.2189 -#3878 := (iff #2973 #3877)
  3.2190 -#3875 := (iff #2893 #3872)
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  3.2195 -#3910 := [monotonicity #3879 #3907]: #3909
  3.2196 -#3913 := [monotonicity #3910]: #3912
  3.2197 -#3916 := [monotonicity #3913]: #3915
  3.2198 -#3919 := [monotonicity #3916]: #3918
  3.2199 -#3869 := (iff #1182 #3868)
  3.2200 -#3866 := (iff #1179 #3863)
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  3.2205 -#3922 := [monotonicity #3870 #3919]: #3921
  3.2206 -#3925 := [monotonicity #3922]: #3924
  3.2207 -#3928 := [monotonicity #3925]: #3927
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  3.2210 -#3937 := [monotonicity #3934]: #3936
  3.2211 -#3940 := [monotonicity #3937]: #3939
  3.2212 -#3943 := [monotonicity #3940]: #3942
  3.2213 -#3861 := (iff #673 #3860)
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  3.2217 -#3859 := [quant-intro #3857]: #3858
  3.2218 -#3862 := [monotonicity #3859]: #3861
  3.2219 -#3946 := [monotonicity #3862 #3943]: #3945
  3.2220 -#3949 := [monotonicity #3946]: #3948
  3.2221 -#3952 := [monotonicity #3949]: #3951
  3.2222 -#3955 := [monotonicity #3952]: #3954
  3.2223 -#3852 := (iff #1173 #3851)
  3.2224 -#3849 := (iff #1170 #3846)
  3.2225 -#3847 := (iff #1165 #1165)
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  3.2227 -#3850 := [quant-intro #3848]: #3849
  3.2228 -#3853 := [monotonicity #3850]: #3852
  3.2229 -#3958 := [monotonicity #3853 #3955]: #3957
  3.2230 -#3961 := [monotonicity #3958]: #3960
  3.2231 -#3964 := [monotonicity #3961]: #3963
  3.2232 -#3967 := [monotonicity #3964]: #3966
  3.2233 -#3844 := (iff #3040 #3843)
  3.2234 -#3841 := (iff #2847 #3838)
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  3.2237 -#3842 := [quant-intro #3840]: #3841
  3.2238 -#3845 := [monotonicity #3842]: #3844
  3.2239 -#3836 := (iff #3039 #3835)
  3.2240 -#3833 := (iff #2841 #3830)
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  3.2243 -#3834 := [quant-intro #3832]: #3833
  3.2244 -#3837 := [monotonicity #3834]: #3836
  3.2245 -#3826 := (iff #1318 #3825)
  3.2246 -#3823 := (iff #1315 #3820)
  3.2247 -#3821 := (iff #1312 #1312)
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  3.2249 -#3824 := [quant-intro #3822]: #3823
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  3.2251 -#3970 := [monotonicity #3827 #3837 #3845 #3967]: #3969
  3.2252 -#3973 := [monotonicity #3970]: #3972
  3.2253 -#3818 := (iff #2817 #3817)
  3.2254 -#3815 := (iff #2816 #3814)
  3.2255 -#3812 := (iff #2815 #3811)
  3.2256 -#3809 := (iff #2808 #3808)
  3.2257 -#3806 := (iff #2803 #3805)
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  3.2263 -#3788 := (iff #2787 #3787)
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  3.2267 -#3786 := [quant-intro #3784]: #3785
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  3.2270 -#3795 := [monotonicity #3792]: #3794
  3.2271 -#3798 := [monotonicity #3795]: #3797
  3.2272 -#3801 := [monotonicity #3798]: #3800
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  3.2280 -#3807 := [monotonicity #3804]: #3806
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  3.2291 -#3810 := [monotonicity #3773 #3807]: #3809
  3.2292 -#3813 := [monotonicity #3810]: #3812
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  3.2346 -#3991 := [monotonicity #3988]: #3990
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  3.2356 -#4003 := [monotonicity #4000]: #4002
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  3.2395 -#1982 := (and #1979 #1981)
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  3.2444 -#2233 := (forall (vars (?v0 S2)) #2230)
  3.2445 -#2454 := (and #2233 #111 #1397 #1388 #1377 #2275 #2451)
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  3.2447 -#1631 := (and #1625 #77 #1630)
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  3.2449 -#1643 := (forall (vars (?v1 S2)) #1640)
  3.2450 -#2191 := (and #1615 #1620 #1643)
  3.2451 -#2457 := (or #2191 #2454)
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  3.2454 -#1592 := (and #1584 #1591)
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  3.2461 -#1561 := (and #1558 #1560)
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  3.2463 -#1568 := (or #1562 #1567)
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  3.2465 -#2469 := (or #1569 #2466)
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  3.2467 -#2475 := (or #1542 #2472)
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  3.2469 -#2481 := (or #868 #2478)
  3.2470 -#3120 := (iff #2481 #3119)
  3.2471 -#3117 := (iff #2478 #3114)
  3.2472 -#3109 := (and #81 #3106)
  3.2473 -#3115 := (iff #3109 #3114)
  3.2474 -#3116 := [rewrite]: #3115
  3.2475 -#3110 := (iff #2478 #3109)
  3.2476 -#3107 := (iff #2475 #3106)
  3.2477 -#3104 := (iff #2472 #3101)
  3.2478 -#3096 := (and #917 #3093)
  3.2479 -#3102 := (iff #3096 #3101)
  3.2480 -#3103 := [rewrite]: #3102
  3.2481 -#3097 := (iff #2472 #3096)
  3.2482 -#3094 := (iff #2469 #3093)
  3.2483 -#3091 := (iff #2466 #3088)
  3.2484 -#3082 := (and #2500 #3079)
  3.2485 -#3089 := (iff #3082 #3088)
  3.2486 -#3090 := [rewrite]: #3089
  3.2487 -#3083 := (iff #2466 #3082)
  3.2488 -#3080 := (iff #2463 #3079)
  3.2489 -#3077 := (iff #2460 #3074)
  3.2490 -#3068 := (and #2545 #3065)
  3.2491 -#3075 := (iff #3068 #3074)
  3.2492 -#3076 := [rewrite]: #3075
  3.2493 -#3069 := (iff #2460 #3068)
  3.2494 -#3066 := (iff #2457 #3065)
  3.2495 -#3063 := (iff #2454 #3060)
  3.2496 -#3051 := (and #2598 #111 #1397 #2621 #2643 #2671 #3048)
  3.2497 -#3061 := (iff #3051 #3060)
  3.2498 -#3062 := [rewrite]: #3061
  3.2499 -#3052 := (iff #2454 #3051)
  3.2500 -#3049 := (iff #2451 #3048)
  3.2501 -#3046 := (iff #2446 #3043)
  3.2502 -#3036 := (and #1875 #1880 #184 #1323 #1315 #194 #2841 #2847 #3033)
  3.2503 -#3044 := (iff #3036 #3043)
  3.2504 -#3045 := [rewrite]: #3044
  3.2505 -#3037 := (iff #2446 #3036)
  3.2506 -#3034 := (iff #2440 #3033)
  3.2507 -#3031 := (iff #2437 #3028)
  3.2508 -#3023 := (and #1170 #3020)
  3.2509 -#3029 := (iff #3023 #3028)
  3.2510 -#3030 := [rewrite]: #3029
  3.2511 -#3024 := (iff #2437 #3023)
  3.2512 -#3021 := (iff #2434 #3020)
  3.2513 -#3018 := (iff #2431 #3015)
  3.2514 -#3010 := (and #563 #3007)
  3.2515 -#3016 := (iff #3010 #3015)
  3.2516 -#3017 := [rewrite]: #3016
  3.2517 -#3011 := (iff #2431 #3010)
  3.2518 -#3008 := (iff #2428 #3007)
  3.2519 -#3005 := (iff #2425 #3002)
  3.2520 -#2997 := (and #217 #2994)
  3.2521 -#3003 := (iff #2997 #3002)
  3.2522 -#3004 := [rewrite]: #3003
  3.2523 -#2998 := (iff #2425 #2997)
  3.2524 -#2995 := (iff #2422 #2994)
  3.2525 -#2992 := (iff #2419 #2989)
  3.2526 -#2984 := (and #1179 #2981)
  3.2527 -#2990 := (iff #2984 #2989)
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  3.2529 -#2985 := (iff #2419 #2984)
  3.2530 -#2982 := (iff #2416 #2981)
  3.2531 -#2979 := (iff #2413 #2976)
  3.2532 -#2970 := (and #2893 #2967)
  3.2533 -#2977 := (iff #2970 #2976)
  3.2534 -#2978 := [rewrite]: #2977
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  3.2536 -#2968 := (iff #2410 #2967)
  3.2537 -#2965 := (iff #2405 #2962)
  3.2538 -#2956 := (and #2938 #2036 #2041 #2953)
  3.2539 -#2963 := (iff #2956 #2962)
  3.2540 -#2964 := [rewrite]: #2963
  3.2541 -#2957 := (iff #2405 #2956)
  3.2542 -#2954 := (iff #2396 #2953)
  3.2543 -#2951 := (iff #2393 #2942)
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  3.2545 -#2946 := (not #2943)
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  3.2548 -#2947 := (iff #2393 #2946)
  3.2549 -#2944 := (iff #2390 #2943)
  3.2550 -#2945 := [rewrite]: #2944
  3.2551 -#2948 := [monotonicity #2945]: #2947
  3.2552 -#2952 := [trans #2948 #2950]: #2951
  3.2553 -#2955 := [quant-intro #2952]: #2954
  3.2554 -#2939 := (iff #1212 #2938)
  3.2555 -#2936 := (iff #1209 #2933)
  3.2556 -#2919 := (or #220 #940)
  3.2557 -#2930 := (or #2919 #1205)
  3.2558 -#2934 := (iff #2930 #2933)
  3.2559 -#2935 := [rewrite]: #2934
  3.2560 -#2931 := (iff #1209 #2930)
  3.2561 -#2928 := (iff #1202 #2919)
  3.2562 -#2920 := (not #2919)
  3.2563 -#2923 := (not #2920)
  3.2564 -#2926 := (iff #2923 #2919)
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  3.2566 -#2924 := (iff #1202 #2923)
  3.2567 -#2921 := (iff #1199 #2920)
  3.2568 -#2922 := [rewrite]: #2921
  3.2569 -#2925 := [monotonicity #2922]: #2924
  3.2570 -#2929 := [trans #2925 #2927]: #2928
  3.2571 -#2932 := [monotonicity #2929]: #2931
  3.2572 -#2937 := [trans #2932 #2935]: #2936
  3.2573 -#2940 := [quant-intro #2937]: #2939
  3.2574 -#2958 := [monotonicity #2940 #2955]: #2957
  3.2575 -#2966 := [trans #2958 #2964]: #2965
  3.2576 -#2917 := (iff #2022 #2916)
  3.2577 -#2914 := (iff #2021 #2911)
  3.2578 -#2897 := (or #2896 #2011)
  3.2579 -#2908 := (or #2897 #2020)
  3.2580 -#2912 := (iff #2908 #2911)
  3.2581 -#2913 := [rewrite]: #2912
  3.2582 -#2909 := (iff #2021 #2908)
  3.2583 -#2906 := (iff #2014 #2897)
  3.2584 -#2898 := (not #2897)
  3.2585 -#2901 := (not #2898)
  3.2586 -#2904 := (iff #2901 #2897)
  3.2587 -#2905 := [rewrite]: #2904
  3.2588 -#2902 := (iff #2014 #2901)
  3.2589 -#2899 := (iff #2013 #2898)
  3.2590 -#2900 := [rewrite]: #2899
  3.2591 -#2903 := [monotonicity #2900]: #2902
  3.2592 -#2907 := [trans #2903 #2905]: #2906
  3.2593 -#2910 := [monotonicity #2907]: #2909
  3.2594 -#2915 := [trans #2910 #2913]: #2914
  3.2595 -#2918 := [monotonicity #2915]: #2917
  3.2596 -#2969 := [monotonicity #2918 #2966]: #2968
  3.2597 -#2894 := (iff #1193 #2893)
  3.2598 -#2891 := (iff #1190 #2888)
  3.2599 -#2874 := (or #213 #2873)
  3.2600 -#2885 := (or #2874 #1185)
  3.2601 -#2889 := (iff #2885 #2888)
  3.2602 -#2890 := [rewrite]: #2889
  3.2603 -#2886 := (iff #1190 #2885)
  3.2604 -#2883 := (iff #566 #2874)
  3.2605 -#2875 := (not #2874)
  3.2606 -#2878 := (not #2875)
  3.2607 -#2881 := (iff #2878 #2874)
  3.2608 -#2882 := [rewrite]: #2881
  3.2609 -#2879 := (iff #566 #2878)
  3.2610 -#2876 := (iff #223 #2875)
  3.2611 -#2877 := [rewrite]: #2876
  3.2612 -#2880 := [monotonicity #2877]: #2879
  3.2613 -#2884 := [trans #2880 #2882]: #2883
  3.2614 -#2887 := [monotonicity #2884]: #2886
  3.2615 -#2892 := [trans #2887 #2890]: #2891
  3.2616 -#2895 := [quant-intro #2892]: #2894
  3.2617 -#2972 := [monotonicity #2895 #2969]: #2971
  3.2618 -#2980 := [trans #2972 #2978]: #2979
  3.2619 -#2871 := (iff #1990 #2870)
  3.2620 -#2868 := (iff #1989 #2865)
  3.2621 -#2851 := (or #1978 #2850)
  3.2622 -#2862 := (or #2851 #1988)
  3.2623 -#2866 := (iff #2862 #2865)
  3.2624 -#2867 := [rewrite]: #2866
  3.2625 -#2863 := (iff #1989 #2862)
  3.2626 -#2860 := (iff #1983 #2851)
  3.2627 -#2852 := (not #2851)
  3.2628 -#2855 := (not #2852)
  3.2629 -#2858 := (iff #2855 #2851)
  3.2630 -#2859 := [rewrite]: #2858
  3.2631 -#2856 := (iff #1983 #2855)
  3.2632 -#2853 := (iff #1982 #2852)
  3.2633 -#2854 := [rewrite]: #2853
  3.2634 -#2857 := [monotonicity #2854]: #2856
  3.2635 -#2861 := [trans #2857 #2859]: #2860
  3.2636 -#2864 := [monotonicity #2861]: #2863
  3.2637 -#2869 := [trans #2864 #2867]: #2868
  3.2638 -#2872 := [monotonicity #2869]: #2871
  3.2639 -#2983 := [monotonicity #2872 #2980]: #2982
  3.2640 -#2986 := [monotonicity #2983]: #2985
  3.2641 -#2993 := [trans #2986 #2991]: #2992
  3.2642 -#2996 := [monotonicity #2993]: #2995
  3.2643 -#2999 := [monotonicity #2996]: #2998
  3.2644 -#3006 := [trans #2999 #3004]: #3005
  3.2645 -#3009 := [monotonicity #3006]: #3008
  3.2646 -#3012 := [monotonicity #3009]: #3011
  3.2647 -#3019 := [trans #3012 #3017]: #3018
  3.2648 -#3022 := [monotonicity #3019]: #3021
  3.2649 -#3025 := [monotonicity #3022]: #3024
  3.2650 -#3032 := [trans #3025 #3030]: #3031
  3.2651 -#3035 := [monotonicity #3032]: #3034
  3.2652 -#2848 := (iff #1159 #2847)
  3.2653 -#2845 := (iff #1156 #2844)
  3.2654 -#2824 := (iff #1153 #2823)
  3.2655 -#2825 := [rewrite]: #2824
  3.2656 -#2846 := [monotonicity #2825]: #2845
  3.2657 -#2849 := [quant-intro #2846]: #2848
  3.2658 -#2842 := (iff #1302 #2841)
  3.2659 -#2839 := (iff #1299 #2836)
  3.2660 -#2833 := (or #2822 #1294)
  3.2661 -#2837 := (iff #2833 #2836)
  3.2662 -#2838 := [rewrite]: #2837
  3.2663 -#2834 := (iff #1299 #2833)
  3.2664 -#2831 := (iff #1291 #2822)
  3.2665 -#2826 := (not #2823)
  3.2666 -#2829 := (iff #2826 #2822)
  3.2667 -#2830 := [rewrite]: #2829
  3.2668 -#2827 := (iff #1291 #2826)
  3.2669 -#2828 := [monotonicity #2825]: #2827
  3.2670 -#2832 := [trans #2828 #2830]: #2831
  3.2671 -#2835 := [monotonicity #2832]: #2834
  3.2672 -#2840 := [trans #2835 #2838]: #2839
  3.2673 -#2843 := [quant-intro #2840]: #2842
  3.2674 -#3038 := [monotonicity #2843 #2849 #3035]: #3037
  3.2675 -#3047 := [trans #3038 #3045]: #3046
  3.2676 -#2820 := (iff #2374 #2817)
  3.2677 -#2811 := (and #2685 #144 #147 #149 #152 #2808)
  3.2678 -#2818 := (iff #2811 #2817)
  3.2679 -#2819 := [rewrite]: #2818
  3.2680 -#2812 := (iff #2374 #2811)
  3.2681 -#2809 := (iff #2371 #2808)
  3.2682 -#2806 := (iff #2368 #2803)
  3.2683 -#2797 := (and #2737 #2794)
  3.2684 -#2804 := (iff #2797 #2803)
  3.2685 -#2805 := [rewrite]: #2804
  3.2686 -#2798 := (iff #2368 #2797)
  3.2687 -#2795 := (iff #2365 #2794)
  3.2688 -#2792 := (iff #1852 #2789)
  3.2689 -#2784 := (and #2781 #1849)
  3.2690 -#2790 := (iff #2784 #2789)
  3.2691 -#2791 := [rewrite]: #2790
  3.2692 -#2785 := (iff #1852 #2784)
  3.2693 -#2782 := (iff #1096 #2781)
  3.2694 -#2779 := (iff #1093 #2776)
  3.2695 -#2762 := (or #1049 #940)
  3.2696 -#2773 := (or #2762 #1090)
  3.2697 -#2777 := (iff #2773 #2776)
  3.2698 -#2778 := [rewrite]: #2777
  3.2699 -#2774 := (iff #1093 #2773)
  3.2700 -#2771 := (iff #1087 #2762)
  3.2701 -#2763 := (not #2762)
  3.2702 -#2766 := (not #2763)
  3.2703 -#2769 := (iff #2766 #2762)
  3.2704 -#2770 := [rewrite]: #2769
  3.2705 -#2767 := (iff #1087 #2766)
  3.2706 -#2764 := (iff #1084 #2763)
  3.2707 -#2765 := [rewrite]: #2764
  3.2708 -#2768 := [monotonicity #2765]: #2767
  3.2709 -#2772 := [trans #2768 #2770]: #2771
  3.2710 -#2775 := [monotonicity #2772]: #2774
  3.2711 -#2780 := [trans #2775 #2778]: #2779
  3.2712 -#2783 := [quant-intro #2780]: #2782
  3.2713 -#2786 := [monotonicity #2783]: #2785
  3.2714 -#2793 := [trans #2786 #2791]: #2792
  3.2715 -#2760 := (iff #2362 #2759)
  3.2716 -#2757 := (iff #2359 #2754)
  3.2717 -#2740 := (or #1820 #1827)
  3.2718 -#2751 := (or #2740 #2356)
  3.2719 -#2755 := (iff #2751 #2754)
  3.2720 -#2756 := [rewrite]: #2755
  3.2721 -#2752 := (iff #2359 #2751)
  3.2722 -#2749 := (iff #1830 #2740)
  3.2723 -#2741 := (not #2740)
  3.2724 -#2744 := (not #2741)
  3.2725 -#2747 := (iff #2744 #2740)
  3.2726 -#2748 := [rewrite]: #2747
  3.2727 -#2745 := (iff #1830 #2744)
  3.2728 -#2742 := (iff #1829 #2741)
  3.2729 -#2743 := [rewrite]: #2742
  3.2730 -#2746 := [monotonicity #2743]: #2745
  3.2731 -#2750 := [trans #2746 #2748]: #2749
  3.2732 -#2753 := [monotonicity #2750]: #2752
  3.2733 -#2758 := [trans #2753 #2756]: #2757
  3.2734 -#2761 := [monotonicity #2758]: #2760
  3.2735 -#2796 := [monotonicity #2761 #2793]: #2795
  3.2736 -#2738 := (iff #2349 #2737)
  3.2737 -#2735 := (iff #2346 #2732)
  3.2738 -#2713 := (or #66 #1049)
  3.2739 -#2729 := (or #2713 #2726)
  3.2740 -#2733 := (iff #2729 #2732)
  3.2741 -#2734 := [rewrite]: #2733
  3.2742 -#2730 := (iff #2346 #2729)
  3.2743 -#2727 := (iff #2343 #2726)
  3.2744 -#2728 := [rewrite]: #2727
  3.2745 -#2722 := (iff #1056 #2713)
  3.2746 -#2714 := (not #2713)
  3.2747 -#2717 := (not #2714)
  3.2748 -#2720 := (iff #2717 #2713)
  3.2749 -#2721 := [rewrite]: #2720
  3.2750 -#2718 := (iff #1056 #2717)
  3.2751 -#2715 := (iff #1053 #2714)
  3.2752 -#2716 := [rewrite]: #2715
  3.2753 -#2719 := [monotonicity #2716]: #2718
  3.2754 -#2723 := [trans #2719 #2721]: #2722
  3.2755 -#2731 := [monotonicity #2723 #2728]: #2730
  3.2756 -#2736 := [trans #2731 #2734]: #2735
  3.2757 -#2739 := [quant-intro #2736]: #2738
  3.2758 -#2799 := [monotonicity #2739 #2796]: #2798
  3.2759 -#2807 := [trans #2799 #2805]: #2806
  3.2760 -#2711 := (iff #2307 #2708)
  3.2761 -#2703 := (and #1753 #1758 #2700)
  3.2762 -#2709 := (iff #2703 #2708)
  3.2763 -#2710 := [rewrite]: #2709
  3.2764 -#2704 := (iff #2307 #2703)
  3.2765 -#2701 := (iff #2301 #2700)
  3.2766 -#2698 := (iff #2298 #2689)
  3.2767 -#2690 := (not #2689)
  3.2768 -#2693 := (not #2690)
  3.2769 -#2696 := (iff #2693 #2689)
  3.2770 -#2697 := [rewrite]: #2696
  3.2771 -#2694 := (iff #2298 #2693)
  3.2772 -#2691 := (iff #2295 #2690)
  3.2773 -#2692 := [rewrite]: #2691
  3.2774 -#2695 := [monotonicity #2692]: #2694
  3.2775 -#2699 := [trans #2695 #2697]: #2698
  3.2776 -#2702 := [quant-intro #2699]: #2701
  3.2777 -#2705 := [monotonicity #2702]: #2704
  3.2778 -#2712 := [trans #2705 #2710]: #2711
  3.2779 -#2810 := [monotonicity #2712 #2807]: #2809
  3.2780 -#2686 := (iff #1736 #2685)
  3.2781 -#2683 := (iff #1733 #2674)
  3.2782 -#2675 := (not #2674)
  3.2783 -#2678 := (not #2675)
  3.2784 -#2681 := (iff #2678 #2674)
  3.2785 -#2682 := [rewrite]: #2681
  3.2786 -#2679 := (iff #1733 #2678)
  3.2787 -#2676 := (iff #1114 #2675)
  3.2788 -#2677 := [rewrite]: #2676
  3.2789 -#2680 := [monotonicity #2677]: #2679
  3.2790 -#2684 := [trans #2680 #2682]: #2683
  3.2791 -#2687 := [quant-intro #2684]: #2686
  3.2792 -#2813 := [monotonicity #2687 #2810]: #2812
  3.2793 -#2821 := [trans #2813 #2819]: #2820
  3.2794 -#3050 := [monotonicity #2821 #3047]: #3049
  3.2795 -#2672 := (iff #2275 #2671)
  3.2796 -#2669 := (iff #2272 #2666)
  3.2797 -#2646 := (or #66 #1004)
  3.2798 -#2663 := (or #2646 #2660)
  3.2799 -#2667 := (iff #2663 #2666)
  3.2800 -#2668 := [rewrite]: #2667
  3.2801 -#2664 := (iff #2272 #2663)
  3.2802 -#2661 := (iff #2269 #2660)
  3.2803 -#2662 := [rewrite]: #2661
  3.2804 -#2655 := (iff #1011 #2646)
  3.2805 -#2647 := (not #2646)
  3.2806 -#2650 := (not #2647)
  3.2807 -#2653 := (iff #2650 #2646)
  3.2808 -#2654 := [rewrite]: #2653
  3.2809 -#2651 := (iff #1011 #2650)
  3.2810 -#2648 := (iff #1008 #2647)
  3.2811 -#2649 := [rewrite]: #2648
  3.2812 -#2652 := [monotonicity #2649]: #2651
  3.2813 -#2656 := [trans #2652 #2654]: #2655
  3.2814 -#2665 := [monotonicity #2656 #2662]: #2664
  3.2815 -#2670 := [trans #2665 #2668]: #2669
  3.2816 -#2673 := [quant-intro #2670]: #2672
  3.2817 -#2644 := (iff #1377 #2643)
  3.2818 -#2641 := (iff #1374 #2638)
  3.2819 -#2624 := (or #118 #940)
  3.2820 -#2635 := (or #2624 #1371)
  3.2821 -#2639 := (iff #2635 #2638)
  3.2822 -#2640 := [rewrite]: #2639
  3.2823 -#2636 := (iff #1374 #2635)
  3.2824 -#2633 := (iff #1368 #2624)
  3.2825 -#2625 := (not #2624)
  3.2826 -#2628 := (not #2625)
  3.2827 -#2631 := (iff #2628 #2624)
  3.2828 -#2632 := [rewrite]: #2631
  3.2829 -#2629 := (iff #1368 #2628)
  3.2830 -#2626 := (iff #1365 #2625)
  3.2831 -#2627 := [rewrite]: #2626
  3.2832 -#2630 := [monotonicity #2627]: #2629
  3.2833 -#2634 := [trans #2630 #2632]: #2633
  3.2834 -#2637 := [monotonicity #2634]: #2636
  3.2835 -#2642 := [trans #2637 #2640]: #2641
  3.2836 -#2645 := [quant-intro #2642]: #2644
  3.2837 -#2622 := (iff #1388 #2621)
  3.2838 -#2619 := (iff #1385 #2616)
  3.2839 -#2602 := (or #117 #2601)
  3.2840 -#2613 := (or #2602 #1020)
  3.2841 -#2617 := (iff #2613 #2616)
  3.2842 -#2618 := [rewrite]: #2617
  3.2843 -#2614 := (iff #1385 #2613)
  3.2844 -#2611 := (iff #377 #2602)
  3.2845 -#2603 := (not #2602)
  3.2846 -#2606 := (not #2603)
  3.2847 -#2609 := (iff #2606 #2602)
  3.2848 -#2610 := [rewrite]: #2609
  3.2849 -#2607 := (iff #377 #2606)
  3.2850 -#2604 := (iff #121 #2603)
  3.2851 -#2605 := [rewrite]: #2604
  3.2852 -#2608 := [monotonicity #2605]: #2607
  3.2853 -#2612 := [trans #2608 #2610]: #2611
  3.2854 -#2615 := [monotonicity #2612]: #2614
  3.2855 -#2620 := [trans #2615 #2618]: #2619
  3.2856 -#2623 := [quant-intro #2620]: #2622
  3.2857 -#2599 := (iff #2233 #2598)
  3.2858 -#2596 := (iff #2230 #2593)
  3.2859 -#2573 := (or #66 #966)
  3.2860 -#2590 := (or #2573 #2587)
  3.2861 -#2594 := (iff #2590 #2593)
  3.2862 -#2595 := [rewrite]: #2594
  3.2863 -#2591 := (iff #2230 #2590)
  3.2864 -#2588 := (iff #2227 #2587)
  3.2865 -#2589 := [rewrite]: #2588
  3.2866 -#2582 := (iff #973 #2573)
  3.2867 -#2574 := (not #2573)
  3.2868 -#2577 := (not #2574)
  3.2869 -#2580 := (iff #2577 #2573)
  3.2870 -#2581 := [rewrite]: #2580
  3.2871 -#2578 := (iff #973 #2577)
  3.2872 -#2575 := (iff #970 #2574)
  3.2873 -#2576 := [rewrite]: #2575
  3.2874 -#2579 := [monotonicity #2576]: #2578
  3.2875 -#2583 := [trans #2579 #2581]: #2582
  3.2876 -#2592 := [monotonicity #2583 #2589]: #2591
  3.2877 -#2597 := [trans #2592 #2595]: #2596
  3.2878 -#2600 := [quant-intro #2597]: #2599
  3.2879 -#3053 := [monotonicity #2600 #2623 #2645 #2673 #3050]: #3052
  3.2880 -#3064 := [trans #3053 #3062]: #3063
  3.2881 -#2571 := (iff #2191 #2568)
  3.2882 -#2563 := (and #1615 #1620 #2560)
  3.2883 -#2569 := (iff #2563 #2568)
  3.2884 -#2570 := [rewrite]: #2569
  3.2885 -#2564 := (iff #2191 #2563)
  3.2886 -#2561 := (iff #1643 #2560)
  3.2887 -#2558 := (iff #1640 #2549)
  3.2888 -#2550 := (not #2549)
  3.2889 -#2553 := (not #2550)
  3.2890 -#2556 := (iff #2553 #2549)
  3.2891 -#2557 := [rewrite]: #2556
  3.2892 -#2554 := (iff #1640 #2553)
  3.2893 -#2551 := (iff #1631 #2550)
  3.2894 -#2552 := [rewrite]: #2551
  3.2895 -#2555 := [monotonicity #2552]: #2554
  3.2896 -#2559 := [trans #2555 #2557]: #2558
  3.2897 -#2562 := [quant-intro #2559]: #2561
  3.2898 -#2565 := [monotonicity #2562]: #2564
  3.2899 -#2572 := [trans #2565 #2570]: #2571
  3.2900 -#3067 := [monotonicity #2572 #3064]: #3066
  3.2901 -#2546 := (iff #958 #2545)
  3.2902 -#2543 := (iff #955 #2540)
  3.2903 -#2526 := (or #78 #940)
  3.2904 -#2537 := (or #2526 #951)
  3.2905 -#2541 := (iff #2537 #2540)
  3.2906 -#2542 := [rewrite]: #2541
  3.2907 -#2538 := (iff #955 #2537)
  3.2908 -#2535 := (iff #947 #2526)
  3.2909 -#2527 := (not #2526)
  3.2910 -#2530 := (not #2527)
  3.2911 -#2533 := (iff #2530 #2526)
  3.2912 -#2534 := [rewrite]: #2533
  3.2913 -#2531 := (iff #947 #2530)
  3.2914 -#2528 := (iff #944 #2527)
  3.2915 -#2529 := [rewrite]: #2528
  3.2916 -#2532 := [monotonicity #2529]: #2531
  3.2917 -#2536 := [trans #2532 #2534]: #2535
  3.2918 -#2539 := [monotonicity #2536]: #2538
  3.2919 -#2544 := [trans #2539 #2542]: #2543
  3.2920 -#2547 := [quant-intro #2544]: #2546
  3.2921 -#3070 := [monotonicity #2547 #3067]: #3069
  3.2922 -#3078 := [trans #3070 #3076]: #3077
  3.2923 -#2524 := (iff #2183 #2523)
  3.2924 -#2521 := (iff #2180 #2518)
  3.2925 -#2504 := (or #2503 #1590)
  3.2926 -#2515 := (or #2504 #2177)
  3.2927 -#2519 := (iff #2515 #2518)
  3.2928 -#2520 := [rewrite]: #2519
  3.2929 -#2516 := (iff #2180 #2515)
  3.2930 -#2513 := (iff #1593 #2504)
  3.2931 -#2505 := (not #2504)
  3.2932 -#2508 := (not #2505)
  3.2933 -#2511 := (iff #2508 #2504)
  3.2934 -#2512 := [rewrite]: #2511
  3.2935 -#2509 := (iff #1593 #2508)
  3.2936 -#2506 := (iff #1592 #2505)
  3.2937 -#2507 := [rewrite]: #2506
  3.2938 -#2510 := [monotonicity #2507]: #2509
  3.2939 -#2514 := [trans #2510 #2512]: #2513
  3.2940 -#2517 := [monotonicity #2514]: #2516
  3.2941 -#2522 := [trans #2517 #2520]: #2521
  3.2942 -#2525 := [monotonicity #2522]: #2524
  3.2943 -#3081 := [monotonicity #2525 #3078]: #3080
  3.2944 -#2501 := (iff #932 #2500)
  3.2945 -#2498 := (iff #929 #2495)
  3.2946 -#1670 := (or #77 #1605)
  3.2947 -#2492 := (or #1670 #925)
  3.2948 -#2496 := (iff #2492 #2495)
  3.2949 -#2497 := [rewrite]: #2496
  3.2950 -#2493 := (iff #929 #2492)
  3.2951 -#2490 := (iff #356 #1670)
  3.2952 -#1671 := (not #1670)
  3.2953 -#2485 := (not #1671)
  3.2954 -#2488 := (iff #2485 #1670)
  3.2955 -#2489 := [rewrite]: #2488
  3.2956 -#2486 := (iff #356 #2485)
  3.2957 -#2170 := (iff #86 #1671)
  3.2958 -#2484 := [rewrite]: #2170
  3.2959 -#2487 := [monotonicity #2484]: #2486
  3.2960 -#2491 := [trans #2487 #2489]: #2490
  3.2961 -#2494 := [monotonicity #2491]: #2493
  3.2962 -#2499 := [trans #2494 #2497]: #2498
  3.2963 -#2502 := [quant-intro #2499]: #2501
  3.2964 -#3084 := [monotonicity #2502 #3081]: #3083
  3.2965 -#3092 := [trans #3084 #3090]: #3091
  3.2966 -#1947 := (iff #1569 #1946)
  3.2967 -#1966 := (iff #1568 #1841)
  3.2968 -#1885 := (or #1557 #1884)
  3.2969 -#1545 := (or #1885 #1567)
  3.2970 -#1926 := (iff #1545 #1841)
  3.2971 -#1927 := [rewrite]: #1926
  3.2972 -#1546 := (iff #1568 #1545)
  3.2973 -#1572 := (iff #1562 #1885)
  3.2974 -#1804 := (not #1885)
  3.2975 -#2026 := (not #1804)
  3.2976 -#1993 := (iff #2026 #1885)
  3.2977 -#1994 := [rewrite]: #1993
  3.2978 -#1722 := (iff #1562 #2026)
  3.2979 -#1805 := (iff #1561 #1804)
  3.2980 -#2025 := [rewrite]: #1805
  3.2981 -#1723 := [monotonicity #2025]: #1722
  3.2982 -#1573 := [trans #1723 #1994]: #1572
  3.2983 -#1840 := [monotonicity #1573]: #1546
  3.2984 -#1967 := [trans #1840 #1927]: #1966
  3.2985 -#1604 := [monotonicity #1967]: #1947
  3.2986 -#3095 := [monotonicity #1604 #3092]: #3094
  3.2987 -#3098 := [monotonicity #3095]: #3097
  3.2988 -#3105 := [trans #3098 #3103]: #3104
  3.2989 -#3108 := [monotonicity #3105]: #3107
  3.2990 -#3111 := [monotonicity #3108]: #3110
  3.2991 -#3118 := [trans #3111 #3116]: #3117
  3.2992 -#3121 := [monotonicity #3118]: #3120
  3.2993 -#2049 := (+ #2048 #2044)
  3.2994 -#2050 := (= #2049 0::Int)
  3.2995 -#2051 := (and #2046 #213 #2050)
  3.2996 -#2061 := (not #2051)
  3.2997 -#2064 := (forall (vars (?v1 S2)) #2061)
  3.2998 -#2042 := (and #2036 #2041)
  3.2999 -#2043 := (not #2042)
  3.3000 -#2058 := (not #2043)
  3.3001 -#2068 := (and #2058 #2064)
  3.3002 -#2073 := (and #1212 #2068)
  3.3003 -#2077 := (or #2022 #2073)
  3.3004 -#2081 := (and #1193 #2077)
  3.3005 -#2085 := (or #1990 #2081)
  3.3006 -#2089 := (and #1179 #2085)
  3.3007 -#2093 := (or #1963 #2089)
  3.3008 -#1957 := (not #661)
  3.3009 -#2097 := (and #1957 #2093)
  3.3010 -#2101 := (or #661 #2097)
  3.3011 -#2105 := (and #563 #2101)
  3.3012 -#2109 := (or #1943 #2105)
  3.3013 -#2113 := (and #1170 #2109)
  3.3014 -#2117 := (or #1923 #2113)
  3.3015 -#1900 := (not #715)
  3.3016 -#1881 := (and #1875 #1880)
  3.3017 -#2121 := (and #1881 #184 #1323 #1315 #1900 #1302 #1159 #2117)
  3.3018 -#1833 := (+ #1817 #1832)
  3.3019 -#1834 := (+ #1824 #1833)
  3.3020 -#1835 := (>= #1834 0::Int)
  3.3021 -#1836 := (or #1830 #1835)
  3.3022 -#1837 := (not #1836)
  3.3023 -#1856 := (or #1837 #1852)
  3.3024 -#1793 := (+ #1792 #1047)
  3.3025 -#1799 := (+ #1798 #1793)
  3.3026 -#1800 := (= #1799 0::Int)
  3.3027 -#1794 := (>= #1793 0::Int)
  3.3028 -#1795 := (not #1794)
  3.3029 -#1801 := (and #1795 #1800)
  3.3030 -#1806 := (or #1056 #1801)
  3.3031 -#1809 := (forall (vars (?v0 S2)) #1806)
  3.3032 -#1860 := (and #1809 #1856)
  3.3033 -#1766 := (+ #1765 #1761)
  3.3034 -#1767 := (= #1766 0::Int)
  3.3035 -#1768 := (and #1763 #1767)
  3.3036 -#1777 := (not #1768)
  3.3037 -#1780 := (forall (vars (?v1 S2)) #1777)
  3.3038 -#1759 := (and #1753 #1758)
  3.3039 -#1760 := (not #1759)
  3.3040 -#1774 := (not #1760)
  3.3041 -#1784 := (and #1774 #1780)
  3.3042 -#1864 := (or #1784 #1860)
  3.3043 -#1748 := (not #494)
  3.3044 -#1745 := (not #503)
  3.3045 -#1742 := (not #512)
  3.3046 -#1739 := (not #521)
  3.3047 -#1868 := (and #1736 #1739 #1742 #1745 #1748 #1864)
  3.3048 -#2125 := (or #1868 #2121)
  3.3049 -#1709 := (+ #1708 #1002)
  3.3050 -#1717 := (+ #1716 #1709)
  3.3051 -#1718 := (= #1717 0::Int)
  3.3052 -#1710 := (>= #1709 0::Int)
  3.3053 -#1711 := (not #1710)
  3.3054 -#1719 := (and #1711 #1713 #1718)
  3.3055 -#1724 := (or #1011 #1719)
  3.3056 -#1727 := (forall (vars (?v0 S2)) #1724)
  3.3057 -#1681 := (not #804)
  3.3058 -#1664 := (+ #964 #1663)
  3.3059 -#1665 := (+ #1655 #1664)
  3.3060 -#1666 := (= #1665 0::Int)
  3.3061 -#1656 := (+ #1655 #964)
  3.3062 -#1657 := (>= #1656 0::Int)
  3.3063 -#1658 := (not #1657)
  3.3064 -#1667 := (and #1658 #1660 #1666)
  3.3065 -#1672 := (or #973 #1667)
  3.3066 -#1675 := (forall (vars (?v0 S2)) #1672)
  3.3067 -#2129 := (and #1675 #1681 #1397 #1388 #1377 #1727 #2125)
  3.3068 -#1621 := (and #1615 #1620)
  3.3069 -#1622 := (not #1621)
  3.3070 -#1637 := (not #1622)
  3.3071 -#1647 := (and #1637 #1643)
  3.3072 -#2133 := (or #1647 #2129)
  3.3073 -#2137 := (and #958 #2133)
  3.3074 -#1597 := (+ #1596 #1587)
  3.3075 -#1598 := (+ #1594 #1597)
  3.3076 -#1599 := (>= #1598 0::Int)
  3.3077 -#1600 := (or #1593 #1599)
  3.3078 -#1601 := (not #1600)
  3.3079 -#2141 := (or #1601 #2137)
  3.3080 -#2145 := (and #932 #2141)
  3.3081 -#2149 := (or #1569 #2145)
  3.3082 -#2153 := (and #917 #2149)
  3.3083 -#2157 := (or #1542 #2153)
  3.3084 -#1504 := (not #868)
  3.3085 -#2161 := (and #1504 #2157)
  3.3086 -#2165 := (or #868 #2161)
  3.3087 -#2482 := (iff #2165 #2481)
  3.3088 -#2479 := (iff #2161 #2478)
  3.3089 -#2476 := (iff #2157 #2475)
  3.3090 -#2473 := (iff #2153 #2472)
  3.3091 -#2470 := (iff #2149 #2469)
  3.3092 -#2467 := (iff #2145 #2466)
  3.3093 -#2464 := (iff #2141 #2463)
  3.3094 -#2461 := (iff #2137 #2460)
  3.3095 -#2458 := (iff #2133 #2457)
  3.3096 -#2455 := (iff #2129 #2454)
  3.3097 -#2452 := (iff #2125 #2451)
  3.3098 -#2449 := (iff #2121 #2446)
  3.3099 -#2443 := (and #1881 #184 #1323 #1315 #194 #1302 #1159 #2440)
  3.3100 -#2447 := (iff #2443 #2446)
  3.3101 -#2448 := [rewrite]: #2447
  3.3102 -#2444 := (iff #2121 #2443)
  3.3103 -#2441 := (iff #2117 #2440)
  3.3104 -#2438 := (iff #2113 #2437)
  3.3105 -#2435 := (iff #2109 #2434)
  3.3106 -#2432 := (iff #2105 #2431)
  3.3107 -#2429 := (iff #2101 #2428)
  3.3108 -#2426 := (iff #2097 #2425)
  3.3109 -#2423 := (iff #2093 #2422)
  3.3110 -#2420 := (iff #2089 #2419)
  3.3111 -#2417 := (iff #2085 #2416)
  3.3112 -#2414 := (iff #2081 #2413)
  3.3113 -#2411 := (iff #2077 #2410)
  3.3114 -#2408 := (iff #2073 #2405)
  3.3115 -#2399 := (and #2042 #2396)
  3.3116 -#2402 := (and #1212 #2399)
  3.3117 -#2406 := (iff #2402 #2405)
  3.3118 -#2407 := [rewrite]: #2406
  3.3119 -#2403 := (iff #2073 #2402)
  3.3120 -#2400 := (iff #2068 #2399)
  3.3121 -#2397 := (iff #2064 #2396)
  3.3122 -#2394 := (iff #2061 #2393)
  3.3123 -#2391 := (iff #2051 #2390)
  3.3124 -#2388 := (iff #2050 #2387)
  3.3125 -#2385 := (= #2049 #2384)
  3.3126 -#2386 := [rewrite]: #2385
  3.3127 -#2389 := [monotonicity #2386]: #2388
  3.3128 -#2392 := [monotonicity #2389]: #2391
  3.3129 -#2395 := [monotonicity #2392]: #2394
  3.3130 -#2398 := [quant-intro #2395]: #2397
  3.3131 -#2381 := (iff #2058 #2042)
  3.3132 -#2382 := [rewrite]: #2381
  3.3133 -#2401 := [monotonicity #2382 #2398]: #2400
  3.3134 -#2404 := [monotonicity #2401]: #2403
  3.3135 -#2409 := [trans #2404 #2407]: #2408
  3.3136 -#2412 := [monotonicity #2409]: #2411
  3.3137 -#2415 := [monotonicity #2412]: #2414
  3.3138 -#2418 := [monotonicity #2415]: #2417
  3.3139 -#2421 := [monotonicity #2418]: #2420
  3.3140 -#2424 := [monotonicity #2421]: #2423
  3.3141 -#2379 := (iff #1957 #217)
  3.3142 -#2380 := [rewrite]: #2379
  3.3143 -#2427 := [monotonicity #2380 #2424]: #2426
  3.3144 -#2430 := [monotonicity #2427]: #2429
  3.3145 -#2433 := [monotonicity #2430]: #2432
  3.3146 -#2436 := [monotonicity #2433]: #2435
  3.3147 -#2439 := [monotonicity #2436]: #2438
  3.3148 -#2442 := [monotonicity #2439]: #2441
  3.3149 -#2377 := (iff #1900 #194)
  3.3150 -#2378 := [rewrite]: #2377
  3.3151 -#2445 := [monotonicity #2378 #2442]: #2444
  3.3152 -#2450 := [trans #2445 #2448]: #2449
  3.3153 -#2375 := (iff #1868 #2374)
  3.3154 -#2372 := (iff #1864 #2371)
  3.3155 -#2369 := (iff #1860 #2368)
  3.3156 -#2366 := (iff #1856 #2365)
  3.3157 -#2363 := (iff #1837 #2362)
  3.3158 -#2360 := (iff #1836 #2359)
  3.3159 -#2357 := (iff #1835 #2356)
  3.3160 -#2354 := (= #1834 #2353)
  3.3161 -#2355 := [rewrite]: #2354
  3.3162 -#2358 := [monotonicity #2355]: #2357
  3.3163 -#2361 := [monotonicity #2358]: #2360
  3.3164 -#2364 := [monotonicity #2361]: #2363
  3.3165 -#2367 := [monotonicity #2364]: #2366
  3.3166 -#2350 := (iff #1809 #2349)
  3.3167 -#2347 := (iff #1806 #2346)
  3.3168 -#2344 := (iff #1801 #2343)
  3.3169 -#2341 := (iff #1800 #2338)
  3.3170 -#2328 := (+ #1792 #1798)
  3.3171 -#2329 := (+ #1047 #2328)
  3.3172 -#2332 := (= #2329 0::Int)
  3.3173 -#2339 := (iff #2332 #2338)
  3.3174 -#2340 := [rewrite]: #2339
  3.3175 -#2333 := (iff #1800 #2332)
  3.3176 -#2330 := (= #1799 #2329)
  3.3177 -#2331 := [rewrite]: #2330
  3.3178 -#2334 := [monotonicity #2331]: #2333
  3.3179 -#2342 := [trans #2334 #2340]: #2341
  3.3180 -#2326 := (iff #1795 #2325)
  3.3181 -#2323 := (iff #1794 #2320)
  3.3182 -#2312 := (+ #1047 #1792)
  3.3183 -#2315 := (>= #2312 0::Int)
  3.3184 -#2321 := (iff #2315 #2320)
  3.3185 -#2322 := [rewrite]: #2321
  3.3186 -#2316 := (iff #1794 #2315)
  3.3187 -#2313 := (= #1793 #2312)
  3.3188 -#2314 := [rewrite]: #2313
  3.3189 -#2317 := [monotonicity #2314]: #2316
  3.3190 -#2324 := [trans #2317 #2322]: #2323
  3.3191 -#2327 := [monotonicity #2324]: #2326
  3.3192 -#2345 := [monotonicity #2327 #2342]: #2344
  3.3193 -#2348 := [monotonicity #2345]: #2347
  3.3194 -#2351 := [quant-intro #2348]: #2350
  3.3195 -#2370 := [monotonicity #2351 #2367]: #2369
  3.3196 -#2310 := (iff #1784 #2307)
  3.3197 -#2304 := (and #1759 #2301)
  3.3198 -#2308 := (iff #2304 #2307)
  3.3199 -#2309 := [rewrite]: #2308
  3.3200 -#2305 := (iff #1784 #2304)
  3.3201 -#2302 := (iff #1780 #2301)
  3.3202 -#2299 := (iff #1777 #2298)
  3.3203 -#2296 := (iff #1768 #2295)
  3.3204 -#2293 := (iff #1767 #2292)
  3.3205 -#2290 := (= #1766 #2289)
  3.3206 -#2291 := [rewrite]: #2290
  3.3207 -#2294 := [monotonicity #2291]: #2293
  3.3208 -#2297 := [monotonicity #2294]: #2296
  3.3209 -#2300 := [monotonicity #2297]: #2299
  3.3210 -#2303 := [quant-intro #2300]: #2302
  3.3211 -#2286 := (iff #1774 #1759)
  3.3212 -#2287 := [rewrite]: #2286
  3.3213 -#2306 := [monotonicity #2287 #2303]: #2305
  3.3214 -#2311 := [trans #2306 #2309]: #2310
  3.3215 -#2373 := [monotonicity #2311 #2370]: #2372
  3.3216 -#2284 := (iff #1748 #152)
  3.3217 -#2285 := [rewrite]: #2284
  3.3218 -#2282 := (iff #1745 #149)
  3.3219 -#2283 := [rewrite]: #2282
  3.3220 -#2280 := (iff #1742 #147)
  3.3221 -#2281 := [rewrite]: #2280
  3.3222 -#2278 := (iff #1739 #144)
  3.3223 -#2279 := [rewrite]: #2278
  3.3224 -#2376 := [monotonicity #2279 #2281 #2283 #2285 #2373]: #2375
  3.3225 -#2453 := [monotonicity #2376 #2450]: #2452
  3.3226 -#2276 := (iff #1727 #2275)
  3.3227 -#2273 := (iff #1724 #2272)
  3.3228 -#2270 := (iff #1719 #2269)
  3.3229 -#2267 := (iff #1718 #2264)
  3.3230 -#2254 := (+ #1708 #1716)
  3.3231 -#2255 := (+ #1002 #2254)
  3.3232 -#2258 := (= #2255 0::Int)
  3.3233 -#2265 := (iff #2258 #2264)
  3.3234 -#2266 := [rewrite]: #2265
  3.3235 -#2259 := (iff #1718 #2258)
  3.3236 -#2256 := (= #1717 #2255)
  3.3237 -#2257 := [rewrite]: #2256
  3.3238 -#2260 := [monotonicity #2257]: #2259
  3.3239 -#2268 := [trans #2260 #2266]: #2267
  3.3240 -#2252 := (iff #1711 #2251)
  3.3241 -#2249 := (iff #1710 #2246)
  3.3242 -#2238 := (+ #1002 #1708)
  3.3243 -#2241 := (>= #2238 0::Int)
  3.3244 -#2247 := (iff #2241 #2246)
  3.3245 -#2248 := [rewrite]: #2247
  3.3246 -#2242 := (iff #1710 #2241)
  3.3247 -#2239 := (= #1709 #2238)
  3.3248 -#2240 := [rewrite]: #2239
  3.3249 -#2243 := [monotonicity #2240]: #2242
  3.3250 -#2250 := [trans #2243 #2248]: #2249
  3.3251 -#2253 := [monotonicity #2250]: #2252
  3.3252 -#2271 := [monotonicity #2253 #2268]: #2270
  3.3253 -#2274 := [monotonicity #2271]: #2273
  3.3254 -#2277 := [quant-intro #2274]: #2276
  3.3255 -#2236 := (iff #1681 #111)
  3.3256 -#2237 := [rewrite]: #2236
  3.3257 -#2234 := (iff #1675 #2233)
  3.3258 -#2231 := (iff #1672 #2230)
  3.3259 -#2228 := (iff #1667 #2227)
  3.3260 -#2225 := (iff #1666 #2222)
  3.3261 -#2212 := (+ #1655 #1663)
  3.3262 -#2213 := (+ #964 #2212)
  3.3263 -#2216 := (= #2213 0::Int)
  3.3264 -#2223 := (iff #2216 #2222)
  3.3265 -#2224 := [rewrite]: #2223
  3.3266 -#2217 := (iff #1666 #2216)
  3.3267 -#2214 := (= #1665 #2213)
  3.3268 -#2215 := [rewrite]: #2214
  3.3269 -#2218 := [monotonicity #2215]: #2217
  3.3270 -#2226 := [trans #2218 #2224]: #2225
  3.3271 -#2210 := (iff #1658 #2209)
  3.3272 -#2207 := (iff #1657 #2204)
  3.3273 -#2196 := (+ #964 #1655)
  3.3274 -#2199 := (>= #2196 0::Int)
  3.3275 -#2205 := (iff #2199 #2204)
  3.3276 -#2206 := [rewrite]: #2205
  3.3277 -#2200 := (iff #1657 #2199)
  3.3278 -#2197 := (= #1656 #2196)
  3.3279 -#2198 := [rewrite]: #2197
  3.3280 -#2201 := [monotonicity #2198]: #2200
  3.3281 -#2208 := [trans #2201 #2206]: #2207
  3.3282 -#2211 := [monotonicity #2208]: #2210
  3.3283 -#2229 := [monotonicity #2211 #2226]: #2228
  3.3284 -#2232 := [monotonicity #2229]: #2231
  3.3285 -#2235 := [quant-intro #2232]: #2234
  3.3286 -#2456 := [monotonicity #2235 #2237 #2277 #2453]: #2455
  3.3287 -#2194 := (iff #1647 #2191)
  3.3288 -#2188 := (and #1621 #1643)
  3.3289 -#2192 := (iff #2188 #2191)
  3.3290 -#2193 := [rewrite]: #2192
  3.3291 -#2189 := (iff #1647 #2188)
  3.3292 -#2186 := (iff #1637 #1621)
  3.3293 -#2187 := [rewrite]: #2186
  3.3294 -#2190 := [monotonicity #2187]: #2189
  3.3295 -#2195 := [trans #2190 #2193]: #2194
  3.3296 -#2459 := [monotonicity #2195 #2456]: #2458
  3.3297 -#2462 := [monotonicity #2459]: #2461
  3.3298 -#2184 := (iff #1601 #2183)
  3.3299 -#2181 := (iff #1600 #2180)
  3.3300 -#2178 := (iff #1599 #2177)
  3.3301 -#2175 := (= #1598 #2174)
  3.3302 -#2176 := [rewrite]: #2175
  3.3303 -#2179 := [monotonicity #2176]: #2178
  3.3304 -#2182 := [monotonicity #2179]: #2181
  3.3305 -#2185 := [monotonicity #2182]: #2184
  3.3306 -#2465 := [monotonicity #2185 #2462]: #2464
  3.3307 -#2468 := [monotonicity #2465]: #2467
  3.3308 -#2471 := [monotonicity #2468]: #2470
  3.3309 -#2474 := [monotonicity #2471]: #2473
  3.3310 -#2477 := [monotonicity #2474]: #2476
  3.3311 -#2171 := (iff #1504 #81)
  3.3312 -#2172 := [rewrite]: #2171
  3.3313 -#2480 := [monotonicity #2172 #2477]: #2479
  3.3314 -#2483 := [monotonicity #2480]: #2482
  3.3315 -#1479 := (not #1453)
  3.3316 -#2166 := (~ #1479 #2165)
  3.3317 -#2162 := (not #1450)
  3.3318 -#2163 := (~ #2162 #2161)
  3.3319 -#2158 := (not #1447)
  3.3320 -#2159 := (~ #2158 #2157)
  3.3321 -#2154 := (not #1444)
  3.3322 -#2155 := (~ #2154 #2153)
  3.3323 -#2150 := (not #1441)
  3.3324 -#2151 := (~ #2150 #2149)
  3.3325 -#2146 := (not #1438)
  3.3326 -#2147 := (~ #2146 #2145)
  3.3327 -#2142 := (not #1435)
  3.3328 -#2143 := (~ #2142 #2141)
  3.3329 -#2138 := (not #1432)
  3.3330 -#2139 := (~ #2138 #2137)
  3.3331 -#2134 := (not #1429)
  3.3332 -#2135 := (~ #2134 #2133)
  3.3333 -#2130 := (not #1424)
  3.3334 -#2131 := (~ #2130 #2129)
  3.3335 -#2126 := (not #1362)
  3.3336 -#2127 := (~ #2126 #2125)
  3.3337 -#2122 := (not #1357)
  3.3338 -#2123 := (~ #2122 #2121)
  3.3339 -#2118 := (not #1288)
  3.3340 -#2119 := (~ #2118 #2117)
  3.3341 -#2114 := (not #1285)
  3.3342 -#2115 := (~ #2114 #2113)
  3.3343 -#2110 := (not #1282)
  3.3344 -#2111 := (~ #2110 #2109)
  3.3345 -#2106 := (not #1279)
  3.3346 -#2107 := (~ #2106 #2105)
  3.3347 -#2102 := (not #1276)
  3.3348 -#2103 := (~ #2102 #2101)
  3.3349 -#2098 := (not #1273)
  3.3350 -#2099 := (~ #2098 #2097)
  3.3351 -#2094 := (not #1270)
  3.3352 -#2095 := (~ #2094 #2093)
  3.3353 -#2090 := (not #1267)
  3.3354 -#2091 := (~ #2090 #2089)
  3.3355 -#2086 := (not #1264)
  3.3356 -#2087 := (~ #2086 #2085)
  3.3357 -#2082 := (not #1261)
  3.3358 -#2083 := (~ #2082 #2081)
  3.3359 -#2078 := (not #1258)
  3.3360 -#2079 := (~ #2078 #2077)
  3.3361 -#2074 := (not #1255)
  3.3362 -#2075 := (~ #2074 #2073)
  3.3363 -#2055 := (not #1252)
  3.3364 -#2071 := (~ #2055 #2068)
  3.3365 -#2052 := (exists (vars (?v1 S2)) #2051)
  3.3366 -#2053 := (or #2043 #2052)
  3.3367 -#2054 := (not #2053)
  3.3368 -#2069 := (~ #2054 #2068)
  3.3369 -#2065 := (not #2052)
  3.3370 -#2066 := (~ #2065 #2064)
  3.3371 -#2062 := (~ #2061 #2061)
  3.3372 -#2063 := [refl]: #2062
  3.3373 -#2067 := [nnf-neg #2063]: #2066
  3.3374 -#2059 := (~ #2058 #2058)
  3.3375 -#2060 := [refl]: #2059
  3.3376 -#2070 := [nnf-neg #2060 #2067]: #2069
  3.3377 -#2056 := (~ #2055 #2054)
  3.3378 -#2057 := [sk]: #2056
  3.3379 -#2072 := [trans #2057 #2070]: #2071
  3.3380 -#2031 := (not #1215)
  3.3381 -#2032 := (~ #2031 #1212)
  3.3382 -#2029 := (~ #1212 #1212)
  3.3383 -#2027 := (~ #1209 #1209)
  3.3384 -#2028 := [refl]: #2027
  3.3385 -#2030 := [nnf-pos #2028]: #2029
  3.3386 -#2033 := [nnf-neg #2030]: #2032
  3.3387 -#2076 := [nnf-neg #2033 #2072]: #2075
  3.3388 -#2023 := (~ #1215 #2022)
  3.3389 -#2024 := [sk]: #2023
  3.3390 -#2080 := [nnf-neg #2024 #2076]: #2079
  3.3391 -#1999 := (not #1196)
  3.3392 -#2000 := (~ #1999 #1193)
  3.3393 -#1997 := (~ #1193 #1193)
  3.3394 -#1995 := (~ #1190 #1190)
  3.3395 -#1996 := [refl]: #1995
  3.3396 -#1998 := [nnf-pos #1996]: #1997
  3.3397 -#2001 := [nnf-neg #1998]: #2000
  3.3398 -#2084 := [nnf-neg #2001 #2080]: #2083
  3.3399 -#1991 := (~ #1196 #1990)
  3.3400 -#1992 := [sk]: #1991
  3.3401 -#2088 := [nnf-neg #1992 #2084]: #2087
  3.3402 -#1972 := (not #1182)
  3.3403 -#1973 := (~ #1972 #1179)
  3.3404 -#1970 := (~ #1179 #1179)
  3.3405 -#1968 := (~ #1176 #1176)
  3.3406 -#1969 := [refl]: #1968
  3.3407 -#1971 := [nnf-pos #1969]: #1970
  3.3408 -#1974 := [nnf-neg #1971]: #1973
  3.3409 -#2092 := [nnf-neg #1974 #2088]: #2091
  3.3410 -#1964 := (~ #1182 #1963)
  3.3411 -#1965 := [sk]: #1964
  3.3412 -#2096 := [nnf-neg #1965 #2092]: #2095
  3.3413 -#1958 := (~ #1957 #1957)
  3.3414 -#1959 := [refl]: #1958
  3.3415 -#2100 := [nnf-neg #1959 #2096]: #2099
  3.3416 -#1955 := (~ #661 #661)
  3.3417 -#1956 := [refl]: #1955
  3.3418 -#2104 := [nnf-neg #1956 #2100]: #2103
  3.3419 -#1952 := (not #673)
  3.3420 -#1953 := (~ #1952 #563)
  3.3421 -#1950 := (~ #563 #563)
  3.3422 -#1948 := (~ #560 #560)
  3.3423 -#1949 := [refl]: #1948
  3.3424 -#1951 := [nnf-pos #1949]: #1950
  3.3425 -#1954 := [nnf-neg #1951]: #1953
  3.3426 -#2108 := [nnf-neg #1954 #2104]: #2107
  3.3427 -#1944 := (~ #673 #1943)
  3.3428 -#1945 := [sk]: #1944
  3.3429 -#2112 := [nnf-neg #1945 #2108]: #2111
  3.3430 -#1932 := (not #1173)
  3.3431 -#1933 := (~ #1932 #1170)
  3.3432 -#1930 := (~ #1170 #1170)
  3.3433 -#1928 := (~ #1165 #1165)
  3.3434 -#1929 := [refl]: #1928
  3.3435 -#1931 := [nnf-pos #1929]: #1930
  3.3436 -#1934 := [nnf-neg #1931]: #1933
  3.3437 -#2116 := [nnf-neg #1934 #2112]: #2115
  3.3438 -#1924 := (~ #1173 #1923)
  3.3439 -#1925 := [sk]: #1924
  3.3440 -#2120 := [nnf-neg #1925 #2116]: #2119
  3.3441 -#1914 := (not #1162)
  3.3442 -#1915 := (~ #1914 #1159)
  3.3443 -#1912 := (~ #1159 #1159)
  3.3444 -#1910 := (~ #1156 #1156)
  3.3445 -#1911 := [refl]: #1910
  3.3446 -#1913 := [nnf-pos #1911]: #1912
  3.3447 -#1916 := [nnf-neg #1913]: #1915
  3.3448 -#1907 := (not #1305)
  3.3449 -#1908 := (~ #1907 #1302)
  3.3450 -#1905 := (~ #1302 #1302)
  3.3451 -#1903 := (~ #1299 #1299)
  3.3452 -#1904 := [refl]: #1903
  3.3453 -#1906 := [nnf-pos #1904]: #1905
  3.3454 -#1909 := [nnf-neg #1906]: #1908
  3.3455 -#1901 := (~ #1900 #1900)
  3.3456 -#1902 := [refl]: #1901
  3.3457 -#1897 := (not #1318)
  3.3458 -#1898 := (~ #1897 #1315)
  3.3459 -#1895 := (~ #1315 #1315)
  3.3460 -#1893 := (~ #1312 #1312)
  3.3461 -#1894 := [refl]: #1893
  3.3462 -#1896 := [nnf-pos #1894]: #1895
  3.3463 -#1899 := [nnf-neg #1896]: #1898
  3.3464 -#1891 := (~ #1323 #1323)
  3.3465 -#1892 := [refl]: #1891
  3.3466 -#1889 := (~ #184 #184)
  3.3467 -#1890 := [refl]: #1889
  3.3468 -#1886 := (not #1333)
  3.3469 -#1887 := (~ #1886 #1881)
  3.3470 -#1882 := (~ #1117 #1881)
  3.3471 -#1883 := [sk]: #1882
  3.3472 -#1888 := [nnf-neg #1883]: #1887
  3.3473 -#2124 := [nnf-neg #1888 #1890 #1892 #1899 #1902 #1909 #1916 #2120]: #2123
  3.3474 -#1869 := (not #1135)
  3.3475 -#1870 := (~ #1869 #1868)
  3.3476 -#1865 := (not #1111)
  3.3477 -#1866 := (~ #1865 #1864)
  3.3478 -#1861 := (not #1108)
  3.3479 -#1862 := (~ #1861 #1860)
  3.3480 -#1857 := (not #1105)
  3.3481 -#1858 := (~ #1857 #1856)
  3.3482 -#1853 := (not #1102)
  3.3483 -#1854 := (~ #1853 #1852)
  3.3484 -#1850 := (~ #1849 #1849)
  3.3485 -#1851 := [refl]: #1850
  3.3486 -#1846 := (not #1099)
  3.3487 -#1847 := (~ #1846 #1096)
  3.3488 -#1844 := (~ #1096 #1096)
  3.3489 -#1842 := (~ #1093 #1093)
  3.3490 -#1843 := [refl]: #1842
  3.3491 -#1845 := [nnf-pos #1843]: #1844
  3.3492 -#1848 := [nnf-neg #1845]: #1847
  3.3493 -#1855 := [nnf-neg #1848 #1851]: #1854
  3.3494 -#1838 := (~ #1099 #1837)
  3.3495 -#1839 := [sk]: #1838
  3.3496 -#1859 := [nnf-neg #1839 #1855]: #1858
  3.3497 -#1812 := (not #1081)
  3.3498 -#1813 := (~ #1812 #1809)
  3.3499 -#1810 := (~ #1078 #1809)
  3.3500 -#1807 := (~ #1075 #1806)
  3.3501 -#1802 := (~ #1072 #1801)
  3.3502 -#1803 := [sk]: #1802
  3.3503 -#1789 := (~ #1056 #1056)
  3.3504 -#1790 := [refl]: #1789
  3.3505 -#1808 := [monotonicity #1790 #1803]: #1807
  3.3506 -#1811 := [nnf-pos #1808]: #1810
  3.3507 -#1814 := [nnf-neg #1811]: #1813
  3.3508 -#1863 := [nnf-neg #1814 #1859]: #1862
  3.3509 -#1787 := (~ #1081 #1784)
  3.3510 -#1769 := (exists (vars (?v1 S2)) #1768)
  3.3511 -#1770 := (or #1760 #1769)
  3.3512 -#1771 := (not #1770)
  3.3513 -#1785 := (~ #1771 #1784)
  3.3514 -#1781 := (not #1769)
  3.3515 -#1782 := (~ #1781 #1780)
  3.3516 -#1778 := (~ #1777 #1777)
  3.3517 -#1779 := [refl]: #1778
  3.3518 -#1783 := [nnf-neg #1779]: #1782
  3.3519 -#1775 := (~ #1774 #1774)
  3.3520 -#1776 := [refl]: #1775
  3.3521 -#1786 := [nnf-neg #1776 #1783]: #1785
  3.3522 -#1772 := (~ #1081 #1771)
  3.3523 -#1773 := [sk]: #1772
  3.3524 -#1788 := [trans #1773 #1786]: #1787
  3.3525 -#1867 := [nnf-neg #1788 #1863]: #1866
  3.3526 -#1749 := (~ #1748 #1748)
  3.3527 -#1750 := [refl]: #1749
  3.3528 -#1746 := (~ #1745 #1745)
  3.3529 -#1747 := [refl]: #1746
  3.3530 -#1743 := (~ #1742 #1742)
  3.3531 -#1744 := [refl]: #1743
  3.3532 -#1740 := (~ #1739 #1739)
  3.3533 -#1741 := [refl]: #1740
  3.3534 -#1737 := (~ #1333 #1736)
  3.3535 -#1734 := (~ #1733 #1733)
  3.3536 -#1735 := [refl]: #1734
  3.3537 -#1738 := [nnf-neg #1735]: #1737
  3.3538 -#1871 := [nnf-neg #1738 #1741 #1744 #1747 #1750 #1867]: #1870
  3.3539 -#2128 := [nnf-neg #1871 #2124]: #2127
  3.3540 -#1730 := (not #1044)
  3.3541 -#1731 := (~ #1730 #1727)
  3.3542 -#1728 := (~ #1041 #1727)
  3.3543 -#1725 := (~ #1038 #1724)
  3.3544 -#1720 := (~ #1035 #1719)
  3.3545 -#1721 := [sk]: #1720
  3.3546 -#1705 := (~ #1011 #1011)
  3.3547 -#1706 := [refl]: #1705
  3.3548 -#1726 := [monotonicity #1706 #1721]: #1725
  3.3549 -#1729 := [nnf-pos #1726]: #1728
  3.3550 -#1732 := [nnf-neg #1729]: #1731
  3.3551 -#1702 := (not #1380)
  3.3552 -#1703 := (~ #1702 #1377)
  3.3553 -#1700 := (~ #1377 #1377)
  3.3554 -#1698 := (~ #1374 #1374)
  3.3555 -#1699 := [refl]: #1698
  3.3556 -#1701 := [nnf-pos #1699]: #1700
  3.3557 -#1704 := [nnf-neg #1701]: #1703
  3.3558 -#1695 := (not #1391)
  3.3559 -#1696 := (~ #1695 #1388)
  3.3560 -#1693 := (~ #1388 #1388)
  3.3561 -#1691 := (~ #1385 #1385)
  3.3562 -#1692 := [refl]: #1691
  3.3563 -#1694 := [nnf-pos #1692]: #1693
  3.3564 -#1697 := [nnf-neg #1694]: #1696
  3.3565 -#1688 := (not #1400)
  3.3566 -#1689 := (~ #1688 #1397)
  3.3567 -#1686 := (~ #1397 #1397)
  3.3568 -#1684 := (~ #1394 #1394)
  3.3569 -#1685 := [refl]: #1684
  3.3570 -#1687 := [nnf-pos #1685]: #1686
  3.3571 -#1690 := [nnf-neg #1687]: #1689
  3.3572 -#1682 := (~ #1681 #1681)
  3.3573 -#1683 := [refl]: #1682
  3.3574 -#1678 := (not #1403)
  3.3575 -#1679 := (~ #1678 #1675)
  3.3576 -#1676 := (~ #999 #1675)
  3.3577 -#1673 := (~ #996 #1672)
  3.3578 -#1668 := (~ #993 #1667)
  3.3579 -#1669 := [sk]: #1668
  3.3580 -#1652 := (~ #973 #973)
  3.3581 -#1653 := [refl]: #1652
  3.3582 -#1674 := [monotonicity #1653 #1669]: #1673
  3.3583 -#1677 := [nnf-pos #1674]: #1676
  3.3584 -#1680 := [nnf-neg #1677]: #1679
  3.3585 -#2132 := [nnf-neg #1680 #1683 #1690 #1697 #1704 #1732 #2128]: #2131
  3.3586 -#1650 := (~ #1403 #1647)
  3.3587 -#1632 := (exists (vars (?v1 S2)) #1631)
  3.3588 -#1633 := (or #1622 #1632)
  3.3589 -#1634 := (not #1633)
  3.3590 -#1648 := (~ #1634 #1647)
  3.3591 -#1644 := (not #1632)
  3.3592 -#1645 := (~ #1644 #1643)
  3.3593 -#1641 := (~ #1640 #1640)
  3.3594 -#1642 := [refl]: #1641
  3.3595 -#1646 := [nnf-neg #1642]: #1645
  3.3596 -#1638 := (~ #1637 #1637)
  3.3597 -#1639 := [refl]: #1638
  3.3598 -#1649 := [nnf-neg #1639 #1646]: #1648
  3.3599 -#1635 := (~ #1403 #1634)
  3.3600 -#1636 := [sk]: #1635
  3.3601 -#1651 := [trans #1636 #1649]: #1650
  3.3602 -#2136 := [nnf-neg #1651 #2132]: #2135
  3.3603 -#1610 := (not #961)
  3.3604 -#1611 := (~ #1610 #958)
  3.3605 -#1608 := (~ #958 #958)
  3.3606 -#1606 := (~ #955 #955)
  3.3607 -#1607 := [refl]: #1606
  3.3608 -#1609 := [nnf-pos #1607]: #1608
  3.3609 -#1612 := [nnf-neg #1609]: #1611
  3.3610 -#2140 := [nnf-neg #1612 #2136]: #2139
  3.3611 -#1602 := (~ #961 #1601)
  3.3612 -#1603 := [sk]: #1602
  3.3613 -#2144 := [nnf-neg #1603 #2140]: #2143
  3.3614 -#1578 := (not #935)
  3.3615 -#1579 := (~ #1578 #932)
  3.3616 -#1576 := (~ #932 #932)
  3.3617 -#1574 := (~ #929 #929)
  3.3618 -#1575 := [refl]: #1574
  3.3619 -#1577 := [nnf-pos #1575]: #1576
  3.3620 -#1580 := [nnf-neg #1577]: #1579
  3.3621 -#2148 := [nnf-neg #1580 #2144]: #2147
  3.3622 -#1570 := (~ #935 #1569)
  3.3623 -#1571 := [sk]: #1570
  3.3624 -#2152 := [nnf-neg #1571 #2148]: #2151
  3.3625 -#1551 := (not #920)
  3.3626 -#1552 := (~ #1551 #917)
  3.3627 -#1549 := (~ #917 #917)
  3.3628 -#1547 := (~ #916 #916)
  3.3629 -#1548 := [refl]: #1547
  3.3630 -#1550 := [nnf-pos #1548]: #1549
  3.3631 -#1553 := [nnf-neg #1550]: #1552
  3.3632 -#2156 := [nnf-neg #1553 #2152]: #2155
  3.3633 -#1543 := (~ #920 #1542)
  3.3634 -#1544 := [sk]: #1543
  3.3635 -#2160 := [nnf-neg #1544 #2156]: #2159
  3.3636 -#1505 := (~ #1504 #1504)
  3.3637 -#1538 := [refl]: #1505
  3.3638 -#2164 := [nnf-neg #1538 #2160]: #2163
  3.3639 -#1536 := (~ #868 #868)
  3.3640 -#1537 := [refl]: #1536
  3.3641 -#2167 := [nnf-neg #1537 #2164]: #2166
  3.3642 -#1480 := [not-or-elim #1475]: #1479
  3.3643 -#2168 := [mp~ #1480 #2167]: #2165
  3.3644 -#2169 := [mp #2168 #2483]: #2481
  3.3645 -#3122 := [mp #2169 #3121]: #3119
  3.3646 -#4037 := [mp #3122 #4036]: #4034
  3.3647 -#7144 := [unit-resolution #4037 #4122]: #4031
  3.3648 -#3361 := (or #4028 #4022)
  3.3649 -#3351 := [def-axiom]: #3361
  3.3650 -#7145 := [unit-resolution #3351 #7144]: #4022
  3.3651 -#3357 := (or #4025 #1542 #4019)
  3.3652 -#3359 := [def-axiom]: #3357
  3.3653 -#7146 := [unit-resolution #3359 #7145 #4053]: #4019
  3.3654 -#3355 := (or #4016 #4010)
  3.3655 -#3358 := [def-axiom]: #3355
  3.3656 -#7147 := [unit-resolution #3358 #7146]: #4010
  3.3657 -#4245 := [hypothesis]: #1560
  3.3658 -#3661 := (forall (vars (?v0 S2)) (:pat #3660) #78)
  3.3659 -#3664 := (iff #79 #3661)
  3.3660 -#3662 := (iff #78 #78)
  3.3661 -#3663 := [refl]: #3662
  3.3662 -#3665 := [quant-intro #3663]: #3664
  3.3663 -#1502 := (~ #79 #79)
  3.3664 -#1533 := (~ #78 #78)
  3.3665 -#1534 := [refl]: #1533
  3.3666 -#1503 := [nnf-pos #1534]: #1502
  3.3667 -#1478 := [not-or-elim #1475]: #79
  3.3668 -#1535 := [mp~ #1478 #1503]: #79
  3.3669 -#3666 := [mp #1535 #3665]: #3661
  3.3670 -#6940 := (not #3661)
  3.3671 -#4154 := (or #6940 #1884)
  3.3672 -#4155 := [quant-inst #1555]: #4154
  3.3673 -#4251 := [unit-resolution #4155 #3666 #4245]: false
  3.3674 -#4288 := [lemma #4251]: #1884
  3.3675 -#3186 := (or #1841 #1560)
  3.3676 -#3272 := [def-axiom]: #3186
  3.3677 -#7148 := [unit-resolution #3272 #4288]: #1841
  3.3678 -#3217 := (or #4013 #1946 #4007)
  3.3679 -#3375 := [def-axiom]: #3217
  3.3680 -#7149 := [unit-resolution #3375 #7148 #7147]: #4007
  3.3681 -#3397 := (or #4004 #3998)
  3.3682 -#3367 := [def-axiom]: #3397
  3.3683 -#7150 := [unit-resolution #3367 #7149]: #3998
  3.3684 -#6160 := [hypothesis]: #1584
  3.3685 -#6331 := (or #6940 #2503)
  3.3686 -#6332 := [quant-inst #1581]: #6331
  3.3687 -#6161 := [unit-resolution #6332 #3666 #6160]: false
  3.3688 -#6581 := [lemma #6161]: #2503
  3.3689 -#3277 := (or #2518 #1584)
  3.3690 -#3274 := [def-axiom]: #3277
  3.3691 -#7151 := [unit-resolution #3274 #6581]: #2518
  3.3692 -#3394 := (or #4001 #2523 #3995)
  3.3693 -#3395 := [def-axiom]: #3394
  3.3694 -#7152 := [unit-resolution #3395 #7151 #7150]: #3995
  3.3695 -#3378 := (or #3992 #3986)
  3.3696 -#3385 := [def-axiom]: #3378
  3.3697 -#7153 := [unit-resolution #3385 #7152]: #3986
  3.3698 -#3415 := (or #3989 #3705 #3983)
  3.3699 -#3400 := [def-axiom]: #3415
  3.3700 -#7154 := [unit-resolution #3400 #7153]: #3986
  3.3701 -#7155 := [unit-resolution #7154 #6633]: #3983
  3.3702 -#3407 := (or #3980 #3974)
  3.3703 -#3408 := [def-axiom]: #3407
  3.3704 -#7801 := [unit-resolution #3408 #7155]: #3974
  3.3705 -#6893 := [hypothesis]: #3817
  3.3706 -#3559 := (or #3814 #149)
  3.3707 -#3554 := [def-axiom]: #3559
  3.3708 -#6888 := [unit-resolution #3554 #6893]: #149
  3.3709 -#3555 := (or #3814 #3751)
  3.3710 -#3556 := [def-axiom]: #3555
  3.3711 -#6808 := [unit-resolution #3556 #6893]: #3751
  3.3712 -#3431 := (or #3980 #111)
  3.3713 -#3432 := [def-axiom]: #3431
  3.3714 -#6894 := [unit-resolution #3432 #7155]: #111
  3.3715 -#4278 := (or #503 #169 #804)
  3.3716 -#4273 := [hypothesis]: #111
  3.3717 -#4275 := (= #168 #110)
  3.3718 -#4274 := [hypothesis]: #149
  3.3719 -#4276 := [monotonicity #4274]: #4275
  3.3720 -#4271 := [trans #4276 #4273]: #169
  3.3721 -#4158 := [hypothesis]: #1849
  3.3722 -#4277 := [unit-resolution #4158 #4271]: false
  3.3723 -#4279 := [lemma #4277]: #4278
  3.3724 -#6895 := [unit-resolution #4279 #6888 #6894]: #169
  3.3725 -#3298 := (or #3790 #1849)
  3.3726 -#3299 := [def-axiom]: #3298
  3.3727 -#6896 := [unit-resolution #3299 #6895]: #3790
  3.3728 -#3402 := (or #3814 #3808)
  3.3729 -#3403 := [def-axiom]: #3402
  3.3730 -#6861 := [unit-resolution #3403 #6893]: #3808
  3.3731 -#7454 := (or #3768 #503)
  3.3732 -#6806 := (?v1!7 ?v0!8)
  3.3733 -#7010 := (f19 f25 #6806)
  3.3734 -#7056 := (* -1::Int #7010)
  3.3735 -#6807 := (f19 f20 #6806)
  3.3736 -#7278 := (+ #6807 #7056)
  3.3737 -#7328 := (>= #7278 0::Int)
  3.3738 -#7277 := (= #6807 #7010)
  3.3739 -#7409 := (= #7010 #6807)
  3.3740 -#7410 := [monotonicity #4274]: #7409
  3.3741 -#7411 := [symm #7410]: #7277
  3.3742 -#7412 := (not #7277)
  3.3743 -#7413 := (or #7412 #7328)
  3.3744 -#7414 := [th-lemma arith triangle-eq]: #7413
  3.3745 -#7415 := [unit-resolution #7414 #7411]: #7328
  3.3746 -#6897 := (* -1::Int #6807)
  3.3747 -#6741 := (f19 f20 ?v0!8)
  3.3748 -#6898 := (+ #6741 #6897)
  3.3749 -#6903 := (<= #6898 0::Int)
  3.3750 -#6821 := (not #6903)
  3.3751 -#6850 := (f6 f7 #6806)
  3.3752 -#6853 := (f5 #6850 ?v0!8)
  3.3753 -#6889 := (f4 #6853)
  3.3754 -#6890 := (* -1::Int #6889)
  3.3755 -#6908 := (+ #6897 #6890)
  3.3756 -#6925 := (+ #6741 #6908)
  3.3757 -#5298 := (= #6925 0::Int)
  3.3758 -#6077 := (not #5298)
  3.3759 -#6904 := (f11 f21 #6806)
  3.3760 -#6851 := (= #6904 f1)
  3.3761 -#6852 := (not #6851)
  3.3762 -#6078 := (or #6903 #6852 #6077)
  3.3763 -#6102 := (not #6078)
  3.3764 -#6742 := (* -1::Int #6741)
  3.3765 -#6772 := (+ f3 #6742)
  3.3766 -#6773 := (<= #6772 0::Int)
  3.3767 -#7378 := (not #6773)
  3.3768 -#7416 := [hypothesis]: #3771
  3.3769 -#3249 := (or #3768 #1758)
  3.3770 -#3591 := [def-axiom]: #3249
  3.3771 -#7417 := [unit-resolution #3591 #7416]: #1758
  3.3772 -#7026 := (+ #1754 #6742)
  3.3773 -#7012 := (>= #7026 0::Int)
  3.3774 -#7025 := (= #1754 #6741)
  3.3775 -#7418 := (= #6741 #1754)
  3.3776 -#6982 := (= f20 f25)
  3.3777 -#6983 := [symm #4274]: #6982
  3.3778 -#7419 := [monotonicity #6983]: #7418
  3.3779 -#7420 := [symm #7419]: #7025
  3.3780 -#7421 := (not #7025)
  3.3781 -#7422 := (or #7421 #7012)
  3.3782 -#7423 := [th-lemma arith triangle-eq]: #7422
  3.3783 -#7424 := [unit-resolution #7423 #7420]: #7012
  3.3784 -#7379 := (not #7012)
  3.3785 -#7380 := (or #7378 #7379 #1757)
  3.3786 -#7368 := [hypothesis]: #1758
  3.3787 -#7369 := [hypothesis]: #6773
  3.3788 -#7376 := [hypothesis]: #7012
  3.3789 -#7377 := [th-lemma arith farkas 1 -1 1 #7376 #7369 #7368]: false
  3.3790 -#7381 := [lemma #7377]: #7380
  3.3791 -#7425 := [unit-resolution #7381 #7424 #7417]: #7378
  3.3792 -#7428 := (or #6773 #6102)
  3.3793 -#3589 := (or #3768 #1753)
  3.3794 -#3254 := [def-axiom]: #3589
  3.3795 -#7426 := [unit-resolution #3254 #7416]: #1753
  3.3796 -#3405 := (or #3980 #3742)
  3.3797 -#3406 := [def-axiom]: #3405
  3.3798 -#7427 := [unit-resolution #3406 #7155]: #3742
  3.3799 -#6227 := (or #3747 #1752 #6773 #6102)
  3.3800 -#6103 := (or #1752 #6773 #6102)
  3.3801 -#6189 := (or #3747 #6103)
  3.3802 -#6704 := (iff #6189 #6227)
  3.3803 -#6805 := [rewrite]: #6704
  3.3804 -#6190 := [quant-inst #1751]: #6189
  3.3805 -#6797 := [mp #6190 #6805]: #6227
  3.3806 -#7429 := [unit-resolution #6797 #7427 #7426]: #7428
  3.3807 -#7430 := [unit-resolution #7429 #7425]: #6102
  3.3808 -#6854 := (or #6078 #6821)
  3.3809 -#6860 := [def-axiom]: #6854
  3.3810 -#7431 := [unit-resolution #6860 #7430]: #6821
  3.3811 -#7057 := (+ #1754 #7056)
  3.3812 -#7058 := (<= #7057 0::Int)
  3.3813 -#7101 := (+ #6890 #7056)
  3.3814 -#7102 := (+ #1754 #7101)
  3.3815 -#7105 := (= #7102 0::Int)
  3.3816 -#7195 := (<= #7102 0::Int)
  3.3817 -#7327 := (<= #7278 0::Int)
  3.3818 -#7432 := (or #7412 #7327)
  3.3819 -#7433 := [th-lemma arith triangle-eq]: #7432
  3.3820 -#7434 := [unit-resolution #7433 #7411]: #7327
  3.3821 -#6815 := (<= #6925 0::Int)
  3.3822 -#6862 := (or #6078 #5298)
  3.3823 -#6863 := [def-axiom]: #6862
  3.3824 -#7435 := [unit-resolution #6863 #7430]: #5298
  3.3825 -#7436 := (or #6077 #6815)
  3.3826 -#7437 := [th-lemma arith triangle-eq]: #7436
  3.3827 -#7438 := [unit-resolution #7437 #7435]: #6815
  3.3828 -#7011 := (<= #7026 0::Int)
  3.3829 -#7439 := (or #7421 #7011)
  3.3830 -#7440 := [th-lemma arith triangle-eq]: #7439
  3.3831 -#7441 := [unit-resolution #7440 #7420]: #7011
  3.3832 -#7390 := (not #7327)
  3.3833 -#7389 := (not #6815)
  3.3834 -#7388 := (not #7011)
  3.3835 -#7391 := (or #7195 #7388 #7389 #7390)
  3.3836 -#7375 := [hypothesis]: #7327
  3.3837 -#7128 := [hypothesis]: #6815
  3.3838 -#7384 := [hypothesis]: #7011
  3.3839 -#7385 := (not #7195)
  3.3840 -#7386 := [hypothesis]: #7385
  3.3841 -#7387 := [th-lemma arith farkas -1 1 1 1 #7386 #7384 #7128 #7375]: false
  3.3842 -#7392 := [lemma #7387]: #7391
  3.3843 -#7442 := [unit-resolution #7392 #7441 #7438 #7434]: #7195
  3.3844 -#7196 := (>= #7102 0::Int)
  3.3845 -#6820 := (>= #6925 0::Int)
  3.3846 -#7443 := (or #6077 #6820)
  3.3847 -#7444 := [th-lemma arith triangle-eq]: #7443
  3.3848 -#7445 := [unit-resolution #7444 #7435]: #6820
  3.3849 -#7406 := (not #7328)
  3.3850 -#7405 := (not #6820)
  3.3851 -#7407 := (or #7196 #7379 #7405 #7406)
  3.3852 -#7400 := [hypothesis]: #7328
  3.3853 -#7401 := [hypothesis]: #6820
  3.3854 -#7402 := (not #7196)
  3.3855 -#7403 := [hypothesis]: #7402
  3.3856 -#7404 := [th-lemma arith farkas -1 1 1 1 #7403 #7376 #7401 #7400]: false
  3.3857 -#7408 := [lemma #7404]: #7407
  3.3858 -#7446 := [unit-resolution #7408 #7424 #7445 #7415]: #7196
  3.3859 -#7447 := (or #7105 #7385 #7402)
  3.3860 -#7448 := [th-lemma arith triangle-eq]: #7447
  3.3861 -#7449 := [unit-resolution #7448 #7446 #7442]: #7105
  3.3862 -#7114 := (not #7105)
  3.3863 -#7122 := (or #7058 #7114)
  3.3864 -#3234 := (or #3768 #3760)
  3.3865 -#3575 := [def-axiom]: #3234
  3.3866 -#7450 := [unit-resolution #3575 #7416]: #3760
  3.3867 -#7125 := (or #3765 #7058 #7114)
  3.3868 -#7015 := (+ #1755 #6889)
  3.3869 -#7028 := (+ #7010 #7015)
  3.3870 -#7029 := (= #7028 0::Int)
  3.3871 -#7049 := (not #7029)
  3.3872 -#7013 := (+ #7010 #1755)
  3.3873 -#7014 := (>= #7013 0::Int)
  3.3874 -#7050 := (or #7014 #7049)
  3.3875 -#7126 := (or #3765 #7050)
  3.3876 -#7119 := (iff #7126 #7125)
  3.3877 -#6981 := (or #3765 #7122)
  3.3878 -#7017 := (iff #6981 #7125)
  3.3879 -#7118 := [rewrite]: #7017
  3.3880 -#7016 := (iff #7126 #6981)
  3.3881 -#7123 := (iff #7050 #7122)
  3.3882 -#7115 := (iff #7049 #7114)
  3.3883 -#7113 := (iff #7029 #7105)
  3.3884 -#7091 := (+ #6889 #7010)
  3.3885 -#7086 := (+ #1755 #7091)
  3.3886 -#7094 := (= #7086 0::Int)
  3.3887 -#7106 := (iff #7094 #7105)
  3.3888 -#7112 := [rewrite]: #7106
  3.3889 -#7095 := (iff #7029 #7094)
  3.3890 -#7092 := (= #7028 #7086)
  3.3891 -#7093 := [rewrite]: #7092
  3.3892 -#7096 := [monotonicity #7093]: #7095
  3.3893 -#7111 := [trans #7096 #7112]: #7113
  3.3894 -#7116 := [monotonicity #7111]: #7115
  3.3895 -#7089 := (iff #7014 #7058)
  3.3896 -#7051 := (+ #1755 #7010)
  3.3897 -#7048 := (>= #7051 0::Int)
  3.3898 -#7087 := (iff #7048 #7058)
  3.3899 -#7088 := [rewrite]: #7087
  3.3900 -#7054 := (iff #7014 #7048)
  3.3901 -#7052 := (= #7013 #7051)
  3.3902 -#7053 := [rewrite]: #7052
  3.3903 -#7055 := [monotonicity #7053]: #7054
  3.3904 -#7090 := [trans #7055 #7088]: #7089
  3.3905 -#7121 := [monotonicity #7090 #7116]: #7123
  3.3906 -#7124 := [monotonicity #7121]: #7016
  3.3907 -#7120 := [trans #7124 #7118]: #7119
  3.3908 -#6980 := [quant-inst #6806]: #7126
  3.3909 -#7127 := [mp #6980 #7120]: #7125
  3.3910 -#7451 := [unit-resolution #7127 #7450]: #7122
  3.3911 -#7452 := [unit-resolution #7451 #7449]: #7058
  3.3912 -#7453 := [th-lemma arith farkas 1 -1 1 1 #7424 #7452 #7431 #7415]: false
  3.3913 -#7455 := [lemma #7453]: #7454
  3.3914 -#6859 := [unit-resolution #7455 #6888]: #3768
  3.3915 -#3562 := (or #3811 #3771 #3805)
  3.3916 -#3566 := [def-axiom]: #3562
  3.3917 -#6864 := [unit-resolution #3566 #6859 #6861]: #3805
  3.3918 -#3283 := (or #3802 #3796)
  3.3919 -#3284 := [def-axiom]: #3283
  3.3920 -#6869 := [unit-resolution #3284 #6864]: #3796
  3.3921 -#3571 := (or #3799 #2759 #3793)
  3.3922 -#3568 := [def-axiom]: #3571
  3.3923 -#6935 := [unit-resolution #3568 #6869 #6896]: #2759
  3.3924 -#3225 := (or #2754 #1828)
  3.3925 -#3226 := [def-axiom]: #3225
  3.3926 -#6870 := [unit-resolution #3226 #6935]: #1828
  3.3927 -#6589 := (f19 f20 ?v1!10)
  3.3928 -#6584 := (* -1::Int #6589)
  3.3929 -#6868 := (+ #1817 #6584)
  3.3930 -#6946 := (>= #6868 0::Int)
  3.3931 -#4646 := (or #6946 #503)
  3.3932 -#6329 := (= #1817 #6589)
  3.3933 -#6605 := (= #6589 #1817)
  3.3934 -#6606 := [monotonicity #6983]: #6605
  3.3935 -#6585 := [symm #6606]: #6329
  3.3936 -#7134 := (not #6946)
  3.3937 -#6586 := [hypothesis]: #7134
  3.3938 -#6330 := (not #6329)
  3.3939 -#6322 := (or #6330 #6946)
  3.3940 -#6328 := [th-lemma arith triangle-eq]: #6322
  3.3941 -#6580 := [unit-resolution #6328 #6586 #6585]: false
  3.3942 -#4567 := [lemma #6580]: #4646
  3.3943 -#6867 := [unit-resolution #4567 #6888]: #6946
  3.3944 -#3583 := (or #2754 #1821)
  3.3945 -#3585 := [def-axiom]: #3583
  3.3946 -#6945 := [unit-resolution #3585 #6935]: #1821
  3.3947 -#3586 := (not #2356)
  3.3948 -#3584 := (or #2754 #3586)
  3.3949 -#3587 := [def-axiom]: #3584
  3.3950 -#6866 := [unit-resolution #3587 #6935]: #3586
  3.3951 -#7019 := (or #7134 #3756 #1827 #2356 #1820 #503)
  3.3952 -#6765 := (f19 f20 ?v0!11)
  3.3953 -#6766 := (* -1::Int #6765)
  3.3954 -#6948 := (+ #1831 #6766)
  3.3955 -#6949 := (<= #6948 0::Int)
  3.3956 -#6947 := (= #1831 #6765)
  3.3957 -#6984 := (= #6765 #1831)
  3.3958 -#6985 := [monotonicity #6983]: #6984
  3.3959 -#6986 := [symm #6985]: #6947
  3.3960 -#6987 := (not #6947)
  3.3961 -#6988 := (or #6987 #6949)
  3.3962 -#6975 := [th-lemma arith triangle-eq]: #6988
  3.3963 -#6976 := [unit-resolution #6975 #6986]: #6949
  3.3964 -#7130 := [hypothesis]: #3586
  3.3965 -#7143 := [hypothesis]: #1828
  3.3966 -#7140 := [hypothesis]: #3751
  3.3967 -#7131 := [hypothesis]: #6946
  3.3968 -#6572 := (+ f3 #6584)
  3.3969 -#6576 := (<= #6572 0::Int)
  3.3970 -#7138 := (not #6576)
  3.3971 -#6974 := [hypothesis]: #1821
  3.3972 -#6977 := (or #7138 #1820 #7134)
  3.3973 -#6978 := [th-lemma arith assign-bounds -1 -1]: #6977
  3.3974 -#6979 := [unit-resolution #6978 #7131 #6974]: #7138
  3.3975 -#7133 := (not #6949)
  3.3976 -#7160 := (or #6576 #1827 #3756 #7134 #2356 #7133)
  3.3977 -#6907 := (+ #6589 #6766)
  3.3978 -#6926 := (+ #1824 #6907)
  3.3979 -#6924 := (>= #6926 0::Int)
  3.3980 -#7132 := (not #6924)
  3.3981 -#7129 := [hypothesis]: #6949
  3.3982 -#7135 := (or #7132 #7133 #2356 #7134)
  3.3983 -#7136 := [th-lemma arith assign-bounds -1 -1 1]: #7135
  3.3984 -#7137 := [unit-resolution #7136 #7131 #7130 #7129]: #7132
  3.3985 -#6587 := (f11 f21 ?v1!10)
  3.3986 -#6588 := (= #6587 f1)
  3.3987 -#7139 := [hypothesis]: #7138
  3.3988 -#5703 := (or #6588 #6576)
  3.3989 -#6635 := (or #3756 #6588 #6576)
  3.3990 -#6636 := (or #3756 #5703)
  3.3991 -#6638 := (iff #6636 #6635)
  3.3992 -#6211 := [rewrite]: #6638
  3.3993 -#6637 := [quant-inst #1815]: #6636
  3.3994 -#6252 := [mp #6637 #6211]: #6635
  3.3995 -#7141 := [unit-resolution #6252 #7140]: #5703
  3.3996 -#7142 := [unit-resolution #7141 #7139]: #6588
  3.3997 -#6849 := (not #6588)
  3.3998 -#7157 := (or #6849 #6924)
  3.3999 -#3399 := (or #3980 #3734)
  3.4000 -#3404 := [def-axiom]: #3399
  3.4001 -#7156 := [unit-resolution #3404 #7155]: #3734
  3.4002 -#6930 := (or #3739 #6849 #1827 #6924)
  3.4003 -#6927 := (or #6849 #1827 #6924)
  3.4004 -#6931 := (or #3739 #6927)
  3.4005 -#3348 := (iff #6931 #6930)
  3.4006 -#3221 := [rewrite]: #3348
  3.4007 -#6932 := [quant-inst #1816 #1815]: #6931
  3.4008 -#4127 := [mp #6932 #3221]: #6930
  3.4009 -#7158 := [unit-resolution #4127 #7156 #7143]: #7157
  3.4010 -#7159 := [unit-resolution #7158 #7142 #7137]: false
  3.4011 -#7161 := [lemma #7159]: #7160
  3.4012 -#7018 := [unit-resolution #7161 #6979 #7131 #7140 #7143 #7130 #6976]: false
  3.4013 -#7020 := [lemma #7018]: #7019
  3.4014 -#6950 := [unit-resolution #7020 #6866 #6945 #6867 #6870 #6808 #6888]: false
  3.4015 -#7021 := [lemma #6950]: #3814
  3.4016 -#3419 := (or #3977 #3817 #3971)
  3.4017 -#3421 := [def-axiom]: #3419
  3.4018 -#7802 := [unit-resolution #3421 #7021 #7801]: #3971
  3.4019 -#3459 := (or #3968 #194)
  3.4020 -#3464 := [def-axiom]: #3459
  3.4021 -#8144 := [unit-resolution #3464 #7802]: #194
  3.4022 -#8146 := [symm #8144]: #8145
  3.4023 -#16380 := [monotonicity #8146]: #16289
  3.4024 -#16388 := [monotonicity #16380]: #16359
  3.4025 -#16389 := [symm #16388]: #16382
  3.4026 -#16391 := [monotonicity #16389]: #16390
  3.4027 -#19086 := [hypothesis]: #4534
  3.4028 -#5090 := (or #4541 #5087)
  3.4029 -#8395 := [hypothesis]: #1943
  3.4030 -#3547 := (or #1942 #1937)
  3.4031 -#3543 := [def-axiom]: #3547
  3.4032 -#8389 := [unit-resolution #3543 #8395]: #1937
  3.4033 -#3548 := (not #1941)
  3.4034 -#3542 := (or #1942 #3548)
  3.4035 -#3549 := [def-axiom]: #3542
  3.4036 -#8396 := [unit-resolution #3549 #8395]: #3548
  3.4037 -#5879 := (* -1::Int #1940)
  3.4038 -#5980 := (+ #185 #5879)
  3.4039 -#7760 := (>= #5980 0::Int)
  3.4040 -#4329 := (f11 f21 ?v0!14)
  3.4041 -#4316 := (= #4329 f1)
  3.4042 -#4315 := (= ?v0!14 f28)
  3.4043 -#4345 := (or #4315 #4316)
  3.4044 -#4328 := (f11 #193 ?v0!14)
  3.4045 -#4330 := (= #4328 f1)
  3.4046 -#4348 := (iff #4330 #4345)
  3.4047 -#8073 := (or #7518 #4348)
  3.4048 -#4314 := (if #4315 #4057 #4316)
  3.4049 -#4317 := (iff #4330 #4314)
  3.4050 -#8074 := (or #7518 #4317)
  3.4051 -#8078 := (iff #8074 #8073)
  3.4052 -#8080 := (iff #8073 #8073)
  3.4053 -#8081 := [rewrite]: #8080
  3.4054 -#4337 := (iff #4317 #4348)
  3.4055 -#4344 := (iff #4314 #4345)
  3.4056 -#4318 := (if #4315 true #4316)
  3.4057 -#4346 := (iff #4318 #4345)
  3.4058 -#4338 := [rewrite]: #4346
  3.4059 -#4319 := (iff #4314 #4318)
  3.4060 -#4332 := [monotonicity #4060]: #4319
  3.4061 -#4347 := [trans #4332 #4338]: #4344
  3.4062 -#4349 := [monotonicity #4347]: #4337
  3.4063 -#8079 := [monotonicity #4349]: #8078
  3.4064 -#8082 := [trans #8079 #8081]: #8078
  3.4065 -#8077 := [quant-inst #115 #181 #3 #1935]: #8074
  3.4066 -#8083 := [mp #8077 #8082]: #8073
  3.4067 -#8113 := [unit-resolution #8083 #3646]: #4348
  3.4068 -#8114 := [hypothesis]: #1937
  3.4069 -#8147 := (= #4328 #1936)
  3.4070 -#8148 := [monotonicity #8146]: #8147
  3.4071 -#8149 := [trans #8148 #8114]: #4330
  3.4072 -#8094 := (not #4330)
  3.4073 -#8091 := (not #4348)
  3.4074 -#8095 := (or #8091 #8094 #4345)
  3.4075 -#8096 := [def-axiom]: #8095
  3.4076 -#8150 := [unit-resolution #8096 #8149 #8113]: #4345
  3.4077 -#8088 := (not #4345)
  3.4078 -#8152 := (or #8088 #4316)
  3.4079 -#7690 := (not #4315)
  3.4080 -#7795 := [hypothesis]: #3548
  3.4081 -#7815 := (or #7690 #1941)
  3.4082 -#7809 := (= #185 #1940)
  3.4083 -#7807 := (= #1940 #185)
  3.4084 -#7796 := [hypothesis]: #4315
  3.4085 -#7808 := [monotonicity #7796]: #7807
  3.4086 -#7810 := [symm #7808]: #7809
  3.4087 -#7811 := (= #1939 #185)
  3.4088 -#4131 := (= #4078 #185)
  3.4089 -#4082 := (f5 #195 f28)
  3.4090 -#4083 := (f4 #4082)
  3.4091 -#4101 := (>= #4083 0::Int)
  3.4092 -#4086 := (* -1::Int #4083)
  3.4093 -#4087 := (+ f3 #4086)
  3.4094 -#4088 := (<= #4087 0::Int)
  3.4095 -#4133 := (or #4088 #4101)
  3.4096 -#6365 := (= #4083 0::Int)
  3.4097 -#6474 := (not #6365)
  3.4098 -#6475 := [hypothesis]: #6474
  3.4099 -#14 := (f6 f7 #10)
  3.4100 -#15 := (f5 #14 #11)
  3.4101 -#3600 := (pattern #15)
  3.4102 -#16 := (f4 #15)
  3.4103 -#17 := (= #16 0::Int)
  3.4104 -#12 := (= #10 #11)
  3.4105 -#20 := (not #12)
  3.4106 -#306 := (or #20 #17)
  3.4107 -#3601 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3600) #306)
  3.4108 -#314 := (forall (vars (?v0 S2) (?v1 S2)) #306)
  3.4109 -#3604 := (iff #314 #3601)
  3.4110 -#3602 := (iff #306 #306)
  3.4111 -#3603 := [refl]: #3602
  3.4112 -#3605 := [quant-intro #3603]: #3604
  3.4113 -#1510 := (~ #314 #314)
  3.4114 -#1508 := (~ #306 #306)
  3.4115 -#1509 := [refl]: #1508
  3.4116 -#1511 := [nnf-pos #1509]: #1510
  3.4117 -#18 := (implies #12 #17)
  3.4118 -#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
  3.4119 -#315 := (iff #19 #314)
  3.4120 -#312 := (iff #18 #306)
  3.4121 -#313 := [rewrite]: #312
  3.4122 -#316 := [quant-intro #313]: #315
  3.4123 -#305 := [asserted]: #19
  3.4124 -#319 := [mp #305 #316]: #314
  3.4125 -#1484 := [mp~ #319 #1511]: #314
  3.4126 -#3606 := [mp #1484 #3605]: #3601
  3.4127 -#6226 := (not #3601)
  3.4128 -#6401 := (or #6226 #6365)
  3.4129 -#4403 := (= f28 f28)
  3.4130 -#6358 := (not #4403)
  3.4131 -#6369 := (or #6358 #6365)
  3.4132 -#6400 := (or #6226 #6369)
  3.4133 -#6403 := (iff #6400 #6401)
  3.4134 -#6471 := (iff #6401 #6401)
  3.4135 -#6466 := [rewrite]: #6471
  3.4136 -#6387 := (iff #6369 #6365)
  3.4137 -#6377 := (or false #6365)
  3.4138 -#6382 := (iff #6377 #6365)
  3.4139 -#6386 := [rewrite]: #6382
  3.4140 -#6383 := (iff #6369 #6377)
  3.4141 -#6378 := (iff #6358 false)
  3.4142 -#6370 := (iff #6358 #6910)
  3.4143 -#4406 := (iff #4403 true)
  3.4144 -#4407 := [rewrite]: #4406
  3.4145 -#6375 := [monotonicity #4407]: #6370
  3.4146 -#6379 := [trans #6375 #6914]: #6378
  3.4147 -#6384 := [monotonicity #6379]: #6383
  3.4148 -#6398 := [trans #6384 #6386]: #6387
  3.4149 -#6439 := [monotonicity #6398]: #6403
  3.4150 -#6470 := [trans #6439 #6466]: #6403
  3.4151 -#6402 := [quant-inst #181 #181]: #6400
  3.4152 -#6472 := [mp #6402 #6470]: #6401
  3.4153 -#6476 := [unit-resolution #6472 #3606 #6475]: false
  3.4154 -#6482 := [lemma #6476]: #6365
  3.4155 -#7797 := (or #6474 #4101)
  3.4156 -#7798 := [th-lemma arith triangle-eq]: #7797
  3.4157 -#7799 := [unit-resolution #7798 #6482]: #4101
  3.4158 -#7285 := (not #4101)
  3.4159 -#7283 := (or #4133 #7285)
  3.4160 -#7286 := [def-axiom]: #7283
  3.4161 -#7800 := [unit-resolution #7286 #7799]: #4133
  3.4162 -#3445 := (or #3968 #3838)
  3.4163 -#3426 := [def-axiom]: #3445
  3.4164 -#7803 := [unit-resolution #3426 #7802]: #3838
  3.4165 -#4136 := (not #4133)
  3.4166 -#7259 := (or #3843 #4136 #4131)
  3.4167 -#4089 := (+ #1146 #4086)
  3.4168 -#4090 := (+ #185 #4089)
  3.4169 -#4091 := (<= #4090 0::Int)
  3.4170 -#4129 := (or #4088 #4091)
  3.4171 -#4130 := (not #4129)
  3.4172 -#4132 := (or #4130 #4131)
  3.4173 -#7260 := (or #3843 #4132)
  3.4174 -#7266 := (iff #7260 #7259)
  3.4175 -#4139 := (or #4136 #4131)
  3.4176 -#7262 := (or #3843 #4139)
  3.4177 -#7265 := (iff #7262 #7259)
  3.4178 -#7261 := [rewrite]: #7265
  3.4179 -#7263 := (iff #7260 #7262)
  3.4180 -#4140 := (iff #4132 #4139)
  3.4181 -#4137 := (iff #4130 #4136)
  3.4182 -#4134 := (iff #4129 #4133)
  3.4183 -#4104 := (iff #4091 #4101)
  3.4184 -#4098 := (<= #4086 0::Int)
  3.4185 -#4102 := (iff #4098 #4101)
  3.4186 -#4103 := [rewrite]: #4102
  3.4187 -#4099 := (iff #4091 #4098)
  3.4188 -#4096 := (= #4090 #4086)
  3.4189 -#4097 := [rewrite]: #4096
  3.4190 -#4100 := [monotonicity #4097]: #4099
  3.4191 -#4105 := [trans #4100 #4103]: #4104
  3.4192 -#4135 := [monotonicity #4105]: #4134
  3.4193 -#4138 := [monotonicity #4135]: #4137
  3.4194 -#4141 := [monotonicity #4138]: #4140
  3.4195 -#7264 := [monotonicity #4141]: #7263
  3.4196 -#7271 := [trans #7264 #7261]: #7266
  3.4197 -#7256 := [quant-inst #181]: #7260
  3.4198 -#7272 := [mp #7256 #7271]: #7259
  3.4199 -#7804 := [unit-resolution #7272 #7803 #7800]: #4131
  3.4200 -#7805 := (= #1939 #4078)
  3.4201 -#7806 := [monotonicity #7796]: #7805
  3.4202 -#7812 := [trans #7806 #7804]: #7811
  3.4203 -#7813 := [trans #7812 #7810]: #1941
  3.4204 -#7814 := [unit-resolution #7795 #7813]: false
  3.4205 -#7816 := [lemma #7814]: #7815
  3.4206 -#8151 := [unit-resolution #7816 #7795]: #7690
  3.4207 -#8089 := (or #8088 #4315 #4316)
  3.4208 -#8090 := [def-axiom]: #8089
  3.4209 -#8153 := [unit-resolution #8090 #8151]: #8152
  3.4210 -#8154 := [unit-resolution #8153 #8150]: #4316
  3.4211 -#3456 := (or #3968 #184)
  3.4212 -#3457 := [def-axiom]: #3456
  3.4213 -#8155 := [unit-resolution #3457 #7802]: #184
  3.4214 -#3443 := (or #3980 #3726)
  3.4215 -#3398 := [def-axiom]: #3443
  3.4216 -#8156 := [unit-resolution #3398 #7155]: #3726
  3.4217 -#7693 := (not #4316)
  3.4218 -#8138 := (or #3731 #183 #7693 #7760)
  3.4219 -#7761 := (or #183 #7693 #7760)
  3.4220 -#8139 := (or #3731 #7761)
  3.4221 -#8141 := (iff #8139 #8138)
  3.4222 -#8142 := [rewrite]: #8141
  3.4223 -#8140 := [quant-inst #1935 #181]: #8139
  3.4224 -#8143 := [mp #8140 #8142]: #8138
  3.4225 -#8157 := [unit-resolution #8143 #8156 #8155 #8154]: #7760
  3.4226 -#6005 := (f5 #195 ?v0!14)
  3.4227 -#6011 := (f4 #6005)
  3.4228 -#6036 := (+ #5879 #6011)
  3.4229 -#6037 := (+ #185 #6036)
  3.4230 -#6038 := (>= #6037 0::Int)
  3.4231 -#8046 := (not #6038)
  3.4232 -#6012 := (* -1::Int #6011)
  3.4233 -#6010 := (+ f3 #6012)
  3.4234 -#6014 := (<= #6010 0::Int)
  3.4235 -#6049 := (or #6014 #6038)
  3.4236 -#6056 := (not #6049)
  3.4237 -#8032 := (or #3843 #6056 #1941)
  3.4238 -#6015 := (+ #1146 #6012)
  3.4239 -#6013 := (+ #1940 #6015)
  3.4240 -#6017 := (<= #6013 0::Int)
  3.4241 -#6051 := (or #6014 #6017)
  3.4242 -#6052 := (not #6051)
  3.4243 -#6054 := (or #6052 #1941)
  3.4244 -#8033 := (or #3843 #6054)
  3.4245 -#8040 := (iff #8033 #8032)
  3.4246 -#6067 := (or #6056 #1941)
  3.4247 -#8035 := (or #3843 #6067)
  3.4248 -#8038 := (iff #8035 #8032)
  3.4249 -#8039 := [rewrite]: #8038
  3.4250 -#8036 := (iff #8033 #8035)
  3.4251 -#6068 := (iff #6054 #6067)
  3.4252 -#6057 := (iff #6052 #6056)
  3.4253 -#6055 := (iff #6051 #6049)
  3.4254 -#6043 := (iff #6017 #6038)
  3.4255 -#6027 := (+ #1940 #6012)
  3.4256 -#6030 := (+ #1146 #6027)
  3.4257 -#6034 := (<= #6030 0::Int)
  3.4258 -#6039 := (iff #6034 #6038)
  3.4259 -#6040 := [rewrite]: #6039
  3.4260 -#6035 := (iff #6017 #6034)
  3.4261 -#6031 := (= #6013 #6030)
  3.4262 -#6032 := [rewrite]: #6031
  3.4263 -#6033 := [monotonicity #6032]: #6035
  3.4264 -#6044 := [trans #6033 #6040]: #6043
  3.4265 -#6053 := [monotonicity #6044]: #6055
  3.4266 -#6058 := [monotonicity #6053]: #6057
  3.4267 -#6045 := [monotonicity #6058]: #6068
  3.4268 -#8037 := [monotonicity #6045]: #8036
  3.4269 -#8041 := [trans #8037 #8039]: #8040
  3.4270 -#8034 := [quant-inst #1935]: #8033
  3.4271 -#8042 := [mp #8034 #8041]: #8032
  3.4272 -#8158 := [unit-resolution #8042 #7803 #7795]: #6056
  3.4273 -#8047 := (or #6049 #8046)
  3.4274 -#8048 := [def-axiom]: #8047
  3.4275 -#8159 := [unit-resolution #8048 #8158]: #8046
  3.4276 -#8125 := (>= #6011 0::Int)
  3.4277 -#6251 := (<= #6011 0::Int)
  3.4278 -#6224 := (not #6251)
  3.4279 -#6208 := (= f28 ?v0!14)
  3.4280 -#6209 := (not #6208)
  3.4281 -#8164 := (iff #7690 #6209)
  3.4282 -#8162 := (iff #4315 #6208)
  3.4283 -#8160 := (iff #6208 #4315)
  3.4284 -#8161 := [commutativity]: #8160
  3.4285 -#8163 := [symm #8161]: #8162
  3.4286 -#8165 := [monotonicity #8163]: #8164
  3.4287 -#8166 := [mp #8151 #8165]: #6209
  3.4288 -#6225 := (or #6208 #6224)
  3.4289 -#325 := (<= #16 0::Int)
  3.4290 -#326 := (not #325)
  3.4291 -#329 := (or #12 #326)
  3.4292 -#3607 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #3600) #329)
  3.4293 -#332 := (forall (vars (?v0 S2) (?v1 S2)) #329)
  3.4294 -#3610 := (iff #332 #3607)
  3.4295 -#3608 := (iff #329 #329)
  3.4296 -#3609 := [refl]: #3608
  3.4297 -#3611 := [quant-intro #3609]: #3610
  3.4298 -#1486 := (~ #332 #332)
  3.4299 -#1485 := (~ #329 #329)
  3.4300 -#1482 := [refl]: #1485
  3.4301 -#1487 := [nnf-pos #1482]: #1486
  3.4302 -#21 := (< 0::Int #16)
  3.4303 -#22 := (implies #20 #21)
  3.4304 -#23 := (forall (vars (?v0 S2) (?v1 S2)) #22)
  3.4305 -#335 := (iff #23 #332)
  3.4306 -#318 := (or #12 #21)
  3.4307 -#322 := (forall (vars (?v0 S2) (?v1 S2)) #318)
  3.4308 -#333 := (iff #322 #332)
  3.4309 -#330 := (iff #318 #329)
  3.4310 -#327 := (iff #21 #326)
  3.4311 -#328 := [rewrite]: #327
  3.4312 -#331 := [monotonicity #328]: #330
  3.4313 -#334 := [quant-intro #331]: #333
  3.4314 -#323 := (iff #23 #322)
  3.4315 -#320 := (iff #22 #318)
  3.4316 -#321 := [rewrite]: #320
  3.4317 -#324 := [quant-intro #321]: #323
  3.4318 -#336 := [trans #324 #334]: #335
  3.4319 -#317 := [asserted]: #23
  3.4320 -#337 := [mp #317 #336]: #332
  3.4321 -#1483 := [mp~ #337 #1487]: #332
  3.4322 -#3612 := [mp #1483 #3611]: #3607
  3.4323 -#7600 := (not #3607)
  3.4324 -#8126 := (or #7600 #6208 #6224)
  3.4325 -#8127 := (or #7600 #6225)
  3.4326 -#8129 := (iff #8127 #8126)
  3.4327 -#8130 := [rewrite]: #8129
  3.4328 -#8128 := [quant-inst #181 #1935]: #8127
  3.4329 -#8131 := [mp #8128 #8130]: #8126
  3.4330 -#8167 := [unit-resolution #8131 #3612]: #6225
  3.4331 -#8168 := [unit-resolution #8167 #8166]: #6224
  3.4332 -#8169 := (or #8125 #6251)
  3.4333 -#8170 := [th-lemma arith farkas 1 1]: #8169
  3.4334 -#8171 := [unit-resolution #8170 #8168]: #8125
  3.4335 -#8172 := [th-lemma arith farkas 1 -1 1 #8171 #8159 #8157]: false
  3.4336 -#8173 := [lemma #8172]: #1942
  3.4337 -#8376 := [unit-resolution #8173 #8396 #8389]: false
  3.4338 -#8397 := [lemma #8376]: #1942
  3.4339 -#3450 := (or #3968 #3962)
  3.4340 -#3451 := [def-axiom]: #3450
  3.4341 -#7966 := [unit-resolution #3451 #7802]: #3962
  3.4342 -#3444 := (or #3968 #3830)
  3.4343 -#3390 := [def-axiom]: #3444
  3.4344 -#7967 := [unit-resolution #3390 #7802]: #3830
  3.4345 -#5748 := (or #1922 #3835 #3843)
  3.4346 -#4760 := (f5 #195 ?v0!13)
  3.4347 -#4761 := (f4 #4760)
  3.4348 -#4791 := (+ #1920 #4761)
  3.4349 -#4792 := (+ #185 #4791)
  3.4350 -#4951 := (>= #4792 0::Int)
  3.4351 -#4794 := (= #4792 0::Int)
  3.4352 -#4766 := (* -1::Int #4761)
  3.4353 -#4767 := (+ f3 #4766)
  3.4354 -#4768 := (<= #4767 0::Int)
  3.4355 -#5036 := (not #4768)
  3.4356 -#4703 := (* -1::Int #1918)
  3.4357 -#4881 := (+ #4703 #4761)
  3.4358 -#4879 := (+ #185 #4881)
  3.4359 -#4882 := (>= #4879 0::Int)
  3.4360 -#4975 := (or #4768 #4882)
  3.4361 -#4979 := (not #4975)
  3.4362 -#4945 := (= #1919 #1918)
  3.4363 -#5470 := (not #4945)
  3.4364 -#5031 := (= #1918 #1919)
  3.4365 -#5429 := (not #5031)
  3.4366 -#5471 := (iff #5429 #5470)
  3.4367 -#5469 := (iff #5031 #4945)
  3.4368 -#5468 := [commutativity]: #5469
  3.4369 -#5472 := [monotonicity #5468]: #5471
  3.4370 -#5428 := [hypothesis]: #1923
  3.4371 -#5431 := (or #5429 #1922)
  3.4372 -#5467 := [th-lemma arith triangle-eq]: #5431
  3.4373 -#5466 := [unit-resolution #5467 #5428]: #5429
  3.4374 -#5474 := [mp #5466 #5472]: #5470
  3.4375 -#4981 := (or #4979 #4945)
  3.4376 -#5494 := [hypothesis]: #3838
  3.4377 -#4983 := (or #3843 #4979 #4945)
  3.4378 -#4769 := (+ #1146 #4766)
  3.4379 -#4770 := (+ #1918 #4769)
  3.4380 -#4798 := (<= #4770 0::Int)
  3.4381 -#4954 := (or #4768 #4798)
  3.4382 -#4955 := (not #4954)
  3.4383 -#4974 := (or #4955 #4945)
  3.4384 -#5002 := (or #3843 #4974)
  3.4385 -#5074 := (iff #5002 #4983)
  3.4386 -#5004 := (or #3843 #4981)
  3.4387 -#5066 := (iff #5004 #4983)
  3.4388 -#5067 := [rewrite]: #5066
  3.4389 -#5064 := (iff #5002 #5004)
  3.4390 -#4977 := (iff #4974 #4981)
  3.4391 -#4980 := (iff #4955 #4979)
  3.4392 -#4976 := (iff #4954 #4975)
  3.4393 -#4889 := (iff #4798 #4882)
  3.4394 -#4871 := (+ #1918 #4766)
  3.4395 -#4872 := (+ #1146 #4871)
  3.4396 -#4874 := (<= #4872 0::Int)
  3.4397 -#4883 := (iff #4874 #4882)
  3.4398 -#4884 := [rewrite]: #4883
  3.4399 -#4875 := (iff #4798 #4874)
  3.4400 -#4870 := (= #4770 #4872)
  3.4401 -#4873 := [rewrite]: #4870
  3.4402 -#4880 := [monotonicity #4873]: #4875
  3.4403 -#4890 := [trans #4880 #4884]: #4889
  3.4404 -#4978 := [monotonicity #4890]: #4976
  3.4405 -#4973 := [monotonicity #4978]: #4980
  3.4406 -#4982 := [monotonicity #4973]: #4977
  3.4407 -#5065 := [monotonicity #4982]: #5064
  3.4408 -#5075 := [trans #5065 #5067]: #5074
  3.4409 -#5003 := [quant-inst #1917]: #5002
  3.4410 -#5035 := [mp #5003 #5075]: #4983
  3.4411 -#5473 := [unit-resolution #5035 #5494]: #4981
  3.4412 -#5495 := [unit-resolution #5473 #5474]: #4979
  3.4413 -#5008 := (or #4975 #5036)
  3.4414 -#5009 := [def-axiom]: #5008
  3.4415 -#5496 := [unit-resolution #5009 #5495]: #5036
  3.4416 -#5005 := (not #4882)
  3.4417 -#5010 := (or #4975 #5005)
  3.4418 -#5011 := [def-axiom]: #5010
  3.4419 -#5497 := [unit-resolution #5011 #5495]: #5005
  3.4420 -#4796 := (or #4768 #4882 #4794)
  3.4421 -#5498 := [hypothesis]: #3830
  3.4422 -#4854 := (or #3835 #4768 #4882 #4794)
  3.4423 -#4799 := (+ #4761 #1920)
  3.4424 -#4864 := (+ #185 #4799)
  3.4425 -#4865 := (= #4864 0::Int)
  3.4426 -#4866 := (or #4768 #4798 #4865)
  3.4427 -#4852 := (or #3835 #4866)
  3.4428 -#4863 := (iff #4852 #4854)
  3.4429 -#4855 := (or #3835 #4796)
  3.4430 -#4857 := (iff #4855 #4854)
  3.4431 -#4862 := [rewrite]: #4857
  3.4432 -#4888 := (iff #4852 #4855)
  3.4433 -#4797 := (iff #4866 #4796)
  3.4434 -#4789 := (iff #4865 #4794)
  3.4435 -#4790 := (= #4864 #4792)
  3.4436 -#4793 := [rewrite]: #4790
  3.4437 -#4795 := [monotonicity #4793]: #4789
  3.4438 -#4891 := [monotonicity #4890 #4795]: #4797
  3.4439 -#4856 := [monotonicity #4891]: #4888
  3.4440 -#4861 := [trans #4856 #4862]: #4863
  3.4441 -#4853 := [quant-inst #1917]: #4852
  3.4442 -#4952 := [mp #4853 #4861]: #4854
  3.4443 -#5493 := [unit-resolution #4952 #5498]: #4796
  3.4444 -#5450 := [unit-resolution #5493 #5497 #5496]: #4794
  3.4445 -#5424 := (not #4794)
  3.4446 -#5366 := (or #5424 #4951)
  3.4447 -#5425 := [th-lemma arith triangle-eq]: #5366
  3.4448 -#5423 := [unit-resolution #5425 #5450]: #4951
  3.4449 -#5032 := (<= #1921 0::Int)
  3.4450 -#5426 := (or #5032 #1922)
  3.4451 -#5743 := [th-lemma arith farkas 1 1]: #5426
  3.4452 -#5746 := [unit-resolution #5743 #5428]: #5032
  3.4453 -#5747 := [th-lemma arith farkas 1 -1 1 #5746 #5497 #5423]: false
  3.4454 -#5749 := [lemma #5747]: #5748
  3.4455 -#7968 := [unit-resolution #5749 #7803 #7967]: #1922
  3.4456 -#3449 := (or #3965 #1923 #3959)
  3.4457 -#3342 := [def-axiom]: #3449
  3.4458 -#7969 := [unit-resolution #3342 #7968 #7966]: #3959
  3.4459 -#3470 := (or #3956 #3950)
  3.4460 -#3471 := [def-axiom]: #3470
  3.4461 -#10050 := [unit-resolution #3471 #7969]: #3950
  3.4462 -#3469 := (or #3953 #1943 #3947)
  3.4463 -#3465 := [def-axiom]: #3469
  3.4464 -#10051 := [unit-resolution #3465 #10050]: #3950
  3.4465 -#10052 := [unit-resolution #10051 #8397]: #3947
  3.4466 -#3497 := (or #3944 #3855)
  3.4467 -#3475 := [def-axiom]: #3497
  3.4468 -#10053 := [unit-resolution #3475 #10052]: #3855
  3.4469 -#10974 := (or #3860 #4541 #5087)
  3.4470 -#11004 := (or #3860 #5090)
  3.4471 -#10996 := (iff #11004 #10974)
  3.4472 -#11018 := [rewrite]: #10996
  3.4473 -#10999 := [quant-inst #2034]: #11004
  3.4474 -#11019 := [mp #10999 #11018]: #10974
  3.4475 -#19095 := [unit-resolution #11019 #10053]: #5090
  3.4476 -#19096 := [unit-resolution #19095 #19086]: #5087
  3.4477 -#11867 := (not #5087)
  3.4478 -#11974 := (or #11867 #12022)
  3.4479 -#12636 := [th-lemma arith triangle-eq]: #11974
  3.4480 -#19097 := [unit-resolution #12636 #19096]: #12022
  3.4481 -#13344 := (+ #5343 #13327)
  3.4482 -#13366 := (>= #13344 0::Int)
  3.4483 -#3466 := (or #3956 #3846)
  3.4484 -#3467 := [def-axiom]: #3466
  3.4485 -#7970 := [unit-resolution #3467 #7969]: #3846
  3.4486 -#18080 := (or #3851 #13366)
  3.4487 -#18086 := [quant-inst #5342]: #18080
  3.4488 -#19087 := [unit-resolution #18086 #7970]: #13366
  3.4489 -#15969 := (not #12022)
  3.4490 -#19098 := (or #15968 #15969)
  3.4491 -#3538 := (not #1988)
  3.4492 -#5971 := [hypothesis]: #2870
  3.4493 -#3541 := (or #2865 #3538)
  3.4494 -#3425 := [def-axiom]: #3541
  3.4495 -#5972 := [unit-resolution #3425 #5971]: #3538
  3.4496 -#3536 := (or #2865 #1979)
  3.4497 -#3539 := [def-axiom]: #3536
  3.4498 -#5974 := [unit-resolution #3539 #5971]: #1979
  3.4499 -#3537 := (or #2865 #1981)
  3.4500 -#3540 := [def-axiom]: #3537
  3.4501 -#5973 := [unit-resolution #3540 #5971]: #1981
  3.4502 -#10629 := (or #2850 #1988 #1978)
  3.4503 -#5727 := (= ?v1!16 f28)
  3.4504 -#9301 := (= f28 ?v1!16)
  3.4505 -#5888 := (f5 #195 ?v1!16)
  3.4506 -#5889 := (f4 #5888)
  3.4507 -#9302 := (<= #5889 0::Int)
  3.4508 -#9711 := [hypothesis]: #3538
  3.4509 -#5985 := (+ #1985 #4079)
  3.4510 -#9236 := (<= #5985 0::Int)
  3.4511 -#5682 := (f11 f21 ?v0!17)
  3.4512 -#5683 := (= #5682 f1)
  3.4513 -#5681 := (= ?v0!17 f28)
  3.4514 -#5689 := (or #5681 #5683)
  3.4515 -#5671 := (f11 #193 ?v0!17)
  3.4516 -#5672 := (= #5671 f1)
  3.4517 -#5694 := (iff #5672 #5689)
  3.4518 -#9981 := (or #7518 #5694)
  3.4519 -#5684 := (if #5681 #4057 #5683)
  3.4520 -#5685 := (iff #5672 #5684)
  3.4521 -#9982 := (or #7518 #5685)
  3.4522 -#9550 := (iff #9982 #9981)
  3.4523 -#9683 := (iff #9981 #9981)
  3.4524 -#9737 := [rewrite]: #9683
  3.4525 -#5695 := (iff #5685 #5694)
  3.4526 -#5692 := (iff #5684 #5689)
  3.4527 -#5686 := (if #5681 true #5683)
  3.4528 -#5690 := (iff #5686 #5689)
  3.4529 -#5691 := [rewrite]: #5690
  3.4530 -#5687 := (iff #5684 #5686)
  3.4531 -#5688 := [monotonicity #4060]: #5687
  3.4532 -#5693 := [trans #5688 #5691]: #5692
  3.4533 -#5696 := [monotonicity #5693]: #5695
  3.4534 -#9267 := [monotonicity #5696]: #9550
  3.4535 -#9960 := [trans #9267 #9737]: #9550
  3.4536 -#9682 := [quant-inst #115 #181 #3 #1976]: #9982
  3.4537 -#9972 := [mp #9682 #9960]: #9981
  3.4538 -#10602 := [unit-resolution #9972 #3646]: #5694
  3.4539 -#10603 := [hypothesis]: #1981
  3.4540 -#10604 := (= #5671 #1980)
  3.4541 -#10599 := [monotonicity #8146]: #10604
  3.4542 -#10571 := [trans #10599 #10603]: #5672
  3.4543 -#9787 := (not #5672)
  3.4544 -#9971 := (not #5694)
  3.4545 -#9963 := (or #9971 #9787 #5689)
  3.4546 -#9964 := [def-axiom]: #9963
  3.4547 -#10605 := [unit-resolution #9964 #10571 #10602]: #5689
  3.4548 -#8065 := (not #5689)
  3.4549 -#10754 := (or #9236 #8065)
  3.4550 -#9774 := (not #9236)
  3.4551 -#10735 := [hypothesis]: #9774
  3.4552 -#5652 := (f19 f20 ?v0!17)
  3.4553 -#5545 := (* -1::Int #5652)
  3.4554 -#5605 := (+ #1985 #5545)
  3.4555 -#5610 := (<= #5605 0::Int)
  3.4556 -#8385 := (or #3851 #5610)
  3.4557 -#5582 := (+ #5652 #1986)
  3.4558 -#5595 := (>= #5582 0::Int)
  3.4559 -#8384 := (or #3851 #5595)
  3.4560 -#7710 := (iff #8384 #8385)
  3.4561 -#7667 := (iff #8385 #8385)
  3.4562 -#8392 := [rewrite]: #7667
  3.4563 -#5612 := (iff #5595 #5610)
  3.4564 -#5596 := (+ #1986 #5652)
  3.4565 -#5600 := (>= #5596 0::Int)
  3.4566 -#5611 := (iff #5600 #5610)
  3.4567 -#5609 := [rewrite]: #5611
  3.4568 -#5603 := (iff #5595 #5600)
  3.4569 -#5601 := (= #5582 #5596)
  3.4570 -#5602 := [rewrite]: #5601
  3.4571 -#5604 := [monotonicity #5602]: #5603
  3.4572 -#5613 := [trans #5604 #5609]: #5612
  3.4573 -#7791 := [monotonicity #5613]: #7710
  3.4574 -#7912 := [trans #7791 #8392]: #7710
  3.4575 -#8393 := [quant-inst #1976]: #8384
  3.4576 -#8060 := [mp #8393 #7912]: #8385
  3.4577 -#9712 := [unit-resolution #8060 #7970]: #5610
  3.4578 -#5540 := (+ #185 #5545)
  3.4579 -#9420 := (>= #5540 0::Int)
  3.4580 -#9400 := [hypothesis]: #5689
  3.4581 -#8193 := (not #5681)
  3.4582 -#9234 := (= #1985 #4078)
  3.4583 -#9689 := (not #9234)
  3.4584 -#9518 := (or #9689 #9236)
  3.4585 -#9690 := [th-lemma arith triangle-eq]: #9518
  3.4586 -#10715 := [unit-resolution #9690 #10735]: #9689
  3.4587 -#10725 := (or #8193 #9234)
  3.4588 -#9309 := [hypothesis]: #5681
  3.4589 -#10737 := [monotonicity #9309]: #9234
  3.4590 -#10736 := [hypothesis]: #9689
  3.4591 -#10724 := [unit-resolution #10736 #10737]: false
  3.4592 -#10726 := [lemma #10724]: #10725
  3.4593 -#10727 := [unit-resolution #10726 #10715]: #8193
  3.4594 -#8066 := (or #8065 #5681 #5683)
  3.4595 -#8067 := [def-axiom]: #8066
  3.4596 -#10723 := [unit-resolution #8067 #10727 #9400]: #5683
  3.4597 -#8196 := (not #5683)
  3.4598 -#9377 := (or #8196 #9420)
  3.4599 -#9723 := (not #9420)
  3.4600 -#9387 := [hypothesis]: #9723
  3.4601 -#9362 := [hypothesis]: #5683
  3.4602 -#9219 := (or #3731 #183 #8196 #9420)
  3.4603 -#9438 := (or #183 #8196 #9420)
  3.4604 -#9235 := (or #3731 #9438)
  3.4605 -#9246 := (iff #9235 #9219)
  3.4606 -#9220 := [rewrite]: #9246
  3.4607 -#9237 := [quant-inst #1976 #181]: #9235
  3.4608 -#8778 := [mp #9237 #9220]: #9219
  3.4609 -#9376 := [unit-resolution #8778 #8156 #8155 #9362 #9387]: false
  3.4610 -#9457 := [lemma #9376]: #9377
  3.4611 -#10721 := [unit-resolution #9457 #10723]: #9420
  3.4612 -#4080 := (+ #185 #4079)
  3.4613 -#4439 := (<= #4080 0::Int)
  3.4614 -#7295 := (= #185 #4078)
  3.4615 -#10741 := (iff #4131 #7295)
  3.4616 -#10728 := (iff #7295 #4131)
  3.4617 -#10729 := [commutativity]: #10728
  3.4618 -#10742 := [symm #10729]: #10741
  3.4619 -#10743 := [mp #7804 #10742]: #7295
  3.4620 -#10747 := (not #7295)
  3.4621 -#10748 := (or #10747 #4439)
  3.4622 -#10750 := [th-lemma arith triangle-eq]: #10748
  3.4623 -#10752 := [unit-resolution #10750 #10743]: #4439
  3.4624 -#10753 := [th-lemma arith farkas -1 1 -1 1 #10752 #10721 #9712 #10735]: false
  3.4625 -#10749 := [lemma #10753]: #10754
  3.4626 -#10606 := [unit-resolution #10749 #10605]: #9236
  3.4627 -#4081 := (>= #4080 0::Int)
  3.4628 -#7188 := (or #3851 #4081)
  3.4629 -#7230 := [quant-inst #181]: #7188
  3.4630 -#9459 := [unit-resolution #7230 #7970]: #4081
  3.4631 -#4492 := (* -1::Int #1984)
  3.4632 -#5947 := (+ #4492 #5889)
  3.4633 -#5948 := (+ #185 #5947)
  3.4634 -#7908 := (<= #5948 0::Int)
  3.4635 -#5951 := (= #5948 0::Int)
  3.4636 -#5855 := (f19 f20 ?v1!16)
  3.4637 -#5872 := (* -1::Int #5855)
  3.4638 -#5907 := (+ #5872 #5889)
  3.4639 -#5908 := (+ #185 #5907)
  3.4640 -#5909 := (>= #5908 0::Int)
  3.4641 -#5890 := (* -1::Int #5889)
  3.4642 -#5891 := (+ f3 #5890)
  3.4643 -#5892 := (<= #5891 0::Int)
  3.4644 -#5914 := (or #5892 #5909)
  3.4645 -#5917 := (not #5914)
  3.4646 -#5898 := (= #1984 #5855)
  3.4647 -#10613 := (not #5898)
  3.4648 -#5873 := (+ #1984 #5872)
  3.4649 -#8314 := (>= #5873 0::Int)
  3.4650 -#9718 := (not #8314)
  3.4651 -#4924 := (+ #185 #5872)
  3.4652 -#4925 := (<= #4924 0::Int)
  3.4653 -#5728 := (f11 f21 ?v1!16)
  3.4654 -#5729 := (= #5728 f1)
  3.4655 -#9937 := (not #5729)
  3.4656 -#5735 := (or #5727 #5729)
  3.4657 -#9563 := (not #5735)
  3.4658 -#5725 := (f11 #193 ?v1!16)
  3.4659 -#5726 := (= #5725 f1)
  3.4660 -#5740 := (iff #5726 #5735)
  3.4661 -#9884 := (or #7518 #5740)
  3.4662 -#5730 := (if #5727 #4057 #5729)
  3.4663 -#5731 := (iff #5726 #5730)
  3.4664 -#9851 := (or #7518 #5731)
  3.4665 -#9678 := (iff #9851 #9884)
  3.4666 -#9677 := (iff #9884 #9884)
  3.4667 -#9566 := [rewrite]: #9677
  3.4668 -#5741 := (iff #5731 #5740)
  3.4669 -#5738 := (iff #5730 #5735)
  3.4670 -#5732 := (if #5727 true #5729)
  3.4671 -#5736 := (iff #5732 #5735)
  3.4672 -#5737 := [rewrite]: #5736
  3.4673 -#5733 := (iff #5730 #5732)
  3.4674 -#5734 := [monotonicity #4060]: #5733
  3.4675 -#5739 := [trans #5734 #5737]: #5738
  3.4676 -#5742 := [monotonicity #5739]: #5741
  3.4677 -#9679 := [monotonicity #5742]: #9678
  3.4678 -#8478 := [trans #9679 #9566]: #9678
  3.4679 -#9932 := [quant-inst #115 #181 #3 #1975]: #9851
  3.4680 -#7394 := [mp #9932 #8478]: #9884
  3.4681 -#10476 := [unit-resolution #7394 #3646]: #5740
  3.4682 -#8333 := (not #5726)
  3.4683 -#10578 := (iff #1979 #8333)
  3.4684 -#10579 := (iff #1978 #5726)
  3.4685 -#10551 := (iff #5726 #1978)
  3.4686 -#10541 := (= #5725 #1977)
  3.4687 -#10544 := [monotonicity #8146]: #10541
  3.4688 -#10552 := [monotonicity #10544]: #10551
  3.4689 -#10580 := [symm #10552]: #10579
  3.4690 -#10581 := [monotonicity #10580]: #10578
  3.4691 -#10477 := [hypothesis]: #1979
  3.4692 -#10600 := [mp #10477 #10581]: #8333
  3.4693 -#8954 := (not #5740)
  3.4694 -#9175 := (or #8954 #5726 #9563)
  3.4695 -#7890 := [def-axiom]: #9175
  3.4696 -#10601 := [unit-resolution #7890 #10600 #10476]: #9563
  3.4697 -#8489 := (or #5735 #9937)
  3.4698 -#9914 := [def-axiom]: #8489
  3.4699 -#10607 := [unit-resolution #9914 #10601]: #9937
  3.4700 -#4948 := (or #5729 #4925)
  3.4701 -#3462 := (or #3968 #3820)
  3.4702 -#3463 := [def-axiom]: #3462
  3.4703 -#9789 := [unit-resolution #3463 #7802]: #3820
  3.4704 -#9716 := (or #3825 #5729 #4925)
  3.4705 -#4892 := (+ #5855 #1146)
  3.4706 -#4893 := (>= #4892 0::Int)
  3.4707 -#4918 := (or #5729 #4893)
  3.4708 -#9628 := (or #3825 #4918)
  3.4709 -#10139 := (iff #9628 #9716)
  3.4710 -#10115 := (or #3825 #4948)
  3.4711 -#10118 := (iff #10115 #9716)
  3.4712 -#10138 := [rewrite]: #10118
  3.4713 -#10117 := (iff #9628 #10115)
  3.4714 -#4949 := (iff #4918 #4948)
  3.4715 -#4946 := (iff #4893 #4925)
  3.4716 -#4919 := (+ #1146 #5855)
  3.4717 -#4922 := (>= #4919 0::Int)
  3.4718 -#4926 := (iff #4922 #4925)
  3.4719 -#4927 := [rewrite]: #4926
  3.4720 -#4917 := (iff #4893 #4922)
  3.4721 -#4920 := (= #4892 #4919)
  3.4722 -#4921 := [rewrite]: #4920
  3.4723 -#4923 := [monotonicity #4921]: #4917
  3.4724 -#4947 := [trans #4923 #4927]: #4946
  3.4725 -#4950 := [monotonicity #4947]: #4949
  3.4726 -#10112 := [monotonicity #4950]: #10117
  3.4727 -#10140 := [trans #10112 #10138]: #10139
  3.4728 -#10116 := [quant-inst #1975]: #9628
  3.4729 -#10141 := [mp #10116 #10140]: #9716
  3.4730 -#10608 := [unit-resolution #10141 #9789]: #4948
  3.4731 -#10609 := [unit-resolution #10608 #10607]: #4925
  3.4732 -#11010 := (not #4925)
  3.4733 -#11011 := (or #9774 #9718 #1988 #11010)
  3.4734 -#11006 := [hypothesis]: #4925
  3.4735 -#9759 := [hypothesis]: #9236
  3.4736 -#9707 := [hypothesis]: #8314
  3.4737 -#11009 := [th-lemma arith farkas -1 1 1 -1 1 #9707 #9759 #9711 #9459 #11006]: false
  3.4738 -#11012 := [lemma #11009]: #11011
  3.4739 -#10612 := [unit-resolution #11012 #10606 #9711 #10609]: #9718
  3.4740 -#10614 := (or #10613 #8314)
  3.4741 -#10615 := [th-lemma arith triangle-eq]: #10614
  3.4742 -#10610 := [unit-resolution #10615 #10612]: #10613
  3.4743 -#5920 := (or #5917 #5898)
  3.4744 -#10033 := (or #3843 #5917 #5898)
  3.4745 -#5893 := (+ #1146 #5890)
  3.4746 -#5894 := (+ #5855 #5893)
  3.4747 -#5895 := (<= #5894 0::Int)
  3.4748 -#5896 := (or #5892 #5895)
  3.4749 -#5897 := (not #5896)
  3.4750 -#5899 := (or #5897 #5898)
  3.4751 -#10016 := (or #3843 #5899)
  3.4752 -#9991 := (iff #10016 #10033)
  3.4753 -#10017 := (or #3843 #5920)
  3.4754 -#10008 := (iff #10017 #10033)
  3.4755 -#10004 := [rewrite]: #10008
  3.4756 -#9989 := (iff #10016 #10017)
  3.4757 -#5921 := (iff #5899 #5920)
  3.4758 -#5918 := (iff #5897 #5917)
  3.4759 -#5915 := (iff #5896 #5914)
  3.4760 -#5912 := (iff #5895 #5909)
  3.4761 -#5900 := (+ #5855 #5890)
  3.4762 -#5901 := (+ #1146 #5900)
  3.4763 -#5904 := (<= #5901 0::Int)
  3.4764 -#5910 := (iff #5904 #5909)
  3.4765 -#5911 := [rewrite]: #5910
  3.4766 -#5905 := (iff #5895 #5904)
  3.4767 -#5902 := (= #5894 #5901)
  3.4768 -#5903 := [rewrite]: #5902
  3.4769 -#5906 := [monotonicity #5903]: #5905
  3.4770 -#5913 := [trans #5906 #5911]: #5912
  3.4771 -#5916 := [monotonicity #5913]: #5915
  3.4772 -#5919 := [monotonicity #5916]: #5918
  3.4773 -#5922 := [monotonicity #5919]: #5921
  3.4774 -#10005 := [monotonicity #5922]: #9989
  3.4775 -#10002 := [trans #10005 #10004]: #9991
  3.4776 -#9962 := [quant-inst #1975]: #10016
  3.4777 -#10010 := [mp #9962 #10002]: #10033
  3.4778 -#10611 := [unit-resolution #10010 #7803]: #5920
  3.4779 -#10616 := [unit-resolution #10611 #10610]: #5917
  3.4780 -#9749 := (or #5914 #5951)
  3.4781 -#9732 := (not #5951)
  3.4782 -#9742 := [hypothesis]: #9732
  3.4783 -#8264 := (not #5892)
  3.4784 -#9745 := [hypothesis]: #5917
  3.4785 -#8000 := (or #5914 #8264)
  3.4786 -#8092 := [def-axiom]: #8000
  3.4787 -#9727 := [unit-resolution #8092 #9745]: #8264
  3.4788 -#8284 := (not #5909)
  3.4789 -#8311 := (or #5914 #8284)
  3.4790 -#8280 := [def-axiom]: #8311
  3.4791 -#9746 := [unit-resolution #8280 #9745]: #8284
  3.4792 -#5954 := (or #5892 #5909 #5951)
  3.4793 -#8310 := (or #3835 #5892 #5909 #5951)
  3.4794 -#5943 := (+ #5889 #4492)
  3.4795 -#5944 := (+ #185 #5943)
  3.4796 -#5945 := (= #5944 0::Int)
  3.4797 -#5946 := (or #5892 #5895 #5945)
  3.4798 -#8334 := (or #3835 #5946)
  3.4799 -#8377 := (iff #8334 #8310)
  3.4800 -#8335 := (or #3835 #5954)
  3.4801 -#8378 := (iff #8335 #8310)
  3.4802 -#8379 := [rewrite]: #8378
  3.4803 -#8336 := (iff #8334 #8335)
  3.4804 -#5955 := (iff #5946 #5954)
  3.4805 -#5952 := (iff #5945 #5951)
  3.4806 -#5949 := (= #5944 #5948)
  3.4807 -#5950 := [rewrite]: #5949
  3.4808 -#5953 := [monotonicity #5950]: #5952
  3.4809 -#5956 := [monotonicity #5913 #5953]: #5955
  3.4810 -#8337 := [monotonicity #5956]: #8336
  3.4811 -#8371 := [trans #8337 #8379]: #8377
  3.4812 -#8279 := [quant-inst #1975]: #8334
  3.4813 -#8381 := [mp #8279 #8371]: #8310
  3.4814 -#9747 := [unit-resolution #8381 #7967]: #5954
  3.4815 -#9748 := [unit-resolution #9747 #9746 #9727 #9742]: false
  3.4816 -#9750 := [lemma #9748]: #9749
  3.4817 -#10617 := [unit-resolution #9750 #10616]: #5951
  3.4818 -#10618 := (or #9732 #7908)
  3.4819 -#10619 := [th-lemma arith triangle-eq]: #10618
  3.4820 -#10620 := [unit-resolution #10619 #10617]: #7908
  3.4821 -#10624 := (not #4081)
  3.4822 -#10623 := (not #7908)
  3.4823 -#10625 := (or #9302 #10623 #1988 #9774 #10624)
  3.4824 -#10626 := [th-lemma arith assign-bounds 1 1 1 1]: #10625
  3.4825 -#10621 := [unit-resolution #10626 #10620 #9459 #10606 #9711]: #9302
  3.4826 -#9349 := (not #9302)
  3.4827 -#10411 := (or #7600 #9301 #9349)
  3.4828 -#9385 := (or #9301 #9349)
  3.4829 -#10539 := (or #7600 #9385)
  3.4830 -#10540 := (iff #10539 #10411)
  3.4831 -#10542 := [rewrite]: #10540
  3.4832 -#10381 := [quant-inst #181 #1975]: #10539
  3.4833 -#10543 := [mp #10381 #10542]: #10411
  3.4834 -#10622 := [unit-resolution #10543 #3612 #10621]: #9301
  3.4835 -#10627 := [symm #10622]: #5727
  3.4836 -#7819 := (not #5727)
  3.4837 -#9916 := (or #5735 #7819)
  3.4838 -#9935 := [def-axiom]: #9916
  3.4839 -#10577 := [unit-resolution #9935 #10601]: #7819
  3.4840 -#10628 := [unit-resolution #10577 #10627]: false
  3.4841 -#10630 := [lemma #10628]: #10629
  3.4842 -#9889 := [unit-resolution #10630 #5973 #5974 #5972]: false
  3.4843 -#9891 := [lemma #9889]: #2865
  3.4844 -#8784 := (or #1962 #3860)
  3.4845 -#4183 := (>= #185 0::Int)
  3.4846 -#3442 := (or #3980 #3717)
  3.4847 -#3422 := [def-axiom]: #3442
  3.4848 -#7614 := [unit-resolution #3422 #7155]: #3717
  3.4849 -#7345 := (or #3722 #4183)
  3.4850 -#7351 := [quant-inst #181]: #7345
  3.4851 -#7620 := [unit-resolution #7351 #7614]: #4183
  3.4852 -#6537 := (f5 #195 ?v0!15)
  3.4853 -#6538 := (f4 #6537)
  3.4854 -#4488 := (* -1::Int #1961)
  3.4855 -#6594 := (+ #4488 #6538)
  3.4856 -#6595 := (+ #185 #6594)
  3.4857 -#8465 := (<= #6595 0::Int)
  3.4858 -#6598 := (= #6595 0::Int)
  3.4859 -#6496 := (f19 f20 ?v0!15)
  3.4860 -#6521 := (* -1::Int #6496)
  3.4861 -#6555 := (+ #6521 #6538)
  3.4862 -#6556 := (+ #185 #6555)
  3.4863 -#6557 := (>= #6556 0::Int)
  3.4864 -#6539 := (* -1::Int #6538)
  3.4865 -#6540 := (+ f3 #6539)
  3.4866 -#6541 := (<= #6540 0::Int)
  3.4867 -#6562 := (or #6541 #6557)
  3.4868 -#6565 := (not #6562)
  3.4869 -#6497 := (= #1961 #6496)
  3.4870 -#9674 := (not #6497)
  3.4871 -#6522 := (+ #1961 #6521)
  3.4872 -#9653 := (>= #6522 0::Int)
  3.4873 -#9661 := (not #9653)
  3.4874 -#6618 := [hypothesis]: #1963
  3.4875 -#9453 := (or #9661 #1962)
  3.4876 -#8190 := (>= #6496 0::Int)
  3.4877 -#8498 := (or #3722 #8190)
  3.4878 -#8474 := [quant-inst #1960]: #8498
  3.4879 -#9421 := [unit-resolution #8474 #7614]: #8190
  3.4880 -#9654 := [hypothesis]: #9653
  3.4881 -#9452 := [th-lemma arith farkas -1 1 1 #6618 #9654 #9421]: false
  3.4882 -#9454 := [lemma #9452]: #9453
  3.4883 -#8733 := [unit-resolution #9454 #6618]: #9661
  3.4884 -#9675 := (or #9674 #9653)
  3.4885 -#8499 := [hypothesis]: #9661
  3.4886 -#8502 := [hypothesis]: #6497
  3.4887 -#9676 := [th-lemma arith triangle-eq]: #9675
  3.4888 -#8503 := [unit-resolution #9676 #8502 #8499]: false
  3.4889 -#8506 := [lemma #8503]: #9675
  3.4890 -#8735 := [unit-resolution #8506 #8733]: #9674
  3.4891 -#6568 := (or #6565 #6497)
  3.4892 -#8443 := (or #3843 #6565 #6497)
  3.4893 -#6542 := (+ #1146 #6539)
  3.4894 -#6543 := (+ #6496 #6542)
  3.4895 -#6544 := (<= #6543 0::Int)
  3.4896 -#6545 := (or #6541 #6544)
  3.4897 -#6546 := (not #6545)
  3.4898 -#6547 := (or #6546 #6497)
  3.4899 -#8444 := (or #3843 #6547)
  3.4900 -#8433 := (iff #8444 #8443)
  3.4901 -#8446 := (or #3843 #6568)
  3.4902 -#8449 := (iff #8446 #8443)
  3.4903 -#8432 := [rewrite]: #8449
  3.4904 -#8447 := (iff #8444 #8446)
  3.4905 -#6569 := (iff #6547 #6568)
  3.4906 -#6566 := (iff #6546 #6565)
  3.4907 -#6563 := (iff #6545 #6562)
  3.4908 -#6560 := (iff #6544 #6557)
  3.4909 -#6548 := (+ #6496 #6539)
  3.4910 -#6549 := (+ #1146 #6548)
  3.4911 -#6552 := (<= #6549 0::Int)
  3.4912 -#6558 := (iff #6552 #6557)
  3.4913 -#6559 := [rewrite]: #6558
  3.4914 -#6553 := (iff #6544 #6552)
  3.4915 -#6550 := (= #6543 #6549)
  3.4916 -#6551 := [rewrite]: #6550
  3.4917 -#6554 := [monotonicity #6551]: #6553
  3.4918 -#6561 := [trans #6554 #6559]: #6560
  3.4919 -#6564 := [monotonicity #6561]: #6563
  3.4920 -#6567 := [monotonicity #6564]: #6566
  3.4921 -#6570 := [monotonicity #6567]: #6569
  3.4922 -#8448 := [monotonicity #6570]: #8447
  3.4923 -#8434 := [trans #8448 #8432]: #8433
  3.4924 -#8445 := [quant-inst #1960]: #8444
  3.4925 -#8435 := [mp #8445 #8434]: #8443
  3.4926 -#9672 := [unit-resolution #8435 #7803]: #6568
  3.4927 -#8736 := [unit-resolution #9672 #8735]: #6565
  3.4928 -#9651 := (or #6562 #6598)
  3.4929 -#9644 := (not #6598)
  3.4930 -#9645 := [hypothesis]: #9644
  3.4931 -#8436 := (not #6541)
  3.4932 -#9646 := [hypothesis]: #6565
  3.4933 -#8431 := (or #6562 #8436)
  3.4934 -#8437 := [def-axiom]: #8431
  3.4935 -#9647 := [unit-resolution #8437 #9646]: #8436
  3.4936 -#8438 := (not #6557)
  3.4937 -#8439 := (or #6562 #8438)
  3.4938 -#8440 := [def-axiom]: #8439
  3.4939 -#9648 := [unit-resolution #8440 #9646]: #8438
  3.4940 -#6601 := (or #6541 #6557 #6598)
  3.4941 -#8452 := (or #3835 #6541 #6557 #6598)
  3.4942 -#6590 := (+ #6538 #4488)
  3.4943 -#6591 := (+ #185 #6590)
  3.4944 -#6592 := (= #6591 0::Int)
  3.4945 -#6593 := (or #6541 #6544 #6592)
  3.4946 -#8453 := (or #3835 #6593)
  3.4947 -#8459 := (iff #8453 #8452)
  3.4948 -#8455 := (or #3835 #6601)
  3.4949 -#8457 := (iff #8455 #8452)
  3.4950 -#8458 := [rewrite]: #8457
  3.4951 -#8450 := (iff #8453 #8455)
  3.4952 -#6602 := (iff #6593 #6601)
  3.4953 -#6599 := (iff #6592 #6598)
  3.4954 -#6596 := (= #6591 #6595)
  3.4955 -#6597 := [rewrite]: #6596
  3.4956 -#6600 := [monotonicity #6597]: #6599
  3.4957 -#6603 := [monotonicity #6561 #6600]: #6602
  3.4958 -#8456 := [monotonicity #6603]: #8450
  3.4959 -#8460 := [trans #8456 #8458]: #8459
  3.4960 -#8454 := [quant-inst #1960]: #8453
  3.4961 -#8464 := [mp #8454 #8460]: #8452
  3.4962 -#9649 := [unit-resolution #8464 #7967]: #6601
  3.4963 -#9650 := [unit-resolution #9649 #9648 #9647 #9645]: false
  3.4964 -#9652 := [lemma #9650]: #9651
  3.4965 -#8729 := [unit-resolution #9652 #8736]: #6598
  3.4966 -#9668 := (or #9644 #8465)
  3.4967 -#9669 := [th-lemma arith triangle-eq]: #9668
  3.4968 -#8737 := [unit-resolution #9669 #8729]: #8465
  3.4969 -#8633 := (>= #6538 0::Int)
  3.4970 -#9565 := (<= #6538 0::Int)
  3.4971 -#9568 := (not #9565)
  3.4972 -#9564 := (= f28 ?v0!15)
  3.4973 -#9601 := (not #9564)
  3.4974 -#9422 := (= ?v0!15 f28)
  3.4975 -#9445 := (not #9422)
  3.4976 -#9602 := (iff #9445 #9601)
  3.4977 -#9625 := (iff #9422 #9564)
  3.4978 -#9571 := (iff #9564 #9422)
  3.4979 -#9624 := [commutativity]: #9571
  3.4980 -#9626 := [symm #9624]: #9625
  3.4981 -#9603 := [monotonicity #9626]: #9602
  3.4982 -#8093 := (f11 f21 ?v0!15)
  3.4983 -#8097 := (= #8093 f1)
  3.4984 -#9428 := (or #9422 #8097)
  3.4985 -#9451 := (not #9428)
  3.4986 -#9414 := (f11 #193 ?v0!15)
  3.4987 -#9415 := (= #9414 f1)
  3.4988 -#9433 := (iff #9415 #9428)
  3.4989 -#8508 := (or #7518 #9433)
  3.4990 -#9423 := (if #9422 #4057 #8097)
  3.4991 -#9424 := (iff #9415 #9423)
  3.4992 -#8509 := (or #7518 #9424)
  3.4993 -#8511 := (iff #8509 #8508)
  3.4994 -#8510 := (iff #8508 #8508)
  3.4995 -#8514 := [rewrite]: #8510
  3.4996 -#9434 := (iff #9424 #9433)
  3.4997 -#9431 := (iff #9423 #9428)
  3.4998 -#9425 := (if #9422 true #8097)
  3.4999 -#9429 := (iff #9425 #9428)
  3.5000 -#9430 := [rewrite]: #9429
  3.5001 -#9426 := (iff #9423 #9425)
  3.5002 -#9427 := [monotonicity #4060]: #9426
  3.5003 -#9432 := [trans #9427 #9430]: #9431
  3.5004 -#9435 := [monotonicity #9432]: #9434
  3.5005 -#8512 := [monotonicity #9435]: #8511
  3.5006 -#8515 := [trans #8512 #8514]: #8511
  3.5007 -#8507 := [quant-inst #115 #181 #3 #1960]: #8509
  3.5008 -#8513 := [mp #8507 #8515]: #8508
  3.5009 -#8738 := [unit-resolution #8513 #3646]: #9433
  3.5010 -#8520 := (not #9415)
  3.5011 -#4485 := (f11 f29 ?v0!15)
  3.5012 -#4486 := (= #4485 f1)
  3.5013 -#4487 := (not #4486)
  3.5014 -#8754 := (iff #4487 #8520)
  3.5015 -#8755 := (iff #4486 #9415)
  3.5016 -#8702 := (iff #9415 #4486)
  3.5017 -#8748 := (= #9414 #4485)
  3.5018 -#8749 := [monotonicity #8146]: #8748
  3.5019 -#8703 := [monotonicity #8749]: #8702
  3.5020 -#8756 := [symm #8703]: #8755
  3.5021 -#8757 := [monotonicity #8756]: #8754
  3.5022 -#6506 := (or #4487 #6497)
  3.5023 -#8739 := [hypothesis]: #3855
  3.5024 -#8421 := (or #3860 #4487 #6497)
  3.5025 -#8422 := (or #3860 #6506)
  3.5026 -#8406 := (iff #8422 #8421)
  3.5027 -#8424 := [rewrite]: #8406
  3.5028 -#8423 := [quant-inst #1960]: #8422
  3.5029 -#8405 := [mp #8423 #8424]: #8421
  3.5030 -#8744 := [unit-resolution #8405 #8739]: #6506
  3.5031 -#8745 := [unit-resolution #8744 #8735]: #4487
  3.5032 -#8758 := [mp #8745 #8757]: #8520
  3.5033 -#8518 := (not #9433)
  3.5034 -#8519 := (or #8518 #9415 #9451)
  3.5035 -#8517 := [def-axiom]: #8519
  3.5036 -#8767 := [unit-resolution #8517 #8758 #8738]: #9451
  3.5037 -#9446 := (or #9428 #9445)
  3.5038 -#9447 := [def-axiom]: #9446
  3.5039 -#8768 := [unit-resolution #9447 #8767]: #9445
  3.5040 -#8774 := [mp #8768 #9603]: #9601
  3.5041 -#9572 := (or #9564 #9568)
  3.5042 -#9574 := (or #7600 #9564 #9568)
  3.5043 -#9575 := (or #7600 #9572)
  3.5044 -#9579 := (iff #9575 #9574)
  3.5045 -#9580 := [rewrite]: #9579
  3.5046 -#9576 := [quant-inst #181 #1960]: #9575
  3.5047 -#9578 := [mp #9576 #9580]: #9574
  3.5048 -#9605 := [unit-resolution #9578 #3612]: #9572
  3.5049 -#8775 := [unit-resolution #9605 #8774]: #9568
  3.5050 -#8773 := (or #8633 #9565)
  3.5051 -#8776 := [th-lemma arith farkas 1 1]: #8773
  3.5052 -#8769 := [unit-resolution #8776 #8775]: #8633
  3.5053 -#8777 := [th-lemma arith farkas 1 1 -1 1 #6618 #8769 #8737 #7620]: false
  3.5054 -#8782 := [lemma #8777]: #8784
  3.5055 -#10054 := [unit-resolution #8782 #10053]: #1962
  3.5056 -#4342 := (f5 #195 f16)
  3.5057 -#4343 := (f4 #4342)
  3.5058 -#7596 := (<= #4343 0::Int)
  3.5059 -#7588 := (not #7596)
  3.5060 -#4163 := (= f28 f16)
  3.5061 -#7583 := (not #4163)
  3.5062 -#7834 := [hypothesis]: #661
  3.5063 -#7847 := (or #7583 #217)
  3.5064 -#4358 := (= #216 #110)
  3.5065 -#7840 := (= #185 #110)
  3.5066 -#7835 := [hypothesis]: #4163
  3.5067 -#7841 := [monotonicity #7835]: #7840
  3.5068 -#7842 := (= #216 #185)
  3.5069 -#7838 := (= #216 #4078)
  3.5070 -#7836 := (= f16 f28)
  3.5071 -#7837 := [symm #7835]: #7836
  3.5072 -#7839 := [monotonicity #7837]: #7838
  3.5073 -#7843 := [trans #7839 #7804]: #7842
  3.5074 -#7844 := [trans #7843 #7841]: #4358
  3.5075 -#7845 := [trans #7844 #6894]: #217
  3.5076 -#7846 := [unit-resolution #7834 #7845]: false
  3.5077 -#7848 := [lemma #7846]: #7847
  3.5078 -#7599 := [unit-resolution #7848 #7834]: #7583
  3.5079 -#7589 := (or #4163 #7588)
  3.5080 -#7601 := (or #7600 #4163 #7588)
  3.5081 -#7602 := (or #7600 #7589)
  3.5082 -#7604 := (iff #7602 #7601)
  3.5083 -#7605 := [rewrite]: #7604
  3.5084 -#7603 := [quant-inst #181 #65]: #7602
  3.5085 -#7606 := [mp #7603 #7605]: #7601
  3.5086 -#7607 := [unit-resolution #7606 #3612]: #7589
  3.5087 -#7598 := [unit-resolution #7607 #7599]: #7588
  3.5088 -#4350 := (* -1::Int #4343)
  3.5089 -#4353 := (+ #1146 #4350)
  3.5090 -#4354 := (+ #110 #4353)
  3.5091 -#4355 := (<= #4354 0::Int)
  3.5092 -#7500 := (not #4355)
  3.5093 -#4351 := (+ f3 #4350)
  3.5094 -#4352 := (<= #4351 0::Int)
  3.5095 -#4356 := (or #4352 #4355)
  3.5096 -#4357 := (not #4356)
  3.5097 -#7612 := (not #4358)
  3.5098 -#7613 := (iff #661 #7612)
  3.5099 -#7610 := (iff #217 #4358)
  3.5100 -#7608 := (iff #4358 #217)
  3.5101 -#7609 := [monotonicity #6894]: #7608
  3.5102 -#7611 := [symm #7609]: #7610
  3.5103 -#7615 := [monotonicity #7611]: #7613
  3.5104 -#7616 := [mp #7834 #7615]: #7612
  3.5105 -#4359 := (or #4357 #4358)
  3.5106 -#7491 := (or #3843 #4357 #4358)
  3.5107 -#7492 := (or #3843 #4359)
  3.5108 -#7494 := (iff #7492 #7491)
  3.5109 -#7495 := [rewrite]: #7494
  3.5110 -#7493 := [quant-inst #65]: #7492
  3.5111 -#7496 := [mp #7493 #7495]: #7491
  3.5112 -#7617 := [unit-resolution #7496 #7803]: #4359
  3.5113 -#7618 := [unit-resolution #7617 #7616]: #4357
  3.5114 -#7501 := (or #4356 #7500)
  3.5115 -#7502 := [def-axiom]: #7501
  3.5116 -#7619 := [unit-resolution #7502 #7618]: #7500
  3.5117 -#4504 := (<= #110 0::Int)
  3.5118 -#7621 := (or #804 #4504)
  3.5119 -#7622 := [th-lemma arith triangle-eq]: #7621
  3.5120 -#7623 := [unit-resolution #7622 #6894]: #4504
  3.5121 -#7624 := [th-lemma arith farkas 1 1 1 1 #7623 #7620 #7619 #7598]: false
  3.5122 -#7626 := [lemma #7624]: #217
  3.5123 -#3476 := (or #3944 #3938)
  3.5124 -#3478 := [def-axiom]: #3476
  3.5125 -#10055 := [unit-resolution #3478 #10052]: #3938
  3.5126 -#3496 := (or #3941 #661 #3935)
  3.5127 -#3486 := [def-axiom]: #3496
  3.5128 -#10056 := [unit-resolution #3486 #10055 #7626]: #3935
  3.5129 -#3488 := (or #3932 #3926)
  3.5130 -#3489 := [def-axiom]: #3488
  3.5131 -#10057 := [unit-resolution #3489 #10056]: #3926
  3.5132 -#3504 := (or #3929 #1963 #3923)
  3.5133 -#3484 := [def-axiom]: #3504
  3.5134 -#10058 := [unit-resolution #3484 #10057 #10054]: #3923
  3.5135 -#3507 := (or #3920 #3914)
  3.5136 -#3512 := [def-axiom]: #3507
  3.5137 -#18172 := [unit-resolution #3512 #10058]: #3914
  3.5138 -#3508 := (or #3917 #2870 #3911)
  3.5139 -#3509 := [def-axiom]: #3508
  3.5140 -#18183 := [unit-resolution #3509 #18172]: #3914
  3.5141 -#18184 := [unit-resolution #18183 #9891]: #3911
  3.5142 -#3517 := (or #3908 #3902)
  3.5143 -#3518 := [def-axiom]: #3517
  3.5144 -#18185 := [unit-resolution #3518 #18184]: #3902
  3.5145 -#18186 := (or #3905 #3899)
  3.5146 -#15845 := [hypothesis]: #2916
  3.5147 -#3530 := (or #2911 #2012)
  3.5148 -#3533 := [def-axiom]: #3530
  3.5149 -#15846 := [unit-resolution #3533 #15845]: #2012
  3.5150 -#6483 := (f5 #195 ?v0!19)
  3.5151 -#6481 := (f4 #6483)
  3.5152 -#6484 := (* -1::Int #6481)
  3.5153 -#15446 := (+ #2008 #6484)
  3.5154 -#15535 := (>= #15446 0::Int)
  3.5155 -#15445 := (= #2008 #6481)
  3.5156 -#15962 := (= #2007 #6483)
  3.5157 -#15956 := (= #2006 #195)
  3.5158 -#5407 := (= ?v1!18 f28)
  3.5159 -#5408 := (f11 f21 ?v1!18)
  3.5160 -#5409 := (= #5408 f1)
  3.5161 -#5415 := (or #5407 #5409)
  3.5162 -#5397 := (f11 #193 ?v1!18)
  3.5163 -#5398 := (= #5397 f1)
  3.5164 -#5420 := (iff #5398 #5415)
  3.5165 -#14616 := (or #7518 #5420)
  3.5166 -#5410 := (if #5407 #4057 #5409)
  3.5167 -#5411 := (iff #5398 #5410)
  3.5168 -#14606 := (or #7518 #5411)
  3.5169 -#14610 := (iff #14606 #14616)
  3.5170 -#14613 := (iff #14616 #14616)
  3.5171 -#14619 := [rewrite]: #14613
  3.5172 -#5421 := (iff #5411 #5420)
  3.5173 -#5418 := (iff #5410 #5415)
  3.5174 -#5412 := (if #5407 true #5409)
  3.5175 -#5416 := (iff #5412 #5415)
  3.5176 -#5417 := [rewrite]: #5416
  3.5177 -#5413 := (iff #5410 #5412)
  3.5178 -#5414 := [monotonicity #4060]: #5413
  3.5179 -#5419 := [trans #5414 #5417]: #5418
  3.5180 -#5422 := [monotonicity #5419]: #5421
  3.5181 -#14620 := [monotonicity #5422]: #14610
  3.5182 -#14630 := [trans #14620 #14619]: #14610
  3.5183 -#14618 := [quant-inst #115 #181 #3 #2002]: #14606
  3.5184 -#14662 := [mp #14618 #14630]: #14616
  3.5185 -#15893 := [unit-resolution #14662 #3646]: #5420
  3.5186 -#3434 := (or #2911 #2005)
  3.5187 -#3529 := [def-axiom]: #3434
  3.5188 -#15907 := [unit-resolution #3529 #15845]: #2005
  3.5189 -#15926 := (= #5397 #2004)
  3.5190 -#15928 := [monotonicity #8146]: #15926
  3.5191 -#15908 := [trans #15928 #15907]: #5398
  3.5192 -#11373 := (not #5398)
  3.5193 -#15102 := (not #5420)
  3.5194 -#15199 := (or #15102 #11373 #5415)
  3.5195 -#15197 := [def-axiom]: #15199
  3.5196 -#15929 := [unit-resolution #15197 #15908 #15893]: #5415
  3.5197 -#6623 := (not #5409)
  3.5198 -#6374 := (f19 f20 ?v0!19)
  3.5199 -#6445 := (* -1::Int #6374)
  3.5200 -#5362 := (f19 f20 ?v1!18)
  3.5201 -#6639 := (+ #5362 #6445)
  3.5202 -#6640 := (+ #2008 #6639)
  3.5203 -#6641 := (>= #6640 0::Int)
  3.5204 -#15933 := (not #6641)
  3.5205 -#3418 := (not #2020)
  3.5206 -#3433 := (or #2911 #3418)
  3.5207 -#3435 := [def-axiom]: #3433
  3.5208 -#15930 := [unit-resolution #3435 #15845]: #3418
  3.5209 -#6446 := (+ #2016 #6445)
  3.5210 -#6447 := (<= #6446 0::Int)
  3.5211 -#12992 := (not #6447)
  3.5212 -#12993 := [hypothesis]: #12992
  3.5213 -#12524 := (or #3851 #6447)
  3.5214 -#6389 := (+ #6374 #2017)
  3.5215 -#6399 := (>= #6389 0::Int)
  3.5216 -#12525 := (or #3851 #6399)
  3.5217 -#12527 := (iff #12525 #12524)
  3.5218 -#12530 := (iff #12524 #12524)
  3.5219 -#12531 := [rewrite]: #12530
  3.5220 -#6468 := (iff #6399 #6447)
  3.5221 -#6440 := (+ #2017 #6374)
  3.5222 -#6443 := (>= #6440 0::Int)
  3.5223 -#6448 := (iff #6443 #6447)
  3.5224 -#6467 := [rewrite]: #6448
  3.5225 -#6438 := (iff #6399 #6443)
  3.5226 -#6441 := (= #6389 #6440)
  3.5227 -#6442 := [rewrite]: #6441
  3.5228 -#6444 := [monotonicity #6442]: #6438
  3.5229 -#6469 := [trans #6444 #6467]: #6468
  3.5230 -#12529 := [monotonicity #6469]: #12527
  3.5231 -#12532 := [trans #12529 #12531]: #12527
  3.5232 -#12526 := [quant-inst #2003]: #12525
  3.5233 -#12533 := [mp #12526 #12532]: #12524
  3.5234 -#12610 := [unit-resolution #12533 #7970 #12993]: false
  3.5235 -#12611 := [lemma #12610]: #6447
  3.5236 -#5459 := (* -1::Int #5362)
  3.5237 -#5460 := (+ #2015 #5459)
  3.5238 -#12226 := (>= #5460 0::Int)
  3.5239 -#5380 := (= #2015 #5362)
  3.5240 -#12307 := (or #3860 #2896 #5380)
  3.5241 -#5383 := (or #2896 #5380)
  3.5242 -#12303 := (or #3860 #5383)
  3.5243 -#12279 := (iff #12303 #12307)
  3.5244 -#12410 := [rewrite]: #12279
  3.5245 -#12304 := [quant-inst #2002]: #12303
  3.5246 -#12398 := [mp #12304 #12410]: #12307
  3.5247 -#15925 := [unit-resolution #12398 #10053 #15907]: #5380
  3.5248 -#15889 := (not #5380)
  3.5249 -#15931 := (or #15889 #12226)
  3.5250 -#15927 := [th-lemma arith triangle-eq]: #15931
  3.5251 -#15932 := [unit-resolution #15927 #15925]: #12226
  3.5252 -#15883 := (not #12226)
  3.5253 -#15934 := (or #15933 #15883 #12992 #2020)
  3.5254 -#15935 := [th-lemma arith assign-bounds 1 -1 -1]: #15934
  3.5255 -#15955 := [unit-resolution #15935 #15932 #12611 #15930]: #15933
  3.5256 -#15957 := (or #6623 #6641)
  3.5257 -#15290 := (or #3739 #6623 #2011 #6641)
  3.5258 -#6642 := (or #6623 #2011 #6641)
  3.5259 -#15291 := (or #3739 #6642)
  3.5260 -#15288 := (iff #15291 #15290)
  3.5261 -#15308 := [rewrite]: #15288
  3.5262 -#15270 := [quant-inst #2003 #2002]: #15291
  3.5263 -#15282 := [mp #15270 #15308]: #15290
  3.5264 -#15958 := [unit-resolution #15282 #7156 #15846]: #15957
  3.5265 -#15954 := [unit-resolution #15958 #15955]: #6623
  3.5266 -#15090 := (not #5415)
  3.5267 -#15098 := (or #15090 #5407 #5409)
  3.5268 -#15091 := [def-axiom]: #15098
  3.5269 -#15960 := [unit-resolution #15091 #15954 #15929]: #5407
  3.5270 -#15961 := [monotonicity #15960]: #15956
  3.5271 -#15959 := [monotonicity #15961]: #15962
  3.5272 -#15963 := [monotonicity #15959]: #15445
  3.5273 -#15964 := (not #15445)
  3.5274 -#13461 := (or #15964 #15535)
  3.5275 -#11575 := [th-lemma arith triangle-eq]: #13461
  3.5276 -#14042 := [unit-resolution #11575 #15963]: #15535
  3.5277 -#6485 := (+ f3 #6484)
  3.5278 -#6486 := (<= #6485 0::Int)
  3.5279 -#6610 := (+ #2017 #6481)
  3.5280 -#6611 := (+ #185 #6610)
  3.5281 -#6614 := (= #6611 0::Int)
  3.5282 -#15542 := (not #6614)
  3.5283 -#14614 := (>= #6611 0::Int)
  3.5284 -#13597 := (not #14614)
  3.5285 -#6363 := (+ #2015 #4079)
  3.5286 -#6364 := (>= #6363 0::Int)
  3.5287 -#7961 := (= #2015 #4078)
  3.5288 -#14062 := [monotonicity #15960]: #7961
  3.5289 -#15213 := (not #7961)
  3.5290 -#15268 := (or #15213 #6364)
  3.5291 -#15479 := [th-lemma arith triangle-eq]: #15268
  3.5292 -#15484 := [unit-resolution #15479 #14062]: #6364
  3.5293 -#12694 := (not #15535)
  3.5294 -#14493 := (not #4439)
  3.5295 -#15269 := (not #6364)
  3.5296 -#12544 := (or #13597 #2020 #15269 #14493 #12694)
  3.5297 -#14974 := [th-lemma arith assign-bounds -1 1 -1 1]: #12544
  3.5298 -#15581 := [unit-resolution #14974 #15930 #10752 #15484 #14042]: #13597
  3.5299 -#15702 := (or #15542 #14614)
  3.5300 -#15714 := [th-lemma arith triangle-eq]: #15702
  3.5301 -#15715 := [unit-resolution #15714 #15581]: #15542
  3.5302 -#6511 := (+ #6445 #6481)
  3.5303 -#6509 := (+ #185 #6511)
  3.5304 -#6512 := (>= #6509 0::Int)
  3.5305 -#13034 := (not #6512)
  3.5306 -#15736 := (or #13034 #12992 #2020 #15269 #14493 #12694)
  3.5307 -#15582 := [th-lemma arith assign-bounds -1 -1 1 -1 1]: #15736
  3.5308 -#15841 := [unit-resolution #15582 #15930 #12611 #10752 #15484 #14042]: #13034
  3.5309 -#5073 := (or #6486 #6512 #6614)
  3.5310 -#14397 := (or #3835 #6486 #6512 #6614)
  3.5311 -#6607 := (+ #6481 #2017)
  3.5312 -#6608 := (+ #185 #6607)
  3.5313 -#6609 := (= #6608 0::Int)
  3.5314 -#6491 := (+ #1146 #6484)
  3.5315 -#6492 := (+ #6374 #6491)
  3.5316 -#6490 := (<= #6492 0::Int)
  3.5317 -#6604 := (or #6486 #6490 #6609)
  3.5318 -#12671 := (or #3835 #6604)
  3.5319 -#14485 := (iff #12671 #14397)
  3.5320 -#14423 := (or #3835 #5073)
  3.5321 -#14478 := (iff #14423 #14397)
  3.5322 -#14483 := [rewrite]: #14478
  3.5323 -#14389 := (iff #12671 #14423)
  3.5324 -#5263 := (iff #6604 #5073)
  3.5325 -#5033 := (iff #6609 #6614)
  3.5326 -#6612 := (= #6608 #6611)
  3.5327 -#6613 := [rewrite]: #6612
  3.5328 -#5034 := [monotonicity #6613]: #5033
  3.5329 -#6529 := (iff #6490 #6512)
  3.5330 -#6499 := (+ #6374 #6484)
  3.5331 -#6500 := (+ #1146 #6499)
  3.5332 -#6502 := (<= #6500 0::Int)
  3.5333 -#6513 := (iff #6502 #6512)
  3.5334 -#6514 := [rewrite]: #6513
  3.5335 -#6503 := (iff #6490 #6502)
  3.5336 -#6498 := (= #6492 #6500)
  3.5337 -#6501 := [rewrite]: #6498
  3.5338 -#6510 := [monotonicity #6501]: #6503
  3.5339 -#6530 := [trans #6510 #6514]: #6529
  3.5340 -#5264 := [monotonicity #6530 #5034]: #5263
  3.5341 -#14396 := [monotonicity #5264]: #14389
  3.5342 -#14472 := [trans #14396 #14483]: #14485
  3.5343 -#14422 := [quant-inst #2003]: #12671
  3.5344 -#14486 := [mp #14422 #14472]: #14397
  3.5345 -#15735 := [unit-resolution #14486 #7967]: #5073
  3.5346 -#15853 := [unit-resolution #15735 #15841 #15715]: #6486
  3.5347 -#15854 := [th-lemma arith farkas -1 1 1 #15853 #14042 #15846]: false
  3.5348 -#15894 := [lemma #15854]: #2911
  3.5349 -#3526 := (or #3905 #2916 #3899)
  3.5350 -#3527 := [def-axiom]: #3526
  3.5351 -#18187 := [unit-resolution #3527 #15894]: #18186
  3.5352 -#18188 := [unit-resolution #18187 #18185]: #3899
  3.5353 -#3441 := (or #3896 #2041)
  3.5354 -#3534 := [def-axiom]: #3441
  3.5355 -#18189 := [unit-resolution #3534 #18188]: #2041
  3.5356 -#15970 := (or #15968 #15969 #2040)
  3.5357 -#13634 := [hypothesis]: #2041
  3.5358 -#15965 := [hypothesis]: #12022
  3.5359 -#15966 := [hypothesis]: #5341
  3.5360 -#15967 := [th-lemma arith farkas -1 1 1 #15966 #15965 #13634]: false
  3.5361 -#15971 := [lemma #15967]: #15970
  3.5362 -#19099 := [unit-resolution #15971 #18189]: #19098
  3.5363 -#19100 := [unit-resolution #19099 #19097]: #15968
  3.5364 -#15703 := (or #5341 #5359)
  3.5365 -#3439 := (or #3896 #2036)
  3.5366 -#3440 := [def-axiom]: #3439
  3.5367 -#19101 := [unit-resolution #3440 #18188]: #2036
  3.5368 -#12207 := (or #3747 #2035 #5341 #5359)
  3.5369 -#5360 := (or #2035 #5341 #5359)
  3.5370 -#12245 := (or #3747 #5360)
  3.5371 -#12251 := (iff #12245 #12207)
  3.5372 -#12352 := [rewrite]: #12251
  3.5373 -#12240 := [quant-inst #2034]: #12245
  3.5374 -#12292 := [mp #12240 #12352]: #12207
  3.5375 -#19102 := [unit-resolution #12292 #7427 #19101]: #15703
  3.5376 -#19103 := [unit-resolution #19102 #19100]: #5359
  3.5377 -#15553 := (or #5358 #5356)
  3.5378 -#15554 := [def-axiom]: #15553
  3.5379 -#18351 := [unit-resolution #15554 #19103]: #5356
  3.5380 -#18355 := (or #5357 #15530)
  3.5381 -#18361 := [th-lemma arith triangle-eq]: #18355
  3.5382 -#18362 := [unit-resolution #18361 #18351]: #15530
  3.5383 -#19106 := (not #13366)
  3.5384 -#18364 := (not #15530)
  3.5385 -#18350 := (or #18243 #18364 #15969 #19106)
  3.5386 -#18365 := [th-lemma arith assign-bounds 1 1 1]: #18350
  3.5387 -#18367 := [unit-resolution #18365 #18362 #19087 #19097]: #18243
  3.5388 -#14134 := (<= #14210 0::Int)
  3.5389 -#14035 := (+ f3 #5353)
  3.5390 -#14131 := (<= #14035 0::Int)
  3.5391 -#18369 := (not #14131)
  3.5392 -#13911 := (>= #5343 0::Int)
  3.5393 -#18177 := (or #3722 #13911)
  3.5394 -#18180 := [quant-inst #5342]: #18177
  3.5395 -#18368 := [unit-resolution #18180 #7614]: #13911
  3.5396 -#18363 := (not #13911)
  3.5397 -#18372 := (or #18369 #18363 #18364 #15969)
  3.5398 -#18371 := (or #18369 #18363 #18364 #2040 #15969)
  3.5399 -#18366 := [th-lemma arith assign-bounds -1 -1 -1 -1]: #18371
  3.5400 -#18373 := [unit-resolution #18366 #18189]: #18372
  3.5401 -#18378 := [unit-resolution #18373 #18368 #18362 #19097]: #18369
  3.5402 -#13322 := (f11 f29 #5342)
  3.5403 -#13321 := (= #13322 f1)
  3.5404 -#15207 := (+ #2037 #13327)
  3.5405 -#15217 := (<= #15207 0::Int)
  3.5406 -#19105 := (not #15217)
  3.5407 -#12311 := (not #5346)
  3.5408 -#12351 := (or #5358 #12311)
  3.5409 -#12297 := [def-axiom]: #12351
  3.5410 -#19104 := [unit-resolution #12297 #19103]: #12311
  3.5411 -#19107 := (or #19105 #5346 #15969 #19106)
  3.5412 -#19108 := [th-lemma arith assign-bounds 1 1 1]: #19107
  3.5413 -#19109 := [unit-resolution #19108 #19104 #19097 #19087]: #19105
  3.5414 -#15548 := (or #13321 #4541 #15217)
  3.5415 -#3523 := (or #3908 #3872)
  3.5416 -#3528 := [def-axiom]: #3523
  3.5417 -#18201 := [unit-resolution #3528 #18184]: #3872
  3.5418 -#10669 := (or #3877 #13321 #4541 #15217)
  3.5419 -#14133 := (+ #13325 #2038)
  3.5420 -#15115 := (>= #14133 0::Int)
  3.5421 -#15556 := (or #13321 #4541 #15115)
  3.5422 -#10675 := (or #3877 #15556)
  3.5423 -#10689 := (iff #10675 #10669)
  3.5424 -#10671 := (or #3877 #15548)
  3.5425 -#10662 := (iff #10671 #10669)
  3.5426 -#10672 := [rewrite]: #10662
  3.5427 -#10679 := (iff #10675 #10671)
  3.5428 -#15557 := (iff #15556 #15548)
  3.5429 -#15222 := (iff #15115 #15217)
  3.5430 -#15259 := (+ #2038 #13325)
  3.5431 -#15255 := (>= #15259 0::Int)
  3.5432 -#15218 := (iff #15255 #15217)
  3.5433 -#15261 := [rewrite]: #15218
  3.5434 -#15208 := (iff #15115 #15255)
  3.5435 -#15253 := (= #14133 #15259)
  3.5436 -#15258 := [rewrite]: #15253
  3.5437 -#15216 := [monotonicity #15258]: #15208
  3.5438 -#15202 := [trans #15216 #15261]: #15222
  3.5439 -#15555 := [monotonicity #15202]: #15557
  3.5440 -#10681 := [monotonicity #15555]: #10679
  3.5441 -#10677 := [trans #10681 #10672]: #10689
  3.5442 -#10676 := [quant-inst #2034 #5342]: #10675
  3.5443 -#10678 := [mp #10676 #10677]: #10669
  3.5444 -#19114 := [unit-resolution #10678 #18201]: #15548
  3.5445 -#18370 := [unit-resolution #19114 #19109 #19086]: #13321
  3.5446 -#13323 := (not #13321)
  3.5447 -#11985 := (or #13323 #14131 #14134)
  3.5448 -#3437 := (or #3896 #3880)
  3.5449 -#3438 := [def-axiom]: #3437
  3.5450 -#18542 := [unit-resolution #3438 #18188]: #3880
  3.5451 -#18156 := (or #3885 #13323 #14131 #14134)
  3.5452 -#14205 := (+ #5352 #14133)
  3.5453 -#12308 := (>= #14205 0::Int)
  3.5454 -#11983 := (or #13323 #14131 #12308)
  3.5455 -#18152 := (or #3885 #11983)
  3.5456 -#18167 := (iff #18152 #18156)
  3.5457 -#18181 := (or #3885 #11985)
  3.5458 -#17096 := (iff #18181 #18156)
  3.5459 -#18166 := [rewrite]: #17096
  3.5460 -#18182 := (iff #18152 #18181)
  3.5461 -#12007 := (iff #11983 #11985)
  3.5462 -#14226 := (iff #12308 #14134)
  3.5463 -#11853 := (+ #5352 #13325)
  3.5464 -#14129 := (+ #2038 #11853)
  3.5465 -#14155 := (>= #14129 0::Int)
  3.5466 -#8205 := (iff #14155 #14134)
  3.5467 -#14211 := [rewrite]: #8205
  3.5468 -#14206 := (iff #12308 #14155)
  3.5469 -#12309 := (= #14205 #14129)
  3.5470 -#12299 := [rewrite]: #12309
  3.5471 -#14118 := [monotonicity #12299]: #14206
  3.5472 -#14132 := [trans #14118 #14211]: #14226
  3.5473 -#11847 := [monotonicity #14132]: #12007
  3.5474 -#17095 := [monotonicity #11847]: #18182
  3.5475 -#18163 := [trans #17095 #18166]: #18167
  3.5476 -#18175 := [quant-inst #2034 #5342]: #18152
  3.5477 -#18168 := [mp #18175 #18163]: #18156
  3.5478 -#18379 := [unit-resolution #18168 #18542]: #11985
  3.5479 -#18376 := [unit-resolution #18379 #18370 #18378]: #14134
  3.5480 -#15298 := (= #14210 0::Int)
  3.5481 -#15302 := (not #15298)
  3.5482 -#15303 := (or #15217 #13323 #15302)
  3.5483 -#3531 := (or #3896 #3888)
  3.5484 -#3535 := [def-axiom]: #3531
  3.5485 -#18380 := [unit-resolution #3535 #18188]: #3888
  3.5486 -#18219 := (or #3893 #15217 #13323 #15302)
  3.5487 -#15198 := (+ #2038 #5352)
  3.5488 -#15203 := (+ #13325 #15198)
  3.5489 -#15204 := (= #15203 0::Int)
  3.5490 -#15256 := (not #15204)
  3.5491 -#15257 := (or #15115 #13323 #15256)
  3.5492 -#18220 := (or #3893 #15257)
  3.5493 -#18239 := (iff #18220 #18219)
  3.5494 -#18247 := (or #3893 #15303)
  3.5495 -#18237 := (iff #18247 #18219)
  3.5496 -#18238 := [rewrite]: #18237
  3.5497 -#18253 := (iff #18220 #18247)
  3.5498 -#15292 := (iff #15257 #15303)
  3.5499 -#15304 := (iff #15256 #15302)
  3.5500 -#15275 := (iff #15204 #15298)
  3.5501 -#15285 := (= #14129 0::Int)
  3.5502 -#15299 := (iff #15285 #15298)
  3.5503 -#15297 := [rewrite]: #15299
  3.5504 -#15279 := (iff #15204 #15285)
  3.5505 -#15264 := (= #15203 #14129)
  3.5506 -#15254 := [rewrite]: #15264
  3.5507 -#15284 := [monotonicity #15254]: #15279
  3.5508 -#15300 := [trans #15284 #15297]: #15275
  3.5509 -#15289 := [monotonicity #15300]: #15304
  3.5510 -#15301 := [monotonicity #15202 #15289]: #15292
  3.5511 -#18254 := [monotonicity #15301]: #18253
  3.5512 -#18236 := [trans #18254 #18238]: #18239
  3.5513 -#18252 := [quant-inst #5342]: #18220
  3.5514 -#18242 := [mp #18252 #18236]: #18219
  3.5515 -#18381 := [unit-resolution #18242 #18380]: #15303
  3.5516 -#18382 := [unit-resolution #18381 #18370 #19109]: #15302
  3.5517 -#18393 := (not #18243)
  3.5518 -#18392 := (not #14134)
  3.5519 -#18388 := (or #15298 #18392 #18393)
  3.5520 -#18394 := [th-lemma arith triangle-eq]: #18388
  3.5521 -#18396 := [unit-resolution #18394 #18382 #18376 #18367]: false
  3.5522 -#18397 := [lemma #18396]: #4541
  3.5523 -#16386 := [mp #18397 #16391]: #9410
  3.5524 -#9307 := (not #9956)
  3.5525 -#9346 := (or #9307 #9944 #9685)
  3.5526 -#9347 := [def-axiom]: #9346
  3.5527 -#16392 := [unit-resolution #9347 #16386 #16374]: #9685
  3.5528 -#9688 := (or #9951 #9687)
  3.5529 -#9684 := [def-axiom]: #9688
  3.5530 -#16383 := [unit-resolution #9684 #16392]: #9687
  3.5531 -#16395 := [unit-resolution #16383 #16394]: false
  3.5532 -#16405 := [lemma #16395]: #15368
  3.5533 -#16379 := [hypothesis]: #15340
  3.5534 -#15365 := (or #7600 #15327 #15358)
  3.5535 -#15362 := (or #15327 #15358)
  3.5536 -#15360 := (or #7600 #15362)
  3.5537 -#15351 := (iff #15360 #15365)
  3.5538 -#15352 := [rewrite]: #15351
  3.5539 -#15364 := [quant-inst #181 #2034]: #15360
  3.5540 -#15353 := [mp #15364 #15352]: #15365
  3.5541 -#16275 := [unit-resolution #15353 #3612 #16379 #16405]: false
  3.5542 -#16404 := [lemma #16275]: #15358
  3.5543 -#16322 := [hypothesis]: #12121
  3.5544 -#16307 := (or #15340 #15379 #15402)
  3.5545 -#15400 := (or #15340 #15379 #15402 #10624)
  3.5546 -#15403 := [th-lemma arith assign-bounds -1 -1 1]: #15400
  3.5547 -#16283 := [unit-resolution #15403 #9459]: #16307
  3.5548 -#16319 := [unit-resolution #16283 #16322 #16404]: #15402
  3.5549 -#5241 := (+ #4079 #5123)
  3.5550 -#5242 := (+ #2037 #5241)
  3.5551 -#5243 := (= #5242 0::Int)
  3.5552 -#12167 := (>= #5242 0::Int)
  3.5553 -#16360 := (or #12167 #15379)
  3.5554 -#15382 := (or #12167 #10624 #15379)
  3.5555 -#14315 := [th-lemma arith assign-bounds -1 1]: #15382
  3.5556 -#16376 := [unit-resolution #14315 #9459]: #16360
  3.5557 -#16377 := [unit-resolution #16376 #16322]: #12167
  3.5558 -#15390 := (not #12167)
  3.5559 -#16258 := (or #5243 #15390)
  3.5560 -#12074 := (<= #5242 0::Int)
  3.5561 -#4339 := (+ #110 #1146)
  3.5562 -#7776 := (<= #4339 0::Int)
  3.5563 -#4340 := (>= #4339 0::Int)
  3.5564 -#9693 := (not #4340)
  3.5565 -#4164 := (?v1!7 f28)
  3.5566 -#4165 := (f19 f20 #4164)
  3.5567 -#4166 := (* -1::Int #4165)
  3.5568 -#4167 := (+ #185 #4166)
  3.5569 -#4168 := (<= #4167 0::Int)
  3.5570 -#7320 := (not #4168)
  3.5571 -#4172 := (f6 f7 #4164)
  3.5572 -#4173 := (f5 #4172 f28)
  3.5573 -#4174 := (f4 #4173)
  3.5574 -#4175 := (* -1::Int #4174)
  3.5575 -#4176 := (+ #4166 #4175)
  3.5576 -#4177 := (+ #185 #4176)
  3.5577 -#4178 := (= #4177 0::Int)
  3.5578 -#4179 := (not #4178)
  3.5579 -#4169 := (f11 f21 #4164)
  3.5580 -#4170 := (= #4169 f1)
  3.5581 -#4171 := (not #4170)
  3.5582 -#4180 := (or #4168 #4171 #4179)
  3.5583 -#4181 := (not #4180)
  3.5584 -#4335 := (f11 f21 f16)
  3.5585 -#4336 := (= #4335 f1)
  3.5586 -#13038 := (or #3896 #2040 #4336)
  3.5587 -#12906 := [hypothesis]: #3899
  3.5588 -#12800 := [unit-resolution #3535 #12906]: #3888
  3.5589 -#7302 := (not #4336)
  3.5590 -#15705 := [hypothesis]: #7302
  3.5591 -#4341 := (or #4336 #4340)
  3.5592 -#7485 := (or #3825 #4336 #4340)
  3.5593 -#7486 := (or #3825 #4341)
  3.5594 -#7488 := (iff #7486 #7485)
  3.5595 -#7489 := [rewrite]: #7488
  3.5596 -#7487 := [quant-inst #65]: #7486
  3.5597 -#7490 := [mp #7487 #7489]: #7485
  3.5598 -#15712 := [unit-resolution #7490 #9789]: #4341
  3.5599 -#15713 := [unit-resolution #15712 #15705]: #4340
  3.5600 -#15716 := (or #9693 #4168)
  3.5601 -#7756 := (>= #4165 0::Int)
  3.5602 -#7707 := (not #7756)
  3.5603 -#7708 := [hypothesis]: #7707
  3.5604 -#7822 := (or #3722 #7756)
  3.5605 -#7824 := [quant-inst #4164]: #7822
  3.5606 -#7859 := [unit-resolution #7824 #7614 #7708]: false
  3.5607 -#7860 := [lemma #7859]: #7756
  3.5608 -#15719 := (or #9693 #7707 #4168)
  3.5609 -#7972 := (not #4504)
  3.5610 -#15717 := (or #9693 #7972 #7707 #4168)
  3.5611 -#15718 := [th-lemma arith assign-bounds -1 1 1]: #15717
  3.5612 -#15721 := [unit-resolution #15718 #7623]: #15719
  3.5613 -#15722 := [unit-resolution #15721 #7860]: #15716
  3.5614 -#15723 := [unit-resolution #15722 #15713]: #4168
  3.5615 -#7326 := (or #4180 #7320)
  3.5616 -#7330 := [def-axiom]: #7326
  3.5617 -#15728 := [unit-resolution #7330 #15723]: #4180
  3.5618 -#7978 := (or #4163 #4181)
  3.5619 -#3458 := (or #3968 #1323)
  3.5620 -#3461 := [def-axiom]: #3458
  3.5621 -#7977 := [unit-resolution #3461 #7802]: #1323
  3.5622 -#7294 := (or #3747 #4163 #1322 #4181)
  3.5623 -#4182 := (or #4163 #1322 #4181)
  3.5624 -#7297 := (or #3747 #4182)
  3.5625 -#7321 := (iff #7297 #7294)
  3.5626 -#7323 := [rewrite]: #7321
  3.5627 -#7298 := [quant-inst #181]: #7297
  3.5628 -#7324 := [mp #7298 #7323]: #7294
  3.5629 -#7979 := [unit-resolution #7324 #7427 #7977]: #7978
  3.5630 -#15748 := [unit-resolution #7979 #15728]: #4163
  3.5631 -#11585 := [unit-resolution #3440 #12906]: #2036
  3.5632 -#15405 := (or #15374 #2035 #7583 #3893)
  3.5633 -#15369 := (iff #2036 #15368)
  3.5634 -#15350 := (iff #2035 #15327)
  3.5635 -#15367 := (iff #15327 #2035)
  3.5636 -#12076 := (= f16 ?v0!20)
  3.5637 -#15366 := (iff #12076 #2035)
  3.5638 -#15354 := [commutativity]: #15366
  3.5639 -#15357 := (iff #15327 #12076)
  3.5640 -#15317 := [monotonicity #7835]: #15357
  3.5641 -#15318 := [trans #15317 #15354]: #15367
  3.5642 -#15336 := [symm #15318]: #15350
  3.5643 -#15370 := [monotonicity #15336]: #15369
  3.5644 -#15363 := [hypothesis]: #2036
  3.5645 -#15373 := [mp #15363 #15370]: #15368
  3.5646 -#15335 := [hypothesis]: #5182
  3.5647 -#15375 := (or #15374 #12121)
  3.5648 -#15376 := [th-lemma arith triangle-eq]: #15375
  3.5649 -#15378 := [unit-resolution #15376 #15335]: #12121
  3.5650 -#15381 := [unit-resolution #14315 #15378 #9459]: #12167
  3.5651 -#12123 := (>= #5179 0::Int)
  3.5652 -#14322 := (or #15374 #12123)
  3.5653 -#11027 := [th-lemma arith triangle-eq]: #14322
  3.5654 -#15349 := [unit-resolution #11027 #15335]: #12123
  3.5655 -#15265 := (not #12123)
  3.5656 -#14563 := (or #12074 #14493 #15265)
  3.5657 -#15266 := [th-lemma arith assign-bounds -1 1]: #14563
  3.5658 -#15286 := [unit-resolution #15266 #15349 #10752]: #12074
  3.5659 -#14562 := (not #12074)
  3.5660 -#15295 := (or #5243 #14562 #15390)
  3.5661 -#15391 := [th-lemma arith triangle-eq]: #15295
  3.5662 -#15392 := [unit-resolution #15391 #15286 #15381]: #5243
  3.5663 -#5248 := (not #5243)
  3.5664 -#15394 := (or #5229 #5248)
  3.5665 -#4429 := (f11 f29 f28)
  3.5666 -#4430 := (= #4429 f1)
  3.5667 -#4055 := (f11 #193 f28)
  3.5668 -#4056 := (= #4055 f1)
  3.5669 -#43 := (:var 0 S1)
  3.5670 -#40 := (:var 2 S7)
  3.5671 -#41 := (f14 f15 #40)
  3.5672 -#42 := (f13 #41 #10)
  3.5673 -#44 := (f12 #42 #43)
  3.5674 -#3633 := (pattern #44)
  3.5675 -#47 := (= #43 f1)
  3.5676 -#45 := (f11 #44 #10)
  3.5677 -#46 := (= #45 f1)
  3.5678 -#48 := (iff #46 #47)
  3.5679 -#3634 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) (:pat #3633) #48)
  3.5680 -#49 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) #48)
  3.5681 -#3637 := (iff #49 #3634)
  3.5682 -#3635 := (iff #48 #48)
  3.5683 -#3636 := [refl]: #3635
  3.5684 -#3638 := [quant-intro #3636]: #3637
  3.5685 -#1494 := (~ #49 #49)
  3.5686 -#1521 := (~ #48 #48)
  3.5687 -#1522 := [refl]: #1521
  3.5688 -#1495 := [nnf-pos #1522]: #1494
  3.5689 -#341 := [asserted]: #49
  3.5690 -#1523 := [mp~ #341 #1495]: #49
  3.5691 -#3639 := [mp #1523 #3638]: #3634
  3.5692 -#7192 := (not #3634)
  3.5693 -#7205 := (or #7192 #4056)
  3.5694 -#4058 := (iff #4056 #4057)
  3.5695 -#7206 := (or #7192 #4058)
  3.5696 -#7227 := (iff #7206 #7205)
  3.5697 -#7229 := (iff #7205 #7205)
  3.5698 -#7200 := [rewrite]: #7229
  3.5699 -#4066 := (iff #4058 #4056)
  3.5700 -#4061 := (iff #4056 true)
  3.5701 -#4064 := (iff #4061 #4056)
  3.5702 -#4065 := [rewrite]: #4064
  3.5703 -#4062 := (iff #4058 #4061)
  3.5704 -#4063 := [monotonicity #4060]: #4062
  3.5705 -#4067 := [trans #4063 #4065]: #4066
  3.5706 -#7228 := [monotonicity #4067]: #7227
  3.5707 -#7201 := [trans #7228 #7200]: #7227
  3.5708 -#7226 := [quant-inst #115 #181 #3]: #7206
  3.5709 -#7199 := [mp #7226 #7201]: #7205
  3.5710 -#15296 := [unit-resolution #7199 #3639]: #4056
  3.5711 -#14014 := (= #4429 #4055)
  3.5712 -#15393 := [monotonicity #8144]: #14014
  3.5713 -#15395 := [trans #15393 #15296]: #4430
  3.5714 -#15396 := [hypothesis]: #3888
  3.5715 -#4431 := (not #4430)
  3.5716 -#12122 := (or #3893 #5229 #4431 #5248)
  3.5717 -#5219 := (+ #4078 #5178)
  3.5718 -#5220 := (= #5219 0::Int)
  3.5719 -#5221 := (not #5220)
  3.5720 -#5209 := (+ #4078 #2038)
  3.5721 -#5210 := (>= #5209 0::Int)
  3.5722 -#5222 := (or #5210 #4431 #5221)
  3.5723 -#12125 := (or #3893 #5222)
  3.5724 -#12149 := (iff #12125 #12122)
  3.5725 -#5251 := (or #5229 #4431 #5248)
  3.5726 -#12146 := (or #3893 #5251)
  3.5727 -#12083 := (iff #12146 #12122)
  3.5728 -#12143 := [rewrite]: #12083
  3.5729 -#12131 := (iff #12125 #12146)
  3.5730 -#5252 := (iff #5222 #5251)
  3.5731 -#5249 := (iff #5221 #5248)
  3.5732 -#5246 := (iff #5220 #5243)
  3.5733 -#5234 := (+ #4078 #5122)
  3.5734 -#5235 := (+ #2038 #5234)
  3.5735 -#5238 := (= #5235 0::Int)
  3.5736 -#5244 := (iff #5238 #5243)
  3.5737 -#5245 := [rewrite]: #5244
  3.5738 -#5239 := (iff #5220 #5238)
  3.5739 -#5236 := (= #5219 #5235)
  3.5740 -#5237 := [rewrite]: #5236
  3.5741 -#5240 := [monotonicity #5237]: #5239
  3.5742 -#5247 := [trans #5240 #5245]: #5246
  3.5743 -#5250 := [monotonicity #5247]: #5249
  3.5744 -#5232 := (iff #5210 #5229)
  3.5745 -#5223 := (+ #2038 #4078)
  3.5746 -#5226 := (>= #5223 0::Int)
  3.5747 -#5230 := (iff #5226 #5229)
  3.5748 -#5231 := [rewrite]: #5230
  3.5749 -#5227 := (iff #5210 #5226)
  3.5750 -#5224 := (= #5209 #5223)
  3.5751 -#5225 := [rewrite]: #5224
  3.5752 -#5228 := [monotonicity #5225]: #5227
  3.5753 -#5233 := [trans #5228 #5231]: #5232
  3.5754 -#5253 := [monotonicity #5233 #5250]: #5252
  3.5755 -#12082 := [monotonicity #5253]: #12131
  3.5756 -#12147 := [trans #12082 #12143]: #12149
  3.5757 -#12075 := [quant-inst #181]: #12125
  3.5758 -#12124 := [mp #12075 #12147]: #12122
  3.5759 -#15399 := [unit-resolution #12124 #15396 #15395]: #15394
  3.5760 -#15401 := [unit-resolution #15399 #15392]: #5229
  3.5761 -#15397 := [unit-resolution #15403 #15378 #15401 #9459]: #15340
  3.5762 -#15398 := [unit-resolution #15353 #3612]: #15362
  3.5763 -#15404 := [unit-resolution #15398 #15397 #15373]: false
  3.5764 -#15406 := [lemma #15404]: #15405
  3.5765 -#11721 := [unit-resolution #15406 #11585 #15748 #12800]: #15374
  3.5766 -#12105 := (not #5125)
  3.5767 -#5149 := (not #5146)
  3.5768 -#15784 := (or #15969 #4336 #2040 #2035)
  3.5769 -#15708 := [unit-resolution #15971 #15965 #13634]: #15968
  3.5770 -#15709 := [unit-resolution #12292 #7427 #15363]: #15703
  3.5771 -#15710 := [unit-resolution #15709 #15708]: #5359
  3.5772 -#12264 := (or #5358 #5348)
  3.5773 -#12306 := [def-axiom]: #12264
  3.5774 -#15453 := [unit-resolution #12306 #15710]: #5348
  3.5775 -#15775 := (= #4335 #5347)
  3.5776 -#15780 := (= #182 #5347)
  3.5777 -#15777 := (= f28 #5342)
  3.5778 -#15752 := (= f16 #5342)
  3.5779 -#13856 := (= #5342 f16)
  3.5780 -#13857 := (?v1!7 #5342)
  3.5781 -#13952 := (f6 f7 #13857)
  3.5782 -#13906 := (f5 #13952 #5342)
  3.5783 -#13881 := (f4 #13906)
  3.5784 -#13913 := (* -1::Int #13881)
  3.5785 -#13835 := (f19 f20 #13857)
  3.5786 -#13871 := (* -1::Int #13835)
  3.5787 -#13806 := (+ #13871 #13913)
  3.5788 -#11518 := (+ #5343 #13806)
  3.5789 -#11879 := (= #11518 0::Int)
  3.5790 -#13861 := (not #11879)
  3.5791 -#13937 := (f11 f21 #13857)
  3.5792 -#13943 := (= #13937 f1)
  3.5793 -#13938 := (not #13943)
  3.5794 -#13870 := (+ #5343 #13871)
  3.5795 -#13936 := (<= #13870 0::Int)
  3.5796 -#11576 := (or #13936 #13938 #13861)
  3.5797 -#12649 := (+ #185 #5344)
  3.5798 -#12802 := (>= #12649 0::Int)
  3.5799 -#11633 := (or #3731 #183 #5349 #12802)
  3.5800 -#11028 := (or #183 #5349 #12802)
  3.5801 -#12259 := (or #3731 #11028)
  3.5802 -#11754 := (iff #12259 #11633)
  3.5803 -#12879 := [rewrite]: #11754
  3.5804 -#12287 := [quant-inst #5342 #181]: #12259
  3.5805 -#12883 := [mp #12287 #12879]: #11633
  3.5806 -#15747 := [unit-resolution #12883 #8156 #8155 #15453]: #12802
  3.5807 -#17243 := (not #12802)
  3.5808 -#17244 := (or #13936 #9693 #17243)
  3.5809 -#17239 := [hypothesis]: #12802
  3.5810 -#14038 := (not #13936)
  3.5811 -#17240 := [hypothesis]: #14038
  3.5812 -#17043 := (>= #13835 0::Int)
  3.5813 -#17063 := (or #3722 #17043)
  3.5814 -#17064 := [quant-inst #13857]: #17063
  3.5815 -#17241 := [unit-resolution #17064 #7614]: #17043
  3.5816 -#9714 := [hypothesis]: #4340
  3.5817 -#17242 := [th-lemma arith farkas -1 1 1 1 1 #7623 #9714 #17241 #17240 #17239]: false
  3.5818 -#17245 := [lemma #17242]: #17244
  3.5819 -#15749 := [unit-resolution #17245 #15747 #15713]: #13936
  3.5820 -#14010 := (or #11576 #14038)
  3.5821 -#14095 := [def-axiom]: #14010
  3.5822 -#15750 := [unit-resolution #14095 #15749]: #11576
  3.5823 -#13847 := (+ f3 #5344)
  3.5824 -#13841 := (<= #13847 0::Int)
  3.5825 -#16579 := (not #13841)
  3.5826 -#15746 := [unit-resolution #12297 #15710]: #12311
  3.5827 -#16524 := (or #16579 #2040 #15969 #5346)
  3.5828 -#16576 := [hypothesis]: #13841
  3.5829 -#16577 := [hypothesis]: #12311
  3.5830 -#16578 := [th-lemma arith farkas 1 1 1 1 #13634 #15965 #16577 #16576]: false
  3.5831 -#16580 := [lemma #16578]: #16524
  3.5832 -#15711 := [unit-resolution #16580 #15965 #13634 #15746]: #16579
  3.5833 -#13912 := (not #11576)
  3.5834 -#13915 := (or #13856 #13841 #13912)
  3.5835 -#14033 := (or #3747 #13856 #13841 #13912)
  3.5836 -#14036 := (or #3747 #13915)
  3.5837 -#14009 := (iff #14036 #14033)
  3.5838 -#14008 := [rewrite]: #14009
  3.5839 -#14011 := [quant-inst #5342]: #14036
  3.5840 -#14037 := [mp #14011 #14008]: #14033
  3.5841 -#15720 := [unit-resolution #14037 #7427]: #13915
  3.5842 -#15751 := [unit-resolution #15720 #15711 #15750]: #13856
  3.5843 -#15753 := [symm #15751]: #15752
  3.5844 -#15778 := [trans #15748 #15753]: #15777
  3.5845 -#15754 := [monotonicity #15778]: #15780
  3.5846 -#15776 := (= #4335 #182)
  3.5847 -#15727 := [symm #15748]: #7836
  3.5848 -#15779 := [monotonicity #15727]: #15776
  3.5849 -#15782 := [trans #15779 #15754]: #15775
  3.5850 -#15783 := [trans #15782 #15453]: #4336
  3.5851 -#15781 := [unit-resolution #15705 #15783]: false
  3.5852 -#15786 := [lemma #15781]: #15784
  3.5853 -#12801 := [unit-resolution #15786 #11585 #13634 #15705]: #15969
  3.5854 -#12564 := [unit-resolution #12636 #12801]: #11867
  3.5855 -#5152 := (or #5149 #5087)
  3.5856 -#11970 := (or #3843 #5149 #5087)
  3.5857 -#5126 := (+ #1146 #5123)
  3.5858 -#5127 := (+ #5080 #5126)
  3.5859 -#5128 := (<= #5127 0::Int)
  3.5860 -#5129 := (or #5125 #5128)
  3.5861 -#5130 := (not #5129)
  3.5862 -#5131 := (or #5130 #5087)
  3.5863 -#12023 := (or #3843 #5131)
  3.5864 -#12067 := (iff #12023 #11970)
  3.5865 -#12068 := (or #3843 #5152)
  3.5866 -#12042 := (iff #12068 #11970)
  3.5867 -#12107 := [rewrite]: #12042
  3.5868 -#12058 := (iff #12023 #12068)
  3.5869 -#5153 := (iff #5131 #5152)
  3.5870 -#5150 := (iff #5130 #5149)
  3.5871 -#5147 := (iff #5129 #5146)
  3.5872 -#5144 := (iff #5128 #5141)
  3.5873 -#5132 := (+ #5080 #5123)
  3.5874 -#5133 := (+ #1146 #5132)
  3.5875 -#5136 := (<= #5133 0::Int)
  3.5876 -#5142 := (iff #5136 #5141)
  3.5877 -#5143 := [rewrite]: #5142
  3.5878 -#5137 := (iff #5128 #5136)
  3.5879 -#5134 := (= #5127 #5133)
  3.5880 -#5135 := [rewrite]: #5134
  3.5881 -#5138 := [monotonicity #5135]: #5137
  3.5882 -#5145 := [trans #5138 #5143]: #5144
  3.5883 -#5148 := [monotonicity #5145]: #5147
  3.5884 -#5151 := [monotonicity #5148]: #5150
  3.5885 -#5154 := [monotonicity #5151]: #5153
  3.5886 -#12062 := [monotonicity #5154]: #12058
  3.5887 -#12070 := [trans #12062 #12107]: #12067
  3.5888 -#12017 := [quant-inst #2034]: #12023
  3.5889 -#12084 := [mp #12017 #12070]: #11970
  3.5890 -#9728 := [unit-resolution #12084 #7803]: #5152
  3.5891 -#12860 := [unit-resolution #9728 #12564]: #5149
  3.5892 -#12072 := (or #5146 #12105)
  3.5893 -#12071 := [def-axiom]: #12072
  3.5894 -#13044 := [unit-resolution #12071 #12860]: #12105
  3.5895 -#12081 := (not #5141)
  3.5896 -#12073 := (or #5146 #12081)
  3.5897 -#12118 := [def-axiom]: #12073
  3.5898 -#13025 := [unit-resolution #12118 #12860]: #12081
  3.5899 -#5185 := (or #5125 #5141 #5182)
  3.5900 -#12077 := (or #3835 #5125 #5141 #5182)
  3.5901 -#5174 := (+ #5122 #2038)
  3.5902 -#5175 := (+ #185 #5174)
  3.5903 -#5176 := (= #5175 0::Int)
  3.5904 -#5177 := (or #5125 #5128 #5176)
  3.5905 -#12079 := (or #3835 #5177)
  3.5906 -#12130 := (iff #12079 #12077)
  3.5907 -#12113 := (or #3835 #5185)
  3.5908 -#12114 := (iff #12113 #12077)
  3.5909 -#12129 := [rewrite]: #12114
  3.5910 -#12117 := (iff #12079 #12113)
  3.5911 -#5186 := (iff #5177 #5185)
  3.5912 -#5183 := (iff #5176 #5182)
  3.5913 -#5180 := (= #5175 #5179)
  3.5914 -#5181 := [rewrite]: #5180
  3.5915 -#5184 := [monotonicity #5181]: #5183
  3.5916 -#5187 := [monotonicity #5145 #5184]: #5186
  3.5917 -#12115 := [monotonicity #5187]: #12117
  3.5918 -#12109 := [trans #12115 #12129]: #12130
  3.5919 -#12120 := [quant-inst #2034]: #12079
  3.5920 -#12128 := [mp #12120 #12109]: #12077
  3.5921 -#11095 := [unit-resolution #12128 #7967]: #5185
  3.5922 -#13026 := [unit-resolution #11095 #13025 #13044 #11721]: false
  3.5923 -#11841 := [lemma #13026]: #13038
  3.5924 -#18190 := [unit-resolution #11841 #18188 #18189]: #4336
  3.5925 -#9665 := (or #7583 #7302)
  3.5926 -#8260 := [hypothesis]: #4336
  3.5927 -#9629 := (= #182 #4335)
  3.5928 -#9567 := [monotonicity #7835]: #9629
  3.5929 -#7820 := [trans #9567 #8260]: #183
  3.5930 -#7888 := [unit-resolution #8155 #7820]: false
  3.5931 -#7765 := [lemma #7888]: #9665
  3.5932 -#18191 := [unit-resolution #7765 #18190]: #7583
  3.5933 -#18192 := [unit-resolution #7979 #18191]: #4181
  3.5934 -#18193 := [unit-resolution #7330 #18192]: #7320
  3.5935 -#16378 := [unit-resolution #15722 #18193]: #9693
  3.5936 -#16277 := (or #7776 #4340)
  3.5937 -#16270 := [th-lemma arith farkas 1 1]: #16277
  3.5938 -#16406 := [unit-resolution #16270 #16378]: #7776
  3.5939 -#9345 := (not #7776)
  3.5940 -#12779 := (or #12074 #9345 #2040 #3885)
  3.5941 -#12732 := [hypothesis]: #14562
  3.5942 -#12904 := (or #5125 #12074)
  3.5943 -#12870 := [hypothesis]: #3880
  3.5944 -#12757 := (or #3885 #4431 #5125 #12074)
  3.5945 -#15309 := (+ #5122 #5209)
  3.5946 -#15305 := (>= #15309 0::Int)
  3.5947 -#15310 := (or #4431 #5125 #15305)
  3.5948 -#12733 := (or #3885 #15310)
  3.5949 -#12657 := (iff #12733 #12757)
  3.5950 -#15344 := (or #4431 #5125 #12074)
  3.5951 -#12731 := (or #3885 #15344)
  3.5952 -#12778 := (iff #12731 #12757)
  3.5953 -#12664 := [rewrite]: #12778
  3.5954 -#12760 := (iff #12733 #12731)
  3.5955 -#15345 := (iff #15310 #15344)
  3.5956 -#15319 := (iff #15305 #12074)
  3.5957 -#15287 := (>= #5235 0::Int)
  3.5958 -#15315 := (iff #15287 #12074)
  3.5959 -#15321 := [rewrite]: #15315
  3.5960 -#15312 := (iff #15305 #15287)
  3.5961 -#15307 := (= #15309 #5235)
  3.5962 -#15311 := [rewrite]: #15307
  3.5963 -#15313 := [monotonicity #15311]: #15312
  3.5964 -#15342 := [trans #15313 #15321]: #15319
  3.5965 -#15343 := [monotonicity #15342]: #15345
  3.5966 -#12770 := [monotonicity #15343]: #12760
  3.5967 -#12730 := [trans #12770 #12664]: #12657
  3.5968 -#12432 := [quant-inst #2034 #181]: #12733
  3.5969 -#12772 := [mp #12432 #12730]: #12757
  3.5970 -#12909 := [unit-resolution #12772 #12870 #15395]: #12904
  3.5971 -#12907 := [unit-resolution #12909 #12732]: #5125
  3.5972 -#12775 := (or #12167 #12074)
  3.5973 -#12881 := [th-lemma arith farkas 1 1]: #12775
  3.5974 -#12865 := [unit-resolution #12881 #12732]: #12167
  3.5975 -#9736 := [hypothesis]: #7776
  3.5976 -#3233 := (>= #110 0::Int)
  3.5977 -#4506 := (or #3722 #3233)
  3.5978 -#4549 := [quant-inst #65]: #4506
  3.5979 -#9790 := [unit-resolution #4549 #7614]: #3233
  3.5980 -#12861 := [th-lemma arith farkas 1 1 1 1 -1 1 #10752 #9790 #9736 #12865 #12907 #13634]: false
  3.5981 -#12858 := [lemma #12861]: #12779
  3.5982 -#16384 := [unit-resolution #12858 #16406 #18189 #18542]: #12074
  3.5983 -#16235 := [unit-resolution #15391 #16384]: #16258
  3.5984 -#16285 := [unit-resolution #16235 #16377]: #5243
  3.5985 -#16416 := [unit-resolution #12124 #18380]: #5251
  3.5986 -#16417 := [unit-resolution #16416 #15395]: #15394
  3.5987 -#16408 := [unit-resolution #16417 #16285 #16319]: false
  3.5988 -#16407 := [lemma #16408]: #15379
  3.5989 -#16321 := [unit-resolution #15376 #16407]: #15374
  3.5990 -#16309 := [hypothesis]: #5149
  3.5991 -#16410 := [unit-resolution #12071 #16309]: #12105
  3.5992 -#16431 := [unit-resolution #12118 #16309]: #12081
  3.5993 -#16434 := [unit-resolution #11095 #16431 #16410 #16321]: false
  3.5994 -#16432 := [lemma #16434]: #5146
  3.5995 -#16614 := [unit-resolution #9728 #16432]: #5087
  3.5996 -#16615 := [unit-resolution #12636 #16614]: #12022
  3.5997 -#16603 := [unit-resolution #19099 #16615]: #15968
  3.5998 -#16597 := [unit-resolution #19102 #16603]: #5359
  3.5999 -#16549 := [unit-resolution #15554 #16597]: #5356
  3.6000 -#16573 := [unit-resolution #18361 #16549]: #15530
  3.6001 -#16590 := [unit-resolution #18365 #19087 #16615 #16573]: #18243
  3.6002 -#16554 := [unit-resolution #18373 #18368 #16573 #16615]: #18369
  3.6003 -#16552 := (f11 #193 #5342)
  3.6004 -#16553 := (= #16552 f1)
  3.6005 -#16559 := (= #5342 f28)
  3.6006 -#16561 := (or #16559 #5348)
  3.6007 -#16545 := (iff #16553 #16561)
  3.6008 -#16568 := (or #7518 #16545)
  3.6009 -#16522 := (if #16559 #4057 #5348)
  3.6010 -#16560 := (iff #16553 #16522)
  3.6011 -#16569 := (or #7518 #16560)
  3.6012 -#16571 := (iff #16569 #16568)
  3.6013 -#16563 := (iff #16568 #16568)
  3.6014 -#16588 := [rewrite]: #16563
  3.6015 -#16567 := (iff #16560 #16545)
  3.6016 -#16564 := (iff #16522 #16561)
  3.6017 -#16557 := (if #16559 true #5348)
  3.6018 -#16565 := (iff #16557 #16561)
  3.6019 -#16547 := [rewrite]: #16565
  3.6020 -#16562 := (iff #16522 #16557)
  3.6021 -#16548 := [monotonicity #4060]: #16562
  3.6022 -#16566 := [trans #16548 #16547]: #16564
  3.6023 -#16546 := [monotonicity #16566]: #16567
  3.6024 -#16574 := [monotonicity #16546]: #16571
  3.6025 -#16586 := [trans #16574 #16588]: #16571
  3.6026 -#16572 := [quant-inst #115 #181 #3 #5342]: #16569
  3.6027 -#16589 := [mp #16572 #16586]: #16568
  3.6028 -#16611 := [unit-resolution #16589 #3646]: #16545
  3.6029 -#16373 := (not #16545)
  3.6030 -#16635 := (or #16373 #16553)
  3.6031 -#16598 := [unit-resolution #12306 #16597]: #5348
  3.6032 -#15874 := (or #16561 #5349)
  3.6033 -#16585 := [def-axiom]: #15874
  3.6034 -#16596 := [unit-resolution #16585 #16598]: #16561
  3.6035 -#15886 := (not #16561)
  3.6036 -#16515 := (or #16373 #16553 #15886)
  3.6037 -#16581 := [def-axiom]: #16515
  3.6038 -#16599 := [unit-resolution #16581 #16596]: #16635
  3.6039 -#16620 := [unit-resolution #16599 #16611]: #16553
  3.6040 -#16621 := (= #13322 #16552)
  3.6041 -#16619 := [monotonicity #8144]: #16621
  3.6042 -#16595 := [trans #16619 #16620]: #13321
  3.6043 -#16610 := [hypothesis]: #13323
  3.6044 -#16622 := [unit-resolution #16610 #16595]: false
  3.6045 -#16600 := [lemma #16622]: #13321
  3.6046 -#16372 := [unit-resolution #18379 #16600 #16554]: #14134
  3.6047 -#16550 := [unit-resolution #12297 #16597]: #12311
  3.6048 -#16043 := [unit-resolution #19108 #19087 #16615 #16550]: #19105
  3.6049 -#16044 := [unit-resolution #18381 #16600 #16043]: #15302
  3.6050 -[unit-resolution #18394 #16044 #16372 #16590]: false
  3.6051 -unsat
     4.1 --- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.thy	Tue Jul 23 13:14:14 2013 +0200
     4.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     4.3 @@ -1,93 +0,0 @@
     4.4 -(*  Title:      HOL/Boogie/Examples/Boogie_Dijkstra.thy
     4.5 -    Author:     Sascha Boehme, TU Muenchen
     4.6 -*)
     4.7 -
     4.8 -header {* Boogie example: Dijkstra's algorithm *}
     4.9 -
    4.10 -theory Boogie_Dijkstra
    4.11 -imports Boogie
    4.12 -begin
    4.13 -
    4.14 -text {*
    4.15 -We prove correct the verification condition generated from the following
    4.16 -Boogie code:
    4.17 -
    4.18 -\begin{verbatim}
    4.19 -type Vertex;
    4.20 -const G: [Vertex, Vertex] int;
    4.21 -axiom (forall x: Vertex, y: Vertex ::  x != y ==> 0 < G[x,y]);
    4.22 -axiom (forall x: Vertex, y: Vertex ::  x == y ==> G[x,y] == 0);
    4.23 -
    4.24 -const Infinity: int;
    4.25 -axiom 0 < Infinity;
    4.26 -
    4.27 -const Source: Vertex;
    4.28 -var SP: [Vertex] int;
    4.29 -
    4.30 -procedure Dijkstra();
    4.31 -  modifies SP;
    4.32 -  ensures (SP[Source] == 0);
    4.33 -  ensures (forall z: Vertex, y: Vertex ::
    4.34 -    SP[y] < Infinity && G[y,z] < Infinity ==> SP[z] <= SP[y] + G[y,z]);
    4.35 -  ensures (forall z: Vertex :: z != Source && SP[z] < Infinity ==>
    4.36 -    (exists y: Vertex :: SP[y] < SP[z] && SP[z] == SP[y] + G[y,z]));
    4.37 -
    4.38 -implementation Dijkstra()
    4.39 -{
    4.40 -  var v: Vertex;
    4.41 -  var Visited: [Vertex] bool;
    4.42 -  var oldSP: [Vertex] int;
    4.43 -
    4.44 -  havoc SP;
    4.45 -  assume (forall x: Vertex :: x == Source ==> SP[x] == 0);
    4.46 -  assume (forall x: Vertex :: x != Source ==> SP[x] == Infinity);
    4.47 -
    4.48 -  havoc Visited;
    4.49 -  assume (forall x: Vertex :: !Visited[x]);
    4.50 -
    4.51 -  while ((exists x: Vertex :: !Visited[x] && SP[x] < Infinity))
    4.52 -    invariant (SP[Source] == 0);
    4.53 -    invariant (forall x: Vertex :: SP[x] >= 0);
    4.54 -    invariant (forall y: Vertex, z: Vertex :: 
    4.55 -      !Visited[z] && Visited[y] ==> SP[y] <= SP[z]);
    4.56 -    invariant (forall z: Vertex, y: Vertex ::
    4.57 -      Visited[y] && G[y,z] < Infinity ==> SP[z] <= SP[y] + G[y,z]);
    4.58 -    invariant (forall z: Vertex :: z != Source && SP[z] < Infinity ==>
    4.59 -      (exists y: Vertex :: SP[y] < SP[z] && Visited[y] && 
    4.60 -        SP[z] == SP[y] + G[y,z]));
    4.61 -  {
    4.62 -    havoc v;
    4.63 -    assume (!Visited[v]);
    4.64 -    assume (SP[v] < Infinity); 
    4.65 -    assume (forall x: Vertex :: !Visited[x] ==> SP[v] <= SP[x]);
    4.66 -
    4.67 -    Visited[v] := true;
    4.68 -
    4.69 -    oldSP := SP;
    4.70 -    havoc SP;
    4.71 -    assume (forall u: Vertex :: 
    4.72 -      G[v,u] < Infinity && oldSP[v] + G[v,u] < oldSP[u] ==> 
    4.73 -        SP[u] == oldSP[v] + G[v,u]);
    4.74 -    assume (forall u: Vertex :: 
    4.75 -      !(G[v,u] < Infinity && oldSP[v] + G[v,u] < oldSP[u]) ==> 
    4.76 -        SP[u] == oldSP[u]);
    4.77 -    assert (forall z: Vertex:: SP[z] <= oldSP[z]);
    4.78 -    assert (forall y: Vertex:: Visited[y] ==> SP[y] == oldSP[y]);
    4.79 -  }
    4.80 -}
    4.81 -\end{verbatim}
    4.82 -*}
    4.83 -
    4.84 -
    4.85 -boogie_open "Boogie_Dijkstra.b2i"
    4.86 -
    4.87 -declare [[smt_oracle = false]]
    4.88 -declare [[smt_certificates = "Boogie_Dijkstra.certs"]]
    4.89 -declare [[smt_read_only_certificates = true]]
    4.90 -
    4.91 -boogie_vc Dijkstra
    4.92 -  by boogie
    4.93 -
    4.94 -boogie_end
    4.95 -
    4.96 -end
     5.1 --- a/src/HOL/Boogie/Examples/Boogie_Max.b2i	Tue Jul 23 13:14:14 2013 +0200
     5.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     5.3 @@ -1,748 +0,0 @@
     5.4 -vc max 1
     5.5 -    implies
     5.6 -    label pos 10 7
     5.7 -    true
     5.8 -    implies
     5.9 -    <
    5.10 -    int-num 0
    5.11 -    var length
    5.12 -      int
    5.13 -    implies
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   5.227 -    var max@4
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   5.241 -    label neg 5 3
   5.242 -    exists 1 0 3
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