merged
authorhuffman
Sat, 07 Nov 2009 07:37:20 -0800
changeset 33507 6390cc8d2714
parent 33506 afb577487b15 (current diff)
parent 33501 31872dd275c8 (diff)
child 33508 70026e20fa4c
merged
src/HOL/Boogie/Examples/cert/Boogie_b_Dijkstra
src/HOL/Boogie/Examples/cert/Boogie_b_Dijkstra.proof
src/HOL/Boogie/Examples/cert/Boogie_b_max
src/HOL/Boogie/Examples/cert/Boogie_b_max.proof
src/HOL/Boogie/Examples/cert/VCC_b_maximum
src/HOL/Boogie/Examples/cert/VCC_b_maximum.proof
src/HOL/SizeChange/Correctness.thy
src/HOL/SizeChange/Criterion.thy
src/HOL/SizeChange/Examples.thy
src/HOL/SizeChange/Graphs.thy
src/HOL/SizeChange/Implementation.thy
src/HOL/SizeChange/Interpretation.thy
src/HOL/SizeChange/Misc_Tools.thy
src/HOL/SizeChange/ROOT.ML
src/HOL/SizeChange/Size_Change_Termination.thy
src/HOL/SizeChange/document/root.tex
src/HOL/SizeChange/sct.ML
src/HOL/Tools/Function/induction_scheme.ML
src/HOL/ex/Induction_Scheme.thy
src/HOLCF/Tools/fixrec.ML
--- a/Admin/isatest/isatest-settings	Fri Nov 06 09:50:37 2009 -0800
+++ b/Admin/isatest/isatest-settings	Sat Nov 07 07:37:20 2009 -0800
@@ -11,7 +11,7 @@
 HOME=/home/isatest
 
 ## send email on failure to
-MAILTO="kleing@cse.unsw.edu.au nipkow@in.tum.de berghofe@in.tum.de schirmer@in.tum.de lp15@cam.ac.uk makarius@sketis.net haftmann@in.tum.de krauss@in.tum.de blanchet@in.tum.de bulwahn@in.tum.de"
+MAILTO="kleing@cse.unsw.edu.au nipkow@in.tum.de berghofe@in.tum.de schirmer@in.tum.de lp15@cam.ac.uk makarius@sketis.net haftmann@in.tum.de krauss@in.tum.de blanchet@in.tum.de bulwahn@in.tum.de boehmes@in.tum.de hoelzl@in.tum.de"
 
 LOGPREFIX=$HOME/log
 MASTERLOG=$LOGPREFIX/isatest.log
--- a/NEWS	Fri Nov 06 09:50:37 2009 -0800
+++ b/NEWS	Sat Nov 07 07:37:20 2009 -0800
@@ -54,6 +54,8 @@
 solvers using the oracle mechanism; for the SMT solver Z3,
 this method is proof-producing. Certificates are provided to
 avoid calling the external solvers solely for re-checking proofs.
+Due to a remote SMT service there is no need for installing SMT
+solvers locally.
 
 * New commands to load and prove verification conditions
 generated by the Boogie program verifier or derived systems
@@ -227,6 +229,10 @@
 * Maclauren.DERIV_tac and Maclauren.deriv_tac was removed, they are
 replaced by: (auto intro!: DERIV_intros).  INCOMPATIBILITY.
 
+* Renamed methods:
+    sizechange -> size_change
+    induct_scheme -> induction_schema
+
 
 *** ML ***
 
--- a/src/FOL/ex/LocaleTest.thy	Fri Nov 06 09:50:37 2009 -0800
+++ b/src/FOL/ex/LocaleTest.thy	Sat Nov 07 07:37:20 2009 -0800
@@ -124,6 +124,59 @@
 thm var.test_def
 
 
+text {* Under which circumstances term syntax remains active. *}
+
+locale "syntax" =
+  fixes p1 :: "'a => 'b"
+    and p2 :: "'b => o"
+begin
+
+definition d1 :: "'a => o" where "d1(x) <-> ~ p2(p1(x))"
+definition d2 :: "'b => o" where "d2(x) <-> ~ p2(x)"
+
+thm d1_def d2_def
+
+end
+
+thm syntax.d1_def syntax.d2_def
+
+locale syntax' = "syntax" p1 p2 for p1 :: "'a => 'a" and p2 :: "'a => o"
+begin
+
+thm d1_def d2_def  (* should print as "d1(?x) <-> ..." and "d2(?x) <-> ..." *)
+
+ML {*
+  fun check_syntax ctxt thm expected =
+    let
+      val obtained = PrintMode.setmp [] (Display.string_of_thm ctxt) thm;
+    in
+      if obtained <> expected
+      then error ("Theorem syntax '" ^ obtained ^ "' obtained, but '" ^ expected ^ "' expected.")
+      else ()
+    end;
+*}
+
+ML {*
+  check_syntax @{context} @{thm d1_def} "d1(?x) <-> ~ p2(p1(?x))";
+  check_syntax @{context} @{thm d2_def} "d2(?x) <-> ~ p2(?x)";
+*}
+
+end
+
+locale syntax'' = "syntax" p3 p2 for p3 :: "'a => 'b" and p2 :: "'b => o"
+begin
+
+thm d1_def d2_def
+  (* should print as "syntax.d1(p3, p2, ?x) <-> ..." and "d2(?x) <-> ..." *)
+
+ML {*
+  check_syntax @{context} @{thm d1_def} "syntax.d1(p3, p2, ?x) <-> ~ p2(p3(?x))";
+  check_syntax @{context} @{thm d2_def} "d2(?x) <-> ~ p2(?x)";
+*}
+
+end
+
+
 section {* Foundational versions of theorems *}
 
 thm logic.assoc
--- a/src/HOL/Boogie/Boogie.thy	Fri Nov 06 09:50:37 2009 -0800
+++ b/src/HOL/Boogie/Boogie.thy	Sat Nov 07 07:37:20 2009 -0800
@@ -13,6 +13,22 @@
   ("Tools/boogie_split.ML")
 begin
 
+text {*
+HOL-Boogie and its applications are described in:
+\begin{itemize}
+
+\item Sascha B"ohme, K. Rustan M. Leino, and Burkhart Wolff.
+HOL-Boogie --- An Interactive Prover for the Boogie Program-Verifier.
+Theorem Proving in Higher Order Logics, 2008.
+
+\item Sascha B"ohme, Micha{\l} Moskal, Wolfram Schulte, and Burkhart Wolff.
+HOL-Boogie --- An Interactive Prover-Backend for the Verifying C Compiler.
+Journal of Automated Reasoning, 2009.
+
+\end{itemize}
+*}
+
+
 section {* Built-in types and functions of Boogie *}
 
 subsection {* Labels *}
@@ -177,8 +193,8 @@
 structure Boogie_Axioms = Named_Thms
 (
   val name = "boogie"
-  val description = ("Boogie background axioms" ^
-    " loaded along with Boogie verification conditions")
+  val description =
+    "Boogie background axioms loaded along with Boogie verification conditions"
 )
 *}
 setup Boogie_Axioms.setup
@@ -191,8 +207,8 @@
 structure Split_VC_SMT_Rules = Named_Thms
 (
   val name = "split_vc_smt"
-  val description = ("Theorems given to the SMT sub-tactic" ^
-    " of the split_vc method")
+  val description =
+    "theorems given to the SMT sub-tactic of the split_vc method"
 )
 *}
 setup Split_VC_SMT_Rules.setup
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.thy	Fri Nov 06 09:50:37 2009 -0800
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.thy	Sat Nov 07 07:37:20 2009 -0800
@@ -81,9 +81,9 @@
 
 boogie_open "~~/src/HOL/Boogie/Examples/Boogie_Dijkstra"
 
-boogie_vc b_Dijkstra
+boogie_vc Dijkstra
   unfolding labels
-  using [[smt_cert="~~/src/HOL/Boogie/Examples/cert/Boogie_b_Dijkstra"]]
+  using [[smt_cert="~~/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra"]]
   using [[z3_proofs=true]]
   by (smt boogie)
 
--- a/src/HOL/Boogie/Examples/Boogie_Max.thy	Fri Nov 06 09:50:37 2009 -0800
+++ b/src/HOL/Boogie/Examples/Boogie_Max.thy	Sat Nov 07 07:37:20 2009 -0800
@@ -41,9 +41,9 @@
 text {*
 Approach 1: Discharge the verification condition fully automatically by SMT:
 *}
-boogie_vc b_max
+boogie_vc max
   unfolding labels
-  using [[smt_cert="~~/src/HOL/Boogie/Examples/cert/Boogie_b_max"]]
+  using [[smt_cert="~~/src/HOL/Boogie/Examples/cert/Boogie_max"]]
   using [[z3_proofs=true]]
   by (smt boogie)
 
@@ -53,7 +53,7 @@
 explicit proof. This approach is most useful in an interactive debug-and-fix
 mode. 
 *}
-boogie_vc b_max
+boogie_vc max
 proof (split_vc (verbose) try: fast simp)
   print_cases
   case L_14_5c
--- a/src/HOL/Boogie/Examples/ROOT.ML	Fri Nov 06 09:50:37 2009 -0800
+++ b/src/HOL/Boogie/Examples/ROOT.ML	Sat Nov 07 07:37:20 2009 -0800
@@ -1,3 +1,1 @@
-use_thy "Boogie_Max";
-use_thy "Boogie_Dijkstra";
-use_thy "VCC_Max";
+use_thys ["Boogie_Max", "Boogie_Dijkstra", "VCC_Max"];
--- a/src/HOL/Boogie/Examples/VCC_Max.thy	Fri Nov 06 09:50:37 2009 -0800
+++ b/src/HOL/Boogie/Examples/VCC_Max.thy	Sat Nov 07 07:37:20 2009 -0800
@@ -48,9 +48,9 @@
 
 boogie_status
 
-boogie_vc b_maximum
+boogie_vc maximum
   unfolding labels
-  using [[smt_cert="~~/src/HOL/Boogie/Examples/cert/VCC_b_maximum"]]
+  using [[smt_cert="~~/src/HOL/Boogie/Examples/cert/VCC_maximum"]]
   using [[z3_proofs=true]]
   by (smt boogie)
 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra	Sat Nov 07 07:37:20 2009 -0800
@@ -0,0 +1,43 @@
+(benchmark Isabelle
+:extrasorts ( T1 T4 T3 T5 T2)
+:extrafuns (
+  (uf_2 T1 T2)
+  (uf_3 T1 T2)
+  (uf_1 T2 T2 T1)
+  (uf_8 T5)
+  (uf_7 T4 T2 T5 T4)
+  (uf_5 T3 T2 Int T3)
+  (uf_6 T4 T2 T5)
+  (uf_4 T3 T2 Int)
+  (uf_10 T1 Int)
+  (uf_11 T2)
+  (uf_9 Int)
+  (uf_21 T2)
+  (uf_16 T2)
+  (uf_20 T2)
+  (uf_12 T2 Int)
+  (uf_14 T3)
+  (uf_18 T2 Int)
+  (uf_22 T3)
+  (uf_24 T3)
+  (uf_23 T3)
+  (uf_15 T4)
+  (uf_17 T4)
+  (uf_19 T4)
+ )
+:extrapreds (
+  (up_13 T2)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1) (uf_3 ?x1)) ?x1))
+:assumption (forall (?x2 T2) (?x3 T2) (= (uf_3 (uf_1 ?x2 ?x3)) ?x3))
+:assumption (forall (?x4 T2) (?x5 T2) (= (uf_2 (uf_1 ?x4 ?x5)) ?x4))
+:assumption (forall (?x6 T3) (?x7 T2) (?x8 Int) (?x9 T2) (= (uf_4 (uf_5 ?x6 ?x7 ?x8) ?x9) (ite (= ?x9 ?x7) ?x8 (uf_4 ?x6 ?x9))))
+:assumption (forall (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2) (iff (= (uf_6 (uf_7 ?x10 ?x11 ?x12) ?x13) uf_8) (if_then_else (= ?x13 ?x11) (= ?x12 uf_8) (= (uf_6 ?x10 ?x13) uf_8))))
+:assumption (forall (?x14 T3) (?x15 T2) (?x16 Int) (= (uf_4 (uf_5 ?x14 ?x15 ?x16) ?x15) ?x16))
+:assumption (forall (?x17 T4) (?x18 T2) (?x19 T5) (iff (= (uf_6 (uf_7 ?x17 ?x18 ?x19) ?x18) uf_8) (= ?x19 uf_8)))
+:assumption (< 0 uf_9)
+:assumption (forall (?x20 T2) (?x21 T2) (implies (= ?x20 ?x21) (= (uf_10 (uf_1 ?x20 ?x21)) 0)))
+:assumption (forall (?x22 T2) (?x23 T2) (implies (not (= ?x22 ?x23)) (< 0 (uf_10 (uf_1 ?x22 ?x23)))))
+:assumption (not (implies true (implies true (implies (forall (?x24 T2) (implies (= ?x24 uf_11) (= (uf_12 ?x24) 0))) (implies (forall (?x25 T2) (implies (not (= ?x25 uf_11)) (= (uf_12 ?x25) uf_9))) (implies (forall (?x26 T2) (not (up_13 ?x26))) (implies true (and (implies (= (uf_12 uf_11) 0) (and (implies (forall (?x27 T2) (<= 0 (uf_12 ?x27))) (and (implies (forall (?x28 T2) (?x29 T2) (implies (and (up_13 ?x28) (not (up_13 ?x29))) (<= (uf_12 ?x28) (uf_12 ?x29)))) (and (implies (forall (?x30 T2) (?x31 T2) (implies (and (< (uf_10 (uf_1 ?x31 ?x30)) uf_9) (up_13 ?x31)) (<= (uf_12 ?x30) (+ (uf_12 ?x31) (uf_10 (uf_1 ?x31 ?x30)))))) (and (implies (forall (?x32 T2) (implies (and (< (uf_12 ?x32) uf_9) (not (= ?x32 uf_11))) (exists (?x33 T2) (and (= (uf_12 ?x32) (+ (uf_12 ?x33) (uf_10 (uf_1 ?x33 ?x32)))) (and (up_13 ?x33) (< (uf_12 ?x33) (uf_12 ?x32))))))) (implies true (implies true (implies (= (uf_4 uf_14 uf_11) 0) (implies (forall (?x34 T2) (<= 0 (uf_4 uf_14 ?x34))) (implies (forall (?x35 T2) (?x36 T2) (implies (and (= (uf_6 uf_15 ?x35) uf_8) (not (= (uf_6 uf_15 ?x36) uf_8))) (<= (uf_4 uf_14 ?x35) (uf_4 uf_14 ?x36)))) (implies (forall (?x37 T2) (?x38 T2) (implies (and (< (uf_10 (uf_1 ?x38 ?x37)) uf_9) (= (uf_6 uf_15 ?x38) uf_8)) (<= (uf_4 uf_14 ?x37) (+ (uf_4 uf_14 ?x38) (uf_10 (uf_1 ?x38 ?x37)))))) (implies (forall (?x39 T2) (implies (and (< (uf_4 uf_14 ?x39) uf_9) (not (= ?x39 uf_11))) (exists (?x40 T2) (and (= (uf_4 uf_14 ?x39) (+ (uf_4 uf_14 ?x40) (uf_10 (uf_1 ?x40 ?x39)))) (and (= (uf_6 uf_15 ?x40) uf_8) (< (uf_4 uf_14 ?x40) (uf_4 uf_14 ?x39))))))) (implies true (and (implies true (implies true (implies (exists (?x41 T2) (and (< (uf_4 uf_14 ?x41) uf_9) (not (= (uf_6 uf_15 ?x41) uf_8)))) (implies (not (= (uf_6 uf_15 uf_16) uf_8)) (implies (< (uf_4 uf_14 uf_16) uf_9) (implies (forall (?x42 T2) (implies (not (= (uf_6 uf_15 ?x42) uf_8)) (<= (uf_4 uf_14 uf_16) (uf_4 uf_14 ?x42)))) (implies (= uf_17 (uf_7 uf_15 uf_16 uf_8)) (implies (forall (?x43 T2) (implies (and (< (+ (uf_4 uf_14 uf_16) (uf_10 (uf_1 uf_16 ?x43))) (uf_4 uf_14 ?x43)) (< (uf_10 (uf_1 uf_16 ?x43)) uf_9)) (= (uf_18 ?x43) (+ (uf_4 uf_14 uf_16) (uf_10 (uf_1 uf_16 ?x43)))))) (implies (forall (?x44 T2) (implies (not (and (< (+ (uf_4 uf_14 uf_16) (uf_10 (uf_1 uf_16 ?x44))) (uf_4 uf_14 ?x44)) (< (uf_10 (uf_1 uf_16 ?x44)) uf_9))) (= (uf_18 ?x44) (uf_4 uf_14 ?x44)))) (and (implies (forall (?x45 T2) (<= (uf_18 ?x45) (uf_4 uf_14 ?x45))) (and (implies (forall (?x46 T2) (implies (= (uf_6 uf_17 ?x46) uf_8) (= (uf_18 ?x46) (uf_4 uf_14 ?x46)))) (implies true (implies true (and (implies (= (uf_18 uf_11) 0) (and (implies (forall (?x47 T2) (<= 0 (uf_18 ?x47))) (and (implies (forall (?x48 T2) (?x49 T2) (implies (and (= (uf_6 uf_17 ?x48) uf_8) (not (= (uf_6 uf_17 ?x49) uf_8))) (<= (uf_18 ?x48) (uf_18 ?x49)))) (and (implies (forall (?x50 T2) (?x51 T2) (implies (and (< (uf_10 (uf_1 ?x51 ?x50)) uf_9) (= (uf_6 uf_17 ?x51) uf_8)) (<= (uf_18 ?x50) (+ (uf_18 ?x51) (uf_10 (uf_1 ?x51 ?x50)))))) (and (implies (forall (?x52 T2) (implies (and (< (uf_18 ?x52) uf_9) (not (= ?x52 uf_11))) (exists (?x53 T2) (and (= (uf_18 ?x52) (+ (uf_18 ?x53) (uf_10 (uf_1 ?x53 ?x52)))) (and (= (uf_6 uf_17 ?x53) uf_8) (< (uf_18 ?x53) (uf_18 ?x52))))))) (implies false true)) (forall (?x54 T2) (implies (and (< (uf_18 ?x54) uf_9) (not (= ?x54 uf_11))) (exists (?x55 T2) (and (= (uf_18 ?x54) (+ (uf_18 ?x55) (uf_10 (uf_1 ?x55 ?x54)))) (and (= (uf_6 uf_17 ?x55) uf_8) (< (uf_18 ?x55) (uf_18 ?x54))))))))) (forall (?x56 T2) (?x57 T2) (implies (and (< (uf_10 (uf_1 ?x57 ?x56)) uf_9) (= (uf_6 uf_17 ?x57) uf_8)) (<= (uf_18 ?x56) (+ (uf_18 ?x57) (uf_10 (uf_1 ?x57 ?x56)))))))) (forall (?x58 T2) (?x59 T2) (implies (and (= (uf_6 uf_17 ?x58) uf_8) (not (= (uf_6 uf_17 ?x59) uf_8))) (<= (uf_18 ?x58) (uf_18 ?x59)))))) (forall (?x60 T2) (<= 0 (uf_18 ?x60))))) (= (uf_18 uf_11) 0))))) (forall (?x61 T2) (implies (= (uf_6 uf_17 ?x61) uf_8) (= (uf_18 ?x61) (uf_4 uf_14 ?x61)))))) (forall (?x62 T2) (<= (uf_18 ?x62) (uf_4 uf_14 ?x62))))))))))))) (implies true (implies true (implies (not (exists (?x63 T2) (and (< (uf_4 uf_14 ?x63) uf_9) (not (= (uf_6 uf_15 ?x63) uf_8))))) (implies true (implies true (implies (= uf_19 uf_15) (implies (= uf_20 uf_21) (implies (= uf_22 uf_14) (implies (= uf_23 uf_24) (implies true (and (implies (forall (?x64 T2) (implies (and (< (uf_4 uf_22 ?x64) uf_9) (not (= ?x64 uf_11))) (exists (?x65 T2) (and (= (uf_4 uf_22 ?x64) (+ (uf_4 uf_22 ?x65) (uf_10 (uf_1 ?x65 ?x64)))) (< (uf_4 uf_22 ?x65) (uf_4 uf_22 ?x64)))))) (and (implies (forall (?x66 T2) (?x67 T2) (implies (and (< (uf_10 (uf_1 ?x67 ?x66)) uf_9) (< (uf_4 uf_22 ?x67) uf_9)) (<= (uf_4 uf_22 ?x66) (+ (uf_4 uf_22 ?x67) (uf_10 (uf_1 ?x67 ?x66)))))) (and (implies (= (uf_4 uf_22 uf_11) 0) true) (= (uf_4 uf_22 uf_11) 0))) (forall (?x68 T2) (?x69 T2) (implies (and (< (uf_10 (uf_1 ?x69 ?x68)) uf_9) (< (uf_4 uf_22 ?x69) uf_9)) (<= (uf_4 uf_22 ?x68) (+ (uf_4 uf_22 ?x69) (uf_10 (uf_1 ?x69 ?x68)))))))) (forall (?x70 T2) (implies (and (< (uf_4 uf_22 ?x70) uf_9) (not (= ?x70 uf_11))) (exists (?x71 T2) (and (= (uf_4 uf_22 ?x70) (+ (uf_4 uf_22 ?x71) (uf_10 (uf_1 ?x71 ?x70)))) (< (uf_4 uf_22 ?x71) (uf_4 uf_22 ?x70))))))))))))))))))))))))))) (forall (?x72 T2) (implies (and (< (uf_12 ?x72) uf_9) (not (= ?x72 uf_11))) (exists (?x73 T2) (and (= (uf_12 ?x72) (+ (uf_12 ?x73) (uf_10 (uf_1 ?x73 ?x72)))) (and (up_13 ?x73) (< (uf_12 ?x73) (uf_12 ?x72))))))))) (forall (?x74 T2) (?x75 T2) (implies (and (< (uf_10 (uf_1 ?x75 ?x74)) uf_9) (up_13 ?x75)) (<= (uf_12 ?x74) (+ (uf_12 ?x75) (uf_10 (uf_1 ?x75 ?x74)))))))) (forall (?x76 T2) (?x77 T2) (implies (and (up_13 ?x76) (not (up_13 ?x77))) (<= (uf_12 ?x76) (uf_12 ?x77)))))) (forall (?x78 T2) (<= 0 (uf_12 ?x78))))) (= (uf_12 uf_11) 0)))))))))
+:formula true
+)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Boogie/Examples/cert/Boogie_Dijkstra.proof	Sat Nov 07 07:37:20 2009 -0800
@@ -0,0 +1,7081 @@
+#2 := false
+#55 := 0::int
+decl uf_4 :: (-> T3 T2 int)
+decl ?x40!7 :: (-> T2 T2)
+decl ?x52!15 :: T2
+#2305 := ?x52!15
+#15992 := (?x40!7 ?x52!15)
+decl uf_14 :: T3
+#107 := uf_14
+#15996 := (uf_4 uf_14 #15992)
+#20405 := (>= #15996 0::int)
+#11 := (:var 0 T2)
+#110 := (uf_4 uf_14 #11)
+#4403 := (pattern #110)
+#1843 := (>= #110 0::int)
+#4404 := (forall (vars (?x34 T2)) (:pat #4403) #1843)
+decl uf_10 :: (-> T1 int)
+decl uf_1 :: (-> T2 T2 T1)
+decl ?x66!20 :: T2
+#2511 := ?x66!20
+decl ?x67!19 :: T2
+#2510 := ?x67!19
+#2516 := (uf_1 ?x67!19 ?x66!20)
+#2517 := (uf_10 #2516)
+#1320 := -1::int
+#2524 := (* -1::int #2517)
+decl uf_22 :: T3
+#230 := uf_22
+#2514 := (uf_4 uf_22 ?x67!19)
+#2520 := (* -1::int #2514)
+#3094 := (+ #2520 #2524)
+#2512 := (uf_4 uf_22 ?x66!20)
+#3095 := (+ #2512 #3094)
+#3096 := (<= #3095 0::int)
+decl uf_9 :: int
+#56 := uf_9
+#2525 := (+ uf_9 #2524)
+#2526 := (<= #2525 0::int)
+#2521 := (+ uf_9 #2520)
+#2522 := (<= #2521 0::int)
+#3693 := (or #2522 #2526 #3096)
+#3698 := (not #3693)
+#10 := (:var 1 T2)
+#90 := (uf_1 #11 #10)
+#4379 := (pattern #90)
+#238 := (uf_4 uf_22 #10)
+#1720 := (* -1::int #238)
+#235 := (uf_4 uf_22 #11)
+#1721 := (+ #235 #1720)
+#91 := (uf_10 #90)
+#1727 := (+ #91 #1721)
+#1750 := (>= #1727 0::int)
+#1707 := (* -1::int #235)
+#1708 := (+ uf_9 #1707)
+#1709 := (<= #1708 0::int)
+#1343 := (* -1::int #91)
+#1346 := (+ uf_9 #1343)
+#1347 := (<= #1346 0::int)
+#3661 := (or #1347 #1709 #1750)
+#4633 := (forall (vars (?x66 T2) (?x67 T2)) (:pat #4379) #3661)
+#4638 := (not #4633)
+decl uf_11 :: T2
+#67 := uf_11
+#250 := (uf_4 uf_22 uf_11)
+#251 := (= #250 0::int)
+#4641 := (or #251 #4638)
+#4644 := (not #4641)
+#4647 := (or #4644 #3698)
+#4650 := (not #4647)
+#4609 := (pattern #235)
+decl ?x65!18 :: (-> T2 T2)
+#2487 := (?x65!18 #11)
+#2490 := (uf_1 #2487 #11)
+#2491 := (uf_10 #2490)
+#3064 := (* -1::int #2491)
+#2488 := (uf_4 uf_22 #2487)
+#3047 := (* -1::int #2488)
+#3065 := (+ #3047 #3064)
+#3066 := (+ #235 #3065)
+#3067 := (= #3066 0::int)
+#3631 := (not #3067)
+#3048 := (+ #235 #3047)
+#3049 := (<= #3048 0::int)
+#3632 := (or #3049 #3631)
+#3633 := (not #3632)
+#68 := (= #11 uf_11)
+#3639 := (or #68 #1709 #3633)
+#4625 := (forall (vars (?x64 T2)) (:pat #4609) #3639)
+#4630 := (not #4625)
+#4653 := (or #4630 #4650)
+#4656 := (not #4653)
+decl ?x64!17 :: T2
+#2447 := ?x64!17
+#2451 := (uf_1 #11 ?x64!17)
+#4610 := (pattern #2451)
+#2452 := (uf_10 #2451)
+#2448 := (uf_4 uf_22 ?x64!17)
+#2449 := (* -1::int #2448)
+#3017 := (+ #2449 #2452)
+#3018 := (+ #235 #3017)
+#3021 := (= #3018 0::int)
+#3595 := (not #3021)
+#2450 := (+ #235 #2449)
+#2455 := (>= #2450 0::int)
+#3596 := (or #2455 #3595)
+#4611 := (forall (vars (?x65 T2)) (:pat #4609 #4610) #3596)
+#4616 := (not #4611)
+#2993 := (= uf_11 ?x64!17)
+#2459 := (+ uf_9 #2449)
+#2460 := (<= #2459 0::int)
+#4619 := (or #2460 #2993 #4616)
+#4622 := (not #4619)
+#4659 := (or #4622 #4656)
+#4662 := (not #4659)
+decl uf_6 :: (-> T4 T2 T5)
+decl uf_15 :: T4
+#113 := uf_15
+#116 := (uf_6 uf_15 #11)
+#4445 := (pattern #116)
+#1404 := (* -1::int #110)
+#1405 := (+ uf_9 #1404)
+#1406 := (<= #1405 0::int)
+decl uf_8 :: T5
+#33 := uf_8
+#505 := (= uf_8 #116)
+#3581 := (or #505 #1406)
+#4601 := (forall (vars (?x41 T2)) (:pat #4445 #4403) #3581)
+#4606 := (not #4601)
+#933 := (= uf_14 uf_22)
+#1053 := (not #933)
+decl uf_19 :: T4
+#225 := uf_19
+#930 := (= uf_15 uf_19)
+#1071 := (not #930)
+decl uf_24 :: T3
+#233 := uf_24
+decl uf_23 :: T3
+#232 := uf_23
+#234 := (= uf_23 uf_24)
+#1044 := (not #234)
+decl uf_21 :: T2
+#228 := uf_21
+decl uf_20 :: T2
+#227 := uf_20
+#229 := (= uf_20 uf_21)
+#1062 := (not #229)
+#4665 := (or #1062 #1044 #1071 #1053 #4606 #4662)
+#4668 := (not #4665)
+#2309 := (uf_1 #11 ?x52!15)
+#4514 := (pattern #2309)
+decl uf_18 :: (-> T2 int)
+#158 := (uf_18 #11)
+#4454 := (pattern #158)
+decl uf_17 :: T4
+#149 := uf_17
+#168 := (uf_6 uf_17 #11)
+#4480 := (pattern #168)
+#2310 := (uf_10 #2309)
+#2306 := (uf_18 ?x52!15)
+#2307 := (* -1::int #2306)
+#2917 := (+ #2307 #2310)
+#2918 := (+ #158 #2917)
+#2921 := (= #2918 0::int)
+#3474 := (not #2921)
+#2308 := (+ #158 #2307)
+#2313 := (>= #2308 0::int)
+#630 := (= uf_8 #168)
+#636 := (not #630)
+#3475 := (or #636 #2313 #3474)
+#4515 := (forall (vars (?x53 T2)) (:pat #4480 #4454 #4514) #3475)
+#4520 := (not #4515)
+#180 := (uf_18 #10)
+#1505 := (* -1::int #180)
+#1506 := (+ #158 #1505)
+#1536 := (+ #91 #1506)
+#1534 := (>= #1536 0::int)
+#3466 := (or #636 #1347 #1534)
+#4506 := (forall (vars (?x50 T2) (?x51 T2)) (:pat #4379) #3466)
+#4511 := (not #4506)
+#2893 := (= uf_11 ?x52!15)
+#2317 := (+ uf_9 #2307)
+#2318 := (<= #2317 0::int)
+#4523 := (or #2318 #2893 #4511 #4520)
+#4526 := (not #4523)
+decl ?x50!14 :: T2
+#2275 := ?x50!14
+decl ?x51!13 :: T2
+#2274 := ?x51!13
+#2280 := (uf_1 ?x51!13 ?x50!14)
+#2281 := (uf_10 #2280)
+#2284 := (* -1::int #2281)
+#2278 := (uf_18 ?x51!13)
+#2879 := (* -1::int #2278)
+#2880 := (+ #2879 #2284)
+#2276 := (uf_18 ?x50!14)
+#2881 := (+ #2276 #2880)
+#2882 := (<= #2881 0::int)
+#2288 := (uf_6 uf_17 ?x51!13)
+#2289 := (= uf_8 #2288)
+#3429 := (not #2289)
+#2285 := (+ uf_9 #2284)
+#2286 := (<= #2285 0::int)
+#3444 := (or #2286 #3429 #2882)
+#3449 := (not #3444)
+#4529 := (or #3449 #4526)
+#4532 := (not #4529)
+#4497 := (pattern #158 #180)
+#1504 := (>= #1506 0::int)
+#176 := (uf_6 uf_17 #10)
+#648 := (= uf_8 #176)
+#3406 := (not #648)
+#3421 := (or #630 #3406 #1504)
+#4498 := (forall (vars (?x48 T2) (?x49 T2)) (:pat #4497) #3421)
+#4503 := (not #4498)
+#4535 := (or #4503 #4532)
+#4538 := (not #4535)
+decl ?x49!11 :: T2
+#2247 := ?x49!11
+#2251 := (uf_18 ?x49!11)
+#2853 := (* -1::int #2251)
+decl ?x48!12 :: T2
+#2248 := ?x48!12
+#2249 := (uf_18 ?x48!12)
+#2854 := (+ #2249 #2853)
+#2855 := (<= #2854 0::int)
+#2256 := (uf_6 uf_17 ?x49!11)
+#2257 := (= uf_8 #2256)
+#2254 := (uf_6 uf_17 ?x48!12)
+#2255 := (= uf_8 #2254)
+#3383 := (not #2255)
+#3398 := (or #3383 #2257 #2855)
+#3403 := (not #3398)
+#4541 := (or #3403 #4538)
+#4544 := (not #4541)
+#1495 := (>= #158 0::int)
+#4489 := (forall (vars (?x47 T2)) (:pat #4454) #1495)
+#4494 := (not #4489)
+#4547 := (or #4494 #4544)
+#4550 := (not #4547)
+decl ?x47!10 :: T2
+#2232 := ?x47!10
+#2233 := (uf_18 ?x47!10)
+#2234 := (>= #2233 0::int)
+#2235 := (not #2234)
+#4553 := (or #2235 #4550)
+#4556 := (not #4553)
+#172 := (uf_18 uf_11)
+#173 := (= #172 0::int)
+#1492 := (not #173)
+#4559 := (or #1492 #4556)
+#4562 := (not #4559)
+#4565 := (or #1492 #4562)
+#4568 := (not #4565)
+#616 := (= #110 #158)
+#637 := (or #616 #636)
+#4481 := (forall (vars (?x46 T2)) (:pat #4403 #4454 #4480) #637)
+#4486 := (not #4481)
+#4571 := (or #4486 #4568)
+#4574 := (not #4571)
+decl ?x46!9 :: T2
+#2207 := ?x46!9
+#2212 := (uf_4 uf_14 ?x46!9)
+#2211 := (uf_18 ?x46!9)
+#2825 := (= #2211 #2212)
+#2208 := (uf_6 uf_17 ?x46!9)
+#2209 := (= uf_8 #2208)
+#2210 := (not #2209)
+#2831 := (or #2210 #2825)
+#2836 := (not #2831)
+#4577 := (or #2836 #4574)
+#4580 := (not #4577)
+#1480 := (* -1::int #158)
+#1481 := (+ #110 #1480)
+#1479 := (>= #1481 0::int)
+#4472 := (forall (vars (?x45 T2)) (:pat #4403 #4454) #1479)
+#4477 := (not #4472)
+#4583 := (or #4477 #4580)
+#4586 := (not #4583)
+decl ?x45!8 :: T2
+#2189 := ?x45!8
+#2192 := (uf_4 uf_14 ?x45!8)
+#2815 := (* -1::int #2192)
+#2190 := (uf_18 ?x45!8)
+#2816 := (+ #2190 #2815)
+#2817 := (<= #2816 0::int)
+#2822 := (not #2817)
+#4589 := (or #2822 #4586)
+#4592 := (not #4589)
+decl uf_16 :: T2
+#140 := uf_16
+#152 := (uf_1 uf_16 #11)
+#4455 := (pattern #152)
+#153 := (uf_10 #152)
+#1623 := (+ #153 #1480)
+#144 := (uf_4 uf_14 uf_16)
+#1624 := (+ #144 #1623)
+#1625 := (= #1624 0::int)
+#1450 := (* -1::int #153)
+#1457 := (+ uf_9 #1450)
+#1458 := (<= #1457 0::int)
+#1449 := (* -1::int #144)
+#1451 := (+ #1449 #1450)
+#1452 := (+ #110 #1451)
+#1453 := (<= #1452 0::int)
+#3375 := (or #1453 #1458 #1625)
+#4464 := (forall (vars (?x43 T2)) (:pat #4403 #4455 #4454) #3375)
+#4469 := (not #4464)
+#3355 := (or #1453 #1458)
+#3356 := (not #3355)
+#3359 := (or #616 #3356)
+#4456 := (forall (vars (?x44 T2)) (:pat #4403 #4454 #4455) #3359)
+#4461 := (not #4456)
+decl ?x41!16 :: T2
+#2408 := ?x41!16
+#2414 := (uf_6 uf_15 ?x41!16)
+#2415 := (= uf_8 #2414)
+#2409 := (uf_4 uf_14 ?x41!16)
+#2410 := (* -1::int #2409)
+#2411 := (+ uf_9 #2410)
+#2412 := (<= #2411 0::int)
+#1655 := (+ uf_9 #1449)
+#1656 := (<= #1655 0::int)
+#1638 := (+ #110 #1449)
+#1637 := (>= #1638 0::int)
+#1644 := (or #505 #1637)
+#4446 := (forall (vars (?x42 T2)) (:pat #4445 #4403) #1644)
+#4451 := (not #4446)
+#141 := (uf_6 uf_15 uf_16)
+#585 := (= uf_8 #141)
+decl uf_7 :: (-> T4 T2 T5 T4)
+#150 := (uf_7 uf_15 uf_16 uf_8)
+#151 := (= uf_17 #150)
+#876 := (not #151)
+#4595 := (or #876 #585 #4451 #1656 #2412 #2415 #4461 #4469 #4592)
+#4598 := (not #4595)
+#4671 := (or #4598 #4668)
+#4674 := (not #4671)
+#2152 := (?x40!7 #11)
+#2155 := (uf_1 #2152 #11)
+#2156 := (uf_10 #2155)
+#2790 := (* -1::int #2156)
+#2153 := (uf_4 uf_14 #2152)
+#2773 := (* -1::int #2153)
+#2791 := (+ #2773 #2790)
+#2792 := (+ #110 #2791)
+#2793 := (= #2792 0::int)
+#3339 := (not #2793)
+#2774 := (+ #110 #2773)
+#2775 := (<= #2774 0::int)
+#2161 := (uf_6 uf_15 #2152)
+#2162 := (= uf_8 #2161)
+#3338 := (not #2162)
+#3340 := (or #3338 #2775 #3339)
+#3341 := (not #3340)
+#3347 := (or #68 #1406 #3341)
+#4437 := (forall (vars (?x39 T2)) (:pat #4403) #3347)
+#4442 := (not #4437)
+decl uf_12 :: (-> T2 int)
+#69 := (uf_12 #11)
+#4355 := (pattern #69)
+decl ?x33!6 :: (-> T2 T2)
+#2123 := (?x33!6 #11)
+#2127 := (uf_12 #2123)
+#2728 := (* -1::int #2127)
+#2124 := (uf_1 #2123 #11)
+#2125 := (uf_10 #2124)
+#2745 := (* -1::int #2125)
+#2746 := (+ #2745 #2728)
+#2747 := (+ #69 #2746)
+#2748 := (= #2747 0::int)
+#3311 := (not #2748)
+#2729 := (+ #69 #2728)
+#2730 := (<= #2729 0::int)
+decl up_13 :: (-> T2 bool)
+#2133 := (up_13 #2123)
+#3310 := (not #2133)
+#3312 := (or #3310 #2730 #3311)
+#3313 := (not #3312)
+#1386 := (* -1::int #69)
+#1387 := (+ uf_9 #1386)
+#1388 := (<= #1387 0::int)
+#3319 := (or #68 #1388 #3313)
+#4429 := (forall (vars (?x32 T2)) (:pat #4355) #3319)
+#4434 := (not #4429)
+#114 := (uf_6 uf_15 #10)
+#4420 := (pattern #114 #116)
+#120 := (uf_4 uf_14 #10)
+#1417 := (* -1::int #120)
+#1418 := (+ #110 #1417)
+#1416 := (>= #1418 0::int)
+#502 := (= uf_8 #114)
+#3276 := (not #502)
+#3291 := (or #3276 #505 #1416)
+#4421 := (forall (vars (?x35 T2) (?x36 T2)) (:pat #4420) #3291)
+#4426 := (not #4421)
+#1424 := (+ #91 #1418)
+#1815 := (>= #1424 0::int)
+#508 := (not #505)
+#3268 := (or #508 #1347 #1815)
+#4412 := (forall (vars (?x37 T2) (?x38 T2)) (:pat #4379) #3268)
+#4417 := (not #4412)
+#4409 := (not #4404)
+#108 := (uf_4 uf_14 uf_11)
+#109 := (= #108 0::int)
+#1854 := (not #109)
+#4677 := (or #1854 #4409 #4417 #4426 #4434 #4442 #4674)
+#4680 := (not #4677)
+decl ?x32!5 :: T2
+#2081 := ?x32!5
+#2091 := (uf_1 #11 ?x32!5)
+#4388 := (pattern #2091)
+#77 := (up_13 #11)
+#4348 := (pattern #77)
+#2082 := (uf_12 ?x32!5)
+#2083 := (* -1::int #2082)
+#2096 := (+ #69 #2083)
+#2097 := (>= #2096 0::int)
+#2092 := (uf_10 #2091)
+#2093 := (+ #2083 #2092)
+#2094 := (+ #69 #2093)
+#2095 := (= #2094 0::int)
+#3229 := (not #2095)
+#78 := (not #77)
+#3230 := (or #78 #3229 #2097)
+#4389 := (forall (vars (?x33 T2)) (:pat #4348 #4355 #4388) #3230)
+#4394 := (not #4389)
+#2688 := (= uf_11 ?x32!5)
+#2084 := (+ uf_9 #2083)
+#2085 := (<= #2084 0::int)
+#4397 := (or #2085 #2688 #4394)
+#4400 := (not #4397)
+#4683 := (or #4400 #4680)
+#4686 := (not #4683)
+#86 := (uf_12 #10)
+#1323 := (* -1::int #86)
+#1344 := (+ #1323 #91)
+#1345 := (+ #69 #1344)
+#1342 := (>= #1345 0::int)
+#3221 := (or #78 #1342 #1347)
+#4380 := (forall (vars (?x30 T2) (?x31 T2)) (:pat #4379) #3221)
+#4385 := (not #4380)
+#4689 := (or #4385 #4686)
+#4692 := (not #4689)
+decl ?x31!3 :: T2
+#2051 := ?x31!3
+#2065 := (uf_12 ?x31!3)
+decl ?x30!4 :: T2
+#2052 := ?x30!4
+#2062 := (uf_12 ?x30!4)
+#2063 := (* -1::int #2062)
+#2660 := (+ #2063 #2065)
+#2053 := (uf_1 ?x31!3 ?x30!4)
+#2054 := (uf_10 #2053)
+#2661 := (+ #2054 #2660)
+#2664 := (>= #2661 0::int)
+#2059 := (up_13 ?x31!3)
+#3184 := (not #2059)
+#2055 := (* -1::int #2054)
+#2056 := (+ uf_9 #2055)
+#2057 := (<= #2056 0::int)
+#3199 := (or #2057 #3184 #2664)
+#3204 := (not #3199)
+#4695 := (or #3204 #4692)
+#4698 := (not #4695)
+#84 := (up_13 #10)
+#4370 := (pattern #77 #84)
+#1324 := (+ #69 #1323)
+#1322 := (>= #1324 0::int)
+#2632 := (not #84)
+#3176 := (or #77 #2632 #1322)
+#4371 := (forall (vars (?x28 T2) (?x29 T2)) (:pat #4370) #3176)
+#4376 := (not #4371)
+#4701 := (or #4376 #4698)
+#4704 := (not #4701)
+decl ?x29!1 :: T2
+#2026 := ?x29!1
+#2030 := (uf_12 ?x29!1)
+#2647 := (* -1::int #2030)
+decl ?x28!2 :: T2
+#2027 := ?x28!2
+#2028 := (uf_12 ?x28!2)
+#2648 := (+ #2028 #2647)
+#2649 := (<= #2648 0::int)
+#2034 := (up_13 ?x29!1)
+#2033 := (up_13 ?x28!2)
+#2266 := (not #2033)
+#2166 := (or #2266 #2034 #2649)
+#6004 := [hypothesis]: #2033
+#4349 := (forall (vars (?x26 T2)) (:pat #4348) #78)
+#79 := (forall (vars (?x26 T2)) #78)
+#4352 := (iff #79 #4349)
+#4350 := (iff #78 #78)
+#4351 := [refl]: #4350
+#4353 := [quant-intro #4351]: #4352
+#1965 := (~ #79 #79)
+#2002 := (~ #78 #78)
+#2003 := [refl]: #2002
+#1966 := [nnf-pos #2003]: #1965
+#70 := (= #69 0::int)
+#73 := (not #68)
+#1912 := (or #73 #70)
+#1915 := (forall (vars (?x24 T2)) #1912)
+#1918 := (not #1915)
+#1846 := (forall (vars (?x34 T2)) #1843)
+#1849 := (not #1846)
+#511 := (and #502 #508)
+#517 := (not #511)
+#1832 := (or #517 #1416)
+#1837 := (forall (vars (?x35 T2) (?x36 T2)) #1832)
+#1840 := (not #1837)
+#1348 := (not #1347)
+#1807 := (and #505 #1348)
+#1812 := (not #1807)
+#1818 := (or #1812 #1815)
+#1821 := (forall (vars (?x37 T2) (?x38 T2)) #1818)
+#1824 := (not #1821)
+#1710 := (not #1709)
+#1744 := (and #1348 #1710)
+#1747 := (not #1744)
+#1753 := (or #1747 #1750)
+#1756 := (forall (vars (?x66 T2) (?x67 T2)) #1753)
+#1759 := (not #1756)
+#1767 := (or #251 #1759)
+#1772 := (and #1756 #1767)
+#1725 := (= #1727 0::int)
+#1719 := (>= #1721 0::int)
+#1722 := (not #1719)
+#1729 := (and #1722 #1725)
+#1732 := (exists (vars (?x65 T2)) #1729)
+#1713 := (and #73 #1710)
+#1716 := (not #1713)
+#1735 := (or #1716 #1732)
+#1738 := (forall (vars (?x64 T2)) #1735)
+#1741 := (not #1738)
+#1775 := (or #1741 #1772)
+#1778 := (and #1738 #1775)
+#1407 := (not #1406)
+#1670 := (and #508 #1407)
+#1675 := (exists (vars (?x41 T2)) #1670)
+#1796 := (or #1062 #1044 #1071 #1053 #1675 #1778)
+#1678 := (not #1675)
+#1649 := (forall (vars (?x42 T2)) #1644)
+#1652 := (not #1649)
+#1459 := (not #1458)
+#1454 := (not #1453)
+#1462 := (and #1454 #1459)
+#1620 := (not #1462)
+#1628 := (or #1620 #1625)
+#1631 := (forall (vars (?x43 T2)) #1628)
+#1634 := (not #1631)
+#1561 := (= #1536 0::int)
+#1558 := (not #1504)
+#1570 := (and #630 #1558 #1561)
+#1575 := (exists (vars (?x53 T2)) #1570)
+#1547 := (+ uf_9 #1480)
+#1548 := (<= #1547 0::int)
+#1549 := (not #1548)
+#1552 := (and #73 #1549)
+#1555 := (not #1552)
+#1578 := (or #1555 #1575)
+#1581 := (forall (vars (?x52 T2)) #1578)
+#1526 := (and #630 #1348)
+#1531 := (not #1526)
+#1538 := (or #1531 #1534)
+#1541 := (forall (vars (?x50 T2) (?x51 T2)) #1538)
+#1544 := (not #1541)
+#1584 := (or #1544 #1581)
+#1587 := (and #1541 #1584)
+#656 := (and #636 #648)
+#664 := (not #656)
+#1512 := (or #664 #1504)
+#1517 := (forall (vars (?x48 T2) (?x49 T2)) #1512)
+#1520 := (not #1517)
+#1590 := (or #1520 #1587)
+#1593 := (and #1517 #1590)
+#1498 := (forall (vars (?x47 T2)) #1495)
+#1501 := (not #1498)
+#1596 := (or #1501 #1593)
+#1599 := (and #1498 #1596)
+#1602 := (or #1492 #1599)
+#1605 := (and #173 #1602)
+#642 := (forall (vars (?x46 T2)) #637)
+#824 := (not #642)
+#1608 := (or #824 #1605)
+#1611 := (and #642 #1608)
+#1484 := (forall (vars (?x45 T2)) #1479)
+#1487 := (not #1484)
+#1614 := (or #1487 #1611)
+#1617 := (and #1484 #1614)
+#1468 := (or #616 #1462)
+#1473 := (forall (vars (?x44 T2)) #1468)
+#1476 := (not #1473)
+#1702 := (or #876 #585 #1476 #1617 #1634 #1652 #1656 #1678)
+#1801 := (and #1702 #1796)
+#1422 := (= #1424 0::int)
+#1419 := (not #1416)
+#1432 := (and #505 #1419 #1422)
+#1437 := (exists (vars (?x40 T2)) #1432)
+#1410 := (and #73 #1407)
+#1413 := (not #1410)
+#1440 := (or #1413 #1437)
+#1443 := (forall (vars (?x39 T2)) #1440)
+#1446 := (not #1443)
+#1389 := (not #1388)
+#1392 := (and #73 #1389)
+#1395 := (not #1392)
+#1370 := (= #1345 0::int)
+#1366 := (not #1322)
+#1378 := (and #77 #1366 #1370)
+#1383 := (exists (vars (?x33 T2)) #1378)
+#1398 := (or #1383 #1395)
+#1401 := (forall (vars (?x32 T2)) #1398)
+#1857 := (not #1401)
+#1878 := (or #1854 #1857 #1446 #1801 #1824 #1840 #1849)
+#1883 := (and #1401 #1878)
+#1351 := (and #77 #1348)
+#1354 := (not #1351)
+#1357 := (or #1342 #1354)
+#1360 := (forall (vars (?x30 T2) (?x31 T2)) #1357)
+#1363 := (not #1360)
+#1886 := (or #1363 #1883)
+#1889 := (and #1360 #1886)
+#454 := (and #78 #84)
+#460 := (not #454)
+#1329 := (or #460 #1322)
+#1334 := (forall (vars (?x28 T2) (?x29 T2)) #1329)
+#1337 := (not #1334)
+#1892 := (or #1337 #1889)
+#1895 := (and #1334 #1892)
+#1313 := (>= #69 0::int)
+#1314 := (forall (vars (?x27 T2)) #1313)
+#1317 := (not #1314)
+#1898 := (or #1317 #1895)
+#1901 := (and #1314 #1898)
+#80 := (uf_12 uf_11)
+#81 := (= #80 0::int)
+#1308 := (not #81)
+#1904 := (or #1308 #1901)
+#1907 := (and #81 #1904)
+#437 := (= uf_9 #69)
+#443 := (or #68 #437)
+#448 := (forall (vars (?x25 T2)) #443)
+#1277 := (not #448)
+#1268 := (not #79)
+#1930 := (or #1268 #1277 #1907 #1918)
+#1935 := (not #1930)
+#82 := (<= 0::int #69)
+#83 := (forall (vars (?x27 T2)) #82)
+#87 := (<= #86 #69)
+#85 := (and #84 #78)
+#88 := (implies #85 #87)
+#89 := (forall (vars (?x28 T2) (?x29 T2)) #88)
+#94 := (+ #69 #91)
+#95 := (<= #86 #94)
+#92 := (< #91 uf_9)
+#93 := (and #92 #77)
+#96 := (implies #93 #95)
+#97 := (forall (vars (?x30 T2) (?x31 T2)) #96)
+#101 := (< #69 #86)
+#102 := (and #77 #101)
+#100 := (= #86 #94)
+#103 := (and #100 #102)
+#104 := (exists (vars (?x33 T2)) #103)
+#98 := (< #69 uf_9)
+#99 := (and #98 #73)
+#105 := (implies #99 #104)
+#106 := (forall (vars (?x32 T2)) #105)
+#241 := (< #235 #238)
+#239 := (+ #235 #91)
+#240 := (= #238 #239)
+#242 := (and #240 #241)
+#243 := (exists (vars (?x65 T2)) #242)
+#236 := (< #235 uf_9)
+#237 := (and #236 #73)
+#244 := (implies #237 #243)
+#245 := (forall (vars (?x64 T2)) #244)
+#247 := (<= #238 #239)
+#246 := (and #92 #236)
+#248 := (implies #246 #247)
+#249 := (forall (vars (?x66 T2) (?x67 T2)) #248)
+#1 := true
+#252 := (implies #251 true)
+#253 := (and #252 #251)
+#254 := (implies #249 #253)
+#255 := (and #254 #249)
+#256 := (implies #245 #255)
+#257 := (and #256 #245)
+#258 := (implies true #257)
+#259 := (implies #234 #258)
+#231 := (= uf_22 uf_14)
+#260 := (implies #231 #259)
+#261 := (implies #229 #260)
+#226 := (= uf_19 uf_15)
+#262 := (implies #226 #261)
+#263 := (implies true #262)
+#264 := (implies true #263)
+#117 := (= #116 uf_8)
+#118 := (not #117)
+#129 := (< #110 uf_9)
+#138 := (and #129 #118)
+#139 := (exists (vars (?x41 T2)) #138)
+#224 := (not #139)
+#265 := (implies #224 #264)
+#266 := (implies true #265)
+#267 := (implies true #266)
+#166 := (<= #158 #110)
+#167 := (forall (vars (?x45 T2)) #166)
+#163 := (= #158 #110)
+#169 := (= #168 uf_8)
+#170 := (implies #169 #163)
+#171 := (forall (vars (?x46 T2)) #170)
+#174 := (<= 0::int #158)
+#175 := (forall (vars (?x47 T2)) #174)
+#181 := (<= #180 #158)
+#178 := (not #169)
+#177 := (= #176 uf_8)
+#179 := (and #177 #178)
+#182 := (implies #179 #181)
+#183 := (forall (vars (?x48 T2) (?x49 T2)) #182)
+#185 := (+ #158 #91)
+#186 := (<= #180 #185)
+#184 := (and #92 #169)
+#187 := (implies #184 #186)
+#188 := (forall (vars (?x50 T2) (?x51 T2)) #187)
+#192 := (< #158 #180)
+#193 := (and #169 #192)
+#191 := (= #180 #185)
+#194 := (and #191 #193)
+#195 := (exists (vars (?x53 T2)) #194)
+#189 := (< #158 uf_9)
+#190 := (and #189 #73)
+#196 := (implies #190 #195)
+#197 := (forall (vars (?x52 T2)) #196)
+#198 := (implies false true)
+#199 := (implies #197 #198)
+#200 := (and #199 #197)
+#201 := (implies #188 #200)
+#202 := (and #201 #188)
+#203 := (implies #183 #202)
+#204 := (and #203 #183)
+#205 := (implies #175 #204)
+#206 := (and #205 #175)
+#207 := (implies #173 #206)
+#208 := (and #207 #173)
+#209 := (implies true #208)
+#210 := (implies true #209)
+#211 := (implies #171 #210)
+#212 := (and #211 #171)
+#213 := (implies #167 #212)
+#214 := (and #213 #167)
+#156 := (< #153 uf_9)
+#154 := (+ #144 #153)
+#155 := (< #154 #110)
+#157 := (and #155 #156)
+#162 := (not #157)
+#164 := (implies #162 #163)
+#165 := (forall (vars (?x44 T2)) #164)
+#215 := (implies #165 #214)
+#159 := (= #158 #154)
+#160 := (implies #157 #159)
+#161 := (forall (vars (?x43 T2)) #160)
+#216 := (implies #161 #215)
+#217 := (implies #151 #216)
+#146 := (<= #144 #110)
+#147 := (implies #118 #146)
+#148 := (forall (vars (?x42 T2)) #147)
+#218 := (implies #148 #217)
+#145 := (< #144 uf_9)
+#219 := (implies #145 #218)
+#142 := (= #141 uf_8)
+#143 := (not #142)
+#220 := (implies #143 #219)
+#221 := (implies #139 #220)
+#222 := (implies true #221)
+#223 := (implies true #222)
+#268 := (and #223 #267)
+#269 := (implies true #268)
+#132 := (< #110 #120)
+#133 := (and #117 #132)
+#125 := (+ #110 #91)
+#131 := (= #120 #125)
+#134 := (and #131 #133)
+#135 := (exists (vars (?x40 T2)) #134)
+#130 := (and #129 #73)
+#136 := (implies #130 #135)
+#137 := (forall (vars (?x39 T2)) #136)
+#270 := (implies #137 #269)
+#126 := (<= #120 #125)
+#124 := (and #92 #117)
+#127 := (implies #124 #126)
+#128 := (forall (vars (?x37 T2) (?x38 T2)) #127)
+#271 := (implies #128 #270)
+#121 := (<= #120 #110)
+#115 := (= #114 uf_8)
+#119 := (and #115 #118)
+#122 := (implies #119 #121)
+#123 := (forall (vars (?x35 T2) (?x36 T2)) #122)
+#272 := (implies #123 #271)
+#111 := (<= 0::int #110)
+#112 := (forall (vars (?x34 T2)) #111)
+#273 := (implies #112 #272)
+#274 := (implies #109 #273)
+#275 := (implies true #274)
+#276 := (implies true #275)
+#277 := (implies #106 #276)
+#278 := (and #277 #106)
+#279 := (implies #97 #278)
+#280 := (and #279 #97)
+#281 := (implies #89 #280)
+#282 := (and #281 #89)
+#283 := (implies #83 #282)
+#284 := (and #283 #83)
+#285 := (implies #81 #284)
+#286 := (and #285 #81)
+#287 := (implies true #286)
+#288 := (implies #79 #287)
+#74 := (= #69 uf_9)
+#75 := (implies #73 #74)
+#76 := (forall (vars (?x25 T2)) #75)
+#289 := (implies #76 #288)
+#71 := (implies #68 #70)
+#72 := (forall (vars (?x24 T2)) #71)
+#290 := (implies #72 #289)
+#291 := (implies true #290)
+#292 := (implies true #291)
+#293 := (not #292)
+#1938 := (iff #293 #1935)
+#983 := (= 0::int #250)
+#939 := (+ #91 #235)
+#968 := (<= #238 #939)
+#974 := (not #246)
+#975 := (or #974 #968)
+#980 := (forall (vars (?x66 T2) (?x67 T2)) #975)
+#1003 := (not #980)
+#1004 := (or #1003 #983)
+#1012 := (and #980 #1004)
+#942 := (= #238 #939)
+#948 := (and #241 #942)
+#953 := (exists (vars (?x65 T2)) #948)
+#936 := (and #73 #236)
+#959 := (not #936)
+#960 := (or #959 #953)
+#965 := (forall (vars (?x64 T2)) #960)
+#1020 := (not #965)
+#1021 := (or #1020 #1012)
+#1029 := (and #965 #1021)
+#1045 := (or #1044 #1029)
+#1054 := (or #1053 #1045)
+#1063 := (or #1062 #1054)
+#1072 := (or #1071 #1063)
+#579 := (and #129 #508)
+#582 := (exists (vars (?x41 T2)) #579)
+#1091 := (or #582 #1072)
+#703 := (and #192 #630)
+#676 := (+ #91 #158)
+#697 := (= #180 #676)
+#708 := (and #697 #703)
+#711 := (exists (vars (?x53 T2)) #708)
+#694 := (and #73 #189)
+#717 := (not #694)
+#718 := (or #717 #711)
+#723 := (forall (vars (?x52 T2)) #718)
+#679 := (<= #180 #676)
+#673 := (and #92 #630)
+#685 := (not #673)
+#686 := (or #685 #679)
+#691 := (forall (vars (?x50 T2) (?x51 T2)) #686)
+#745 := (not #691)
+#746 := (or #745 #723)
+#754 := (and #691 #746)
+#665 := (or #181 #664)
+#670 := (forall (vars (?x48 T2) (?x49 T2)) #665)
+#762 := (not #670)
+#763 := (or #762 #754)
+#771 := (and #670 #763)
+#779 := (not #175)
+#780 := (or #779 #771)
+#788 := (and #175 #780)
+#645 := (= 0::int #172)
+#796 := (not #645)
+#797 := (or #796 #788)
+#805 := (and #645 #797)
+#825 := (or #824 #805)
+#833 := (and #642 #825)
+#841 := (not #167)
+#842 := (or #841 #833)
+#850 := (and #167 #842)
+#622 := (or #157 #616)
+#627 := (forall (vars (?x44 T2)) #622)
+#858 := (not #627)
+#859 := (or #858 #850)
+#602 := (= #154 #158)
+#608 := (or #162 #602)
+#613 := (forall (vars (?x43 T2)) #608)
+#867 := (not #613)
+#868 := (or #867 #859)
+#877 := (or #876 #868)
+#594 := (or #146 #505)
+#599 := (forall (vars (?x42 T2)) #594)
+#885 := (not #599)
+#886 := (or #885 #877)
+#894 := (not #145)
+#895 := (or #894 #886)
+#903 := (or #585 #895)
+#911 := (not #582)
+#912 := (or #911 #903)
+#1107 := (and #912 #1091)
+#556 := (and #132 #505)
+#529 := (+ #91 #110)
+#550 := (= #120 #529)
+#561 := (and #550 #556)
+#564 := (exists (vars (?x40 T2)) #561)
+#547 := (and #73 #129)
+#570 := (not #547)
+#571 := (or #570 #564)
+#576 := (forall (vars (?x39 T2)) #571)
+#1120 := (not #576)
+#1121 := (or #1120 #1107)
+#532 := (<= #120 #529)
+#526 := (and #92 #505)
+#538 := (not #526)
+#539 := (or #538 #532)
+#544 := (forall (vars (?x37 T2) (?x38 T2)) #539)
+#1129 := (not #544)
+#1130 := (or #1129 #1121)
+#518 := (or #121 #517)
+#523 := (forall (vars (?x35 T2) (?x36 T2)) #518)
+#1138 := (not #523)
+#1139 := (or #1138 #1130)
+#1147 := (not #112)
+#1148 := (or #1147 #1139)
+#499 := (= 0::int #108)
+#1156 := (not #499)
+#1157 := (or #1156 #1148)
+#484 := (and #73 #98)
+#490 := (not #484)
+#491 := (or #104 #490)
+#496 := (forall (vars (?x32 T2)) #491)
+#1176 := (not #496)
+#1177 := (or #1176 #1157)
+#1185 := (and #496 #1177)
+#469 := (and #77 #92)
+#475 := (not #469)
+#476 := (or #95 #475)
+#481 := (forall (vars (?x30 T2) (?x31 T2)) #476)
+#1193 := (not #481)
+#1194 := (or #1193 #1185)
+#1202 := (and #481 #1194)
+#461 := (or #87 #460)
+#466 := (forall (vars (?x28 T2) (?x29 T2)) #461)
+#1210 := (not #466)
+#1211 := (or #1210 #1202)
+#1219 := (and #466 #1211)
+#1227 := (not #83)
+#1228 := (or #1227 #1219)
+#1236 := (and #83 #1228)
+#451 := (= 0::int #80)
+#1244 := (not #451)
+#1245 := (or #1244 #1236)
+#1253 := (and #451 #1245)
+#1269 := (or #1268 #1253)
+#1278 := (or #1277 #1269)
+#423 := (= 0::int #69)
+#429 := (or #73 #423)
+#434 := (forall (vars (?x24 T2)) #429)
+#1286 := (not #434)
+#1287 := (or #1286 #1278)
+#1303 := (not #1287)
+#1936 := (iff #1303 #1935)
+#1933 := (iff #1287 #1930)
+#1921 := (or #1268 #1907)
+#1924 := (or #1277 #1921)
+#1927 := (or #1918 #1924)
+#1931 := (iff #1927 #1930)
+#1932 := [rewrite]: #1931
+#1928 := (iff #1287 #1927)
+#1925 := (iff #1278 #1924)
+#1922 := (iff #1269 #1921)
+#1908 := (iff #1253 #1907)
+#1905 := (iff #1245 #1904)
+#1902 := (iff #1236 #1901)
+#1899 := (iff #1228 #1898)
+#1896 := (iff #1219 #1895)
+#1893 := (iff #1211 #1892)
+#1890 := (iff #1202 #1889)
+#1887 := (iff #1194 #1886)
+#1884 := (iff #1185 #1883)
+#1881 := (iff #1177 #1878)
+#1860 := (or #1446 #1801)
+#1863 := (or #1824 #1860)
+#1866 := (or #1840 #1863)
+#1869 := (or #1849 #1866)
+#1872 := (or #1854 #1869)
+#1875 := (or #1857 #1872)
+#1879 := (iff #1875 #1878)
+#1880 := [rewrite]: #1879
+#1876 := (iff #1177 #1875)
+#1873 := (iff #1157 #1872)
+#1870 := (iff #1148 #1869)
+#1867 := (iff #1139 #1866)
+#1864 := (iff #1130 #1863)
+#1861 := (iff #1121 #1860)
+#1802 := (iff #1107 #1801)
+#1799 := (iff #1091 #1796)
+#1781 := (or #1044 #1778)
+#1784 := (or #1053 #1781)
+#1787 := (or #1062 #1784)
+#1790 := (or #1071 #1787)
+#1793 := (or #1675 #1790)
+#1797 := (iff #1793 #1796)
+#1798 := [rewrite]: #1797
+#1794 := (iff #1091 #1793)
+#1791 := (iff #1072 #1790)
+#1788 := (iff #1063 #1787)
+#1785 := (iff #1054 #1784)
+#1782 := (iff #1045 #1781)
+#1779 := (iff #1029 #1778)
+#1776 := (iff #1021 #1775)
+#1773 := (iff #1012 #1772)
+#1770 := (iff #1004 #1767)
+#1764 := (or #1759 #251)
+#1768 := (iff #1764 #1767)
+#1769 := [rewrite]: #1768
+#1765 := (iff #1004 #1764)
+#1762 := (iff #983 #251)
+#1763 := [rewrite]: #1762
+#1760 := (iff #1003 #1759)
+#1757 := (iff #980 #1756)
+#1754 := (iff #975 #1753)
+#1751 := (iff #968 #1750)
+#1752 := [rewrite]: #1751
+#1748 := (iff #974 #1747)
+#1745 := (iff #246 #1744)
+#1711 := (iff #236 #1710)
+#1712 := [rewrite]: #1711
+#1349 := (iff #92 #1348)
+#1350 := [rewrite]: #1349
+#1746 := [monotonicity #1350 #1712]: #1745
+#1749 := [monotonicity #1746]: #1748
+#1755 := [monotonicity #1749 #1752]: #1754
+#1758 := [quant-intro #1755]: #1757
+#1761 := [monotonicity #1758]: #1760
+#1766 := [monotonicity #1761 #1763]: #1765
+#1771 := [trans #1766 #1769]: #1770
+#1774 := [monotonicity #1758 #1771]: #1773
+#1742 := (iff #1020 #1741)
+#1739 := (iff #965 #1738)
+#1736 := (iff #960 #1735)
+#1733 := (iff #953 #1732)
+#1730 := (iff #948 #1729)
+#1726 := (iff #942 #1725)
+#1728 := [rewrite]: #1726
+#1723 := (iff #241 #1722)
+#1724 := [rewrite]: #1723
+#1731 := [monotonicity #1724 #1728]: #1730
+#1734 := [quant-intro #1731]: #1733
+#1717 := (iff #959 #1716)
+#1714 := (iff #936 #1713)
+#1715 := [monotonicity #1712]: #1714
+#1718 := [monotonicity #1715]: #1717
+#1737 := [monotonicity #1718 #1734]: #1736
+#1740 := [quant-intro #1737]: #1739
+#1743 := [monotonicity #1740]: #1742
+#1777 := [monotonicity #1743 #1774]: #1776
+#1780 := [monotonicity #1740 #1777]: #1779
+#1783 := [monotonicity #1780]: #1782
+#1786 := [monotonicity #1783]: #1785
+#1789 := [monotonicity #1786]: #1788
+#1792 := [monotonicity #1789]: #1791
+#1676 := (iff #582 #1675)
+#1673 := (iff #579 #1670)
+#1667 := (and #1407 #508)
+#1671 := (iff #1667 #1670)
+#1672 := [rewrite]: #1671
+#1668 := (iff #579 #1667)
+#1408 := (iff #129 #1407)
+#1409 := [rewrite]: #1408
+#1669 := [monotonicity #1409]: #1668
+#1674 := [trans #1669 #1672]: #1673
+#1677 := [quant-intro #1674]: #1676
+#1795 := [monotonicity #1677 #1792]: #1794
+#1800 := [trans #1795 #1798]: #1799
+#1705 := (iff #912 #1702)
+#1681 := (or #1476 #1617)
+#1684 := (or #1634 #1681)
+#1687 := (or #876 #1684)
+#1690 := (or #1652 #1687)
+#1693 := (or #1656 #1690)
+#1696 := (or #585 #1693)
+#1699 := (or #1678 #1696)
+#1703 := (iff #1699 #1702)
+#1704 := [rewrite]: #1703
+#1700 := (iff #912 #1699)
+#1697 := (iff #903 #1696)
+#1694 := (iff #895 #1693)
+#1691 := (iff #886 #1690)
+#1688 := (iff #877 #1687)
+#1685 := (iff #868 #1684)
+#1682 := (iff #859 #1681)
+#1618 := (iff #850 #1617)
+#1615 := (iff #842 #1614)
+#1612 := (iff #833 #1611)
+#1609 := (iff #825 #1608)
+#1606 := (iff #805 #1605)
+#1603 := (iff #797 #1602)
+#1600 := (iff #788 #1599)
+#1597 := (iff #780 #1596)
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+#1560 := [rewrite]: #1559
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+#1563 := [rewrite]: #1562
+#1569 := [monotonicity #1563 #1566]: #1568
+#1574 := [trans #1569 #1572]: #1573
+#1577 := [quant-intro #1574]: #1576
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+#1553 := (iff #694 #1552)
+#1550 := (iff #189 #1549)
+#1551 := [rewrite]: #1550
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+#1557 := [monotonicity #1554]: #1556
+#1580 := [monotonicity #1557 #1577]: #1579
+#1583 := [quant-intro #1580]: #1582
+#1545 := (iff #745 #1544)
+#1542 := (iff #691 #1541)
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+#1523 := (and #1348 #630)
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+#1525 := [monotonicity #1350]: #1524
+#1530 := [trans #1525 #1528]: #1529
+#1533 := [monotonicity #1530]: #1532
+#1540 := [monotonicity #1533 #1537]: #1539
+#1543 := [quant-intro #1540]: #1542
+#1546 := [monotonicity #1543]: #1545
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+#1589 := [monotonicity #1543 #1586]: #1588
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+#1513 := (iff #1509 #1512)
+#1514 := [rewrite]: #1513
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+#1508 := [rewrite]: #1507
+#1511 := [monotonicity #1508]: #1510
+#1516 := [trans #1511 #1514]: #1515
+#1519 := [quant-intro #1516]: #1518
+#1522 := [monotonicity #1519]: #1521
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+#1595 := [monotonicity #1519 #1592]: #1594
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+#1499 := (iff #175 #1498)
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+#1490 := (iff #645 #173)
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+#1613 := [monotonicity #1610]: #1612
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+#1485 := (iff #167 #1484)
+#1482 := (iff #166 #1479)
+#1483 := [rewrite]: #1482
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+#1465 := (or #1462 #616)
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+#1461 := [rewrite]: #1460
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+#1467 := [monotonicity #1464]: #1466
+#1472 := [trans #1467 #1470]: #1471
+#1475 := [quant-intro #1472]: #1474
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+#1633 := [quant-intro #1630]: #1632
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+#1640 := [rewrite]: #1639
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+#1651 := [quant-intro #1648]: #1650
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+#1823 := [quant-intro #1820]: #1822
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+#1030 := (iff #1026 #1029)
+#1031 := [rewrite]: #1030
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+#584 := [quant-intro #581]: #583
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+#626 := [trans #621 #624]: #625
+#629 := [quant-intro #626]: #628
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+#863 := [trans #857 #861]: #862
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+#604 := [rewrite]: #603
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+#615 := [quant-intro #612]: #614
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+#872 := [trans #866 #870]: #871
+#875 := [monotonicity #872]: #874
+#881 := [trans #875 #879]: #880
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+#598 := [trans #593 #596]: #597
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+#890 := [trans #884 #888]: #889
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+#548 := (iff #130 #547)
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+#1209 := [monotonicity #468 #1206]: #1208
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+#1226 := [monotonicity #1223]: #1225
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+#1235 := [monotonicity #1232]: #1234
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+#1249 := [trans #1243 #1247]: #1248
+#1252 := [monotonicity #1249 #453]: #1251
+#1257 := [trans #1252 #1255]: #1256
+#1260 := [monotonicity #1257]: #1259
+#1264 := [trans #1260 #1262]: #1263
+#1267 := [monotonicity #1264]: #1266
+#1273 := [trans #1267 #1271]: #1272
+#449 := (iff #76 #448)
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+#439 := [rewrite]: #438
+#442 := [monotonicity #439]: #441
+#447 := [trans #442 #445]: #446
+#450 := [quant-intro #447]: #449
+#1276 := [monotonicity #450 #1273]: #1275
+#1282 := [trans #1276 #1280]: #1281
+#435 := (iff #72 #434)
+#432 := (iff #71 #429)
+#426 := (implies #68 #423)
+#430 := (iff #426 #429)
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+#427 := (iff #71 #426)
+#424 := (iff #70 #423)
+#425 := [rewrite]: #424
+#428 := [monotonicity #425]: #427
+#433 := [trans #428 #431]: #432
+#436 := [quant-intro #433]: #435
+#1285 := [monotonicity #436 #1282]: #1284
+#1291 := [trans #1285 #1289]: #1290
+#1294 := [monotonicity #1291]: #1293
+#1298 := [trans #1294 #1296]: #1297
+#1300 := [monotonicity #1298]: #1299
+#1302 := [trans #1300 #1296]: #1301
+#1305 := [monotonicity #1302]: #1304
+#1939 := [trans #1305 #1937]: #1938
+#422 := [asserted]: #293
+#1940 := [mp #422 #1939]: #1935
+#1941 := [not-or-elim #1940]: #79
+#2004 := [mp~ #1941 #1966]: #79
+#4354 := [mp #2004 #4353]: #4349
+#5709 := (not #4349)
+#5715 := (or #5709 #2266)
+#5470 := [quant-inst]: #5715
+#6005 := [unit-resolution #5470 #4354 #6004]: false
+#6009 := [lemma #6005]: #2266
+#3870 := (or #2166 #2033)
+#3957 := [def-axiom]: #3870
+#7294 := [unit-resolution #3957 #6009]: #2166
+#2421 := (not #2166)
+#4707 := (or #2421 #4704)
+#4710 := (not #4707)
+#4362 := (forall (vars (?x27 T2)) (:pat #4355) #1313)
+#4367 := (not #4362)
+#4713 := (or #4367 #4710)
+#4716 := (not #4713)
+decl ?x27!0 :: T2
+#2011 := ?x27!0
+#2012 := (uf_12 ?x27!0)
+#2013 := (>= #2012 0::int)
+#2014 := (not #2013)
+#4719 := (or #2014 #4716)
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+#4735 := (forall (vars (?x24 T2)) (:pat #4355) #1912)
+#4738 := (iff #1915 #4735)
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+#4739 := [quant-intro #4737]: #4738
+#2238 := (~ #1915 #1915)
+#2072 := (~ #1912 #1912)
+#2073 := [refl]: #2072
+#2239 := [nnf-pos #2073]: #2238
+#1945 := [not-or-elim #1940]: #1915
+#2265 := [mp~ #1945 #2239]: #1915
+#4740 := [mp #2265 #4739]: #4735
+#5485 := [hypothesis]: #1308
+#5347 := (not #4735)
+#5348 := (or #5347 #81)
+#4030 := (= uf_11 uf_11)
+#4033 := (not #4030)
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+#5346 := [trans #5105 #5107]: #5108
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+#5364 := [trans #5351 #5363]: #5350
+#5349 := [quant-inst]: #5341
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+#5487 := [lemma #5486]: #81
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+#3646 := [quant-intro #3643]: #3645
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+#3168 := [monotonicity #3165]: #3167
+#3172 := [trans #3168 #3170]: #3171
+#3175 := [monotonicity #3172]: #3174
+#3180 := [trans #3175 #3178]: #3179
+#3183 := [quant-intro #3180]: #3182
+#3765 := [monotonicity #3183 #3762]: #3764
+#3773 := [trans #3765 #3771]: #3772
+#2534 := (iff #2657 #2421)
+#2199 := (iff #2654 #2166)
+#2042 := (or #2266 #2034)
+#2297 := (or #2042 #2649)
+#2167 := (iff #2297 #2166)
+#2198 := [rewrite]: #2167
+#2499 := (iff #2654 #2297)
+#2138 := (iff #2638 #2042)
+#1973 := (not #2042)
+#2218 := (not #1973)
+#2018 := (iff #2218 #2042)
+#2137 := [rewrite]: #2018
+#2219 := (iff #2638 #2218)
+#1974 := (iff #2635 #1973)
+#2043 := [rewrite]: #1974
+#2017 := [monotonicity #2043]: #2219
+#2296 := [trans #2017 #2137]: #2138
+#2500 := [monotonicity #2296]: #2499
+#2420 := [trans #2500 #2198]: #2199
+#2535 := [monotonicity #2420]: #2534
+#3776 := [monotonicity #2535 #3773]: #3775
+#3779 := [monotonicity #3776]: #3778
+#3786 := [trans #3779 #3784]: #3785
+#3789 := [monotonicity #3786]: #3788
+#3792 := [monotonicity #3789]: #3791
+#3799 := [trans #3792 #3797]: #3798
+#3802 := [monotonicity #3799]: #3801
+#2513 := (* -1::int #2512)
+#2515 := (+ #2514 #2513)
+#2518 := (+ #2517 #2515)
+#2519 := (>= #2518 0::int)
+#2528 := (and #2527 #2523)
+#2529 := (not #2528)
+#2530 := (or #2529 #2519)
+#2531 := (not #2530)
+#2550 := (or #2531 #2546)
+#2489 := (+ #2488 #1707)
+#2492 := (+ #2491 #2489)
+#2493 := (= #2492 0::int)
+#2494 := (>= #2489 0::int)
+#2495 := (not #2494)
+#2496 := (and #2495 #2493)
+#2501 := (or #1716 #2496)
+#2504 := (forall (vars (?x64 T2)) #2501)
+#2554 := (and #2504 #2550)
+#2453 := (+ #2452 #2450)
+#2454 := (= #2453 0::int)
+#2457 := (and #2456 #2454)
+#2473 := (not #2457)
+#2476 := (forall (vars (?x65 T2)) #2473)
+#2462 := (= ?x64!17 uf_11)
+#2463 := (not #2462)
+#2464 := (and #2463 #2461)
+#2465 := (not #2464)
+#2470 := (not #2465)
+#2480 := (and #2470 #2476)
+#2558 := (or #2480 #2554)
+#2438 := (not #1053)
+#2435 := (not #1071)
+#2432 := (not #1044)
+#2429 := (not #1062)
+#2562 := (and #2429 #2432 #2435 #2438 #2444 #2558)
+#2417 := (and #2416 #2413)
+#2311 := (+ #2310 #2308)
+#2312 := (= #2311 0::int)
+#2315 := (and #630 #2314 #2312)
+#2332 := (not #2315)
+#2335 := (forall (vars (?x53 T2)) #2332)
+#2320 := (= ?x52!15 uf_11)
+#2321 := (not #2320)
+#2322 := (and #2321 #2319)
+#2323 := (not #2322)
+#2329 := (not #2323)
+#2339 := (and #2329 #2335)
+#2344 := (and #1541 #2339)
+#2277 := (* -1::int #2276)
+#2279 := (+ #2278 #2277)
+#2282 := (+ #2281 #2279)
+#2283 := (>= #2282 0::int)
+#2290 := (and #2289 #2287)
+#2291 := (not #2290)
+#2292 := (or #2291 #2283)
+#2293 := (not #2292)
+#2348 := (or #2293 #2344)
+#2352 := (and #1517 #2348)
+#2250 := (* -1::int #2249)
+#2252 := (+ #2251 #2250)
+#2253 := (>= #2252 0::int)
+#2259 := (and #2258 #2255)
+#2260 := (not #2259)
+#2261 := (or #2260 #2253)
+#2262 := (not #2261)
+#2356 := (or #2262 #2352)
+#2360 := (and #1498 #2356)
+#2364 := (or #2235 #2360)
+#2229 := (not #1492)
+#2368 := (and #2229 #2364)
+#2372 := (or #1492 #2368)
+#2376 := (and #642 #2372)
+#2213 := (= #2212 #2211)
+#2214 := (or #2213 #2210)
+#2215 := (not #2214)
+#2380 := (or #2215 #2376)
+#2384 := (and #1484 #2380)
+#2191 := (* -1::int #2190)
+#2193 := (+ #2192 #2191)
+#2194 := (>= #2193 0::int)
+#2195 := (not #2194)
+#2388 := (or #2195 #2384)
+#2177 := (not #876)
+#2425 := (and #2177 #588 #1473 #2388 #1631 #1649 #1657 #2417)
+#2566 := (or #2425 #2562)
+#2154 := (+ #2153 #1404)
+#2157 := (+ #2156 #2154)
+#2158 := (= #2157 0::int)
+#2159 := (>= #2154 0::int)
+#2160 := (not #2159)
+#2163 := (and #2162 #2160 #2158)
+#2168 := (or #1413 #2163)
+#2171 := (forall (vars (?x39 T2)) #2168)
+#2126 := (+ #1386 #2125)
+#2128 := (+ #2127 #2126)
+#2129 := (= #2128 0::int)
+#2130 := (+ #2127 #1386)
+#2131 := (>= #2130 0::int)
+#2132 := (not #2131)
+#2134 := (and #2133 #2132 #2129)
+#2141 := (or #2134 #1395)
+#2144 := (forall (vars (?x32 T2)) #2141)
+#2120 := (not #1854)
+#2591 := (and #2120 #2144 #2171 #2566 #1821 #1837 #1846)
+#2087 := (= ?x32!5 uf_11)
+#2088 := (not #2087)
+#2089 := (and #2088 #2086)
+#2090 := (not #2089)
+#2112 := (not #2090)
+#2099 := (and #77 #2098 #2095)
+#2105 := (not #2099)
+#2108 := (forall (vars (?x33 T2)) #2105)
+#2115 := (and #2108 #2112)
+#2595 := (or #2115 #2591)
+#2599 := (and #1360 #2595)
+#2060 := (and #2059 #2058)
+#2061 := (not #2060)
+#2064 := (+ #2063 #2054)
+#2066 := (+ #2065 #2064)
+#2067 := (>= #2066 0::int)
+#2068 := (or #2067 #2061)
+#2069 := (not #2068)
+#2603 := (or #2069 #2599)
+#2607 := (and #1334 #2603)
+#2029 := (* -1::int #2028)
+#2031 := (+ #2030 #2029)
+#2032 := (>= #2031 0::int)
+#2036 := (and #2035 #2033)
+#2037 := (not #2036)
+#2038 := (or #2037 #2032)
+#2039 := (not #2038)
+#2611 := (or #2039 #2607)
+#2615 := (and #1314 #2611)
+#2619 := (or #2014 #2615)
+#1969 := (not #1308)
+#2623 := (and #1969 #2619)
+#2627 := (or #1308 #2623)
+#3160 := (iff #2627 #3159)
+#3157 := (iff #2623 #3156)
+#3154 := (iff #2619 #3153)
+#3151 := (iff #2615 #3150)
+#3148 := (iff #2611 #3147)
+#3145 := (iff #2607 #3144)
+#3142 := (iff #2603 #3141)
+#3139 := (iff #2599 #3138)
+#3136 := (iff #2595 #3135)
+#3133 := (iff #2591 #3130)
+#3127 := (and #109 #2764 #2804 #3124 #1821 #1837 #1846)
+#3131 := (iff #3127 #3130)
+#3132 := [rewrite]: #3131
+#3128 := (iff #2591 #3127)
+#3125 := (iff #2566 #3124)
+#3122 := (iff #2562 #3121)
+#3119 := (iff #2558 #3118)
+#3116 := (iff #2554 #3115)
+#3113 := (iff #2550 #3110)
+#3107 := (or #3104 #2546)
+#3111 := (iff #3107 #3110)
+#3112 := [rewrite]: #3111
+#3108 := (iff #2550 #3107)
+#3105 := (iff #2531 #3104)
+#3102 := (iff #2530 #3101)
+#3099 := (iff #2519 #3096)
+#3087 := (+ #2514 #2517)
+#3088 := (+ #2513 #3087)
+#3091 := (>= #3088 0::int)
+#3097 := (iff #3091 #3096)
+#3098 := [rewrite]: #3097
+#3092 := (iff #2519 #3091)
+#3089 := (= #2518 #3088)
+#3090 := [rewrite]: #3089
+#3093 := [monotonicity #3090]: #3092
+#3100 := [trans #3093 #3098]: #3099
+#3085 := (iff #2529 #3084)
+#3082 := (iff #2528 #3081)
+#3083 := [rewrite]: #3082
+#3086 := [monotonicity #3083]: #3085
+#3103 := [monotonicity #3086 #3100]: #3102
+#3106 := [monotonicity #3103]: #3105
+#3109 := [monotonicity #3106]: #3108
+#3114 := [trans #3109 #3112]: #3113
+#3079 := (iff #2504 #3078)
+#3076 := (iff #2501 #3075)
+#3073 := (iff #2496 #3072)
+#3070 := (iff #2493 #3067)
+#3057 := (+ #2488 #2491)
+#3058 := (+ #1707 #3057)
+#3061 := (= #3058 0::int)
+#3068 := (iff #3061 #3067)
+#3069 := [rewrite]: #3068
+#3062 := (iff #2493 #3061)
+#3059 := (= #2492 #3058)
+#3060 := [rewrite]: #3059
+#3063 := [monotonicity #3060]: #3062
+#3071 := [trans #3063 #3069]: #3070
+#3055 := (iff #2495 #3054)
+#3052 := (iff #2494 #3049)
+#3041 := (+ #1707 #2488)
+#3044 := (>= #3041 0::int)
+#3050 := (iff #3044 #3049)
+#3051 := [rewrite]: #3050
+#3045 := (iff #2494 #3044)
+#3042 := (= #2489 #3041)
+#3043 := [rewrite]: #3042
+#3046 := [monotonicity #3043]: #3045
+#3053 := [trans #3046 #3051]: #3052
+#3056 := [monotonicity #3053]: #3055
+#3074 := [monotonicity #3056 #3071]: #3073
+#3077 := [monotonicity #3074]: #3076
+#3080 := [quant-intro #3077]: #3079
+#3117 := [monotonicity #3080 #3114]: #3116
+#3039 := (iff #2480 #3036)
+#3002 := (and #2461 #2996)
+#3033 := (and #3002 #3030)
+#3037 := (iff #3033 #3036)
+#3038 := [rewrite]: #3037
+#3034 := (iff #2480 #3033)
+#3031 := (iff #2476 #3030)
+#3028 := (iff #2473 #3027)
+#3025 := (iff #2457 #3024)
+#3022 := (iff #2454 #3021)
+#3019 := (= #2453 #3018)
+#3020 := [rewrite]: #3019
+#3023 := [monotonicity #3020]: #3022
+#3026 := [monotonicity #3023]: #3025
+#3029 := [monotonicity #3026]: #3028
+#3032 := [quant-intro #3029]: #3031
+#3015 := (iff #2470 #3002)
+#3007 := (not #3002)
+#3010 := (not #3007)
+#3013 := (iff #3010 #3002)
+#3014 := [rewrite]: #3013
+#3011 := (iff #2470 #3010)
+#3008 := (iff #2465 #3007)
+#3005 := (iff #2464 #3002)
+#2999 := (and #2996 #2461)
+#3003 := (iff #2999 #3002)
+#3004 := [rewrite]: #3003
+#3000 := (iff #2464 #2999)
+#2997 := (iff #2463 #2996)
+#2994 := (iff #2462 #2993)
+#2995 := [rewrite]: #2994
+#2998 := [monotonicity #2995]: #2997
+#3001 := [monotonicity #2998]: #3000
+#3006 := [trans #3001 #3004]: #3005
+#3009 := [monotonicity #3006]: #3008
+#3012 := [monotonicity #3009]: #3011
+#3016 := [trans #3012 #3014]: #3015
+#3035 := [monotonicity #3016 #3032]: #3034
+#3040 := [trans #3035 #3038]: #3039
+#3120 := [monotonicity #3040 #3117]: #3119
+#2991 := (iff #2438 #933)
+#2992 := [rewrite]: #2991
+#2989 := (iff #2435 #930)
+#2990 := [rewrite]: #2989
+#2987 := (iff #2432 #234)
+#2988 := [rewrite]: #2987
+#2985 := (iff #2429 #229)
+#2986 := [rewrite]: #2985
+#3123 := [monotonicity #2986 #2988 #2990 #2992 #3120]: #3122
+#2983 := (iff #2425 #2980)
+#2977 := (and #151 #588 #1473 #2974 #1631 #1649 #1657 #2417)
+#2981 := (iff #2977 #2980)
+#2982 := [rewrite]: #2981
+#2978 := (iff #2425 #2977)
+#2975 := (iff #2388 #2974)
+#2972 := (iff #2384 #2971)
+#2969 := (iff #2380 #2968)
+#2966 := (iff #2376 #2965)
+#2963 := (iff #2372 #2962)
+#2960 := (iff #2368 #2959)
+#2957 := (iff #2364 #2956)
+#2954 := (iff #2360 #2953)
+#2951 := (iff #2356 #2950)
+#2948 := (iff #2352 #2947)
+#2945 := (iff #2348 #2944)
+#2942 := (iff #2344 #2939)
+#2902 := (and #2319 #2896)
+#2933 := (and #2902 #2930)
+#2936 := (and #1541 #2933)
+#2940 := (iff #2936 #2939)
+#2941 := [rewrite]: #2940
+#2937 := (iff #2344 #2936)
+#2934 := (iff #2339 #2933)
+#2931 := (iff #2335 #2930)
+#2928 := (iff #2332 #2927)
+#2925 := (iff #2315 #2924)
+#2922 := (iff #2312 #2921)
+#2919 := (= #2311 #2918)
+#2920 := [rewrite]: #2919
+#2923 := [monotonicity #2920]: #2922
+#2926 := [monotonicity #2923]: #2925
+#2929 := [monotonicity #2926]: #2928
+#2932 := [quant-intro #2929]: #2931
+#2915 := (iff #2329 #2902)
+#2907 := (not #2902)
+#2910 := (not #2907)
+#2913 := (iff #2910 #2902)
+#2914 := [rewrite]: #2913
+#2911 := (iff #2329 #2910)
+#2908 := (iff #2323 #2907)
+#2905 := (iff #2322 #2902)
+#2899 := (and #2896 #2319)
+#2903 := (iff #2899 #2902)
+#2904 := [rewrite]: #2903
+#2900 := (iff #2322 #2899)
+#2897 := (iff #2321 #2896)
+#2894 := (iff #2320 #2893)
+#2895 := [rewrite]: #2894
+#2898 := [monotonicity #2895]: #2897
+#2901 := [monotonicity #2898]: #2900
+#2906 := [trans #2901 #2904]: #2905
+#2909 := [monotonicity #2906]: #2908
+#2912 := [monotonicity #2909]: #2911
+#2916 := [trans #2912 #2914]: #2915
+#2935 := [monotonicity #2916 #2932]: #2934
+#2938 := [monotonicity #2935]: #2937
+#2943 := [trans #2938 #2941]: #2942
+#2891 := (iff #2293 #2890)
+#2888 := (iff #2292 #2887)
+#2885 := (iff #2283 #2882)
+#2872 := (+ #2278 #2281)
+#2873 := (+ #2277 #2872)
+#2876 := (>= #2873 0::int)
+#2883 := (iff #2876 #2882)
+#2884 := [rewrite]: #2883
+#2877 := (iff #2283 #2876)
+#2874 := (= #2282 #2873)
+#2875 := [rewrite]: #2874
+#2878 := [monotonicity #2875]: #2877
+#2886 := [trans #2878 #2884]: #2885
+#2870 := (iff #2291 #2869)
+#2867 := (iff #2290 #2866)
+#2868 := [rewrite]: #2867
+#2871 := [monotonicity #2868]: #2870
+#2889 := [monotonicity #2871 #2886]: #2888
+#2892 := [monotonicity #2889]: #2891
+#2946 := [monotonicity #2892 #2943]: #2945
+#2949 := [monotonicity #2946]: #2948
+#2864 := (iff #2262 #2863)
+#2861 := (iff #2261 #2860)
+#2858 := (iff #2253 #2855)
+#2847 := (+ #2250 #2251)
+#2850 := (>= #2847 0::int)
+#2856 := (iff #2850 #2855)
+#2857 := [rewrite]: #2856
+#2851 := (iff #2253 #2850)
+#2848 := (= #2252 #2847)
+#2849 := [rewrite]: #2848
+#2852 := [monotonicity #2849]: #2851
+#2859 := [trans #2852 #2857]: #2858
+#2845 := (iff #2260 #2844)
+#2842 := (iff #2259 #2841)
+#2843 := [rewrite]: #2842
+#2846 := [monotonicity #2843]: #2845
+#2862 := [monotonicity #2846 #2859]: #2861
+#2865 := [monotonicity #2862]: #2864
+#2952 := [monotonicity #2865 #2949]: #2951
+#2955 := [monotonicity #2952]: #2954
+#2958 := [monotonicity #2955]: #2957
+#2839 := (iff #2229 #173)
+#2840 := [rewrite]: #2839
+#2961 := [monotonicity #2840 #2958]: #2960
+#2964 := [monotonicity #2961]: #2963
+#2967 := [monotonicity #2964]: #2966
+#2837 := (iff #2215 #2836)
+#2834 := (iff #2214 #2831)
+#2828 := (or #2825 #2210)
+#2832 := (iff #2828 #2831)
+#2833 := [rewrite]: #2832
+#2829 := (iff #2214 #2828)
+#2826 := (iff #2213 #2825)
+#2827 := [rewrite]: #2826
+#2830 := [monotonicity #2827]: #2829
+#2835 := [trans #2830 #2833]: #2834
+#2838 := [monotonicity #2835]: #2837
+#2970 := [monotonicity #2838 #2967]: #2969
+#2973 := [monotonicity #2970]: #2972
+#2823 := (iff #2195 #2822)
+#2820 := (iff #2194 #2817)
+#2809 := (+ #2191 #2192)
+#2812 := (>= #2809 0::int)
+#2818 := (iff #2812 #2817)
+#2819 := [rewrite]: #2818
+#2813 := (iff #2194 #2812)
+#2810 := (= #2193 #2809)
+#2811 := [rewrite]: #2810
+#2814 := [monotonicity #2811]: #2813
+#2821 := [trans #2814 #2819]: #2820
+#2824 := [monotonicity #2821]: #2823
+#2976 := [monotonicity #2824 #2973]: #2975
+#2807 := (iff #2177 #151)
+#2808 := [rewrite]: #2807
+#2979 := [monotonicity #2808 #2976]: #2978
+#2984 := [trans #2979 #2982]: #2983
+#3126 := [monotonicity #2984 #3123]: #3125
+#2805 := (iff #2171 #2804)
+#2802 := (iff #2168 #2801)
+#2799 := (iff #2163 #2798)
+#2796 := (iff #2158 #2793)
+#2783 := (+ #2153 #2156)
+#2784 := (+ #1404 #2783)
+#2787 := (= #2784 0::int)
+#2794 := (iff #2787 #2793)
+#2795 := [rewrite]: #2794
+#2788 := (iff #2158 #2787)
+#2785 := (= #2157 #2784)
+#2786 := [rewrite]: #2785
+#2789 := [monotonicity #2786]: #2788
+#2797 := [trans #2789 #2795]: #2796
+#2781 := (iff #2160 #2780)
+#2778 := (iff #2159 #2775)
+#2767 := (+ #1404 #2153)
+#2770 := (>= #2767 0::int)
+#2776 := (iff #2770 #2775)
+#2777 := [rewrite]: #2776
+#2771 := (iff #2159 #2770)
+#2768 := (= #2154 #2767)
+#2769 := [rewrite]: #2768
+#2772 := [monotonicity #2769]: #2771
+#2779 := [trans #2772 #2777]: #2778
+#2782 := [monotonicity #2779]: #2781
+#2800 := [monotonicity #2782 #2797]: #2799
+#2803 := [monotonicity #2800]: #2802
+#2806 := [quant-intro #2803]: #2805
+#2765 := (iff #2144 #2764)
+#2762 := (iff #2141 #2759)
+#2756 := (or #2753 #1395)
+#2760 := (iff #2756 #2759)
+#2761 := [rewrite]: #2760
+#2757 := (iff #2141 #2756)
+#2754 := (iff #2134 #2753)
+#2751 := (iff #2129 #2748)
+#2738 := (+ #2125 #2127)
+#2739 := (+ #1386 #2738)
+#2742 := (= #2739 0::int)
+#2749 := (iff #2742 #2748)
+#2750 := [rewrite]: #2749
+#2743 := (iff #2129 #2742)
+#2740 := (= #2128 #2739)
+#2741 := [rewrite]: #2740
+#2744 := [monotonicity #2741]: #2743
+#2752 := [trans #2744 #2750]: #2751
+#2736 := (iff #2132 #2735)
+#2733 := (iff #2131 #2730)
+#2722 := (+ #1386 #2127)
+#2725 := (>= #2722 0::int)
+#2731 := (iff #2725 #2730)
+#2732 := [rewrite]: #2731
+#2726 := (iff #2131 #2725)
+#2723 := (= #2130 #2722)
+#2724 := [rewrite]: #2723
+#2727 := [monotonicity #2724]: #2726
+#2734 := [trans #2727 #2732]: #2733
+#2737 := [monotonicity #2734]: #2736
+#2755 := [monotonicity #2737 #2752]: #2754
+#2758 := [monotonicity #2755]: #2757
+#2763 := [trans #2758 #2761]: #2762
+#2766 := [quant-intro #2763]: #2765
+#2720 := (iff #2120 #109)
+#2721 := [rewrite]: #2720
+#3129 := [monotonicity #2721 #2766 #2806 #3126]: #3128
+#3134 := [trans #3129 #3132]: #3133
+#2718 := (iff #2115 #2715)
+#2697 := (and #2086 #2691)
+#2712 := (and #2685 #2697)
+#2716 := (iff #2712 #2715)
+#2717 := [rewrite]: #2716
+#2713 := (iff #2115 #2712)
+#2710 := (iff #2112 #2697)
+#2702 := (not #2697)
+#2705 := (not #2702)
+#2708 := (iff #2705 #2697)
+#2709 := [rewrite]: #2708
+#2706 := (iff #2112 #2705)
+#2703 := (iff #2090 #2702)
+#2700 := (iff #2089 #2697)
+#2694 := (and #2691 #2086)
+#2698 := (iff #2694 #2697)
+#2699 := [rewrite]: #2698
+#2695 := (iff #2089 #2694)
+#2692 := (iff #2088 #2691)
+#2689 := (iff #2087 #2688)
+#2690 := [rewrite]: #2689
+#2693 := [monotonicity #2690]: #2692
+#2696 := [monotonicity #2693]: #2695
+#2701 := [trans #2696 #2699]: #2700
+#2704 := [monotonicity #2701]: #2703
+#2707 := [monotonicity #2704]: #2706
+#2711 := [trans #2707 #2709]: #2710
+#2686 := (iff #2108 #2685)
+#2683 := (iff #2105 #2682)
+#2680 := (iff #2099 #2679)
+#2681 := [rewrite]: #2680
+#2684 := [monotonicity #2681]: #2683
+#2687 := [quant-intro #2684]: #2686
+#2714 := [monotonicity #2687 #2711]: #2713
+#2719 := [trans #2714 #2717]: #2718
+#3137 := [monotonicity #2719 #3134]: #3136
+#3140 := [monotonicity #3137]: #3139
+#2677 := (iff #2069 #2676)
+#2674 := (iff #2068 #2673)
+#2671 := (iff #2061 #2670)
+#2668 := (iff #2060 #2667)
+#2669 := [rewrite]: #2668
+#2672 := [monotonicity #2669]: #2671
+#2665 := (iff #2067 #2664)
+#2662 := (= #2066 #2661)
+#2663 := [rewrite]: #2662
+#2666 := [monotonicity #2663]: #2665
+#2675 := [monotonicity #2666 #2672]: #2674
+#2678 := [monotonicity #2675]: #2677
+#3143 := [monotonicity #2678 #3140]: #3142
+#3146 := [monotonicity #3143]: #3145
+#2658 := (iff #2039 #2657)
+#2655 := (iff #2038 #2654)
+#2652 := (iff #2032 #2649)
+#2641 := (+ #2029 #2030)
+#2644 := (>= #2641 0::int)
+#2650 := (iff #2644 #2649)
+#2651 := [rewrite]: #2650
+#2645 := (iff #2032 #2644)
+#2642 := (= #2031 #2641)
+#2643 := [rewrite]: #2642
+#2646 := [monotonicity #2643]: #2645
+#2653 := [trans #2646 #2651]: #2652
+#2639 := (iff #2037 #2638)
+#2636 := (iff #2036 #2635)
+#2637 := [rewrite]: #2636
+#2640 := [monotonicity #2637]: #2639
+#2656 := [monotonicity #2640 #2653]: #2655
+#2659 := [monotonicity #2656]: #2658
+#3149 := [monotonicity #2659 #3146]: #3148
+#3152 := [monotonicity #3149]: #3151
+#3155 := [monotonicity #3152]: #3154
+#2633 := (iff #1969 #81)
+#2634 := [rewrite]: #2633
+#3158 := [monotonicity #2634 #3155]: #3157
+#3161 := [monotonicity #3158]: #3160
+#1943 := (not #1907)
+#2628 := (~ #1943 #2627)
+#2624 := (not #1904)
+#2625 := (~ #2624 #2623)
+#2620 := (not #1901)
+#2621 := (~ #2620 #2619)
+#2616 := (not #1898)
+#2617 := (~ #2616 #2615)
+#2612 := (not #1895)
+#2613 := (~ #2612 #2611)
+#2608 := (not #1892)
+#2609 := (~ #2608 #2607)
+#2604 := (not #1889)
+#2605 := (~ #2604 #2603)
+#2600 := (not #1886)
+#2601 := (~ #2600 #2599)
+#2596 := (not #1883)
+#2597 := (~ #2596 #2595)
+#2592 := (not #1878)
+#2593 := (~ #2592 #2591)
+#2588 := (not #1849)
+#2589 := (~ #2588 #1846)
+#2586 := (~ #1846 #1846)
+#2584 := (~ #1843 #1843)
+#2585 := [refl]: #2584
+#2587 := [nnf-pos #2585]: #2586
+#2590 := [nnf-neg #2587]: #2589
+#2581 := (not #1840)
+#2582 := (~ #2581 #1837)
+#2579 := (~ #1837 #1837)
+#2577 := (~ #1832 #1832)
+#2578 := [refl]: #2577
+#2580 := [nnf-pos #2578]: #2579
+#2583 := [nnf-neg #2580]: #2582
+#2574 := (not #1824)
+#2575 := (~ #2574 #1821)
+#2572 := (~ #1821 #1821)
+#2570 := (~ #1818 #1818)
+#2571 := [refl]: #2570
+#2573 := [nnf-pos #2571]: #2572
+#2576 := [nnf-neg #2573]: #2575
+#2567 := (not #1801)
+#2568 := (~ #2567 #2566)
+#2563 := (not #1796)
+#2564 := (~ #2563 #2562)
+#2559 := (not #1778)
+#2560 := (~ #2559 #2558)
+#2555 := (not #1775)
+#2556 := (~ #2555 #2554)
+#2551 := (not #1772)
+#2552 := (~ #2551 #2550)
+#2547 := (not #1767)
+#2548 := (~ #2547 #2546)
+#2543 := (not #1759)
+#2544 := (~ #2543 #1756)
+#2541 := (~ #1756 #1756)
+#2539 := (~ #1753 #1753)
+#2540 := [refl]: #2539
+#2542 := [nnf-pos #2540]: #2541
+#2545 := [nnf-neg #2542]: #2544
+#2537 := (~ #2536 #2536)
+#2538 := [refl]: #2537
+#2549 := [nnf-neg #2538 #2545]: #2548
+#2532 := (~ #1759 #2531)
+#2533 := [sk]: #2532
+#2553 := [nnf-neg #2533 #2549]: #2552
+#2507 := (not #1741)
+#2508 := (~ #2507 #2504)
+#2505 := (~ #1738 #2504)
+#2502 := (~ #1735 #2501)
+#2497 := (~ #1732 #2496)
+#2498 := [sk]: #2497
+#2485 := (~ #1716 #1716)
+#2486 := [refl]: #2485
+#2503 := [monotonicity #2486 #2498]: #2502
+#2506 := [nnf-pos #2503]: #2505
+#2509 := [nnf-neg #2506]: #2508
+#2557 := [nnf-neg #2509 #2553]: #2556
+#2483 := (~ #1741 #2480)
+#2458 := (exists (vars (?x65 T2)) #2457)
+#2466 := (or #2465 #2458)
+#2467 := (not #2466)
+#2481 := (~ #2467 #2480)
+#2477 := (not #2458)
+#2478 := (~ #2477 #2476)
+#2474 := (~ #2473 #2473)
+#2475 := [refl]: #2474
+#2479 := [nnf-neg #2475]: #2478
+#2471 := (~ #2470 #2470)
+#2472 := [refl]: #2471
+#2482 := [nnf-neg #2472 #2479]: #2481
+#2468 := (~ #1741 #2467)
+#2469 := [sk]: #2468
+#2484 := [trans #2469 #2482]: #2483
+#2561 := [nnf-neg #2484 #2557]: #2560
+#2445 := (~ #1678 #2444)
+#2442 := (~ #2441 #2441)
+#2443 := [refl]: #2442
+#2446 := [nnf-neg #2443]: #2445
+#2439 := (~ #2438 #2438)
+#2440 := [refl]: #2439
+#2436 := (~ #2435 #2435)
+#2437 := [refl]: #2436
+#2433 := (~ #2432 #2432)
+#2434 := [refl]: #2433
+#2430 := (~ #2429 #2429)
+#2431 := [refl]: #2430
+#2565 := [nnf-neg #2431 #2434 #2437 #2440 #2446 #2561]: #2564
+#2426 := (not #1702)
+#2427 := (~ #2426 #2425)
+#2422 := (not #1678)
+#2423 := (~ #2422 #2417)
+#2418 := (~ #1675 #2417)
+#2419 := [sk]: #2418
+#2424 := [nnf-neg #2419]: #2423
+#2406 := (~ #1657 #1657)
+#2407 := [refl]: #2406
+#2403 := (not #1652)
+#2404 := (~ #2403 #1649)
+#2401 := (~ #1649 #1649)
+#2399 := (~ #1644 #1644)
+#2400 := [refl]: #2399
+#2402 := [nnf-pos #2400]: #2401
+#2405 := [nnf-neg #2402]: #2404
+#2396 := (not #1634)
+#2397 := (~ #2396 #1631)
+#2394 := (~ #1631 #1631)
+#2392 := (~ #1628 #1628)
+#2393 := [refl]: #2392
+#2395 := [nnf-pos #2393]: #2394
+#2398 := [nnf-neg #2395]: #2397
+#2389 := (not #1617)
+#2390 := (~ #2389 #2388)
+#2385 := (not #1614)
+#2386 := (~ #2385 #2384)
+#2381 := (not #1611)
+#2382 := (~ #2381 #2380)
+#2377 := (not #1608)
+#2378 := (~ #2377 #2376)
+#2373 := (not #1605)
+#2374 := (~ #2373 #2372)
+#2369 := (not #1602)
+#2370 := (~ #2369 #2368)
+#2365 := (not #1599)
+#2366 := (~ #2365 #2364)
+#2361 := (not #1596)
+#2362 := (~ #2361 #2360)
+#2357 := (not #1593)
+#2358 := (~ #2357 #2356)
+#2353 := (not #1590)
+#2354 := (~ #2353 #2352)
+#2349 := (not #1587)
+#2350 := (~ #2349 #2348)
+#2345 := (not #1584)
+#2346 := (~ #2345 #2344)
+#2326 := (not #1581)
+#2342 := (~ #2326 #2339)
+#2316 := (exists (vars (?x53 T2)) #2315)
+#2324 := (or #2323 #2316)
+#2325 := (not #2324)
+#2340 := (~ #2325 #2339)
+#2336 := (not #2316)
+#2337 := (~ #2336 #2335)
+#2333 := (~ #2332 #2332)
+#2334 := [refl]: #2333
+#2338 := [nnf-neg #2334]: #2337
+#2330 := (~ #2329 #2329)
+#2331 := [refl]: #2330
+#2341 := [nnf-neg #2331 #2338]: #2340
+#2327 := (~ #2326 #2325)
+#2328 := [sk]: #2327
+#2343 := [trans #2328 #2341]: #2342
+#2302 := (not #1544)
+#2303 := (~ #2302 #1541)
+#2300 := (~ #1541 #1541)
+#2298 := (~ #1538 #1538)
+#2299 := [refl]: #2298
+#2301 := [nnf-pos #2299]: #2300
+#2304 := [nnf-neg #2301]: #2303
+#2347 := [nnf-neg #2304 #2343]: #2346
+#2294 := (~ #1544 #2293)
+#2295 := [sk]: #2294
+#2351 := [nnf-neg #2295 #2347]: #2350
+#2271 := (not #1520)
+#2272 := (~ #2271 #1517)
+#2269 := (~ #1517 #1517)
+#2267 := (~ #1512 #1512)
+#2268 := [refl]: #2267
+#2270 := [nnf-pos #2268]: #2269
+#2273 := [nnf-neg #2270]: #2272
+#2355 := [nnf-neg #2273 #2351]: #2354
+#2263 := (~ #1520 #2262)
+#2264 := [sk]: #2263
+#2359 := [nnf-neg #2264 #2355]: #2358
+#2244 := (not #1501)
+#2245 := (~ #2244 #1498)
+#2242 := (~ #1498 #1498)
+#2240 := (~ #1495 #1495)
+#2241 := [refl]: #2240
+#2243 := [nnf-pos #2241]: #2242
+#2246 := [nnf-neg #2243]: #2245
+#2363 := [nnf-neg #2246 #2359]: #2362
+#2236 := (~ #1501 #2235)
+#2237 := [sk]: #2236
+#2367 := [nnf-neg #2237 #2363]: #2366
+#2230 := (~ #2229 #2229)
+#2231 := [refl]: #2230
+#2371 := [nnf-neg #2231 #2367]: #2370
+#2227 := (~ #1492 #1492)
+#2228 := [refl]: #2227
+#2375 := [nnf-neg #2228 #2371]: #2374
+#2224 := (not #824)
+#2225 := (~ #2224 #642)
+#2222 := (~ #642 #642)
+#2220 := (~ #637 #637)
+#2221 := [refl]: #2220
+#2223 := [nnf-pos #2221]: #2222
+#2226 := [nnf-neg #2223]: #2225
+#2379 := [nnf-neg #2226 #2375]: #2378
+#2216 := (~ #824 #2215)
+#2217 := [sk]: #2216
+#2383 := [nnf-neg #2217 #2379]: #2382
+#2204 := (not #1487)
+#2205 := (~ #2204 #1484)
+#2202 := (~ #1484 #1484)
+#2200 := (~ #1479 #1479)
+#2201 := [refl]: #2200
+#2203 := [nnf-pos #2201]: #2202
+#2206 := [nnf-neg #2203]: #2205
+#2387 := [nnf-neg #2206 #2383]: #2386
+#2196 := (~ #1487 #2195)
+#2197 := [sk]: #2196
+#2391 := [nnf-neg #2197 #2387]: #2390
+#2186 := (not #1476)
+#2187 := (~ #2186 #1473)
+#2184 := (~ #1473 #1473)
+#2182 := (~ #1468 #1468)
+#2183 := [refl]: #2182
+#2185 := [nnf-pos #2183]: #2184
+#2188 := [nnf-neg #2185]: #2187
+#2180 := (~ #588 #588)
+#2181 := [refl]: #2180
+#2178 := (~ #2177 #2177)
+#2179 := [refl]: #2178
+#2428 := [nnf-neg #2179 #2181 #2188 #2391 #2398 #2405 #2407 #2424]: #2427
+#2569 := [nnf-neg #2428 #2565]: #2568
+#2174 := (not #1446)
+#2175 := (~ #2174 #2171)
+#2172 := (~ #1443 #2171)
+#2169 := (~ #1440 #2168)
+#2164 := (~ #1437 #2163)
+#2165 := [sk]: #2164
+#2150 := (~ #1413 #1413)
+#2151 := [refl]: #2150
+#2170 := [monotonicity #2151 #2165]: #2169
+#2173 := [nnf-pos #2170]: #2172
+#2176 := [nnf-neg #2173]: #2175
+#2147 := (not #1857)
+#2148 := (~ #2147 #2144)
+#2145 := (~ #1401 #2144)
+#2142 := (~ #1398 #2141)
+#2139 := (~ #1395 #1395)
+#2140 := [refl]: #2139
+#2135 := (~ #1383 #2134)
+#2136 := [sk]: #2135
+#2143 := [monotonicity #2136 #2140]: #2142
+#2146 := [nnf-pos #2143]: #2145
+#2149 := [nnf-neg #2146]: #2148
+#2121 := (~ #2120 #2120)
+#2122 := [refl]: #2121
+#2594 := [nnf-neg #2122 #2149 #2176 #2569 #2576 #2583 #2590]: #2593
+#2118 := (~ #1857 #2115)
+#2100 := (exists (vars (?x33 T2)) #2099)
+#2101 := (or #2100 #2090)
+#2102 := (not #2101)
+#2116 := (~ #2102 #2115)
+#2113 := (~ #2112 #2112)
+#2114 := [refl]: #2113
+#2109 := (not #2100)
+#2110 := (~ #2109 #2108)
+#2106 := (~ #2105 #2105)
+#2107 := [refl]: #2106
+#2111 := [nnf-neg #2107]: #2110
+#2117 := [nnf-neg #2111 #2114]: #2116
+#2103 := (~ #1857 #2102)
+#2104 := [sk]: #2103
+#2119 := [trans #2104 #2117]: #2118
+#2598 := [nnf-neg #2119 #2594]: #2597
+#2078 := (not #1363)
+#2079 := (~ #2078 #1360)
+#2076 := (~ #1360 #1360)
+#2074 := (~ #1357 #1357)
+#2075 := [refl]: #2074
+#2077 := [nnf-pos #2075]: #2076
+#2080 := [nnf-neg #2077]: #2079
+#2602 := [nnf-neg #2080 #2598]: #2601
+#2070 := (~ #1363 #2069)
+#2071 := [sk]: #2070
+#2606 := [nnf-neg #2071 #2602]: #2605
+#2048 := (not #1337)
+#2049 := (~ #2048 #1334)
+#2046 := (~ #1334 #1334)
+#2044 := (~ #1329 #1329)
+#2045 := [refl]: #2044
+#2047 := [nnf-pos #2045]: #2046
+#2050 := [nnf-neg #2047]: #2049
+#2610 := [nnf-neg #2050 #2606]: #2609
+#2040 := (~ #1337 #2039)
+#2041 := [sk]: #2040
+#2614 := [nnf-neg #2041 #2610]: #2613
+#2023 := (not #1317)
+#2024 := (~ #2023 #1314)
+#2021 := (~ #1314 #1314)
+#2019 := (~ #1313 #1313)
+#2020 := [refl]: #2019
+#2022 := [nnf-pos #2020]: #2021
+#2025 := [nnf-neg #2022]: #2024
+#2618 := [nnf-neg #2025 #2614]: #2617
+#2015 := (~ #1317 #2014)
+#2016 := [sk]: #2015
+#2622 := [nnf-neg #2016 #2618]: #2621
+#1970 := (~ #1969 #1969)
+#2010 := [refl]: #1970
+#2626 := [nnf-neg #2010 #2622]: #2625
+#2008 := (~ #1308 #1308)
+#2009 := [refl]: #2008
+#2629 := [nnf-neg #2009 #2626]: #2628
+#1944 := [not-or-elim #1940]: #1943
+#2630 := [mp~ #1944 #2629]: #2627
+#2631 := [mp #2630 #3161]: #3159
+#3803 := [mp #2631 #3802]: #3800
+#4734 := [mp #3803 #4733]: #4731
+#7295 := [unit-resolution #4734 #5487]: #4728
+#4058 := (or #4725 #4719)
+#4059 := [def-axiom]: #4058
+#7296 := [unit-resolution #4059 #7295]: #4719
+#373 := (<= uf_9 0::int)
+#374 := (not #373)
+#57 := (< 0::int uf_9)
+#375 := (iff #57 #374)
+#376 := [rewrite]: #375
+#369 := [asserted]: #57
+#377 := [mp #369 #376]: #374
+#5901 := (* -1::int #2012)
+#5891 := (+ uf_9 #5901)
+#5892 := (<= #5891 0::int)
+#5472 := (= uf_9 #2012)
+#5745 := (= uf_11 ?x27!0)
+#5918 := (not #5745)
+#5916 := (= #2012 0::int)
+#5836 := (not #5916)
+#5835 := [hypothesis]: #2014
+#5837 := (or #5836 #2013)
+#5896 := [th-lemma]: #5837
+#5922 := [unit-resolution #5896 #5835]: #5836
+#5981 := (or #5347 #5918 #5916)
+#5477 := (= ?x27!0 uf_11)
+#5917 := (not #5477)
+#5890 := (or #5917 #5916)
+#5982 := (or #5347 #5890)
+#5987 := (iff #5982 #5981)
+#5915 := (or #5918 #5916)
+#5984 := (or #5347 #5915)
+#5985 := (iff #5984 #5981)
+#5986 := [rewrite]: #5985
+#6000 := (iff #5982 #5984)
+#5921 := (iff #5890 #5915)
+#5919 := (iff #5917 #5918)
+#5743 := (iff #5477 #5745)
+#5746 := [rewrite]: #5743
+#5920 := [monotonicity #5746]: #5919
+#5980 := [monotonicity #5920]: #5921
+#5979 := [monotonicity #5980]: #6000
+#5988 := [trans #5979 #5986]: #5987
+#5983 := [quant-inst]: #5982
+#6010 := [mp #5983 #5988]: #5981
+#5923 := [unit-resolution #6010 #4740 #5922]: #5918
+#5748 := (or #5472 #5745)
+#4356 := (forall (vars (?x25 T2)) (:pat #4355) #443)
+#4359 := (iff #448 #4356)
+#4357 := (iff #443 #443)
+#4358 := [refl]: #4357
+#4360 := [quant-intro #4358]: #4359
+#1967 := (~ #448 #448)
+#2005 := (~ #443 #443)
+#2006 := [refl]: #2005
+#1968 := [nnf-pos #2006]: #1967
+#1942 := [not-or-elim #1940]: #448
+#2007 := [mp~ #1942 #1968]: #448
+#4361 := [mp #2007 #4360]: #4356
+#5821 := (not #4356)
+#5827 := (or #5821 #5472 #5745)
+#5737 := (or #5477 #5472)
+#5828 := (or #5821 #5737)
+#5894 := (iff #5828 #5827)
+#5830 := (or #5821 #5748)
+#5846 := (iff #5830 #5827)
+#5847 := [rewrite]: #5846
+#5826 := (iff #5828 #5830)
+#5756 := (iff #5737 #5748)
+#5736 := (or #5745 #5472)
+#5752 := (iff #5736 #5748)
+#5753 := [rewrite]: #5752
+#5747 := (iff #5737 #5736)
+#5744 := [monotonicity #5746]: #5747
+#5834 := [trans #5744 #5753]: #5756
+#5831 := [monotonicity #5834]: #5826
+#5895 := [trans #5831 #5847]: #5894
+#5829 := [quant-inst]: #5828
+#5900 := [mp #5829 #5895]: #5827
+#5924 := [unit-resolution #5900 #4361]: #5748
+#5989 := [unit-resolution #5924 #5923]: #5472
+#6012 := (not #5472)
+#6013 := (or #6012 #5892)
+#6014 := [th-lemma]: #6013
+#6042 := [unit-resolution #6014 #5989]: #5892
+#6011 := (<= #2012 0::int)
+#6043 := (or #6011 #2013)
+#6044 := [th-lemma]: #6043
+#6045 := [unit-resolution #6044 #5835]: #6011
+#6046 := [th-lemma #6045 #6042 #377]: false
+#6041 := [lemma #6046]: #2013
+#4053 := (or #4722 #2014 #4716)
+#4054 := [def-axiom]: #4053
+#7297 := [unit-resolution #4054 #6041 #7296]: #4716
+#4077 := (or #4713 #4707)
+#4078 := [def-axiom]: #4077
+#7298 := [unit-resolution #4078 #7297]: #4707
+#4071 := (or #4710 #2421 #4704)
+#4073 := [def-axiom]: #4071
+#7299 := [unit-resolution #4073 #7298 #7294]: #4704
+#4098 := (or #4701 #4695)
+#4099 := [def-axiom]: #4098
+#7300 := [unit-resolution #4099 #7299]: #4695
+#6817 := [hypothesis]: #2059
+#6051 := (or #5709 #3184)
+#6081 := [quant-inst]: #6051
+#6818 := [unit-resolution #6081 #4354 #6817]: false
+#6839 := [lemma #6818]: #3184
+#3960 := (or #3199 #2059)
+#3964 := [def-axiom]: #3960
+#7301 := [unit-resolution #3964 #6839]: #3199
+#4094 := (or #4698 #3204 #4692)
+#4095 := [def-axiom]: #4094
+#7302 := [unit-resolution #4095 #7301 #7300]: #4692
+#4108 := (or #4689 #4683)
+#4129 := [def-axiom]: #4108
+#7303 := [unit-resolution #4129 #7302]: #4683
+#6633 := (= uf_9 #2082)
+#6706 := (not #6633)
+#6684 := [hypothesis]: #4400
+#4274 := (or #4397 #2086)
+#3948 := [def-axiom]: #4274
+#6685 := [unit-resolution #3948 #6684]: #2086
+#6798 := (or #6706 #2085)
+#6840 := [th-lemma]: #6798
+#6835 := [unit-resolution #6840 #6685]: #6706
+#3949 := (or #4397 #2691)
+#4281 := [def-axiom]: #3949
+#6841 := [unit-resolution #4281 #6684]: #2691
+#6695 := (or #5821 #2688 #6633)
+#6680 := (or #2087 #6633)
+#6696 := (or #5821 #6680)
+#6732 := (iff #6696 #6695)
+#6548 := (or #2688 #6633)
+#6694 := (or #5821 #6548)
+#6699 := (iff #6694 #6695)
+#6705 := [rewrite]: #6699
+#6697 := (iff #6696 #6694)
+#6608 := (iff #6680 #6548)
+#6665 := [monotonicity #2690]: #6608
+#6698 := [monotonicity #6665]: #6697
+#6728 := [trans #6698 #6705]: #6732
+#6547 := [quant-inst]: #6696
+#6734 := [mp #6547 #6728]: #6695
+#6842 := [unit-resolution #6734 #4361 #6841 #6835]: false
+#6843 := [lemma #6842]: #4397
+#4116 := (or #4686 #4400 #4680)
+#4117 := [def-axiom]: #4116
+#7304 := [unit-resolution #4117 #6843 #7303]: #4680
+#4149 := (or #4677 #4404)
+#4145 := [def-axiom]: #4149
+#7305 := [unit-resolution #4145 #7304]: #4404
+#24124 := (or #4409 #20405)
+#25438 := [quant-inst]: #24124
+#29563 := [unit-resolution #25438 #7305]: #20405
+#15997 := (* -1::int #15996)
+#15993 := (uf_1 #15992 ?x52!15)
+#15994 := (uf_10 #15993)
+#15995 := (* -1::int #15994)
+#16012 := (+ #15995 #15997)
+#15362 := (uf_4 uf_14 ?x52!15)
+#16013 := (+ #15362 #16012)
+#22006 := (>= #16013 0::int)
+#16016 := (= #16013 0::int)
+#16019 := (not #16016)
+#16004 := (uf_6 uf_15 #15992)
+#16005 := (= uf_8 #16004)
+#16006 := (not #16005)
+#16002 := (+ #15362 #15997)
+#16003 := (<= #16002 0::int)
+#16025 := (or #16003 #16006 #16019)
+#16030 := (not #16025)
+#15397 := (* -1::int #15362)
+#16009 := (+ uf_9 #15397)
+#16010 := (<= #16009 0::int)
+#34324 := (not #16010)
+#15398 := (+ #2306 #15397)
+#14218 := (>= #15398 0::int)
+#15367 := (= #2306 #15362)
+decl uf_3 :: (-> T1 T2)
+#20604 := (uf_3 #15993)
+#32578 := (uf_6 uf_15 #20604)
+#32576 := (= uf_8 #32578)
+#5319 := (uf_6 #150 uf_16)
+#5314 := (= uf_8 #5319)
+decl uf_2 :: (-> T1 T2)
+#6008 := (uf_1 uf_16 uf_11)
+#7128 := (uf_2 #6008)
+#32602 := (= #7128 #20604)
+#32591 := (ite #32602 #5314 #32576)
+#7203 := (uf_7 uf_15 #7128 #5319)
+#32554 := (uf_6 #7203 #20604)
+#32538 := (= uf_8 #32554)
+#32564 := (iff #32538 #32591)
+#30 := (:var 1 T5)
+#20 := (:var 2 T2)
+#29 := (:var 3 T4)
+#31 := (uf_7 #29 #20 #30)
+#32 := (uf_6 #31 #11)
+#4314 := (pattern #32)
+#36 := (uf_6 #29 #11)
+#335 := (= uf_8 #36)
+#35 := (= #30 uf_8)
+#24 := (= #11 #20)
+#338 := (ite #24 #35 #335)
+#34 := (= #32 uf_8)
+#341 := (iff #34 #338)
+#4315 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) (:pat #4314) #341)
+#344 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) #341)
+#4318 := (iff #344 #4315)
+#4316 := (iff #341 #341)
+#4317 := [refl]: #4316
+#4319 := [quant-intro #4317]: #4318
+#1953 := (~ #344 #344)
+#1989 := (~ #341 #341)
+#1990 := [refl]: #1989
+#1954 := [nnf-pos #1990]: #1953
+#37 := (= #36 uf_8)
+#38 := (ite #24 #35 #37)
+#39 := (iff #34 #38)
+#40 := (forall (vars (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2)) #39)
+#345 := (iff #40 #344)
+#342 := (iff #39 #341)
+#339 := (iff #38 #338)
+#336 := (iff #37 #335)
+#337 := [rewrite]: #336
+#340 := [monotonicity #337]: #339
+#343 := [monotonicity #340]: #342
+#346 := [quant-intro #343]: #345
+#333 := [asserted]: #40
+#349 := [mp #333 #346]: #344
+#1991 := [mp~ #349 #1954]: #344
+#4320 := [mp #1991 #4319]: #4315
+#7026 := (not #4315)
+#32561 := (or #7026 #32564)
+#6089 := (= #5319 uf_8)
+#32580 := (= #20604 #7128)
+#32553 := (ite #32580 #6089 #32576)
+#32556 := (= #32554 uf_8)
+#32579 := (iff #32556 #32553)
+#32603 := (or #7026 #32579)
+#32548 := (iff #32603 #32561)
+#32606 := (iff #32561 #32561)
+#32631 := [rewrite]: #32606
+#32629 := (iff #32579 #32564)
+#32535 := (iff #32553 #32591)
+#6101 := (iff #6089 #5314)
+#6102 := [rewrite]: #6101
+#32601 := (iff #32580 #32602)
+#32563 := [rewrite]: #32601
+#32560 := [monotonicity #32563 #6102]: #32535
+#32537 := (iff #32556 #32538)
+#32557 := [rewrite]: #32537
+#32565 := [monotonicity #32557 #32560]: #32629
+#32587 := [monotonicity #32565]: #32548
+#32604 := [trans #32587 #32631]: #32548
+#32558 := [quant-inst]: #32603
+#32623 := [mp #32558 #32604]: #32561
+#32954 := [unit-resolution #32623 #4320]: #32564
+#30313 := (not #32538)
+#8488 := (uf_6 uf_17 ?x52!15)
+#9319 := (= uf_8 #8488)
+#9846 := (not #9319)
+#32968 := (iff #9846 #30313)
+#32955 := (iff #9319 #32538)
+#32985 := (iff #32538 #9319)
+#32980 := (= #32554 #8488)
+#32983 := (= #20604 ?x52!15)
+#20605 := (= ?x52!15 #20604)
+#12 := (uf_1 #10 #11)
+#4294 := (pattern #12)
+#13 := (uf_3 #12)
+#317 := (= #11 #13)
+#4295 := (forall (vars (?x2 T2) (?x3 T2)) (:pat #4294) #317)
+#321 := (forall (vars (?x2 T2) (?x3 T2)) #317)
+#4298 := (iff #321 #4295)
+#4296 := (iff #317 #317)
+#4297 := [refl]: #4296
+#4299 := [quant-intro #4297]: #4298
+#1948 := (~ #321 #321)
+#1980 := (~ #317 #317)
+#1981 := [refl]: #1980
+#1946 := [nnf-pos #1981]: #1948
+#14 := (= #13 #11)
+#15 := (forall (vars (?x2 T2) (?x3 T2)) #14)
+#322 := (iff #15 #321)
+#319 := (iff #14 #317)
+#320 := [rewrite]: #319
+#323 := [quant-intro #320]: #322
+#316 := [asserted]: #15
+#326 := [mp #316 #323]: #321
+#1982 := [mp~ #326 #1946]: #321
+#4300 := [mp #1982 #4299]: #4295
+#5378 := (not #4295)
+#27981 := (or #5378 #20605)
+#27945 := [quant-inst]: #27981
+#32953 := [unit-resolution #27945 #4300]: #20605
+#32984 := [symm #32953]: #32983
+#8596 := (= #7203 uf_17)
+#8594 := (= #150 uf_17)
+#4147 := (or #4677 #109)
+#4148 := [def-axiom]: #4147
+#7307 := [unit-resolution #4148 #7304]: #109
+#4150 := (or #4677 #4412)
+#4130 := [def-axiom]: #4150
+#8027 := [unit-resolution #4130 #7304]: #4412
+#4137 := (or #4677 #4437)
+#4132 := [def-axiom]: #4137
+#8030 := [unit-resolution #4132 #7304]: #4437
+#5284 := (or #4665 #4442 #4417 #1854)
+#4776 := (uf_4 uf_14 ?x64!17)
+#4777 := (* -1::int #4776)
+#4778 := (+ uf_9 #4777)
+#4779 := (<= #4778 0::int)
+#4845 := (?x40!7 ?x64!17)
+#4941 := (uf_6 uf_15 #4845)
+#4942 := (= uf_8 #4941)
+#4943 := (not #4942)
+#4848 := (uf_4 uf_14 #4845)
+#4849 := (* -1::int #4848)
+#4939 := (+ #4776 #4849)
+#4940 := (<= #4939 0::int)
+#4846 := (uf_1 #4845 ?x64!17)
+#4847 := (uf_10 #4846)
+#4842 := (* -1::int #4847)
+#4926 := (+ #4842 #4849)
+#4927 := (+ #4776 #4926)
+#4930 := (= #4927 0::int)
+#4932 := (not #4930)
+#5006 := (or #4932 #4940 #4943)
+#5242 := [hypothesis]: #4668
+#4159 := (or #4665 #933)
+#4154 := [def-axiom]: #4159
+#5243 := [unit-resolution #4154 #5242]: #933
+#4134 := (or #4665 #4659)
+#4135 := [def-axiom]: #4134
+#5244 := [unit-resolution #4135 #5242]: #4659
+#5245 := [hypothesis]: #109
+#5247 := (= #250 #108)
+#5246 := [symm #5243]: #231
+#5248 := [monotonicity #5246]: #5247
+#5249 := [trans #5248 #5245]: #251
+#4193 := (or #4641 #2536)
+#4198 := [def-axiom]: #4193
+#5250 := [unit-resolution #4198 #5249]: #4641
+#5087 := [hypothesis]: #4412
+#4160 := (or #4665 #4601)
+#4133 := [def-axiom]: #4160
+#5230 := [unit-resolution #4133 #5242]: #4601
+#5100 := (or #3693 #4417 #4606 #1053)
+#4862 := (uf_4 uf_14 ?x67!19)
+#3931 := (uf_4 uf_14 ?x66!20)
+#3932 := (* -1::int #3931)
+#4955 := (+ #3932 #4862)
+#4956 := (+ #2517 #4955)
+#4959 := (>= #4956 0::int)
+#4866 := (uf_6 uf_15 ?x67!19)
+#4867 := (= uf_8 #4866)
+#4863 := (* -1::int #4862)
+#4864 := (+ uf_9 #4863)
+#4865 := (<= #4864 0::int)
+#5068 := (not #4865)
+#5072 := [hypothesis]: #3698
+#4189 := (or #3693 #2523)
+#4186 := [def-axiom]: #4189
+#5073 := [unit-resolution #4186 #5072]: #2523
+#5061 := (+ #2514 #4863)
+#5063 := (>= #5061 0::int)
+#5060 := (= #2514 #4862)
+#5075 := (= #4862 #2514)
+#5074 := [hypothesis]: #933
+#5076 := [monotonicity #5074]: #5075
+#5077 := [symm #5076]: #5060
+#5078 := (not #5060)
+#5079 := (or #5078 #5063)
+#5080 := [th-lemma]: #5079
+#5081 := [unit-resolution #5080 #5077]: #5063
+#5069 := (not #5063)
+#5070 := (or #5068 #5069 #2522)
+#5064 := [hypothesis]: #2523
+#5065 := [hypothesis]: #4865
+#5066 := [hypothesis]: #5063
+#5067 := [th-lemma #5066 #5065 #5064]: false
+#5071 := [lemma #5067]: #5070
+#5082 := [unit-resolution #5071 #5081 #5073]: #5068
+#4869 := (or #4865 #4867)
+#5083 := [hypothesis]: #4601
+#4872 := (or #4606 #4865 #4867)
+#4868 := (or #4867 #4865)
+#4873 := (or #4606 #4868)
+#4880 := (iff #4873 #4872)
+#4875 := (or #4606 #4869)
+#4878 := (iff #4875 #4872)
+#4879 := [rewrite]: #4878
+#4876 := (iff #4873 #4875)
+#4870 := (iff #4868 #4869)
+#4871 := [rewrite]: #4870
+#4877 := [monotonicity #4871]: #4876
+#4881 := [trans #4877 #4879]: #4880
+#4874 := [quant-inst]: #4873
+#4882 := [mp #4874 #4881]: #4872
+#5084 := [unit-resolution #4882 #5083]: #4869
+#5085 := [unit-resolution #5084 #5082]: #4867
+#4953 := (not #4867)
+#5088 := (or #4953 #4959)
+#4190 := (or #3693 #2527)
+#4170 := [def-axiom]: #4190
+#5086 := [unit-resolution #4170 #5072]: #2527
+#4970 := (or #4417 #2526 #4953 #4959)
+#4948 := (+ #4862 #3932)
+#4949 := (+ #2517 #4948)
+#4952 := (>= #4949 0::int)
+#4954 := (or #4953 #2526 #4952)
+#4971 := (or #4417 #4954)
+#4978 := (iff #4971 #4970)
+#4965 := (or #2526 #4953 #4959)
+#4973 := (or #4417 #4965)
+#4976 := (iff #4973 #4970)
+#4977 := [rewrite]: #4976
+#4974 := (iff #4971 #4973)
+#4968 := (iff #4954 #4965)
+#4962 := (or #4953 #2526 #4959)
+#4966 := (iff #4962 #4965)
+#4967 := [rewrite]: #4966
+#4963 := (iff #4954 #4962)
+#4960 := (iff #4952 #4959)
+#4957 := (= #4949 #4956)
+#4958 := [rewrite]: #4957
+#4961 := [monotonicity #4958]: #4960
+#4964 := [monotonicity #4961]: #4963
+#4969 := [trans #4964 #4967]: #4968
+#4975 := [monotonicity #4969]: #4974
+#4979 := [trans #4975 #4977]: #4978
+#4972 := [quant-inst]: #4971
+#4980 := [mp #4972 #4979]: #4970
+#5089 := [unit-resolution #4980 #5087 #5086]: #5088
+#5090 := [unit-resolution #5089 #5085]: #4959
+#4171 := (not #3096)
+#4173 := (or #3693 #4171)
+#4174 := [def-axiom]: #4173
+#5091 := [unit-resolution #4174 #5072]: #4171
+#5054 := (+ #2512 #3932)
+#5058 := (<= #5054 0::int)
+#5053 := (= #2512 #3931)
+#5092 := (= #3931 #2512)
+#5093 := [monotonicity #5074]: #5092
+#5094 := [symm #5093]: #5053
+#5095 := (not #5053)
+#5096 := (or #5095 #5058)
+#5097 := [th-lemma]: #5096
+#5098 := [unit-resolution #5097 #5094]: #5058
+#5099 := [th-lemma #5098 #5091 #5081 #5090]: false
+#5101 := [lemma #5099]: #5100
+#5231 := [unit-resolution #5101 #5230 #5087 #5243]: #3693
+#4181 := (or #4650 #4644 #3698)
+#4182 := [def-axiom]: #4181
+#5232 := [unit-resolution #4182 #5231 #5250]: #4650
+#4161 := (or #4653 #4647)
+#4162 := [def-axiom]: #4161
+#5233 := [unit-resolution #4162 #5232]: #4653
+#4169 := (or #4662 #4622 #4656)
+#4155 := [def-axiom]: #4169
+#5234 := [unit-resolution #4155 #5233 #5244]: #4622
+#4194 := (or #4619 #4611)
+#4195 := [def-axiom]: #4194
+#5229 := [unit-resolution #4195 #5234]: #4611
+#5713 := (or #5006 #4616 #1053)
+#5123 := (uf_4 uf_22 #4845)
+#5136 := (* -1::int #5123)
+#5137 := (+ #2448 #5136)
+#5138 := (<= #5137 0::int)
+#5150 := (+ #4842 #5136)
+#5151 := (+ #2448 #5150)
+#5152 := (= #5151 0::int)
+#5382 := (+ #4848 #5136)
+#5387 := (>= #5382 0::int)
+#5381 := (= #4848 #5123)
+#5643 := (= #5123 #4848)
+#5642 := [symm #5074]: #231
+#5644 := [monotonicity #5642]: #5643
+#5645 := [symm #5644]: #5381
+#5646 := (not #5381)
+#5647 := (or #5646 #5387)
+#5648 := [th-lemma]: #5647
+#5649 := [unit-resolution #5648 #5645]: #5387
+#5119 := (+ #2448 #4777)
+#5121 := (>= #5119 0::int)
+#5118 := (= #2448 #4776)
+#5629 := (= #4776 #2448)
+#5630 := [monotonicity #5074]: #5629
+#5631 := [symm #5630]: #5118
+#5632 := (not #5118)
+#5633 := (or #5632 #5121)
+#5628 := [th-lemma]: #5633
+#5634 := [unit-resolution #5628 #5631]: #5121
+#5040 := (>= #4927 0::int)
+#5005 := (not #5006)
+#5635 := [hypothesis]: #5005
+#5042 := (or #5006 #4930)
+#5043 := [def-axiom]: #5042
+#5636 := [unit-resolution #5043 #5635]: #4930
+#5637 := (or #4932 #5040)
+#5638 := [th-lemma]: #5637
+#5653 := [unit-resolution #5638 #5636]: #5040
+#5386 := (<= #5382 0::int)
+#5654 := (or #5646 #5386)
+#5675 := [th-lemma]: #5654
+#5676 := [unit-resolution #5675 #5645]: #5386
+#5120 := (<= #5119 0::int)
+#5677 := (or #5632 #5120)
+#5678 := [th-lemma]: #5677
+#5679 := [unit-resolution #5678 #5631]: #5120
+#5034 := (<= #4927 0::int)
+#5674 := (or #4932 #5034)
+#5680 := [th-lemma]: #5674
+#5681 := [unit-resolution #5680 #5636]: #5034
+#5562 := (not #5387)
+#5567 := (not #5121)
+#5566 := (not #5040)
+#5779 := (not #5386)
+#5778 := (not #5120)
+#5777 := (not #5034)
+#5572 := (or #5152 #5777 #5778 #5779 #5566 #5567 #5562)
+#5774 := [hypothesis]: #5386
+#5775 := [hypothesis]: #5120
+#5776 := [hypothesis]: #5034
+#5157 := (not #5152)
+#5772 := [hypothesis]: #5157
+#5175 := (>= #5151 0::int)
+#5563 := [hypothesis]: #5387
+#5564 := [hypothesis]: #5121
+#5565 := [hypothesis]: #5040
+#5568 := (or #5175 #5566 #5567 #5562)
+#5569 := [th-lemma]: #5568
+#5570 := [unit-resolution #5569 #5565 #5564 #5563]: #5175
+#5784 := (not #5175)
+#5788 := (or #5784 #5152 #5777 #5778 #5779)
+#5773 := [hypothesis]: #5175
+#5174 := (<= #5151 0::int)
+#5780 := (or #5174 #5777 #5778 #5779)
+#5781 := [th-lemma]: #5780
+#5782 := [unit-resolution #5781 #5776 #5775 #5774]: #5174
+#5783 := (not #5174)
+#5785 := (or #5152 #5783 #5784)
+#5786 := [th-lemma]: #5785
+#5787 := [unit-resolution #5786 #5782 #5773 #5772]: false
+#5789 := [lemma #5787]: #5788
+#5571 := [unit-resolution #5789 #5570 #5772 #5776 #5775 #5774]: false
+#5641 := [lemma #5571]: #5572
+#5682 := [unit-resolution #5641 #5681 #5679 #5676 #5653 #5634 #5649]: #5152
+#5160 := (or #5138 #5157)
+#5683 := [hypothesis]: #4611
+#5163 := (or #4616 #5138 #5157)
+#5122 := (+ #2449 #4847)
+#5124 := (+ #5123 #5122)
+#5125 := (= #5124 0::int)
+#5126 := (not #5125)
+#5127 := (+ #5123 #2449)
+#5128 := (>= #5127 0::int)
+#5129 := (or #5128 #5126)
+#5164 := (or #4616 #5129)
+#5171 := (iff #5164 #5163)
+#5166 := (or #4616 #5160)
+#5169 := (iff #5166 #5163)
+#5170 := [rewrite]: #5169
+#5167 := (iff #5164 #5166)
+#5161 := (iff #5129 #5160)
+#5158 := (iff #5126 #5157)
+#5155 := (iff #5125 #5152)
+#5143 := (+ #4847 #5123)
+#5144 := (+ #2449 #5143)
+#5147 := (= #5144 0::int)
+#5153 := (iff #5147 #5152)
+#5154 := [rewrite]: #5153
+#5148 := (iff #5125 #5147)
+#5145 := (= #5124 #5144)
+#5146 := [rewrite]: #5145
+#5149 := [monotonicity #5146]: #5148
+#5156 := [trans #5149 #5154]: #5155
+#5159 := [monotonicity #5156]: #5158
+#5141 := (iff #5128 #5138)
+#5130 := (+ #2449 #5123)
+#5133 := (>= #5130 0::int)
+#5139 := (iff #5133 #5138)
+#5140 := [rewrite]: #5139
+#5134 := (iff #5128 #5133)
+#5131 := (= #5127 #5130)
+#5132 := [rewrite]: #5131
+#5135 := [monotonicity #5132]: #5134
+#5142 := [trans #5135 #5140]: #5141
+#5162 := [monotonicity #5142 #5159]: #5161
+#5168 := [monotonicity #5162]: #5167
+#5172 := [trans #5168 #5170]: #5171
+#5165 := [quant-inst]: #5164
+#5173 := [mp #5165 #5172]: #5163
+#5684 := [unit-resolution #5173 #5683]: #5160
+#5710 := [unit-resolution #5684 #5682]: #5138
+#5041 := (not #4940)
+#5044 := (or #5006 #5041)
+#5045 := [def-axiom]: #5044
+#5711 := [unit-resolution #5045 #5635]: #5041
+#5712 := [th-lemma #5634 #5711 #5649 #5710]: false
+#5714 := [lemma #5712]: #5713
+#5235 := [unit-resolution #5714 #5229 #5243]: #5006
+#5238 := (or #4779 #5005)
+#4191 := (or #4619 #2996)
+#4192 := [def-axiom]: #4191
+#5236 := [unit-resolution #4192 #5234]: #2996
+#5237 := [hypothesis]: #4437
+#5023 := (or #4442 #2993 #4779 #5005)
+#4850 := (+ #4849 #4842)
+#4851 := (+ #4776 #4850)
+#4852 := (= #4851 0::int)
+#4938 := (not #4852)
+#4944 := (or #4943 #4940 #4938)
+#4945 := (not #4944)
+#4946 := (or #2462 #4779 #4945)
+#5025 := (or #4442 #4946)
+#5031 := (iff #5025 #5023)
+#5013 := (or #2993 #4779 #5005)
+#5027 := (or #4442 #5013)
+#5024 := (iff #5027 #5023)
+#5030 := [rewrite]: #5024
+#5028 := (iff #5025 #5027)
+#5014 := (iff #4946 #5013)
+#5011 := (iff #4945 #5005)
+#5009 := (iff #4944 #5006)
+#4935 := (or #4943 #4940 #4932)
+#5007 := (iff #4935 #5006)
+#5008 := [rewrite]: #5007
+#4950 := (iff #4944 #4935)
+#4933 := (iff #4938 #4932)
+#4925 := (iff #4852 #4930)
+#4928 := (= #4851 #4927)
+#4929 := [rewrite]: #4928
+#4931 := [monotonicity #4929]: #4925
+#4934 := [monotonicity #4931]: #4933
+#4951 := [monotonicity #4934]: #4950
+#5010 := [trans #4951 #5008]: #5009
+#5012 := [monotonicity #5010]: #5011
+#5015 := [monotonicity #2995 #5012]: #5014
+#5029 := [monotonicity #5015]: #5028
+#5032 := [trans #5029 #5030]: #5031
+#5026 := [quant-inst]: #5025
+#5033 := [mp #5026 #5032]: #5023
+#5239 := [unit-resolution #5033 #5237 #5236]: #5238
+#5254 := [unit-resolution #5239 #5235]: #4779
+#4200 := (or #4619 #2461)
+#4207 := [def-axiom]: #4200
+#5255 := [unit-resolution #4207 #5234]: #2461
+#5280 := [monotonicity #5243]: #5629
+#5281 := [symm #5280]: #5118
+#5282 := [unit-resolution #5628 #5281]: #5121
+#5283 := [th-lemma #5282 #5255 #5254]: false
+#5279 := [lemma #5283]: #5284
+#8031 := [unit-resolution #5279 #8030 #8027 #7307]: #4665
+#4138 := (or #4677 #4671)
+#4106 := [def-axiom]: #4138
+#7357 := [unit-resolution #4106 #7304]: #4671
+#4143 := (or #4674 #4598 #4668)
+#4144 := [def-axiom]: #4143
+#7389 := [unit-resolution #4144 #7357 #8031]: #4598
+#4125 := (or #4595 #151)
+#4126 := [def-axiom]: #4125
+#8578 := [unit-resolution #4126 #7389]: #151
+#8595 := [symm #8578]: #8594
+#8592 := (= #7203 #150)
+#48 := (:var 0 T5)
+#47 := (:var 2 T4)
+#49 := (uf_7 #47 #10 #48)
+#4329 := (pattern #49)
+#360 := (= uf_8 #48)
+#50 := (uf_6 #49 #10)
+#356 := (= uf_8 #50)
+#363 := (iff #356 #360)
+#4330 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) (:pat #4329) #363)
+#366 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #363)
+#4333 := (iff #366 #4330)
+#4331 := (iff #363 #363)
+#4332 := [refl]: #4331
+#4334 := [quant-intro #4332]: #4333
+#1957 := (~ #366 #366)
+#1995 := (~ #363 #363)
+#1996 := [refl]: #1995
+#1958 := [nnf-pos #1996]: #1957
+#52 := (= #48 uf_8)
+#51 := (= #50 uf_8)
+#53 := (iff #51 #52)
+#54 := (forall (vars (?x17 T4) (?x18 T2) (?x19 T5)) #53)
+#367 := (iff #54 #366)
+#364 := (iff #53 #363)
+#361 := (iff #52 #360)
+#362 := [rewrite]: #361
+#358 := (iff #51 #356)
+#359 := [rewrite]: #358
+#365 := [monotonicity #359 #362]: #364
+#368 := [quant-intro #365]: #367
+#355 := [asserted]: #54
+#371 := [mp #355 #368]: #366
+#1997 := [mp~ #371 #1958]: #366
+#4335 := [mp #1997 #4334]: #4330
+#7014 := (not #4330)
+#7015 := (or #7014 #5314)
+#5318 := (= uf_8 uf_8)
+#5320 := (iff #5314 #5318)
+#7018 := (or #7014 #5320)
+#7020 := (iff #7018 #7015)
+#7022 := (iff #7015 #7015)
+#7023 := [rewrite]: #7022
+#5344 := (iff #5320 #5314)
+#5323 := (iff #5314 true)
+#5342 := (iff #5323 #5314)
+#5343 := [rewrite]: #5342
+#5324 := (iff #5320 #5323)
+#5321 := (iff #5318 true)
+#5322 := [rewrite]: #5321
+#5340 := [monotonicity #5322]: #5324
+#5345 := [trans #5340 #5343]: #5344
+#7021 := [monotonicity #5345]: #7020
+#7024 := [trans #7021 #7023]: #7020
+#7019 := [quant-inst]: #7018
+#7025 := [mp #7019 #7024]: #7015
+#8579 := [unit-resolution #7025 #4335]: #5314
+#8580 := [symm #8579]: #6089
+#8035 := (= #7128 uf_16)
+#7129 := (= uf_16 #7128)
+#16 := (uf_2 #12)
+#325 := (= #10 #16)
+#4301 := (forall (vars (?x4 T2) (?x5 T2)) (:pat #4294) #325)
+#329 := (forall (vars (?x4 T2) (?x5 T2)) #325)
+#4304 := (iff #329 #4301)
+#4302 := (iff #325 #325)
+#4303 := [refl]: #4302
+#4305 := [quant-intro #4303]: #4304
+#1949 := (~ #329 #329)
+#1983 := (~ #325 #325)
+#1984 := [refl]: #1983
+#1950 := [nnf-pos #1984]: #1949
+#17 := (= #16 #10)
+#18 := (forall (vars (?x4 T2) (?x5 T2)) #17)
+#330 := (iff #18 #329)
+#327 := (iff #17 #325)
+#328 := [rewrite]: #327
+#331 := [quant-intro #328]: #330
+#324 := [asserted]: #18
+#334 := [mp #324 #331]: #329
+#1985 := [mp~ #334 #1950]: #329
+#4306 := [mp #1985 #4305]: #4301
+#7136 := (not #4301)
+#7154 := (or #7136 #7129)
+#7155 := [quant-inst]: #7154
+#8034 := [unit-resolution #7155 #4306]: #7129
+#8036 := [symm #8034]: #8035
+#8593 := [monotonicity #8036 #8580]: #8592
+#8591 := [trans #8593 #8595]: #8596
+#32982 := [monotonicity #8591 #32984]: #32980
+#32970 := [monotonicity #32982]: #32985
+#32965 := [symm #32970]: #32955
+#32971 := [monotonicity #32965]: #32968
+#32956 := (not #15367)
+#32950 := [hypothesis]: #32956
+#15373 := (or #9846 #15367)
+#8693 := (= #144 #2212)
+#8633 := (= #2212 #144)
+#6559 := (= ?x46!9 uf_16)
+#7707 := (= ?x46!9 #7128)
+#6330 := (uf_6 uf_15 ?x46!9)
+#6365 := (= uf_8 #6330)
+#7717 := (ite #7707 #5314 #6365)
+#7711 := (uf_6 #7203 ?x46!9)
+#7714 := (= uf_8 #7711)
+#7720 := (iff #7714 #7717)
+#8351 := (or #7026 #7720)
+#7708 := (ite #7707 #6089 #6365)
+#7712 := (= #7711 uf_8)
+#7713 := (iff #7712 #7708)
+#8361 := (or #7026 #7713)
+#8363 := (iff #8361 #8351)
+#8365 := (iff #8351 #8351)
+#8366 := [rewrite]: #8365
+#7721 := (iff #7713 #7720)
+#7718 := (iff #7708 #7717)
+#7719 := [monotonicity #6102]: #7718
+#7715 := (iff #7712 #7714)
+#7716 := [rewrite]: #7715
+#7722 := [monotonicity #7716 #7719]: #7721
+#8364 := [monotonicity #7722]: #8363
+#8367 := [trans #8364 #8366]: #8363
+#8362 := [quant-inst]: #8361
+#8368 := [mp #8362 #8367]: #8351
+#8576 := [unit-resolution #8368 #4320]: #7720
+#8601 := (= #2208 #7711)
+#8597 := (= #7711 #2208)
+#8598 := [monotonicity #8591]: #8597
+#8625 := [symm #8598]: #8601
+#8571 := [hypothesis]: #2836
+#4285 := (or #2831 #2209)
+#4275 := [def-axiom]: #4285
+#8577 := [unit-resolution #4275 #8571]: #2209
+#8626 := [trans #8577 #8625]: #7714
+#8404 := (not #7714)
+#8401 := (not #7720)
+#8405 := (or #8401 #8404 #7717)
+#8400 := [def-axiom]: #8405
+#8627 := [unit-resolution #8400 #8626 #8576]: #7717
+#6393 := (uf_1 uf_16 ?x46!9)
+#6394 := (uf_10 #6393)
+#6337 := (* -1::int #2212)
+#6411 := (+ #6337 #6394)
+#6412 := (+ #144 #6411)
+#6413 := (>= #6412 0::int)
+#8287 := (not #6413)
+#6395 := (* -1::int #6394)
+#6396 := (+ uf_9 #6395)
+#6397 := (<= #6396 0::int)
+#6421 := (or #6397 #6413)
+#6426 := (not #6421)
+#3935 := (not #2825)
+#3940 := (or #2831 #3935)
+#4276 := [def-axiom]: #3940
+#8572 := [unit-resolution #4276 #8571]: #3935
+#4212 := (or #4595 #4456)
+#4213 := [def-axiom]: #4212
+#8574 := [unit-resolution #4213 #7389]: #4456
+#8302 := (or #4461 #2825 #6426)
+#6398 := (+ #1449 #6395)
+#6399 := (+ #2212 #6398)
+#6400 := (<= #6399 0::int)
+#6401 := (or #6400 #6397)
+#6402 := (not #6401)
+#6403 := (or #2213 #6402)
+#8303 := (or #4461 #6403)
+#8310 := (iff #8303 #8302)
+#6429 := (or #2825 #6426)
+#8305 := (or #4461 #6429)
+#8308 := (iff #8305 #8302)
+#8309 := [rewrite]: #8308
+#8306 := (iff #8303 #8305)
+#6430 := (iff #6403 #6429)
+#6427 := (iff #6402 #6426)
+#6424 := (iff #6401 #6421)
+#6418 := (or #6413 #6397)
+#6422 := (iff #6418 #6421)
+#6423 := [rewrite]: #6422
+#6419 := (iff #6401 #6418)
+#6416 := (iff #6400 #6413)
+#6404 := (+ #2212 #6395)
+#6405 := (+ #1449 #6404)
+#6408 := (<= #6405 0::int)
+#6414 := (iff #6408 #6413)
+#6415 := [rewrite]: #6414
+#6409 := (iff #6400 #6408)
+#6406 := (= #6399 #6405)
+#6407 := [rewrite]: #6406
+#6410 := [monotonicity #6407]: #6409
+#6417 := [trans #6410 #6415]: #6416
+#6420 := [monotonicity #6417]: #6419
+#6425 := [trans #6420 #6423]: #6424
+#6428 := [monotonicity #6425]: #6427
+#6431 := [monotonicity #2827 #6428]: #6430
+#8307 := [monotonicity #6431]: #8306
+#8311 := [trans #8307 #8309]: #8310
+#8304 := [quant-inst]: #8303
+#8312 := [mp #8304 #8311]: #8302
+#8628 := [unit-resolution #8312 #8574 #8572]: #6426
+#8288 := (or #6421 #8287)
+#8289 := [def-axiom]: #8288
+#8629 := [unit-resolution #8289 #8628]: #8287
+#8369 := (not #7717)
+#9187 := (or #7707 #6413 #8369)
+#7754 := (uf_1 #7128 ?x46!9)
+#7838 := (uf_3 #7754)
+#9086 := (uf_4 uf_14 #7838)
+#9087 := (* -1::int #9086)
+#7168 := (uf_4 uf_14 #7128)
+#9088 := (+ #7168 #9087)
+#9089 := (>= #9088 0::int)
+#9090 := (uf_6 uf_15 #7838)
+#9091 := (= uf_8 #9090)
+#9139 := (= #6330 #9090)
+#9135 := (= #9090 #6330)
+#9133 := (= #7838 ?x46!9)
+#7839 := (= ?x46!9 #7838)
+#8519 := (or #5378 #7839)
+#8257 := [quant-inst]: #8519
+#9132 := [unit-resolution #8257 #4300]: #7839
+#9134 := [symm #9132]: #9133
+#9136 := [monotonicity #9134]: #9135
+#9140 := [symm #9136]: #9139
+#9129 := [hypothesis]: #7717
+#7733 := (not #7707)
+#9130 := [hypothesis]: #7733
+#8347 := (or #8369 #7707 #6365)
+#8354 := [def-axiom]: #8347
+#9131 := [unit-resolution #8354 #9130 #9129]: #6365
+#9141 := [trans #9131 #9140]: #9091
+#9092 := (not #9091)
+#9154 := (or #9089 #9092)
+#7246 := (uf_6 uf_15 #7128)
+#7247 := (= uf_8 #7246)
+#9149 := (not #7247)
+#9150 := (iff #588 #9149)
+#9147 := (iff #585 #7247)
+#9145 := (iff #7247 #585)
+#9143 := (= #7246 #141)
+#9144 := [monotonicity #8036]: #9143
+#9146 := [monotonicity #9144]: #9145
+#9148 := [symm #9146]: #9147
+#9151 := [monotonicity #9148]: #9150
+#4127 := (or #4595 #588)
+#4220 := [def-axiom]: #4127
+#9142 := [unit-resolution #4220 #7389]: #588
+#9152 := [mp #9142 #9151]: #9149
+#4076 := (or #4677 #4421)
+#4131 := [def-axiom]: #4076
+#9153 := [unit-resolution #4131 #7304]: #4421
+#9097 := (or #4426 #7247 #9089 #9092)
+#9093 := (or #9092 #7247 #9089)
+#9098 := (or #4426 #9093)
+#9105 := (iff #9098 #9097)
+#9094 := (or #7247 #9089 #9092)
+#9100 := (or #4426 #9094)
+#9103 := (iff #9100 #9097)
+#9104 := [rewrite]: #9103
+#9101 := (iff #9098 #9100)
+#9095 := (iff #9093 #9094)
+#9096 := [rewrite]: #9095
+#9102 := [monotonicity #9096]: #9101
+#9106 := [trans #9102 #9104]: #9105
+#9099 := [quant-inst]: #9098
+#9107 := [mp #9099 #9106]: #9097
+#9155 := [unit-resolution #9107 #9153 #9152]: #9154
+#9156 := [unit-resolution #9155 #9141]: #9089
+#9157 := [hypothesis]: #8287
+#7755 := (uf_10 #7754)
+#7756 := (* -1::int #7755)
+#8520 := (+ #6394 #7756)
+#8524 := (>= #8520 0::int)
+#8517 := (= #6394 #7755)
+#9160 := (= #7755 #6394)
+#9158 := (= #7754 #6393)
+#9159 := [monotonicity #8036]: #9158
+#9161 := [monotonicity #9159]: #9160
+#9162 := [symm #9161]: #8517
+#9163 := (not #8517)
+#9164 := (or #9163 #8524)
+#9165 := [th-lemma]: #9164
+#9166 := [unit-resolution #9165 #9162]: #8524
+#8514 := (>= #7755 0::int)
+#7798 := (<= #7755 0::int)
+#7799 := (not #7798)
+#7804 := (or #7707 #7799)
+#59 := (uf_10 #12)
+#409 := (<= #59 0::int)
+#410 := (not #409)
+#58 := (= #10 #11)
+#413 := (or #58 #410)
+#4342 := (forall (vars (?x22 T2) (?x23 T2)) (:pat #4294) #413)
+#416 := (forall (vars (?x22 T2) (?x23 T2)) #413)
+#4345 := (iff #416 #4342)
+#4343 := (iff #413 #413)
+#4344 := [refl]: #4343
+#4346 := [quant-intro #4344]: #4345
+#1963 := (~ #416 #416)
+#1962 := (~ #413 #413)
+#2000 := [refl]: #1962
+#1964 := [nnf-pos #2000]: #1963
+#64 := (< 0::int #59)
+#63 := (not #58)
+#65 := (implies #63 #64)
+#66 := (forall (vars (?x22 T2) (?x23 T2)) #65)
+#419 := (iff #66 #416)
+#403 := (or #58 #64)
+#406 := (forall (vars (?x22 T2) (?x23 T2)) #403)
+#417 := (iff #406 #416)
+#414 := (iff #403 #413)
+#411 := (iff #64 #410)
+#412 := [rewrite]: #411
+#415 := [monotonicity #412]: #414
+#418 := [quant-intro #415]: #417
+#407 := (iff #66 #406)
+#404 := (iff #65 #403)
+#405 := [rewrite]: #404
+#408 := [quant-intro #405]: #407
+#420 := [trans #408 #418]: #419
+#402 := [asserted]: #66
+#421 := [mp #402 #420]: #416
+#2001 := [mp~ #421 #1964]: #416
+#4347 := [mp #2001 #4346]: #4342
+#7093 := (not #4342)
+#8435 := (or #7093 #7707 #7799)
+#7800 := (= #7128 ?x46!9)
+#7801 := (or #7800 #7799)
+#8436 := (or #7093 #7801)
+#8447 := (iff #8436 #8435)
+#8437 := (or #7093 #7804)
+#8443 := (iff #8437 #8435)
+#8444 := [rewrite]: #8443
+#8438 := (iff #8436 #8437)
+#7805 := (iff #7801 #7804)
+#7802 := (iff #7800 #7707)
+#7803 := [rewrite]: #7802
+#7806 := [monotonicity #7803]: #7805
+#8439 := [monotonicity #7806]: #8438
+#8448 := [trans #8439 #8444]: #8447
+#8434 := [quant-inst]: #8436
+#8482 := [mp #8434 #8448]: #8435
+#9167 := [unit-resolution #8482 #4347]: #7804
+#9168 := [unit-resolution #9167 #9130]: #7799
+#9169 := (or #8514 #7798)
+#9170 := [th-lemma]: #9169
+#9171 := [unit-resolution #9170 #9168]: #8514
+#9126 := (+ #2212 #9087)
+#9127 := (<= #9126 0::int)
+#9125 := (= #2212 #9086)
+#9172 := (= #9086 #2212)
+#9173 := [monotonicity #9134]: #9172
+#9174 := [symm #9173]: #9125
+#9175 := (not #9125)
+#9176 := (or #9175 #9127)
+#9177 := [th-lemma]: #9176
+#9178 := [unit-resolution #9177 #9174]: #9127
+#7162 := (* -1::int #7168)
+#7568 := (+ #144 #7162)
+#7572 := (>= #7568 0::int)
+#7233 := (= #144 #7168)
+#9179 := (= #7168 #144)
+#9180 := [monotonicity #8036]: #9179
+#9181 := [symm #9180]: #7233
+#9182 := (not #7233)
+#9183 := (or #9182 #7572)
+#9184 := [th-lemma]: #9183
+#9185 := [unit-resolution #9184 #9181]: #7572
+#9186 := [th-lemma #9185 #9178 #9171 #9166 #9157 #9156]: false
+#9188 := [lemma #9186]: #9187
+#8624 := [unit-resolution #9188 #8629 #8627]: #7707
+#8630 := [trans #8624 #8036]: #6559
+#8634 := [monotonicity #8630]: #8633
+#8694 := [symm #8634]: #8693
+#8695 := (= #2211 #144)
+#5856 := (uf_18 uf_16)
+#8641 := (= #5856 #144)
+#5857 := (= #144 #5856)
+#5844 := (uf_1 uf_16 uf_16)
+#5845 := (uf_10 #5844)
+#5864 := (>= #5845 0::int)
+#5848 := (* -1::int #5845)
+#5849 := (+ uf_9 #5848)
+#5850 := (<= #5849 0::int)
+#5872 := (or #5850 #5864)
+#7965 := (uf_1 #7128 #7128)
+#7966 := (uf_10 #7965)
+#7967 := (* -1::int #7966)
+#8029 := (+ #5845 #7967)
+#8033 := (>= #8029 0::int)
+#8028 := (= #5845 #7966)
+#8039 := (= #5844 #7965)
+#8037 := (= #7965 #5844)
+#8038 := [monotonicity #8036 #8036]: #8037
+#8040 := [symm #8038]: #8039
+#8041 := [monotonicity #8040]: #8028
+#8042 := (not #8028)
+#8043 := (or #8042 #8033)
+#8044 := [th-lemma]: #8043
+#8045 := [unit-resolution #8044 #8041]: #8033
+#7976 := (>= #7966 0::int)
+#7998 := (= #7966 0::int)
+#60 := (= #59 0::int)
+#393 := (or #63 #60)
+#4336 := (forall (vars (?x20 T2) (?x21 T2)) (:pat #4294) #393)
+#396 := (forall (vars (?x20 T2) (?x21 T2)) #393)
+#4339 := (iff #396 #4336)
+#4337 := (iff #393 #393)
+#4338 := [refl]: #4337
+#4340 := [quant-intro #4338]: #4339
+#1959 := (~ #396 #396)
+#1998 := (~ #393 #393)
+#1999 := [refl]: #1998
+#1960 := [nnf-pos #1999]: #1959
+#61 := (implies #58 #60)
+#62 := (forall (vars (?x20 T2) (?x21 T2)) #61)
+#399 := (iff #62 #396)
+#372 := (= 0::int #59)
+#383 := (or #63 #372)
+#388 := (forall (vars (?x20 T2) (?x21 T2)) #383)
+#397 := (iff #388 #396)
+#394 := (iff #383 #393)
+#391 := (iff #372 #60)
+#392 := [rewrite]: #391
+#395 := [monotonicity #392]: #394
+#398 := [quant-intro #395]: #397
+#389 := (iff #62 #388)
+#386 := (iff #61 #383)
+#380 := (implies #58 #372)
+#384 := (iff #380 #383)
+#385 := [rewrite]: #384
+#381 := (iff #61 #380)
+#378 := (iff #60 #372)
+#379 := [rewrite]: #378
+#382 := [monotonicity #379]: #381
+#387 := [trans #382 #385]: #386
+#390 := [quant-intro #387]: #389
+#400 := [trans #390 #398]: #399
+#370 := [asserted]: #62
+#401 := [mp #370 #400]: #396
+#1961 := [mp~ #401 #1960]: #396
+#4341 := [mp #1961 #4340]: #4336
+#6863 := (not #4336)
+#8012 := (or #6863 #7998)
+#7248 := (= #7128 #7128)
+#7999 := (not #7248)
+#8000 := (or #7999 #7998)
+#8013 := (or #6863 #8000)
+#8015 := (iff #8013 #8012)
+#8017 := (iff #8012 #8012)
+#8018 := [rewrite]: #8017
+#8010 := (iff #8000 #7998)
+#8005 := (or false #7998)
+#8008 := (iff #8005 #7998)
+#8009 := [rewrite]: #8008
+#8006 := (iff #8000 #8005)
+#8003 := (iff #7999 false)
+#8001 := (iff #7999 #6849)
+#7256 := (iff #7248 true)
+#7257 := [rewrite]: #7256
+#8002 := [monotonicity #7257]: #8001
+#8004 := [trans #8002 #6853]: #8003
+#8007 := [monotonicity #8004]: #8006
+#8011 := [trans #8007 #8009]: #8010
+#8016 := [monotonicity #8011]: #8015
+#8019 := [trans #8016 #8018]: #8015
+#8014 := [quant-inst]: #8013
+#8020 := [mp #8014 #8019]: #8012
+#8046 := [unit-resolution #8020 #4341]: #7998
+#8047 := (not #7998)
+#8048 := (or #8047 #7976)
+#8049 := [th-lemma]: #8048
+#8050 := [unit-resolution #8049 #8046]: #7976
+#6974 := (not #5864)
+#8051 := [hypothesis]: #6974
+#8052 := [th-lemma #8051 #8050 #8045]: false
+#8053 := [lemma #8052]: #5864
+#6975 := (or #5872 #6974)
+#6976 := [def-axiom]: #6975
+#8573 := [unit-resolution #6976 #8053]: #5872
+#5877 := (not #5872)
+#5880 := (or #5857 #5877)
+#6955 := (or #4461 #5857 #5877)
+#5851 := (+ #1449 #5848)
+#5852 := (+ #144 #5851)
+#5853 := (<= #5852 0::int)
+#5854 := (or #5853 #5850)
+#5855 := (not #5854)
+#5858 := (or #5857 #5855)
+#6956 := (or #4461 #5858)
+#6967 := (iff #6956 #6955)
+#6962 := (or #4461 #5880)
+#6965 := (iff #6962 #6955)
+#6966 := [rewrite]: #6965
+#6963 := (iff #6956 #6962)
+#5881 := (iff #5858 #5880)
+#5878 := (iff #5855 #5877)
+#5875 := (iff #5854 #5872)
+#5869 := (or #5864 #5850)
+#5873 := (iff #5869 #5872)
+#5874 := [rewrite]: #5873
+#5870 := (iff #5854 #5869)
+#5867 := (iff #5853 #5864)
+#5861 := (<= #5848 0::int)
+#5865 := (iff #5861 #5864)
+#5866 := [rewrite]: #5865
+#5862 := (iff #5853 #5861)
+#5859 := (= #5852 #5848)
+#5860 := [rewrite]: #5859
+#5863 := [monotonicity #5860]: #5862
+#5868 := [trans #5863 #5866]: #5867
+#5871 := [monotonicity #5868]: #5870
+#5876 := [trans #5871 #5874]: #5875
+#5879 := [monotonicity #5876]: #5878
+#5882 := [monotonicity #5879]: #5881
+#6964 := [monotonicity #5882]: #6963
+#6968 := [trans #6964 #6966]: #6967
+#6961 := [quant-inst]: #6956
+#6969 := [mp #6961 #6968]: #6955
+#8575 := [unit-resolution #6969 #8574]: #5880
+#8570 := [unit-resolution #8575 #8573]: #5857
+#8642 := [symm #8570]: #8641
+#8631 := (= #2211 #5856)
+#8632 := [monotonicity #8630]: #8631
+#8696 := [trans #8632 #8642]: #8695
+#8697 := [trans #8696 #8694]: #2825
+#8698 := [unit-resolution #8572 #8697]: false
+#8699 := [lemma #8698]: #2831
+#4203 := (or #4595 #4589)
+#4204 := [def-axiom]: #4203
+#9435 := [unit-resolution #4204 #7389]: #4589
+#4209 := (or #4595 #4464)
+#4214 := [def-axiom]: #4209
+#7390 := [unit-resolution #4214 #7389]: #4464
+#6363 := (or #2817 #4469 #4461)
+#6139 := (uf_1 uf_16 ?x45!8)
+#6140 := (uf_10 #6139)
+#6165 := (+ #2191 #6140)
+#6166 := (+ #144 #6165)
+#6192 := (>= #6166 0::int)
+#6169 := (= #6166 0::int)
+#6144 := (* -1::int #6140)
+#6145 := (+ uf_9 #6144)
+#6146 := (<= #6145 0::int)
+#6226 := (not #6146)
+#6158 := (+ #2815 #6140)
+#6159 := (+ #144 #6158)
+#6160 := (>= #6159 0::int)
+#6203 := (or #6146 #6160)
+#6208 := (not #6203)
+#6197 := (= #2190 #2192)
+#6342 := (not #6197)
+#6341 := [hypothesis]: #2822
+#6345 := (or #6342 #2817)
+#6346 := [th-lemma]: #6345
+#6347 := [unit-resolution #6346 #6341]: #6342
+#6348 := [hypothesis]: #4456
+#6214 := (or #4461 #6197 #6208)
+#6147 := (+ #1449 #6144)
+#6148 := (+ #2192 #6147)
+#6149 := (<= #6148 0::int)
+#6193 := (or #6149 #6146)
+#6194 := (not #6193)
+#6195 := (= #2192 #2190)
+#6196 := (or #6195 #6194)
+#6215 := (or #4461 #6196)
+#6222 := (iff #6215 #6214)
+#6211 := (or #6197 #6208)
+#6217 := (or #4461 #6211)
+#6220 := (iff #6217 #6214)
+#6221 := [rewrite]: #6220
+#6218 := (iff #6215 #6217)
+#6212 := (iff #6196 #6211)
+#6209 := (iff #6194 #6208)
+#6206 := (iff #6193 #6203)
+#6200 := (or #6160 #6146)
+#6204 := (iff #6200 #6203)
+#6205 := [rewrite]: #6204
+#6201 := (iff #6193 #6200)
+#6163 := (iff #6149 #6160)
+#6151 := (+ #2192 #6144)
+#6152 := (+ #1449 #6151)
+#6155 := (<= #6152 0::int)
+#6161 := (iff #6155 #6160)
+#6162 := [rewrite]: #6161
+#6156 := (iff #6149 #6155)
+#6153 := (= #6148 #6152)
+#6154 := [rewrite]: #6153
+#6157 := [monotonicity #6154]: #6156
+#6164 := [trans #6157 #6162]: #6163
+#6202 := [monotonicity #6164]: #6201
+#6207 := [trans #6202 #6205]: #6206
+#6210 := [monotonicity #6207]: #6209
+#6198 := (iff #6195 #6197)
+#6199 := [rewrite]: #6198
+#6213 := [monotonicity #6199 #6210]: #6212
+#6219 := [monotonicity #6213]: #6218
+#6223 := [trans #6219 #6221]: #6222
+#6216 := [quant-inst]: #6215
+#6224 := [mp #6216 #6223]: #6214
+#6349 := [unit-resolution #6224 #6348 #6347]: #6208
+#6227 := (or #6203 #6226)
+#6228 := [def-axiom]: #6227
+#6350 := [unit-resolution #6228 #6349]: #6226
+#6229 := (not #6160)
+#6230 := (or #6203 #6229)
+#6231 := [def-axiom]: #6230
+#6351 := [unit-resolution #6231 #6349]: #6229
+#6175 := (or #6146 #6160 #6169)
+#6352 := [hypothesis]: #4464
+#6180 := (or #4469 #6146 #6160 #6169)
+#6141 := (+ #6140 #2191)
+#6142 := (+ #144 #6141)
+#6143 := (= #6142 0::int)
+#6150 := (or #6149 #6146 #6143)
+#6181 := (or #4469 #6150)
+#6188 := (iff #6181 #6180)
+#6183 := (or #4469 #6175)
+#6186 := (iff #6183 #6180)
+#6187 := [rewrite]: #6186
+#6184 := (iff #6181 #6183)
+#6178 := (iff #6150 #6175)
+#6172 := (or #6160 #6146 #6169)
+#6176 := (iff #6172 #6175)
+#6177 := [rewrite]: #6176
+#6173 := (iff #6150 #6172)
+#6170 := (iff #6143 #6169)
+#6167 := (= #6142 #6166)
+#6168 := [rewrite]: #6167
+#6171 := [monotonicity #6168]: #6170
+#6174 := [monotonicity #6164 #6171]: #6173
+#6179 := [trans #6174 #6177]: #6178
+#6185 := [monotonicity #6179]: #6184
+#6189 := [trans #6185 #6187]: #6188
+#6182 := [quant-inst]: #6181
+#6190 := [mp #6182 #6189]: #6180
+#6353 := [unit-resolution #6190 #6352]: #6175
+#6354 := [unit-resolution #6353 #6351 #6350]: #6169
+#6355 := (not #6169)
+#6356 := (or #6355 #6192)
+#6357 := [th-lemma]: #6356
+#6358 := [unit-resolution #6357 #6354]: #6192
+#6225 := (>= #2816 0::int)
+#6359 := (or #6225 #2817)
+#6360 := [th-lemma]: #6359
+#6361 := [unit-resolution #6360 #6341]: #6225
+#6362 := [th-lemma #6361 #6351 #6358]: false
+#6364 := [lemma #6362]: #6363
+#9436 := [unit-resolution #6364 #7390 #8574]: #2817
+#4123 := (or #4592 #2822 #4586)
+#4124 := [def-axiom]: #4123
+#9437 := [unit-resolution #4124 #9436 #9435]: #4586
+#4215 := (or #4583 #4577)
+#4216 := [def-axiom]: #4215
+#9438 := [unit-resolution #4216 #9437]: #4577
+#4111 := (or #4580 #2836 #4574)
+#4070 := [def-axiom]: #4111
+#9439 := [unit-resolution #4070 #9438]: #4577
+#9422 := [unit-resolution #9439 #8699]: #4574
+#4068 := (or #4571 #4481)
+#4069 := [def-axiom]: #4068
+#9423 := [unit-resolution #4069 #9422]: #4481
+#10877 := (or #4486 #9846 #15367)
+#15363 := (= #15362 #2306)
+#15366 := (or #15363 #9846)
+#14529 := (or #4486 #15366)
+#14658 := (iff #14529 #10877)
+#14681 := (or #4486 #15373)
+#14554 := (iff #14681 #10877)
+#14690 := [rewrite]: #14554
+#12540 := (iff #14529 #14681)
+#15376 := (iff #15366 #15373)
+#15370 := (or #15367 #9846)
+#15374 := (iff #15370 #15373)
+#15375 := [rewrite]: #15374
+#15371 := (iff #15366 #15370)
+#15368 := (iff #15363 #15367)
+#15369 := [rewrite]: #15368
+#15372 := [monotonicity #15369]: #15371
+#15377 := [trans #15372 #15375]: #15376
+#14677 := [monotonicity #15377]: #12540
+#14520 := [trans #14677 #14690]: #14658
+#14692 := [quant-inst]: #14529
+#10887 := [mp #14692 #14520]: #10877
+#32978 := [unit-resolution #10887 #9423]: #15373
+#32979 := [unit-resolution #32978 #32950]: #9846
+#32981 := [mp #32979 #32971]: #30313
+#18779 := (= ?x52!15 #7128)
+#32989 := (iff #18779 #32602)
+#32770 := (iff #32602 #18779)
+#25219 := (= #7128 ?x52!15)
+#25223 := (iff #25219 #18779)
+#29787 := [commutativity]: #25223
+#32974 := (iff #32602 #25219)
+#32975 := [monotonicity #32984]: #32974
+#32986 := [trans #32975 #29787]: #32770
+#32991 := [symm #32986]: #32989
+#15413 := (uf_1 uf_16 ?x52!15)
+#15414 := (uf_10 #15413)
+#15439 := (+ #2307 #15414)
+#15440 := (+ #144 #15439)
+#15443 := (= #15440 0::int)
+#15432 := (+ #15397 #15414)
+#15433 := (+ #144 #15432)
+#15434 := (>= #15433 0::int)
+#15418 := (* -1::int #15414)
+#15419 := (+ uf_9 #15418)
+#15420 := (<= #15419 0::int)
+#15473 := (or #15420 #15434)
+#15478 := (not #15473)
+#15481 := (or #15367 #15478)
+#14730 := (or #4461 #15367 #15478)
+#15421 := (+ #1449 #15418)
+#15422 := (+ #15362 #15421)
+#15423 := (<= #15422 0::int)
+#15467 := (or #15423 #15420)
+#15468 := (not #15467)
+#15469 := (or #15363 #15468)
+#14738 := (or #4461 #15469)
+#14986 := (iff #14738 #14730)
+#14556 := (or #4461 #15481)
+#14896 := (iff #14556 #14730)
+#15034 := [rewrite]: #14896
+#14832 := (iff #14738 #14556)
+#15482 := (iff #15469 #15481)
+#15479 := (iff #15468 #15478)
+#15476 := (iff #15467 #15473)
+#15470 := (or #15434 #15420)
+#15474 := (iff #15470 #15473)
+#15475 := [rewrite]: #15474
+#15471 := (iff #15467 #15470)
+#15437 := (iff #15423 #15434)
+#15425 := (+ #15362 #15418)
+#15426 := (+ #1449 #15425)
+#15429 := (<= #15426 0::int)
+#15435 := (iff #15429 #15434)
+#15436 := [rewrite]: #15435
+#15430 := (iff #15423 #15429)
+#15427 := (= #15422 #15426)
+#15428 := [rewrite]: #15427
+#15431 := [monotonicity #15428]: #15430
+#15438 := [trans #15431 #15436]: #15437
+#15472 := [monotonicity #15438]: #15471
+#15477 := [trans #15472 #15475]: #15476
+#15480 := [monotonicity #15477]: #15479
+#15483 := [monotonicity #15369 #15480]: #15482
+#15031 := [monotonicity #15483]: #14832
+#14985 := [trans #15031 #15034]: #14986
+#12501 := [quant-inst]: #14738
+#15678 := [mp #12501 #14985]: #14730
+#32969 := [unit-resolution #15678 #8574]: #15481
+#32952 := [unit-resolution #32969 #32950]: #15478
+#29629 := (or #15473 #15443)
+#25301 := (not #15443)
+#29623 := [hypothesis]: #25301
+#15187 := (not #15420)
+#29624 := [hypothesis]: #15478
+#14833 := (or #15473 #15187)
+#15233 := [def-axiom]: #14833
+#29625 := [unit-resolution #15233 #29624]: #15187
+#8899 := (not #15434)
+#15050 := (or #15473 #8899)
+#15028 := [def-axiom]: #15050
+#29626 := [unit-resolution #15028 #29624]: #8899
+#15449 := (or #15420 #15434 #15443)
+#12503 := (or #4469 #15420 #15434 #15443)
+#15415 := (+ #15414 #2307)
+#15416 := (+ #144 #15415)
+#15417 := (= #15416 0::int)
+#15424 := (or #15423 #15420 #15417)
+#12502 := (or #4469 #15424)
+#14824 := (iff #12502 #12503)
+#14693 := (or #4469 #15449)
+#14698 := (iff #14693 #12503)
+#14734 := [rewrite]: #14698
+#14675 := (iff #12502 #14693)
+#15452 := (iff #15424 #15449)
+#15446 := (or #15434 #15420 #15443)
+#15450 := (iff #15446 #15449)
+#15451 := [rewrite]: #15450
+#15447 := (iff #15424 #15446)
+#15444 := (iff #15417 #15443)
+#15441 := (= #15416 #15440)
+#15442 := [rewrite]: #15441
+#15445 := [monotonicity #15442]: #15444
+#15448 := [monotonicity #15438 #15445]: #15447
+#15453 := [trans #15448 #15451]: #15452
+#14648 := [monotonicity #15453]: #14675
+#14687 := [trans #14648 #14734]: #14824
+#14736 := [quant-inst]: #12502
+#13488 := [mp #14736 #14687]: #12503
+#29627 := [unit-resolution #13488 #7390]: #15449
+#29628 := [unit-resolution #29627 #29626 #29625 #29623]: false
+#29630 := [lemma #29628]: #29629
+#32972 := [unit-resolution #29630 #32952]: #15443
+#29799 := (or #25301 #18779)
+#7126 := (uf_3 #6008)
+#15598 := (uf_1 #7126 ?x52!15)
+#27533 := (uf_3 #15598)
+#28710 := (uf_1 #7128 #27533)
+#28711 := (uf_10 #28710)
+#28714 := (* -1::int #28711)
+#28814 := (+ #15414 #28714)
+#28506 := (>= #28814 0::int)
+#28505 := (= #15414 #28711)
+#29767 := (= #28711 #15414)
+#29765 := (= #28710 #15413)
+#29763 := (= #27533 ?x52!15)
+#27534 := (= ?x52!15 #27533)
+#27563 := (or #5378 #27534)
+#27564 := [quant-inst]: #27563
+#29762 := [unit-resolution #27564 #4300]: #27534
+#29764 := [symm #29762]: #29763
+#29766 := [monotonicity #8036 #29764]: #29765
+#29768 := [monotonicity #29766]: #29767
+#29769 := [symm #29768]: #28505
+#29770 := (not #28505)
+#29771 := (or #29770 #28506)
+#29772 := [th-lemma]: #29771
+#29773 := [unit-resolution #29772 #29769]: #28506
+#5902 := (* -1::int #5856)
+#6232 := (+ #144 #5902)
+#6233 := (>= #6232 0::int)
+#4218 := (or #4583 #4472)
+#4120 := [def-axiom]: #4218
+#14110 := [unit-resolution #4120 #9437]: #4472
+#6959 := (or #4477 #6233)
+#6960 := [quant-inst]: #6959
+#12934 := [unit-resolution #6960 #14110]: #6233
+#7167 := (uf_18 #7128)
+#8141 := (* -1::int #7167)
+#10187 := (+ #5856 #8141)
+#7462 := (>= #10187 0::int)
+#10181 := (= #5856 #7167)
+#14102 := (= #7167 #5856)
+#14103 := [monotonicity #8036]: #14102
+#14104 := [symm #14103]: #10181
+#14105 := (not #10181)
+#25236 := (or #14105 #7462)
+#25243 := [th-lemma]: #25236
+#25235 := [unit-resolution #25243 #14104]: #7462
+#14406 := (<= #15440 0::int)
+#25300 := [hypothesis]: #15443
+#25302 := (or #25301 #14406)
+#25303 := [th-lemma]: #25302
+#25304 := [unit-resolution #25303 #25300]: #14406
+#15344 := (+ #2306 #8141)
+#15518 := (<= #15344 0::int)
+#7164 := (uf_6 uf_17 #7128)
+#7165 := (= uf_8 #7164)
+#25365 := (= #5319 #7164)
+#25361 := (= #7164 #5319)
+#25364 := [monotonicity #8578 #8036]: #25361
+#25366 := [symm #25364]: #25365
+#25367 := [trans #8579 #25366]: #7165
+#15503 := (uf_1 #7128 ?x52!15)
+#15504 := (uf_10 #15503)
+#15530 := (* -1::int #15504)
+#15531 := (+ #8141 #15530)
+#15532 := (+ #2306 #15531)
+#15533 := (= #15532 0::int)
+#25324 := (or #25301 #15533)
+#15538 := (not #15533)
+#25256 := [hypothesis]: #15538
+#14445 := (>= #15532 0::int)
+#14444 := (+ #15414 #15530)
+#14494 := (>= #14444 0::int)
+#14488 := (= #15414 #15504)
+#25275 := (= #15504 #15414)
+#25257 := (= #15503 #15413)
+#25274 := [monotonicity #8036]: #25257
+#25270 := [monotonicity #25274]: #25275
+#25276 := [symm #25270]: #14488
+#25277 := (not #14488)
+#25278 := (or #25277 #14494)
+#25279 := [th-lemma]: #25278
+#25280 := [unit-resolution #25279 #25276]: #14494
+#25306 := (not #14406)
+#25305 := (not #14494)
+#13409 := (not #6233)
+#25299 := (not #7462)
+#25307 := (or #14445 #25299 #13409 #25305 #25306)
+#25308 := [th-lemma]: #25307
+#25309 := [unit-resolution #25308 #25304 #25235 #12934 #25280]: #14445
+#14391 := (<= #15532 0::int)
+#14441 := (<= #14444 0::int)
+#25316 := (or #25277 #14441)
+#25317 := [th-lemma]: #25316
+#25315 := [unit-resolution #25317 #25276]: #14441
+#6970 := (<= #6232 0::int)
+#14098 := (not #5857)
+#14099 := (or #14098 #6970)
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+#10188 := (<= #10187 0::int)
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+#14107 := [th-lemma]: #14106
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+#14435 := (>= #15440 0::int)
+#25318 := (or #25301 #14435)
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+#25320 := [unit-resolution #25319 #25300]: #14435
+#25333 := (not #14435)
+#25332 := (not #14441)
+#12642 := (not #6970)
+#25331 := (not #10188)
+#25334 := (or #14391 #25331 #12642 #25332 #25333)
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+#25336 := [unit-resolution #25335 #25320 #14108 #14101 #25315]: #14391
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+#25337 := (not #14391)
+#25321 := (or #15533 #25337 #25314)
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+#25313 := [lemma #25323]: #25324
+#29774 := [unit-resolution #25313 #25300]: #15533
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+#6002 := (+ #108 #1449)
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+#5931 := (* -1::int #5930)
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+#5957 := (not #5954)
+#5940 := (uf_6 uf_15 #5928)
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+#17980 := (or #9672 #5512 #8252 #5939)
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+#16348 := [unit-resolution #4210 #7389]: #1657
+#6992 := (or #4442 #1656 #5947 #5968)
+#5934 := (+ #5933 #5931)
+#5935 := (+ #144 #5934)
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+#5937 := (not #5936)
+#5943 := (or #5942 #5939 #5937)
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+#7000 := (iff #6993 #6992)
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+#5971 := (or #5947 #1656 #5968)
+#5975 := (iff #5971 #5974)
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+#5972 := (iff #5946 #5971)
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+#5966 := (iff #5943 #5963)
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+#5965 := [rewrite]: #5964
+#5961 := (iff #5943 #5960)
+#5958 := (iff #5937 #5957)
+#5955 := (iff #5936 #5954)
+#5952 := (= #5935 #5951)
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+#5956 := [monotonicity #5953]: #5955
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+#5967 := [trans #5962 #5965]: #5966
+#5970 := [monotonicity #5967]: #5969
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+#5949 := [rewrite]: #5948
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+#5978 := [trans #5973 #5976]: #5977
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+#12009 := [symm #23510]: #5945
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+#8342 := [monotonicity #6664]: #8341
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+#8340 := [quant-inst]: #8314
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+#9352 := [unit-resolution #8353 #9351]: #8360
+#6607 := (or #6540 #6592 #6601)
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+#6581 := [trans #6606 #6580]: #6578
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+#8345 := [quant-inst]: #8344
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+#9353 := [unit-resolution #8321 #7390]: #6607
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+#6061 := (not #6058)
+#6064 := (or #6056 #6061)
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+#25329 := [unit-resolution #25328 #25327]: #6056
+#25356 := [mp #25329 #25355]: #173
+#4237 := (or #4568 #1492 #4562)
+#4066 := [def-axiom]: #4237
+#25358 := [unit-resolution #4066 #25356]: #25357
+#25359 := [unit-resolution #25358 #25326]: #4562
+#4232 := (or #4559 #4553)
+#4233 := [def-axiom]: #4232
+#25339 := [unit-resolution #4233 #25359]: #4553
+#4087 := (or #4556 #2235 #4550)
+#4088 := [def-axiom]: #4087
+#25340 := [unit-resolution #4088 #25339]: #4553
+#29776 := [unit-resolution #25340 #29775]: #4550
+#4242 := (or #4547 #4541)
+#4243 := [def-axiom]: #4242
+#29777 := [unit-resolution #4243 #29776]: #4541
+#25343 := (or #4544 #4538)
+#12812 := (= #2249 #5856)
+#12998 := (= ?x48!12 uf_16)
+#10849 := (= ?x48!12 #7128)
+#10847 := (uf_6 uf_15 ?x48!12)
+#10848 := (= uf_8 #10847)
+#10857 := (ite #10849 #5314 #10848)
+#10851 := (uf_6 #7203 ?x48!12)
+#10854 := (= uf_8 #10851)
+#10860 := (iff #10854 #10857)
+#12152 := (or #7026 #10860)
+#10850 := (ite #10849 #6089 #10848)
+#10852 := (= #10851 uf_8)
+#10853 := (iff #10852 #10850)
+#12155 := (or #7026 #10853)
+#10823 := (iff #12155 #12152)
+#10879 := (iff #12152 #12152)
+#10880 := [rewrite]: #10879
+#10861 := (iff #10853 #10860)
+#10858 := (iff #10850 #10857)
+#10859 := [monotonicity #6102]: #10858
+#10855 := (iff #10852 #10854)
+#10856 := [rewrite]: #10855
+#10862 := [monotonicity #10856 #10859]: #10861
+#10824 := [monotonicity #10862]: #10823
+#11111 := [trans #10824 #10880]: #10823
+#12156 := [quant-inst]: #12155
+#11091 := [mp #12156 #11111]: #12152
+#13286 := [unit-resolution #11091 #4320]: #10860
+#12615 := (= #2254 #10851)
+#12608 := (= #10851 #2254)
+#12613 := [monotonicity #8591]: #12608
+#12730 := [symm #12613]: #12615
+#12965 := [hypothesis]: #3403
+#3920 := (or #3398 #2255)
+#4261 := [def-axiom]: #3920
+#12611 := [unit-resolution #4261 #12965]: #2255
+#13209 := [trans #12611 #12730]: #10854
+#11918 := (not #10854)
+#10920 := (not #10860)
+#11919 := (or #10920 #11918 #10857)
+#12057 := [def-axiom]: #11919
+#13217 := [unit-resolution #12057 #13209 #13286]: #10857
+#10236 := (not #10848)
+#11183 := (uf_4 uf_14 ?x48!12)
+#11200 := (* -1::int #11183)
+#13667 := (+ #7168 #11200)
+#13668 := (>= #13667 0::int)
+#13764 := (not #13668)
+#12813 := (+ #2249 #5902)
+#12814 := (<= #12813 0::int)
+#13407 := (not #12814)
+#11572 := (uf_4 uf_14 ?x49!11)
+#11589 := (* -1::int #11572)
+#11709 := (+ #144 #11589)
+#11710 := (<= #11709 0::int)
+#11467 := (uf_6 uf_15 ?x49!11)
+#11468 := (= uf_8 #11467)
+#12026 := (not #11468)
+#11469 := (= ?x49!11 #7128)
+#11477 := (ite #11469 #5314 #11468)
+#12038 := (not #11477)
+#11471 := (uf_6 #7203 ?x49!11)
+#11474 := (= uf_8 #11471)
+#11480 := (iff #11474 #11477)
+#12030 := (or #7026 #11480)
+#11470 := (ite #11469 #6089 #11468)
+#11472 := (= #11471 uf_8)
+#11473 := (iff #11472 #11470)
+#12028 := (or #7026 #11473)
+#12024 := (iff #12028 #12030)
+#12033 := (iff #12030 #12030)
+#12035 := [rewrite]: #12033
+#11481 := (iff #11473 #11480)
+#11478 := (iff #11470 #11477)
+#11479 := [monotonicity #6102]: #11478
+#11475 := (iff #11472 #11474)
+#11476 := [rewrite]: #11475
+#11482 := [monotonicity #11476 #11479]: #11481
+#12032 := [monotonicity #11482]: #12024
+#12036 := [trans #12032 #12035]: #12024
+#12031 := [quant-inst]: #12028
+#12034 := [mp #12031 #12036]: #12030
+#13262 := [unit-resolution #12034 #4320]: #11480
+#12051 := (not #11474)
+#13387 := (iff #2258 #12051)
+#13353 := (iff #2257 #11474)
+#12939 := (iff #11474 #2257)
+#13219 := (= #11471 #2256)
+#13243 := [monotonicity #8591]: #13219
+#13039 := [monotonicity #13243]: #12939
+#13377 := [symm #13039]: #13353
+#13388 := [monotonicity #13377]: #13387
+#3924 := (or #3398 #2258)
+#3925 := [def-axiom]: #3924
+#12937 := [unit-resolution #3925 #12965]: #2258
+#12543 := [mp #12937 #13388]: #12051
+#12047 := (not #11480)
+#12048 := (or #12047 #11474 #12038)
+#12050 := [def-axiom]: #12048
+#12544 := [unit-resolution #12050 #12543 #13262]: #12038
+#12039 := (not #11469)
+#12539 := (or #11477 #12039)
+#12042 := (or #11477 #12039 #7040)
+#12043 := [def-axiom]: #12042
+#12545 := [unit-resolution #12043 #8579]: #12539
+#12546 := [unit-resolution #12545 #12544]: #12039
+#12044 := (or #11477 #11469 #12026)
+#12045 := [def-axiom]: #12044
+#12548 := [unit-resolution #12045 #12546 #12544]: #12026
+#11715 := (or #11468 #11710)
+#4217 := (or #4595 #4446)
+#4221 := [def-axiom]: #4217
+#12574 := [unit-resolution #4221 #7389]: #4446
+#12438 := (or #4451 #11468 #11710)
+#11700 := (+ #11572 #1449)
+#11701 := (>= #11700 0::int)
+#11702 := (or #11468 #11701)
+#12444 := (or #4451 #11702)
+#12454 := (iff #12444 #12438)
+#12448 := (or #4451 #11715)
+#12452 := (iff #12448 #12438)
+#12453 := [rewrite]: #12452
+#12450 := (iff #12444 #12448)
+#11716 := (iff #11702 #11715)
+#11713 := (iff #11701 #11710)
+#11703 := (+ #1449 #11572)
+#11706 := (>= #11703 0::int)
+#11711 := (iff #11706 #11710)
+#11712 := [rewrite]: #11711
+#11707 := (iff #11701 #11706)
+#11704 := (= #11700 #11703)
+#11705 := [rewrite]: #11704
+#11708 := [monotonicity #11705]: #11707
+#11714 := [trans #11708 #11712]: #11713
+#11717 := [monotonicity #11714]: #11716
+#12451 := [monotonicity #11717]: #12450
+#12449 := [trans #12451 #12453]: #12454
+#12447 := [quant-inst]: #12444
+#12455 := [mp #12447 #12449]: #12438
+#12575 := [unit-resolution #12455 #12574]: #11715
+#12576 := [unit-resolution #12575 #12548]: #11710
+#3926 := (not #2855)
+#3927 := (or #3398 #3926)
+#4263 := [def-axiom]: #3927
+#12577 := [unit-resolution #4263 #12965]: #3926
+#13397 := (not #11710)
+#12612 := (or #13407 #2855 #11469 #13397)
+#11605 := (uf_1 uf_16 ?x49!11)
+#11606 := (uf_10 #11605)
+#11631 := (+ #2853 #11606)
+#11632 := (+ #144 #11631)
+#12233 := (<= #11632 0::int)
+#11635 := (= #11632 0::int)
+#11610 := (* -1::int #11606)
+#11611 := (+ uf_9 #11610)
+#11612 := (<= #11611 0::int)
+#12253 := (not #11612)
+#11624 := (+ #11589 #11606)
+#11625 := (+ #144 #11624)
+#11626 := (>= #11625 0::int)
+#11669 := (or #11612 #11626)
+#11674 := (not #11669)
+#11663 := (= #2251 #11572)
+#13437 := (not #11663)
+#11590 := (+ #2251 #11589)
+#12252 := (>= #11590 0::int)
+#13367 := (not #12252)
+#13284 := [hypothesis]: #11710
+#13478 := [hypothesis]: #3926
+#13215 := [hypothesis]: #12814
+#13389 := (or #13367 #13397 #2855 #13407 #13409)
+#13410 := [th-lemma]: #13389
+#13436 := [unit-resolution #13410 #13215 #13478 #13284 #12934]: #13367
+#13434 := (or #13437 #12252)
+#12573 := [th-lemma]: #13434
+#13419 := [unit-resolution #12573 #13436]: #13437
+#11677 := (or #11663 #11674)
+#12241 := (or #4461 #11663 #11674)
+#11613 := (+ #1449 #11610)
+#11614 := (+ #11572 #11613)
+#11615 := (<= #11614 0::int)
+#11659 := (or #11615 #11612)
+#11660 := (not #11659)
+#11661 := (= #11572 #2251)
+#11662 := (or #11661 #11660)
+#12242 := (or #4461 #11662)
+#12249 := (iff #12242 #12241)
+#12245 := (or #4461 #11677)
+#12247 := (iff #12245 #12241)
+#12248 := [rewrite]: #12247
+#12239 := (iff #12242 #12245)
+#11678 := (iff #11662 #11677)
+#11675 := (iff #11660 #11674)
+#11672 := (iff #11659 #11669)
+#11666 := (or #11626 #11612)
+#11670 := (iff #11666 #11669)
+#11671 := [rewrite]: #11670
+#11667 := (iff #11659 #11666)
+#11629 := (iff #11615 #11626)
+#11617 := (+ #11572 #11610)
+#11618 := (+ #1449 #11617)
+#11621 := (<= #11618 0::int)
+#11627 := (iff #11621 #11626)
+#11628 := [rewrite]: #11627
+#11622 := (iff #11615 #11621)
+#11619 := (= #11614 #11618)
+#11620 := [rewrite]: #11619
+#11623 := [monotonicity #11620]: #11622
+#11630 := [trans #11623 #11628]: #11629
+#11668 := [monotonicity #11630]: #11667
+#11673 := [trans #11668 #11671]: #11672
+#11676 := [monotonicity #11673]: #11675
+#11664 := (iff #11661 #11663)
+#11665 := [rewrite]: #11664
+#11679 := [monotonicity #11665 #11676]: #11678
+#12246 := [monotonicity #11679]: #12239
+#12244 := [trans #12246 #12248]: #12249
+#12243 := [quant-inst]: #12242
+#12251 := [mp #12243 #12244]: #12241
+#13417 := [unit-resolution #12251 #8574]: #11677
+#13423 := [unit-resolution #13417 #13419]: #11674
+#12254 := (or #11669 #12253)
+#12258 := [def-axiom]: #12254
+#13426 := [unit-resolution #12258 #13423]: #12253
+#12250 := (not #11626)
+#12259 := (or #11669 #12250)
+#12257 := [def-axiom]: #12259
+#13412 := [unit-resolution #12257 #13423]: #12250
+#11641 := (or #11612 #11626 #11635)
+#12229 := (or #4469 #11612 #11626 #11635)
+#11607 := (+ #11606 #2853)
+#11608 := (+ #144 #11607)
+#11609 := (= #11608 0::int)
+#11616 := (or #11615 #11612 #11609)
+#12222 := (or #4469 #11616)
+#12236 := (iff #12222 #12229)
+#12231 := (or #4469 #11641)
+#12227 := (iff #12231 #12229)
+#12235 := [rewrite]: #12227
+#12232 := (iff #12222 #12231)
+#11644 := (iff #11616 #11641)
+#11638 := (or #11626 #11612 #11635)
+#11642 := (iff #11638 #11641)
+#11643 := [rewrite]: #11642
+#11639 := (iff #11616 #11638)
+#11636 := (iff #11609 #11635)
+#11633 := (= #11608 #11632)
+#11634 := [rewrite]: #11633
+#11637 := [monotonicity #11634]: #11636
+#11640 := [monotonicity #11630 #11637]: #11639
+#11645 := [trans #11640 #11643]: #11644
+#12234 := [monotonicity #11645]: #12232
+#12237 := [trans #12234 #12235]: #12236
+#12230 := [quant-inst]: #12222
+#12238 := [mp #12230 #12237]: #12229
+#13413 := [unit-resolution #12238 #7390]: #11641
+#13433 := [unit-resolution #13413 #13412 #13426]: #11635
+#13370 := (not #11635)
+#13390 := (or #13370 #12233)
+#13391 := [th-lemma]: #13390
+#13385 := [unit-resolution #13391 #13433]: #12233
+#12787 := (uf_1 #7128 ?x49!11)
+#12788 := (uf_10 #12787)
+#12790 := (* -1::int #12788)
+#13285 := (+ #11606 #12790)
+#13280 := (>= #13285 0::int)
+#13216 := (= #11606 #12788)
+#12644 := (= #12788 #11606)
+#12645 := (= #12787 #11605)
+#13418 := [monotonicity #8036]: #12645
+#12646 := [monotonicity #13418]: #12644
+#12578 := [symm #12646]: #13216
+#12641 := (not #13216)
+#12647 := (or #12641 #13280)
+#12643 := [th-lemma]: #12647
+#12582 := [unit-resolution #12643 #12578]: #13280
+#13068 := (<= #12788 0::int)
+#13063 := (not #13068)
+#12581 := [hypothesis]: #12039
+#13211 := (or #7093 #11469 #13063)
+#12936 := (= #7128 ?x49!11)
+#13162 := (or #12936 #13063)
+#13263 := (or #7093 #13162)
+#13354 := (iff #13263 #13211)
+#13255 := (or #11469 #13063)
+#13161 := (or #7093 #13255)
+#13351 := (iff #13161 #13211)
+#13352 := [rewrite]: #13351
+#13071 := (iff #13263 #13161)
+#13069 := (iff #13162 #13255)
+#13204 := (iff #12936 #11469)
+#13265 := [rewrite]: #13204
+#13210 := [monotonicity #13265]: #13069
+#13163 := [monotonicity #13210]: #13071
+#13067 := [trans #13163 #13352]: #13354
+#13160 := [quant-inst]: #13263
+#13355 := [mp #13160 #13067]: #13211
+#12609 := [unit-resolution #13355 #4347 #12581]: #13063
+#12610 := [th-lemma #13478 #13215 #12934 #12609 #12582 #13385]: false
+#12583 := [lemma #12610]: #12612
+#12780 := [unit-resolution #12583 #12577 #12546 #12576]: #13407
+#11201 := (+ #2249 #11200)
+#11202 := (<= #11201 0::int)
+#12087 := (or #4477 #11202)
+#11190 := (+ #11183 #2250)
+#11193 := (>= #11190 0::int)
+#12088 := (or #4477 #11193)
+#12090 := (iff #12088 #12087)
+#12092 := (iff #12087 #12087)
+#12093 := [rewrite]: #12092
+#11205 := (iff #11193 #11202)
+#11194 := (+ #2250 #11183)
+#11197 := (>= #11194 0::int)
+#11203 := (iff #11197 #11202)
+#11204 := [rewrite]: #11203
+#11198 := (iff #11193 #11197)
+#11195 := (= #11190 #11194)
+#11196 := [rewrite]: #11195
+#11199 := [monotonicity #11196]: #11198
+#11206 := [trans #11199 #11204]: #11205
+#12091 := [monotonicity #11206]: #12090
+#12095 := [trans #12091 #12093]: #12090
+#12085 := [quant-inst]: #12088
+#12097 := [mp #12085 #12095]: #12087
+#13218 := [unit-resolution #12097 #14110]: #11202
+#12617 := (not #11202)
+#12729 := (not #7572)
+#12728 := (or #13764 #12729 #12814 #12617 #12642)
+#12733 := [th-lemma]: #12728
+#12616 := [unit-resolution #12733 #13218 #9185 #14101 #12780]: #13764
+#13844 := (or #10236 #13668)
+#13842 := [hypothesis]: #13764
+#13843 := [hypothesis]: #10848
+#13801 := (or #4426 #7247 #10236 #13668)
+#13669 := (or #10236 #7247 #13668)
+#13802 := (or #4426 #13669)
+#13788 := (iff #13802 #13801)
+#13670 := (or #7247 #10236 #13668)
+#13804 := (or #4426 #13670)
+#13786 := (iff #13804 #13801)
+#13787 := [rewrite]: #13786
+#13805 := (iff #13802 #13804)
+#13665 := (iff #13669 #13670)
+#13671 := [rewrite]: #13665
+#13806 := [monotonicity #13671]: #13805
+#13789 := [trans #13806 #13787]: #13788
+#13803 := [quant-inst]: #13802
+#13790 := [mp #13803 #13789]: #13801
+#13838 := [unit-resolution #13790 #9153 #9152 #13843 #13842]: false
+#13845 := [lemma #13838]: #13844
+#12734 := [unit-resolution #13845 #12616]: #10236
+#11030 := (not #10857)
+#11307 := (or #11030 #10849 #10848)
+#11294 := [def-axiom]: #11307
+#12742 := [unit-resolution #11294 #12734 #13217]: #10849
+#12732 := [trans #12742 #8036]: #12998
+#12743 := [monotonicity #12732]: #12812
+#12969 := (not #12812)
+#12967 := (or #12969 #12814)
+#12973 := [th-lemma]: #12967
+#12786 := [unit-resolution #12973 #12780]: #12969
+#12771 := [unit-resolution #12786 #12743]: false
+#12735 := [lemma #12771]: #3398
+#4251 := (or #4544 #3403 #4538)
+#4248 := [def-axiom]: #4251
+#25338 := [unit-resolution #4248 #12735]: #25343
+#29778 := [unit-resolution #25338 #29777]: #4538
+#3968 := (or #4535 #4529)
+#3969 := [def-axiom]: #3968
+#29779 := [unit-resolution #3969 #29778]: #4529
+#25346 := (or #4532 #4526)
+#17148 := [hypothesis]: #3449
+#4266 := (or #3444 #2287)
+#4267 := [def-axiom]: #4266
+#17149 := [unit-resolution #4267 #17148]: #2287
+#9931 := (uf_1 uf_16 ?x50!14)
+#9932 := (uf_10 #9931)
+#9936 := (* -1::int #9932)
+#17081 := (+ #2281 #9936)
+#17083 := (>= #17081 0::int)
+#17080 := (= #2281 #9932)
+#17180 := (= #2280 #9931)
+#17179 := (= ?x51!13 uf_16)
+#10336 := (= ?x51!13 #7128)
+#10334 := (uf_6 uf_15 ?x51!13)
+#10335 := (= uf_8 #10334)
+#10367 := (not #10335)
+#10193 := (uf_4 uf_14 ?x51!13)
+#9874 := (uf_4 uf_14 ?x50!14)
+#9915 := (* -1::int #9874)
+#10384 := (+ #9915 #10193)
+#10385 := (+ #2281 #10384)
+#10388 := (>= #10385 0::int)
+#17156 := (not #10388)
+#9916 := (+ #2276 #9915)
+#9917 := (<= #9916 0::int)
+#16708 := (or #4477 #9917)
+#9907 := (+ #9874 #2277)
+#9908 := (>= #9907 0::int)
+#16709 := (or #4477 #9908)
+#16711 := (iff #16709 #16708)
+#16713 := (iff #16708 #16708)
+#16714 := [rewrite]: #16713
+#9920 := (iff #9908 #9917)
+#9909 := (+ #2277 #9874)
+#9912 := (>= #9909 0::int)
+#9918 := (iff #9912 #9917)
+#9919 := [rewrite]: #9918
+#9913 := (iff #9908 #9912)
+#9910 := (= #9907 #9909)
+#9911 := [rewrite]: #9910
+#9914 := [monotonicity #9911]: #9913
+#9921 := [trans #9914 #9919]: #9920
+#16712 := [monotonicity #9921]: #16711
+#16715 := [trans #16712 #16714]: #16711
+#16710 := [quant-inst]: #16709
+#16716 := [mp #16710 #16715]: #16708
+#17308 := [unit-resolution #16716 #14110]: #9917
+#3906 := (not #2882)
+#4269 := (or #3444 #3906)
+#4271 := [def-axiom]: #4269
+#17151 := [unit-resolution #4271 #17148]: #3906
+#10228 := (* -1::int #10193)
+#10229 := (+ #2278 #10228)
+#15878 := (>= #10229 0::int)
+#10198 := (= #2278 #10193)
+#4262 := (or #3444 #2289)
+#4268 := [def-axiom]: #4262
+#17152 := [unit-resolution #4268 #17148]: #2289
+#16493 := (or #4486 #3429 #10198)
+#10194 := (= #10193 #2278)
+#10197 := (or #10194 #3429)
+#16494 := (or #4486 #10197)
+#16503 := (iff #16494 #16493)
+#10204 := (or #3429 #10198)
+#16498 := (or #4486 #10204)
+#16501 := (iff #16498 #16493)
+#16502 := [rewrite]: #16501
+#16499 := (iff #16494 #16498)
+#10207 := (iff #10197 #10204)
+#10201 := (or #10198 #3429)
+#10205 := (iff #10201 #10204)
+#10206 := [rewrite]: #10205
+#10202 := (iff #10197 #10201)
+#10199 := (iff #10194 #10198)
+#10200 := [rewrite]: #10199
+#10203 := [monotonicity #10200]: #10202
+#10208 := [trans #10203 #10206]: #10207
+#16500 := [monotonicity #10208]: #16499
+#16504 := [trans #16500 #16502]: #16503
+#16497 := [quant-inst]: #16494
+#16505 := [mp #16497 #16504]: #16493
+#17150 := [unit-resolution #16505 #9423 #17152]: #10198
+#17153 := (not #10198)
+#17154 := (or #17153 #15878)
+#17155 := [th-lemma]: #17154
+#17147 := [unit-resolution #17155 #17150]: #15878
+#17313 := (not #9917)
+#17315 := (not #15878)
+#17157 := (or #17156 #17315 #17313 #2882)
+#17158 := [th-lemma]: #17157
+#17159 := [unit-resolution #17158 #17147 #17151 #17308]: #17156
+#17146 := (or #10367 #10388)
+#16749 := (or #4417 #2286 #10367 #10388)
+#10380 := (+ #10193 #9915)
+#10381 := (+ #2281 #10380)
+#10382 := (>= #10381 0::int)
+#10383 := (or #10367 #2286 #10382)
+#16750 := (or #4417 #10383)
+#16757 := (iff #16750 #16749)
+#10394 := (or #2286 #10367 #10388)
+#16752 := (or #4417 #10394)
+#16755 := (iff #16752 #16749)
+#16756 := [rewrite]: #16755
+#16753 := (iff #16750 #16752)
+#10397 := (iff #10383 #10394)
+#10391 := (or #10367 #2286 #10388)
+#10395 := (iff #10391 #10394)
+#10396 := [rewrite]: #10395
+#10392 := (iff #10383 #10391)
+#10389 := (iff #10382 #10388)
+#10386 := (= #10381 #10385)
+#10387 := [rewrite]: #10386
+#10390 := [monotonicity #10387]: #10389
+#10393 := [monotonicity #10390]: #10392
+#10398 := [trans #10393 #10396]: #10397
+#16754 := [monotonicity #10398]: #16753
+#16758 := [trans #16754 #16756]: #16757
+#16751 := [quant-inst]: #16750
+#16759 := [mp #16751 #16758]: #16749
+#17160 := [unit-resolution #16759 #8027 #17149]: #17146
+#17161 := [unit-resolution #17160 #17159]: #10367
+#10344 := (ite #10336 #5314 #10335)
+#10338 := (uf_6 #7203 ?x51!13)
+#10341 := (= uf_8 #10338)
+#10347 := (iff #10341 #10344)
+#16506 := (or #7026 #10347)
+#10337 := (ite #10336 #6089 #10335)
+#10339 := (= #10338 uf_8)
+#10340 := (iff #10339 #10337)
+#16507 := (or #7026 #10340)
+#16509 := (iff #16507 #16506)
+#16511 := (iff #16506 #16506)
+#16512 := [rewrite]: #16511
+#10348 := (iff #10340 #10347)
+#10345 := (iff #10337 #10344)
+#10346 := [monotonicity #6102]: #10345
+#10342 := (iff #10339 #10341)
+#10343 := [rewrite]: #10342
+#10349 := [monotonicity #10343 #10346]: #10348
+#16510 := [monotonicity #10349]: #16509
+#16513 := [trans #16510 #16512]: #16509
+#16508 := [quant-inst]: #16507
+#16514 := [mp #16508 #16513]: #16506
+#17162 := [unit-resolution #16514 #4320]: #10347
+#17171 := (= #2288 #10338)
+#17163 := (= #10338 #2288)
+#17164 := [monotonicity #8591]: #17163
+#17174 := [symm #17164]: #17171
+#17175 := [trans #17152 #17174]: #10341
+#16528 := (not #10341)
+#16525 := (not #10347)
+#16529 := (or #16525 #16528 #10344)
+#16530 := [def-axiom]: #16529
+#17176 := [unit-resolution #16530 #17175 #17162]: #10344
+#16515 := (not #10344)
+#16519 := (or #16515 #10336 #10335)
+#16520 := [def-axiom]: #16519
+#17178 := [unit-resolution #16520 #17176 #17161]: #10336
+#17177 := [trans #17178 #8036]: #17179
+#17181 := [monotonicity #17177]: #17180
+#17182 := [monotonicity #17181]: #17080
+#17187 := (not #17080)
+#17188 := (or #17187 #17083)
+#17186 := [th-lemma]: #17188
+#17189 := [unit-resolution #17186 #17182]: #17083
+#9937 := (+ uf_9 #9936)
+#9938 := (<= #9937 0::int)
+#9950 := (+ #9915 #9932)
+#9951 := (+ #144 #9950)
+#9952 := (>= #9951 0::int)
+#16744 := (not #9952)
+#10475 := (uf_2 #2280)
+#11002 := (uf_4 uf_14 #10475)
+#11016 := (* -1::int #11002)
+#16798 := (+ #10193 #11016)
+#16800 := (>= #16798 0::int)
+#16797 := (= #10193 #11002)
+#10476 := (= ?x51!13 #10475)
+#16793 := (or #7136 #10476)
+#16794 := [quant-inst]: #16793
+#17292 := [unit-resolution #16794 #4306]: #10476
+#17295 := [monotonicity #17292]: #16797
+#17296 := (not #16797)
+#17297 := (or #17296 #16800)
+#17298 := [th-lemma]: #17297
+#17299 := [unit-resolution #17298 #17295]: #16800
+#11017 := (+ #144 #11016)
+#11018 := (<= #11017 0::int)
+#17065 := (= #144 #11002)
+#17202 := (= #11002 #144)
+#17194 := (= #10475 uf_16)
+#17192 := (= #10475 #7128)
+#17190 := (= #10475 ?x51!13)
+#17191 := [symm #17292]: #17190
+#17193 := [trans #17191 #17178]: #17192
+#17195 := [trans #17193 #8036]: #17194
+#17203 := [monotonicity #17195]: #17202
+#17204 := [symm #17203]: #17065
+#17205 := (not #17065)
+#17206 := (or #17205 #11018)
+#17201 := [th-lemma]: #17206
+#17207 := [unit-resolution #17201 #17204]: #11018
+#17316 := (not #11018)
+#17314 := (not #16800)
+#17208 := (not #17083)
+#17209 := (or #16744 #17208 #17313 #2882 #17314 #17315 #17316)
+#17210 := [th-lemma]: #17209
+#17211 := [unit-resolution #17210 #17207 #17308 #17147 #17151 #17299 #17189]: #16744
+#9957 := (+ #2277 #9932)
+#9958 := (+ #144 #9957)
+#9961 := (= #9958 0::int)
+#17223 := (not #9961)
+#16729 := (>= #9958 0::int)
+#17219 := (not #16729)
+#17220 := (or #17219 #17208 #2882 #17314 #17315 #17316)
+#17221 := [th-lemma]: #17220
+#17222 := [unit-resolution #17221 #17207 #17147 #17151 #17299 #17189]: #17219
+#17218 := (or #17223 #16729)
+#17224 := [th-lemma]: #17218
+#17225 := [unit-resolution #17224 #17222]: #17223
+#9967 := (or #9938 #9952 #9961)
+#16717 := (or #4469 #9938 #9952 #9961)
+#9933 := (+ #9932 #2277)
+#9934 := (+ #144 #9933)
+#9935 := (= #9934 0::int)
+#9939 := (+ #1449 #9936)
+#9940 := (+ #9874 #9939)
+#9941 := (<= #9940 0::int)
+#9942 := (or #9941 #9938 #9935)
+#16718 := (or #4469 #9942)
+#16725 := (iff #16718 #16717)
+#16720 := (or #4469 #9967)
+#16723 := (iff #16720 #16717)
+#16724 := [rewrite]: #16723
+#16721 := (iff #16718 #16720)
+#9970 := (iff #9942 #9967)
+#9964 := (or #9952 #9938 #9961)
+#9968 := (iff #9964 #9967)
+#9969 := [rewrite]: #9968
+#9965 := (iff #9942 #9964)
+#9962 := (iff #9935 #9961)
+#9959 := (= #9934 #9958)
+#9960 := [rewrite]: #9959
+#9963 := [monotonicity #9960]: #9962
+#9955 := (iff #9941 #9952)
+#9943 := (+ #9874 #9936)
+#9944 := (+ #1449 #9943)
+#9947 := (<= #9944 0::int)
+#9953 := (iff #9947 #9952)
+#9954 := [rewrite]: #9953
+#9948 := (iff #9941 #9947)
+#9945 := (= #9940 #9944)
+#9946 := [rewrite]: #9945
+#9949 := [monotonicity #9946]: #9948
+#9956 := [trans #9949 #9954]: #9955
+#9966 := [monotonicity #9956 #9963]: #9965
+#9971 := [trans #9966 #9969]: #9970
+#16722 := [monotonicity #9971]: #16721
+#16726 := [trans #16722 #16724]: #16725
+#16719 := [quant-inst]: #16718
+#16727 := [mp #16719 #16726]: #16717
+#17226 := [unit-resolution #16727 #7390]: #9967
+#17227 := [unit-resolution #17226 #17225 #17211]: #9938
+#17228 := [th-lemma #17227 #17189 #17149]: false
+#17253 := [lemma #17228]: #3444
+#4253 := (or #4532 #3449 #4526)
+#4257 := [def-axiom]: #4253
+#25347 := [unit-resolution #4257 #17253]: #25346
+#29780 := [unit-resolution #25347 #29779]: #4526
+#3983 := (or #4523 #4515)
+#3984 := [def-axiom]: #3983
+#29781 := [unit-resolution #3984 #29780]: #4515
+#20547 := (or #4520 #7166 #15518 #15538)
+#15505 := (+ #2307 #15504)
+#15506 := (+ #7167 #15505)
+#15507 := (= #15506 0::int)
+#15508 := (not #15507)
+#15509 := (+ #7167 #2307)
+#15510 := (>= #15509 0::int)
+#15511 := (or #7166 #15510 #15508)
+#17626 := (or #4520 #15511)
+#20578 := (iff #17626 #20547)
+#20549 := (or #4520 #15541)
+#20516 := (iff #20549 #20547)
+#20517 := [rewrite]: #20516
+#20386 := (iff #17626 #20549)
+#15542 := (iff #15511 #15541)
+#15539 := (iff #15508 #15538)
+#15536 := (iff #15507 #15533)
+#15523 := (+ #7167 #15504)
+#15524 := (+ #2307 #15523)
+#15527 := (= #15524 0::int)
+#15534 := (iff #15527 #15533)
+#15535 := [rewrite]: #15534
+#15528 := (iff #15507 #15527)
+#15525 := (= #15506 #15524)
+#15526 := [rewrite]: #15525
+#15529 := [monotonicity #15526]: #15528
+#15537 := [trans #15529 #15535]: #15536
+#15540 := [monotonicity #15537]: #15539
+#15521 := (iff #15510 #15518)
+#15512 := (+ #2307 #7167)
+#15515 := (>= #15512 0::int)
+#15519 := (iff #15515 #15518)
+#15520 := [rewrite]: #15519
+#15516 := (iff #15510 #15515)
+#15513 := (= #15509 #15512)
+#15514 := [rewrite]: #15513
+#15517 := [monotonicity #15514]: #15516
+#15522 := [trans #15517 #15520]: #15521
+#15543 := [monotonicity #15522 #15540]: #15542
+#20388 := [monotonicity #15543]: #20386
+#20485 := [trans #20388 #20517]: #20578
+#20612 := [quant-inst]: #17626
+#20795 := [mp #20612 #20485]: #20547
+#29782 := [unit-resolution #20795 #29781]: #15541
+#29783 := [unit-resolution #29782 #29774 #25367]: #15518
+#28771 := (<= #28711 0::int)
+#28772 := (not #28771)
+#28773 := (= #7128 #27533)
+#29792 := (not #28773)
+#28056 := (not #18779)
+#29793 := (iff #28056 #29792)
+#29790 := (iff #18779 #28773)
+#29788 := (iff #28773 #18779)
+#29785 := (iff #28773 #25219)
+#29786 := [monotonicity #29764]: #29785
+#29789 := [trans #29786 #29787]: #29788
+#29791 := [symm #29789]: #29790
+#29794 := [monotonicity #29791]: #29793
+#29784 := [hypothesis]: #28056
+#29795 := [mp #29784 #29794]: #29792
+#28775 := (or #28772 #28773)
+#29743 := (or #7093 #28772 #28773)
+#28774 := (or #28773 #28772)
+#29744 := (or #7093 #28774)
+#29751 := (iff #29744 #29743)
+#29746 := (or #7093 #28775)
+#29749 := (iff #29746 #29743)
+#29750 := [rewrite]: #29749
+#29747 := (iff #29744 #29746)
+#28776 := (iff #28774 #28775)
+#28777 := [rewrite]: #28776
+#29748 := [monotonicity #28777]: #29747
+#29752 := [trans #29748 #29750]: #29751
+#29745 := [quant-inst]: #29744
+#29753 := [mp #29745 #29752]: #29743
+#29796 := [unit-resolution #29753 #4347]: #28775
+#29797 := [unit-resolution #29796 #29795]: #28772
+#29798 := [th-lemma #29797 #29783 #25304 #25235 #12934 #29773]: false
+#29800 := [lemma #29798]: #29799
+#32973 := [unit-resolution #29800 #32972]: #18779
+#32992 := [mp #32973 #32991]: #32602
+#32632 := (not #32602)
+#32993 := (or #32591 #32632)
+#29702 := (or #32591 #32632 #7040)
+#30315 := [def-axiom]: #29702
+#32995 := [unit-resolution #30315 #8579]: #32993
+#32996 := [unit-resolution #32995 #32992]: #32591
+#32599 := (not #32591)
+#28920 := (not #32564)
+#30916 := (or #28920 #32538 #32599)
+#31002 := [def-axiom]: #30916
+#32987 := [unit-resolution #31002 #32996 #32981 #32954]: false
+#32997 := [lemma #32987]: #15367
+#39375 := (or #32956 #14218)
+#39376 := [th-lemma]: #39375
+#39377 := [unit-resolution #39376 #32997]: #14218
+#34351 := (not #14218)
+#34357 := (or #34324 #34351)
+#4272 := (or #4523 #2319)
+#4270 := [def-axiom]: #4272
+#34292 := [unit-resolution #4270 #29780]: #2319
+#34293 := [hypothesis]: #14218
+#34291 := [hypothesis]: #16010
+#34294 := [th-lemma #34291 #34293 #34292]: false
+#34641 := [lemma #34294]: #34357
+#39378 := [unit-resolution #34641 #39377]: #34324
+#39380 := (or #16010 #16030)
+#4273 := (or #4523 #2896)
+#4259 := [def-axiom]: #4273
+#39379 := [unit-resolution #4259 #29780]: #2896
+#17785 := (or #4442 #2893 #16010 #16030)
+#15998 := (+ #15997 #15995)
+#15999 := (+ #15362 #15998)
+#16000 := (= #15999 0::int)
+#16001 := (not #16000)
+#16007 := (or #16006 #16003 #16001)
+#16008 := (not #16007)
+#16011 := (or #2320 #16010 #16008)
+#20897 := (or #4442 #16011)
+#21453 := (iff #20897 #17785)
+#16033 := (or #2893 #16010 #16030)
+#21128 := (or #4442 #16033)
+#18084 := (iff #21128 #17785)
+#22003 := [rewrite]: #18084
+#20788 := (iff #20897 #21128)
+#16034 := (iff #16011 #16033)
+#16031 := (iff #16008 #16030)
+#16028 := (iff #16007 #16025)
+#16022 := (or #16006 #16003 #16019)
+#16026 := (iff #16022 #16025)
+#16027 := [rewrite]: #16026
+#16023 := (iff #16007 #16022)
+#16020 := (iff #16001 #16019)
+#16017 := (iff #16000 #16016)
+#16014 := (= #15999 #16013)
+#16015 := [rewrite]: #16014
+#16018 := [monotonicity #16015]: #16017
+#16021 := [monotonicity #16018]: #16020
+#16024 := [monotonicity #16021]: #16023
+#16029 := [trans #16024 #16027]: #16028
+#16032 := [monotonicity #16029]: #16031
+#16035 := [monotonicity #2895 #16032]: #16034
+#21237 := [monotonicity #16035]: #20788
+#21330 := [trans #21237 #22003]: #21453
+#21234 := [quant-inst]: #20897
+#21506 := [mp #21234 #21330]: #17785
+#39381 := [unit-resolution #21506 #8030 #39379]: #39380
+#39382 := [unit-resolution #39381 #39378]: #16030
+#22030 := (or #16025 #16016)
+#18058 := [def-axiom]: #22030
+#32365 := [unit-resolution #18058 #39382]: #16016
+#32368 := (or #16019 #22006)
+#29568 := [th-lemma]: #32368
+#29612 := [unit-resolution #29568 #32365]: #22006
+#20411 := (+ uf_9 #15995)
+#20412 := (<= #20411 0::int)
+#20215 := (uf_6 uf_17 #15992)
+#20216 := (= uf_8 #20215)
+#20606 := (uf_2 #15993)
+#39327 := (uf_6 #7203 #20606)
+#38901 := (= #39327 #20215)
+#38905 := (= #20215 #39327)
+#20607 := (= #15992 #20606)
+#25402 := (or #7136 #20607)
+#25393 := [quant-inst]: #25402
+#39384 := [unit-resolution #25393 #4306]: #20607
+#8247 := (= uf_17 #7203)
+#8291 := (= #150 #7203)
+#8151 := [symm #8593]: #8291
+#8423 := [trans #8578 #8151]: #8247
+#38906 := [monotonicity #8423 #39384]: #38905
+#38907 := [symm #38906]: #38901
+#39330 := (= uf_8 #39327)
+#21345 := (uf_6 uf_15 #20606)
+#21346 := (= uf_8 #21345)
+#39333 := (= #7128 #20606)
+#39336 := (ite #39333 #5314 #21346)
+#39339 := (iff #39330 #39336)
+#38867 := (or #7026 #39339)
+#39325 := (= #20606 #7128)
+#39326 := (ite #39325 #6089 #21346)
+#39328 := (= #39327 uf_8)
+#39329 := (iff #39328 #39326)
+#38877 := (or #7026 #39329)
+#38879 := (iff #38877 #38867)
+#38890 := (iff #38867 #38867)
+#38888 := [rewrite]: #38890
+#39340 := (iff #39329 #39339)
+#39337 := (iff #39326 #39336)
+#39334 := (iff #39325 #39333)
+#39335 := [rewrite]: #39334
+#39338 := [monotonicity #39335 #6102]: #39337
+#39331 := (iff #39328 #39330)
+#39332 := [rewrite]: #39331
+#39341 := [monotonicity #39332 #39338]: #39340
+#38889 := [monotonicity #39341]: #38879
+#38894 := [trans #38889 #38888]: #38879
+#38878 := [quant-inst]: #38877
+#38893 := [mp #38878 #38894]: #38867
+#38919 := [unit-resolution #38893 #4320]: #39339
+#38895 := (not #39339)
+#38922 := (or #38895 #39330)
+#39351 := (not #39336)
+#39371 := [hypothesis]: #39351
+#39352 := (not #39333)
+#39372 := (or #39336 #39352)
+#39357 := (or #39336 #39352 #7040)
+#39358 := [def-axiom]: #39357
+#39373 := [unit-resolution #39358 #8579]: #39372
+#39374 := [unit-resolution #39373 #39371]: #39352
+#39394 := (or #39336 #39333)
+#39391 := (= #16004 #21345)
+#39387 := (= #21345 #16004)
+#39385 := (= #20606 #15992)
+#39386 := [symm #39384]: #39385
+#39388 := [monotonicity #39386]: #39387
+#39392 := [symm #39388]: #39391
+#21698 := (or #16025 #16005)
+#21997 := [def-axiom]: #21698
+#39383 := [unit-resolution #21997 #39382]: #16005
+#39393 := [trans #39383 #39392]: #21346
+#21347 := (not #21346)
+#39359 := (or #39336 #39333 #21347)
+#39360 := [def-axiom]: #39359
+#39395 := [unit-resolution #39360 #39393]: #39394
+#39396 := [unit-resolution #39395 #39374 #39371]: false
+#39397 := [lemma #39396]: #39336
+#38896 := (or #38895 #39330 #39351)
+#38897 := [def-axiom]: #38896
+#38902 := [unit-resolution #38897 #39397]: #38922
+#38903 := [unit-resolution #38902 #38919]: #39330
+#38908 := [trans #38903 #38907]: #20216
+#20217 := (not #20216)
+#38921 := [hypothesis]: #20217
+#38924 := [unit-resolution #38921 #38908]: false
+#38927 := [lemma #38924]: #20216
+#20218 := (uf_18 #15992)
+#20235 := (* -1::int #20218)
+#20421 := (+ #15995 #20235)
+#20422 := (+ #2306 #20421)
+#20423 := (<= #20422 0::int)
+#31764 := (not #20423)
+#26473 := (>= #20422 0::int)
+#20236 := (+ #15996 #20235)
+#20237 := (>= #20236 0::int)
+#25927 := (or #4477 #20237)
+#26030 := [quant-inst]: #25927
+#27294 := [unit-resolution #26030 #14110]: #20237
+#32338 := (not #20237)
+#29920 := (not #22006)
+#29919 := (or #26473 #29920 #34351 #32338)
+#32347 := [th-lemma]: #29919
+#32336 := [unit-resolution #32347 #29612 #27294 #39377]: #26473
+#20465 := (= #20422 0::int)
+#20470 := (not #20465)
+#20454 := (+ #2306 #20235)
+#20455 := (<= #20454 0::int)
+#32331 := (not #20455)
+#22027 := (not #16003)
+#21587 := (or #16025 #22027)
+#21112 := [def-axiom]: #21587
+#32344 := [unit-resolution #21112 #39382]: #22027
+#32343 := (or #32331 #16003 #34351 #32338)
+#32335 := [th-lemma]: #32343
+#32375 := [unit-resolution #32335 #32344 #27294 #39377]: #32331
+#20473 := (or #20217 #20455 #20470)
+#25436 := (or #4520 #20217 #20455 #20470)
+#20442 := (+ #2307 #15994)
+#20443 := (+ #20218 #20442)
+#20444 := (= #20443 0::int)
+#20445 := (not #20444)
+#20406 := (+ #20218 #2307)
+#20446 := (>= #20406 0::int)
+#20447 := (or #20217 #20446 #20445)
+#26505 := (or #4520 #20447)
+#26705 := (iff #26505 #25436)
+#11899 := (or #4520 #20473)
+#26697 := (iff #11899 #25436)
+#26704 := [rewrite]: #26697
+#25435 := (iff #26505 #11899)
+#20474 := (iff #20447 #20473)
+#20471 := (iff #20445 #20470)
+#20468 := (iff #20444 #20465)
+#20414 := (+ #15994 #20218)
+#20415 := (+ #2307 #20414)
+#20462 := (= #20415 0::int)
+#20466 := (iff #20462 #20465)
+#20467 := [rewrite]: #20466
+#20463 := (iff #20444 #20462)
+#20460 := (= #20443 #20415)
+#20461 := [rewrite]: #20460
+#20464 := [monotonicity #20461]: #20463
+#20469 := [trans #20464 #20467]: #20468
+#20472 := [monotonicity #20469]: #20471
+#20458 := (iff #20446 #20455)
+#20448 := (+ #2307 #20218)
+#20451 := (>= #20448 0::int)
+#20456 := (iff #20451 #20455)
+#20457 := [rewrite]: #20456
+#20452 := (iff #20446 #20451)
+#20449 := (= #20406 #20448)
+#20450 := [rewrite]: #20449
+#20453 := [monotonicity #20450]: #20452
+#20459 := [trans #20453 #20457]: #20458
+#20475 := [monotonicity #20459 #20472]: #20474
+#26696 := [monotonicity #20475]: #25435
+#26698 := [trans #26696 #26704]: #26705
+#26504 := [quant-inst]: #26505
+#26615 := [mp #26504 #26698]: #25436
+#29644 := [unit-resolution #26615 #29781]: #20473
+#29611 := [unit-resolution #29644 #38927 #32375]: #20470
+#32349 := (not #26473)
+#31762 := (or #20465 #31764 #32349)
+#29679 := [th-lemma]: #31762
+#32366 := [unit-resolution #29679 #29611 #32336]: #31764
+#20428 := (or #20217 #20412 #20423)
+#4260 := (or #4523 #4506)
+#3982 := [def-axiom]: #4260
+#29894 := [unit-resolution #3982 #29780]: #4506
+#26338 := (or #4511 #20217 #20412 #20423)
+#20407 := (+ #15994 #20406)
+#20410 := (>= #20407 0::int)
+#20413 := (or #20217 #20412 #20410)
+#26340 := (or #4511 #20413)
+#25469 := (iff #26340 #26338)
+#10685 := (or #4511 #20428)
+#25478 := (iff #10685 #26338)
+#25474 := [rewrite]: #25478
+#25437 := (iff #26340 #10685)
+#20429 := (iff #20413 #20428)
+#20426 := (iff #20410 #20423)
+#20418 := (>= #20415 0::int)
+#20424 := (iff #20418 #20423)
+#20425 := [rewrite]: #20424
+#20419 := (iff #20410 #20418)
+#20416 := (= #20407 #20415)
+#20417 := [rewrite]: #20416
+#20420 := [monotonicity #20417]: #20419
+#20427 := [trans #20420 #20425]: #20426
+#20430 := [monotonicity #20427]: #20429
+#25388 := [monotonicity #20430]: #25437
+#25466 := [trans #25388 #25474]: #25469
+#25477 := [quant-inst]: #26340
+#25432 := [mp #25477 #25466]: #26338
+#31826 := [unit-resolution #25432 #29894]: #20428
+#29616 := [unit-resolution #31826 #32366 #38927]: #20412
+[th-lemma #34292 #39377 #29616 #29612 #29563]: false
+unsat
--- a/src/HOL/Boogie/Examples/cert/Boogie_b_Dijkstra	Fri Nov 06 09:50:37 2009 -0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,43 +0,0 @@
-(benchmark Isabelle
-:extrasorts ( T1 T4 T3 T5 T2)
-:extrafuns (
-  (uf_2 T1 T2)
-  (uf_3 T1 T2)
-  (uf_1 T2 T2 T1)
-  (uf_8 T5)
-  (uf_7 T4 T2 T5 T4)
-  (uf_5 T3 T2 Int T3)
-  (uf_6 T4 T2 T5)
-  (uf_4 T3 T2 Int)
-  (uf_10 T1 Int)
-  (uf_11 T2)
-  (uf_9 Int)
-  (uf_21 T2)
-  (uf_16 T2)
-  (uf_20 T2)
-  (uf_12 T2 Int)
-  (uf_14 T3)
-  (uf_18 T2 Int)
-  (uf_22 T3)
-  (uf_24 T3)
-  (uf_23 T3)
-  (uf_15 T4)
-  (uf_17 T4)
-  (uf_19 T4)
- )
-:extrapreds (
-  (up_13 T2)
- )
-:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1) (uf_3 ?x1)) ?x1))
-:assumption (forall (?x2 T2) (?x3 T2) (= (uf_3 (uf_1 ?x2 ?x3)) ?x3))
-:assumption (forall (?x4 T2) (?x5 T2) (= (uf_2 (uf_1 ?x4 ?x5)) ?x4))
-:assumption (forall (?x6 T3) (?x7 T2) (?x8 Int) (?x9 T2) (= (uf_4 (uf_5 ?x6 ?x7 ?x8) ?x9) (ite (= ?x9 ?x7) ?x8 (uf_4 ?x6 ?x9))))
-:assumption (forall (?x10 T4) (?x11 T2) (?x12 T5) (?x13 T2) (iff (= (uf_6 (uf_7 ?x10 ?x11 ?x12) ?x13) uf_8) (if_then_else (= ?x13 ?x11) (= ?x12 uf_8) (= (uf_6 ?x10 ?x13) uf_8))))
-:assumption (forall (?x14 T3) (?x15 T2) (?x16 Int) (= (uf_4 (uf_5 ?x14 ?x15 ?x16) ?x15) ?x16))
-:assumption (forall (?x17 T4) (?x18 T2) (?x19 T5) (iff (= (uf_6 (uf_7 ?x17 ?x18 ?x19) ?x18) uf_8) (= ?x19 uf_8)))
-:assumption (< 0 uf_9)
-:assumption (forall (?x20 T2) (?x21 T2) (implies (= ?x20 ?x21) (= (uf_10 (uf_1 ?x20 ?x21)) 0)))
-:assumption (forall (?x22 T2) (?x23 T2) (implies (not (= ?x22 ?x23)) (< 0 (uf_10 (uf_1 ?x22 ?x23)))))
-:assumption (not (implies true (implies true (implies (forall (?x24 T2) (implies (= ?x24 uf_11) (= (uf_12 ?x24) 0))) (implies (forall (?x25 T2) (implies (not (= ?x25 uf_11)) (= (uf_12 ?x25) uf_9))) (implies (forall (?x26 T2) (not (up_13 ?x26))) (implies true (and (implies (= (uf_12 uf_11) 0) (and (implies (forall (?x27 T2) (<= 0 (uf_12 ?x27))) (and (implies (forall (?x28 T2) (?x29 T2) (implies (and (up_13 ?x28) (not (up_13 ?x29))) (<= (uf_12 ?x28) (uf_12 ?x29)))) (and (implies (forall (?x30 T2) (?x31 T2) (implies (and (< (uf_10 (uf_1 ?x31 ?x30)) uf_9) (up_13 ?x31)) (<= (uf_12 ?x30) (+ (uf_12 ?x31) (uf_10 (uf_1 ?x31 ?x30)))))) (and (implies (forall (?x32 T2) (implies (and (< (uf_12 ?x32) uf_9) (not (= ?x32 uf_11))) (exists (?x33 T2) (and (= (uf_12 ?x32) (+ (uf_12 ?x33) (uf_10 (uf_1 ?x33 ?x32)))) (and (up_13 ?x33) (< (uf_12 ?x33) (uf_12 ?x32))))))) (implies true (implies true (implies (= (uf_4 uf_14 uf_11) 0) (implies (forall (?x34 T2) (<= 0 (uf_4 uf_14 ?x34))) (implies (forall (?x35 T2) (?x36 T2) (implies (and (= (uf_6 uf_15 ?x35) uf_8) (not (= (uf_6 uf_15 ?x36) uf_8))) (<= (uf_4 uf_14 ?x35) (uf_4 uf_14 ?x36)))) (implies (forall (?x37 T2) (?x38 T2) (implies (and (< (uf_10 (uf_1 ?x38 ?x37)) uf_9) (= (uf_6 uf_15 ?x38) uf_8)) (<= (uf_4 uf_14 ?x37) (+ (uf_4 uf_14 ?x38) (uf_10 (uf_1 ?x38 ?x37)))))) (implies (forall (?x39 T2) (implies (and (< (uf_4 uf_14 ?x39) uf_9) (not (= ?x39 uf_11))) (exists (?x40 T2) (and (= (uf_4 uf_14 ?x39) (+ (uf_4 uf_14 ?x40) (uf_10 (uf_1 ?x40 ?x39)))) (and (= (uf_6 uf_15 ?x40) uf_8) (< (uf_4 uf_14 ?x40) (uf_4 uf_14 ?x39))))))) (implies true (and (implies true (implies true (implies (exists (?x41 T2) (and (< (uf_4 uf_14 ?x41) uf_9) (not (= (uf_6 uf_15 ?x41) uf_8)))) (implies (not (= (uf_6 uf_15 uf_16) uf_8)) (implies (< (uf_4 uf_14 uf_16) uf_9) (implies (forall (?x42 T2) (implies (not (= (uf_6 uf_15 ?x42) uf_8)) (<= (uf_4 uf_14 uf_16) (uf_4 uf_14 ?x42)))) (implies (= uf_17 (uf_7 uf_15 uf_16 uf_8)) (implies (forall (?x43 T2) (implies (and (< (+ (uf_4 uf_14 uf_16) (uf_10 (uf_1 uf_16 ?x43))) (uf_4 uf_14 ?x43)) (< (uf_10 (uf_1 uf_16 ?x43)) uf_9)) (= (uf_18 ?x43) (+ (uf_4 uf_14 uf_16) (uf_10 (uf_1 uf_16 ?x43)))))) (implies (forall (?x44 T2) (implies (not (and (< (+ (uf_4 uf_14 uf_16) (uf_10 (uf_1 uf_16 ?x44))) (uf_4 uf_14 ?x44)) (< (uf_10 (uf_1 uf_16 ?x44)) uf_9))) (= (uf_18 ?x44) (uf_4 uf_14 ?x44)))) (and (implies (forall (?x45 T2) (<= (uf_18 ?x45) (uf_4 uf_14 ?x45))) (and (implies (forall (?x46 T2) (implies (= (uf_6 uf_17 ?x46) uf_8) (= (uf_18 ?x46) (uf_4 uf_14 ?x46)))) (implies true (implies true (and (implies (= (uf_18 uf_11) 0) (and (implies (forall (?x47 T2) (<= 0 (uf_18 ?x47))) (and (implies (forall (?x48 T2) (?x49 T2) (implies (and (= (uf_6 uf_17 ?x48) uf_8) (not (= (uf_6 uf_17 ?x49) uf_8))) (<= (uf_18 ?x48) (uf_18 ?x49)))) (and (implies (forall (?x50 T2) (?x51 T2) (implies (and (< (uf_10 (uf_1 ?x51 ?x50)) uf_9) (= (uf_6 uf_17 ?x51) uf_8)) (<= (uf_18 ?x50) (+ (uf_18 ?x51) (uf_10 (uf_1 ?x51 ?x50)))))) (and (implies (forall (?x52 T2) (implies (and (< (uf_18 ?x52) uf_9) (not (= ?x52 uf_11))) (exists (?x53 T2) (and (= (uf_18 ?x52) (+ (uf_18 ?x53) (uf_10 (uf_1 ?x53 ?x52)))) (and (= (uf_6 uf_17 ?x53) uf_8) (< (uf_18 ?x53) (uf_18 ?x52))))))) (implies false true)) (forall (?x54 T2) (implies (and (< (uf_18 ?x54) uf_9) (not (= ?x54 uf_11))) (exists (?x55 T2) (and (= (uf_18 ?x54) (+ (uf_18 ?x55) (uf_10 (uf_1 ?x55 ?x54)))) (and (= (uf_6 uf_17 ?x55) uf_8) (< (uf_18 ?x55) (uf_18 ?x54))))))))) (forall (?x56 T2) (?x57 T2) (implies (and (< (uf_10 (uf_1 ?x57 ?x56)) uf_9) (= (uf_6 uf_17 ?x57) uf_8)) (<= (uf_18 ?x56) (+ (uf_18 ?x57) (uf_10 (uf_1 ?x57 ?x56)))))))) (forall (?x58 T2) (?x59 T2) (implies (and (= (uf_6 uf_17 ?x58) uf_8) (not (= (uf_6 uf_17 ?x59) uf_8))) (<= (uf_18 ?x58) (uf_18 ?x59)))))) (forall (?x60 T2) (<= 0 (uf_18 ?x60))))) (= (uf_18 uf_11) 0))))) (forall (?x61 T2) (implies (= (uf_6 uf_17 ?x61) uf_8) (= (uf_18 ?x61) (uf_4 uf_14 ?x61)))))) (forall (?x62 T2) (<= (uf_18 ?x62) (uf_4 uf_14 ?x62))))))))))))) (implies true (implies true (implies (not (exists (?x63 T2) (and (< (uf_4 uf_14 ?x63) uf_9) (not (= (uf_6 uf_15 ?x63) uf_8))))) (implies true (implies true (implies (= uf_19 uf_15) (implies (= uf_20 uf_21) (implies (= uf_22 uf_14) (implies (= uf_23 uf_24) (implies true (and (implies (forall (?x64 T2) (implies (and (< (uf_4 uf_22 ?x64) uf_9) (not (= ?x64 uf_11))) (exists (?x65 T2) (and (= (uf_4 uf_22 ?x64) (+ (uf_4 uf_22 ?x65) (uf_10 (uf_1 ?x65 ?x64)))) (< (uf_4 uf_22 ?x65) (uf_4 uf_22 ?x64)))))) (and (implies (forall (?x66 T2) (?x67 T2) (implies (and (< (uf_10 (uf_1 ?x67 ?x66)) uf_9) (< (uf_4 uf_22 ?x67) uf_9)) (<= (uf_4 uf_22 ?x66) (+ (uf_4 uf_22 ?x67) (uf_10 (uf_1 ?x67 ?x66)))))) (and (implies (= (uf_4 uf_22 uf_11) 0) true) (= (uf_4 uf_22 uf_11) 0))) (forall (?x68 T2) (?x69 T2) (implies (and (< (uf_10 (uf_1 ?x69 ?x68)) uf_9) (< (uf_4 uf_22 ?x69) uf_9)) (<= (uf_4 uf_22 ?x68) (+ (uf_4 uf_22 ?x69) (uf_10 (uf_1 ?x69 ?x68)))))))) (forall (?x70 T2) (implies (and (< (uf_4 uf_22 ?x70) uf_9) (not (= ?x70 uf_11))) (exists (?x71 T2) (and (= (uf_4 uf_22 ?x70) (+ (uf_4 uf_22 ?x71) (uf_10 (uf_1 ?x71 ?x70)))) (< (uf_4 uf_22 ?x71) (uf_4 uf_22 ?x70))))))))))))))))))))))))))) (forall (?x72 T2) (implies (and (< (uf_12 ?x72) uf_9) (not (= ?x72 uf_11))) (exists (?x73 T2) (and (= (uf_12 ?x72) (+ (uf_12 ?x73) (uf_10 (uf_1 ?x73 ?x72)))) (and (up_13 ?x73) (< (uf_12 ?x73) (uf_12 ?x72))))))))) (forall (?x74 T2) (?x75 T2) (implies (and (< (uf_10 (uf_1 ?x75 ?x74)) uf_9) (up_13 ?x75)) (<= (uf_12 ?x74) (+ (uf_12 ?x75) (uf_10 (uf_1 ?x75 ?x74)))))))) (forall (?x76 T2) (?x77 T2) (implies (and (up_13 ?x76) (not (up_13 ?x77))) (<= (uf_12 ?x76) (uf_12 ?x77)))))) (forall (?x78 T2) (<= 0 (uf_12 ?x78))))) (= (uf_12 uf_11) 0)))))))))
-:formula true
-)
--- a/src/HOL/Boogie/Examples/cert/Boogie_b_Dijkstra.proof	Fri Nov 06 09:50:37 2009 -0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,7081 +0,0 @@
-#2 := false
-#55 := 0::int
-decl uf_4 :: (-> T3 T2 int)
-decl ?x40!7 :: (-> T2 T2)
-decl ?x52!15 :: T2
-#2305 := ?x52!15
-#15992 := (?x40!7 ?x52!15)
-decl uf_14 :: T3
-#107 := uf_14
-#15996 := (uf_4 uf_14 #15992)
-#20405 := (>= #15996 0::int)
-#11 := (:var 0 T2)
-#110 := (uf_4 uf_14 #11)
-#4403 := (pattern #110)
-#1843 := (>= #110 0::int)
-#4404 := (forall (vars (?x34 T2)) (:pat #4403) #1843)
-decl uf_10 :: (-> T1 int)
-decl uf_1 :: (-> T2 T2 T1)
-decl ?x66!20 :: T2
-#2511 := ?x66!20
-decl ?x67!19 :: T2
-#2510 := ?x67!19
-#2516 := (uf_1 ?x67!19 ?x66!20)
-#2517 := (uf_10 #2516)
-#1320 := -1::int
-#2524 := (* -1::int #2517)
-decl uf_22 :: T3
-#230 := uf_22
-#2514 := (uf_4 uf_22 ?x67!19)
-#2520 := (* -1::int #2514)
-#3094 := (+ #2520 #2524)
-#2512 := (uf_4 uf_22 ?x66!20)
-#3095 := (+ #2512 #3094)
-#3096 := (<= #3095 0::int)
-decl uf_9 :: int
-#56 := uf_9
-#2525 := (+ uf_9 #2524)
-#2526 := (<= #2525 0::int)
-#2521 := (+ uf_9 #2520)
-#2522 := (<= #2521 0::int)
-#3693 := (or #2522 #2526 #3096)
-#3698 := (not #3693)
-#10 := (:var 1 T2)
-#90 := (uf_1 #11 #10)
-#4379 := (pattern #90)
-#238 := (uf_4 uf_22 #10)
-#1720 := (* -1::int #238)
-#235 := (uf_4 uf_22 #11)
-#1721 := (+ #235 #1720)
-#91 := (uf_10 #90)
-#1727 := (+ #91 #1721)
-#1750 := (>= #1727 0::int)
-#1707 := (* -1::int #235)
-#1708 := (+ uf_9 #1707)
-#1709 := (<= #1708 0::int)
-#1343 := (* -1::int #91)
-#1346 := (+ uf_9 #1343)
-#1347 := (<= #1346 0::int)
-#3661 := (or #1347 #1709 #1750)
-#4633 := (forall (vars (?x66 T2) (?x67 T2)) (:pat #4379) #3661)
-#4638 := (not #4633)
-decl uf_11 :: T2
-#67 := uf_11
-#250 := (uf_4 uf_22 uf_11)
-#251 := (= #250 0::int)
-#4641 := (or #251 #4638)
-#4644 := (not #4641)
-#4647 := (or #4644 #3698)
-#4650 := (not #4647)
-#4609 := (pattern #235)
-decl ?x65!18 :: (-> T2 T2)
-#2487 := (?x65!18 #11)
-#2490 := (uf_1 #2487 #11)
-#2491 := (uf_10 #2490)
-#3064 := (* -1::int #2491)
-#2488 := (uf_4 uf_22 #2487)
-#3047 := (* -1::int #2488)
-#3065 := (+ #3047 #3064)
-#3066 := (+ #235 #3065)
-#3067 := (= #3066 0::int)
-#3631 := (not #3067)
-#3048 := (+ #235 #3047)
-#3049 := (<= #3048 0::int)
-#3632 := (or #3049 #3631)
-#3633 := (not #3632)
-#68 := (= #11 uf_11)
-#3639 := (or #68 #1709 #3633)
-#4625 := (forall (vars (?x64 T2)) (:pat #4609) #3639)
-#4630 := (not #4625)
-#4653 := (or #4630 #4650)
-#4656 := (not #4653)
-decl ?x64!17 :: T2
-#2447 := ?x64!17
-#2451 := (uf_1 #11 ?x64!17)
-#4610 := (pattern #2451)
-#2452 := (uf_10 #2451)
-#2448 := (uf_4 uf_22 ?x64!17)
-#2449 := (* -1::int #2448)
-#3017 := (+ #2449 #2452)
-#3018 := (+ #235 #3017)
-#3021 := (= #3018 0::int)
-#3595 := (not #3021)
-#2450 := (+ #235 #2449)
-#2455 := (>= #2450 0::int)
-#3596 := (or #2455 #3595)
-#4611 := (forall (vars (?x65 T2)) (:pat #4609 #4610) #3596)
-#4616 := (not #4611)
-#2993 := (= uf_11 ?x64!17)
-#2459 := (+ uf_9 #2449)
-#2460 := (<= #2459 0::int)
-#4619 := (or #2460 #2993 #4616)
-#4622 := (not #4619)
-#4659 := (or #4622 #4656)
-#4662 := (not #4659)
-decl uf_6 :: (-> T4 T2 T5)
-decl uf_15 :: T4
-#113 := uf_15
-#116 := (uf_6 uf_15 #11)
-#4445 := (pattern #116)
-#1404 := (* -1::int #110)
-#1405 := (+ uf_9 #1404)
-#1406 := (<= #1405 0::int)
-decl uf_8 :: T5
-#33 := uf_8
-#505 := (= uf_8 #116)
-#3581 := (or #505 #1406)
-#4601 := (forall (vars (?x41 T2)) (:pat #4445 #4403) #3581)
-#4606 := (not #4601)
-#933 := (= uf_14 uf_22)
-#1053 := (not #933)
-decl uf_19 :: T4
-#225 := uf_19
-#930 := (= uf_15 uf_19)
-#1071 := (not #930)
-decl uf_24 :: T3
-#233 := uf_24
-decl uf_23 :: T3
-#232 := uf_23
-#234 := (= uf_23 uf_24)
-#1044 := (not #234)
-decl uf_21 :: T2
-#228 := uf_21
-decl uf_20 :: T2
-#227 := uf_20
-#229 := (= uf_20 uf_21)
-#1062 := (not #229)
-#4665 := (or #1062 #1044 #1071 #1053 #4606 #4662)
-#4668 := (not #4665)
-#2309 := (uf_1 #11 ?x52!15)
-#4514 := (pattern #2309)
-decl uf_18 :: (-> T2 int)
-#158 := (uf_18 #11)
-#4454 := (pattern #158)
-decl uf_17 :: T4
-#149 := uf_17
-#168 := (uf_6 uf_17 #11)
-#4480 := (pattern #168)
-#2310 := (uf_10 #2309)
-#2306 := (uf_18 ?x52!15)
-#2307 := (* -1::int #2306)
-#2917 := (+ #2307 #2310)
-#2918 := (+ #158 #2917)
-#2921 := (= #2918 0::int)
-#3474 := (not #2921)
-#2308 := (+ #158 #2307)
-#2313 := (>= #2308 0::int)
-#630 := (= uf_8 #168)
-#636 := (not #630)
-#3475 := (or #636 #2313 #3474)
-#4515 := (forall (vars (?x53 T2)) (:pat #4480 #4454 #4514) #3475)
-#4520 := (not #4515)
-#180 := (uf_18 #10)
-#1505 := (* -1::int #180)
-#1506 := (+ #158 #1505)
-#1536 := (+ #91 #1506)
-#1534 := (>= #1536 0::int)
-#3466 := (or #636 #1347 #1534)
-#4506 := (forall (vars (?x50 T2) (?x51 T2)) (:pat #4379) #3466)
-#4511 := (not #4506)
-#2893 := (= uf_11 ?x52!15)
-#2317 := (+ uf_9 #2307)
-#2318 := (<= #2317 0::int)
-#4523 := (or #2318 #2893 #4511 #4520)
-#4526 := (not #4523)
-decl ?x50!14 :: T2
-#2275 := ?x50!14
-decl ?x51!13 :: T2
-#2274 := ?x51!13
-#2280 := (uf_1 ?x51!13 ?x50!14)
-#2281 := (uf_10 #2280)
-#2284 := (* -1::int #2281)
-#2278 := (uf_18 ?x51!13)
-#2879 := (* -1::int #2278)
-#2880 := (+ #2879 #2284)
-#2276 := (uf_18 ?x50!14)
-#2881 := (+ #2276 #2880)
-#2882 := (<= #2881 0::int)
-#2288 := (uf_6 uf_17 ?x51!13)
-#2289 := (= uf_8 #2288)
-#3429 := (not #2289)
-#2285 := (+ uf_9 #2284)
-#2286 := (<= #2285 0::int)
-#3444 := (or #2286 #3429 #2882)
-#3449 := (not #3444)
-#4529 := (or #3449 #4526)
-#4532 := (not #4529)
-#4497 := (pattern #158 #180)
-#1504 := (>= #1506 0::int)
-#176 := (uf_6 uf_17 #10)
-#648 := (= uf_8 #176)
-#3406 := (not #648)
-#3421 := (or #630 #3406 #1504)
-#4498 := (forall (vars (?x48 T2) (?x49 T2)) (:pat #4497) #3421)
-#4503 := (not #4498)
-#4535 := (or #4503 #4532)
-#4538 := (not #4535)
-decl ?x49!11 :: T2
-#2247 := ?x49!11
-#2251 := (uf_18 ?x49!11)
-#2853 := (* -1::int #2251)
-decl ?x48!12 :: T2
-#2248 := ?x48!12
-#2249 := (uf_18 ?x48!12)
-#2854 := (+ #2249 #2853)
-#2855 := (<= #2854 0::int)
-#2256 := (uf_6 uf_17 ?x49!11)
-#2257 := (= uf_8 #2256)
-#2254 := (uf_6 uf_17 ?x48!12)
-#2255 := (= uf_8 #2254)
-#3383 := (not #2255)
-#3398 := (or #3383 #2257 #2855)
-#3403 := (not #3398)
-#4541 := (or #3403 #4538)
-#4544 := (not #4541)
-#1495 := (>= #158 0::int)
-#4489 := (forall (vars (?x47 T2)) (:pat #4454) #1495)
-#4494 := (not #4489)
-#4547 := (or #4494 #4544)
-#4550 := (not #4547)
-decl ?x47!10 :: T2
-#2232 := ?x47!10
-#2233 := (uf_18 ?x47!10)
-#2234 := (>= #2233 0::int)
-#2235 := (not #2234)
-#4553 := (or #2235 #4550)
-#4556 := (not #4553)
-#172 := (uf_18 uf_11)
-#173 := (= #172 0::int)
-#1492 := (not #173)
-#4559 := (or #1492 #4556)
-#4562 := (not #4559)
-#4565 := (or #1492 #4562)
-#4568 := (not #4565)
-#616 := (= #110 #158)
-#637 := (or #616 #636)
-#4481 := (forall (vars (?x46 T2)) (:pat #4403 #4454 #4480) #637)
-#4486 := (not #4481)
-#4571 := (or #4486 #4568)
-#4574 := (not #4571)
-decl ?x46!9 :: T2
-#2207 := ?x46!9
-#2212 := (uf_4 uf_14 ?x46!9)
-#2211 := (uf_18 ?x46!9)
-#2825 := (= #2211 #2212)
-#2208 := (uf_6 uf_17 ?x46!9)
-#2209 := (= uf_8 #2208)
-#2210 := (not #2209)
-#2831 := (or #2210 #2825)
-#2836 := (not #2831)
-#4577 := (or #2836 #4574)
-#4580 := (not #4577)
-#1480 := (* -1::int #158)
-#1481 := (+ #110 #1480)
-#1479 := (>= #1481 0::int)
-#4472 := (forall (vars (?x45 T2)) (:pat #4403 #4454) #1479)
-#4477 := (not #4472)
-#4583 := (or #4477 #4580)
-#4586 := (not #4583)
-decl ?x45!8 :: T2
-#2189 := ?x45!8
-#2192 := (uf_4 uf_14 ?x45!8)
-#2815 := (* -1::int #2192)
-#2190 := (uf_18 ?x45!8)
-#2816 := (+ #2190 #2815)
-#2817 := (<= #2816 0::int)
-#2822 := (not #2817)
-#4589 := (or #2822 #4586)
-#4592 := (not #4589)
-decl uf_16 :: T2
-#140 := uf_16
-#152 := (uf_1 uf_16 #11)
-#4455 := (pattern #152)
-#153 := (uf_10 #152)
-#1623 := (+ #153 #1480)
-#144 := (uf_4 uf_14 uf_16)
-#1624 := (+ #144 #1623)
-#1625 := (= #1624 0::int)
-#1450 := (* -1::int #153)
-#1457 := (+ uf_9 #1450)
-#1458 := (<= #1457 0::int)
-#1449 := (* -1::int #144)
-#1451 := (+ #1449 #1450)
-#1452 := (+ #110 #1451)
-#1453 := (<= #1452 0::int)
-#3375 := (or #1453 #1458 #1625)
-#4464 := (forall (vars (?x43 T2)) (:pat #4403 #4455 #4454) #3375)
-#4469 := (not #4464)
-#3355 := (or #1453 #1458)
-#3356 := (not #3355)
-#3359 := (or #616 #3356)
-#4456 := (forall (vars (?x44 T2)) (:pat #4403 #4454 #4455) #3359)
-#4461 := (not #4456)
-decl ?x41!16 :: T2
-#2408 := ?x41!16
-#2414 := (uf_6 uf_15 ?x41!16)
-#2415 := (= uf_8 #2414)
-#2409 := (uf_4 uf_14 ?x41!16)
-#2410 := (* -1::int #2409)
-#2411 := (+ uf_9 #2410)
-#2412 := (<= #2411 0::int)
-#1655 := (+ uf_9 #1449)
-#1656 := (<= #1655 0::int)
-#1638 := (+ #110 #1449)
-#1637 := (>= #1638 0::int)
-#1644 := (or #505 #1637)
-#4446 := (forall (vars (?x42 T2)) (:pat #4445 #4403) #1644)
-#4451 := (not #4446)
-#141 := (uf_6 uf_15 uf_16)
-#585 := (= uf_8 #141)
-decl uf_7 :: (-> T4 T2 T5 T4)
-#150 := (uf_7 uf_15 uf_16 uf_8)
-#151 := (= uf_17 #150)
-#876 := (not #151)
-#4595 := (or #876 #585 #4451 #1656 #2412 #2415 #4461 #4469 #4592)
-#4598 := (not #4595)
-#4671 := (or #4598 #4668)
-#4674 := (not #4671)
-#2152 := (?x40!7 #11)
-#2155 := (uf_1 #2152 #11)
-#2156 := (uf_10 #2155)
-#2790 := (* -1::int #2156)
-#2153 := (uf_4 uf_14 #2152)
-#2773 := (* -1::int #2153)
-#2791 := (+ #2773 #2790)
-#2792 := (+ #110 #2791)
-#2793 := (= #2792 0::int)
-#3339 := (not #2793)
-#2774 := (+ #110 #2773)
-#2775 := (<= #2774 0::int)
-#2161 := (uf_6 uf_15 #2152)
-#2162 := (= uf_8 #2161)
-#3338 := (not #2162)
-#3340 := (or #3338 #2775 #3339)
-#3341 := (not #3340)
-#3347 := (or #68 #1406 #3341)
-#4437 := (forall (vars (?x39 T2)) (:pat #4403) #3347)
-#4442 := (not #4437)
-decl uf_12 :: (-> T2 int)
-#69 := (uf_12 #11)
-#4355 := (pattern #69)
-decl ?x33!6 :: (-> T2 T2)
-#2123 := (?x33!6 #11)
-#2127 := (uf_12 #2123)
-#2728 := (* -1::int #2127)
-#2124 := (uf_1 #2123 #11)
-#2125 := (uf_10 #2124)
-#2745 := (* -1::int #2125)
-#2746 := (+ #2745 #2728)
-#2747 := (+ #69 #2746)
-#2748 := (= #2747 0::int)
-#3311 := (not #2748)
-#2729 := (+ #69 #2728)
-#2730 := (<= #2729 0::int)
-decl up_13 :: (-> T2 bool)
-#2133 := (up_13 #2123)
-#3310 := (not #2133)
-#3312 := (or #3310 #2730 #3311)
-#3313 := (not #3312)
-#1386 := (* -1::int #69)
-#1387 := (+ uf_9 #1386)
-#1388 := (<= #1387 0::int)
-#3319 := (or #68 #1388 #3313)
-#4429 := (forall (vars (?x32 T2)) (:pat #4355) #3319)
-#4434 := (not #4429)
-#114 := (uf_6 uf_15 #10)
-#4420 := (pattern #114 #116)
-#120 := (uf_4 uf_14 #10)
-#1417 := (* -1::int #120)
-#1418 := (+ #110 #1417)
-#1416 := (>= #1418 0::int)
-#502 := (= uf_8 #114)
-#3276 := (not #502)
-#3291 := (or #3276 #505 #1416)
-#4421 := (forall (vars (?x35 T2) (?x36 T2)) (:pat #4420) #3291)
-#4426 := (not #4421)
-#1424 := (+ #91 #1418)
-#1815 := (>= #1424 0::int)
-#508 := (not #505)
-#3268 := (or #508 #1347 #1815)
-#4412 := (forall (vars (?x37 T2) (?x38 T2)) (:pat #4379) #3268)
-#4417 := (not #4412)
-#4409 := (not #4404)
-#108 := (uf_4 uf_14 uf_11)
-#109 := (= #108 0::int)
-#1854 := (not #109)
-#4677 := (or #1854 #4409 #4417 #4426 #4434 #4442 #4674)
-#4680 := (not #4677)
-decl ?x32!5 :: T2
-#2081 := ?x32!5
-#2091 := (uf_1 #11 ?x32!5)
-#4388 := (pattern #2091)
-#77 := (up_13 #11)
-#4348 := (pattern #77)
-#2082 := (uf_12 ?x32!5)
-#2083 := (* -1::int #2082)
-#2096 := (+ #69 #2083)
-#2097 := (>= #2096 0::int)
-#2092 := (uf_10 #2091)
-#2093 := (+ #2083 #2092)
-#2094 := (+ #69 #2093)
-#2095 := (= #2094 0::int)
-#3229 := (not #2095)
-#78 := (not #77)
-#3230 := (or #78 #3229 #2097)
-#4389 := (forall (vars (?x33 T2)) (:pat #4348 #4355 #4388) #3230)
-#4394 := (not #4389)
-#2688 := (= uf_11 ?x32!5)
-#2084 := (+ uf_9 #2083)
-#2085 := (<= #2084 0::int)
-#4397 := (or #2085 #2688 #4394)
-#4400 := (not #4397)
-#4683 := (or #4400 #4680)
-#4686 := (not #4683)
-#86 := (uf_12 #10)
-#1323 := (* -1::int #86)
-#1344 := (+ #1323 #91)
-#1345 := (+ #69 #1344)
-#1342 := (>= #1345 0::int)
-#3221 := (or #78 #1342 #1347)
-#4380 := (forall (vars (?x30 T2) (?x31 T2)) (:pat #4379) #3221)
-#4385 := (not #4380)
-#4689 := (or #4385 #4686)
-#4692 := (not #4689)
-decl ?x31!3 :: T2
-#2051 := ?x31!3
-#2065 := (uf_12 ?x31!3)
-decl ?x30!4 :: T2
-#2052 := ?x30!4
-#2062 := (uf_12 ?x30!4)
-#2063 := (* -1::int #2062)
-#2660 := (+ #2063 #2065)
-#2053 := (uf_1 ?x31!3 ?x30!4)
-#2054 := (uf_10 #2053)
-#2661 := (+ #2054 #2660)
-#2664 := (>= #2661 0::int)
-#2059 := (up_13 ?x31!3)
-#3184 := (not #2059)
-#2055 := (* -1::int #2054)
-#2056 := (+ uf_9 #2055)
-#2057 := (<= #2056 0::int)
-#3199 := (or #2057 #3184 #2664)
-#3204 := (not #3199)
-#4695 := (or #3204 #4692)
-#4698 := (not #4695)
-#84 := (up_13 #10)
-#4370 := (pattern #77 #84)
-#1324 := (+ #69 #1323)
-#1322 := (>= #1324 0::int)
-#2632 := (not #84)
-#3176 := (or #77 #2632 #1322)
-#4371 := (forall (vars (?x28 T2) (?x29 T2)) (:pat #4370) #3176)
-#4376 := (not #4371)
-#4701 := (or #4376 #4698)
-#4704 := (not #4701)
-decl ?x29!1 :: T2
-#2026 := ?x29!1
-#2030 := (uf_12 ?x29!1)
-#2647 := (* -1::int #2030)
-decl ?x28!2 :: T2
-#2027 := ?x28!2
-#2028 := (uf_12 ?x28!2)
-#2648 := (+ #2028 #2647)
-#2649 := (<= #2648 0::int)
-#2034 := (up_13 ?x29!1)
-#2033 := (up_13 ?x28!2)
-#2266 := (not #2033)
-#2166 := (or #2266 #2034 #2649)
-#6004 := [hypothesis]: #2033
-#4349 := (forall (vars (?x26 T2)) (:pat #4348) #78)
-#79 := (forall (vars (?x26 T2)) #78)
-#4352 := (iff #79 #4349)
-#4350 := (iff #78 #78)
-#4351 := [refl]: #4350
-#4353 := [quant-intro #4351]: #4352
-#1965 := (~ #79 #79)
-#2002 := (~ #78 #78)
-#2003 := [refl]: #2002
-#1966 := [nnf-pos #2003]: #1965
-#70 := (= #69 0::int)
-#73 := (not #68)
-#1912 := (or #73 #70)
-#1915 := (forall (vars (?x24 T2)) #1912)
-#1918 := (not #1915)
-#1846 := (forall (vars (?x34 T2)) #1843)
-#1849 := (not #1846)
-#511 := (and #502 #508)
-#517 := (not #511)
-#1832 := (or #517 #1416)
-#1837 := (forall (vars (?x35 T2) (?x36 T2)) #1832)
-#1840 := (not #1837)
-#1348 := (not #1347)
-#1807 := (and #505 #1348)
-#1812 := (not #1807)
-#1818 := (or #1812 #1815)
-#1821 := (forall (vars (?x37 T2) (?x38 T2)) #1818)
-#1824 := (not #1821)
-#1710 := (not #1709)
-#1744 := (and #1348 #1710)
-#1747 := (not #1744)
-#1753 := (or #1747 #1750)
-#1756 := (forall (vars (?x66 T2) (?x67 T2)) #1753)
-#1759 := (not #1756)
-#1767 := (or #251 #1759)
-#1772 := (and #1756 #1767)
-#1725 := (= #1727 0::int)
-#1719 := (>= #1721 0::int)
-#1722 := (not #1719)
-#1729 := (and #1722 #1725)
-#1732 := (exists (vars (?x65 T2)) #1729)
-#1713 := (and #73 #1710)
-#1716 := (not #1713)
-#1735 := (or #1716 #1732)
-#1738 := (forall (vars (?x64 T2)) #1735)
-#1741 := (not #1738)
-#1775 := (or #1741 #1772)
-#1778 := (and #1738 #1775)
-#1407 := (not #1406)
-#1670 := (and #508 #1407)
-#1675 := (exists (vars (?x41 T2)) #1670)
-#1796 := (or #1062 #1044 #1071 #1053 #1675 #1778)
-#1678 := (not #1675)
-#1649 := (forall (vars (?x42 T2)) #1644)
-#1652 := (not #1649)
-#1459 := (not #1458)
-#1454 := (not #1453)
-#1462 := (and #1454 #1459)
-#1620 := (not #1462)
-#1628 := (or #1620 #1625)
-#1631 := (forall (vars (?x43 T2)) #1628)
-#1634 := (not #1631)
-#1561 := (= #1536 0::int)
-#1558 := (not #1504)
-#1570 := (and #630 #1558 #1561)
-#1575 := (exists (vars (?x53 T2)) #1570)
-#1547 := (+ uf_9 #1480)
-#1548 := (<= #1547 0::int)
-#1549 := (not #1548)
-#1552 := (and #73 #1549)
-#1555 := (not #1552)
-#1578 := (or #1555 #1575)
-#1581 := (forall (vars (?x52 T2)) #1578)
-#1526 := (and #630 #1348)
-#1531 := (not #1526)
-#1538 := (or #1531 #1534)
-#1541 := (forall (vars (?x50 T2) (?x51 T2)) #1538)
-#1544 := (not #1541)
-#1584 := (or #1544 #1581)
-#1587 := (and #1541 #1584)
-#656 := (and #636 #648)
-#664 := (not #656)
-#1512 := (or #664 #1504)
-#1517 := (forall (vars (?x48 T2) (?x49 T2)) #1512)
-#1520 := (not #1517)
-#1590 := (or #1520 #1587)
-#1593 := (and #1517 #1590)
-#1498 := (forall (vars (?x47 T2)) #1495)
-#1501 := (not #1498)
-#1596 := (or #1501 #1593)
-#1599 := (and #1498 #1596)
-#1602 := (or #1492 #1599)
-#1605 := (and #173 #1602)
-#642 := (forall (vars (?x46 T2)) #637)
-#824 := (not #642)
-#1608 := (or #824 #1605)
-#1611 := (and #642 #1608)
-#1484 := (forall (vars (?x45 T2)) #1479)
-#1487 := (not #1484)
-#1614 := (or #1487 #1611)
-#1617 := (and #1484 #1614)
-#1468 := (or #616 #1462)
-#1473 := (forall (vars (?x44 T2)) #1468)
-#1476 := (not #1473)
-#1702 := (or #876 #585 #1476 #1617 #1634 #1652 #1656 #1678)
-#1801 := (and #1702 #1796)
-#1422 := (= #1424 0::int)
-#1419 := (not #1416)
-#1432 := (and #505 #1419 #1422)
-#1437 := (exists (vars (?x40 T2)) #1432)
-#1410 := (and #73 #1407)
-#1413 := (not #1410)
-#1440 := (or #1413 #1437)
-#1443 := (forall (vars (?x39 T2)) #1440)
-#1446 := (not #1443)
-#1389 := (not #1388)
-#1392 := (and #73 #1389)
-#1395 := (not #1392)
-#1370 := (= #1345 0::int)
-#1366 := (not #1322)
-#1378 := (and #77 #1366 #1370)
-#1383 := (exists (vars (?x33 T2)) #1378)
-#1398 := (or #1383 #1395)
-#1401 := (forall (vars (?x32 T2)) #1398)
-#1857 := (not #1401)
-#1878 := (or #1854 #1857 #1446 #1801 #1824 #1840 #1849)
-#1883 := (and #1401 #1878)
-#1351 := (and #77 #1348)
-#1354 := (not #1351)
-#1357 := (or #1342 #1354)
-#1360 := (forall (vars (?x30 T2) (?x31 T2)) #1357)
-#1363 := (not #1360)
-#1886 := (or #1363 #1883)
-#1889 := (and #1360 #1886)
-#454 := (and #78 #84)
-#460 := (not #454)
-#1329 := (or #460 #1322)
-#1334 := (forall (vars (?x28 T2) (?x29 T2)) #1329)
-#1337 := (not #1334)
-#1892 := (or #1337 #1889)
-#1895 := (and #1334 #1892)
-#1313 := (>= #69 0::int)
-#1314 := (forall (vars (?x27 T2)) #1313)
-#1317 := (not #1314)
-#1898 := (or #1317 #1895)
-#1901 := (and #1314 #1898)
-#80 := (uf_12 uf_11)
-#81 := (= #80 0::int)
-#1308 := (not #81)
-#1904 := (or #1308 #1901)
-#1907 := (and #81 #1904)
-#437 := (= uf_9 #69)
-#443 := (or #68 #437)
-#448 := (forall (vars (?x25 T2)) #443)
-#1277 := (not #448)
-#1268 := (not #79)
-#1930 := (or #1268 #1277 #1907 #1918)
-#1935 := (not #1930)
-#82 := (<= 0::int #69)
-#83 := (forall (vars (?x27 T2)) #82)
-#87 := (<= #86 #69)
-#85 := (and #84 #78)
-#88 := (implies #85 #87)
-#89 := (forall (vars (?x28 T2) (?x29 T2)) #88)
-#94 := (+ #69 #91)
-#95 := (<= #86 #94)
-#92 := (< #91 uf_9)
-#93 := (and #92 #77)
-#96 := (implies #93 #95)
-#97 := (forall (vars (?x30 T2) (?x31 T2)) #96)
-#101 := (< #69 #86)
-#102 := (and #77 #101)
-#100 := (= #86 #94)
-#103 := (and #100 #102)
-#104 := (exists (vars (?x33 T2)) #103)
-#98 := (< #69 uf_9)
-#99 := (and #98 #73)
-#105 := (implies #99 #104)
-#106 := (forall (vars (?x32 T2)) #105)
-#241 := (< #235 #238)
-#239 := (+ #235 #91)
-#240 := (= #238 #239)
-#242 := (and #240 #241)
-#243 := (exists (vars (?x65 T2)) #242)
-#236 := (< #235 uf_9)
-#237 := (and #236 #73)
-#244 := (implies #237 #243)
-#245 := (forall (vars (?x64 T2)) #244)
-#247 := (<= #238 #239)
-#246 := (and #92 #236)
-#248 := (implies #246 #247)
-#249 := (forall (vars (?x66 T2) (?x67 T2)) #248)
-#1 := true
-#252 := (implies #251 true)
-#253 := (and #252 #251)
-#254 := (implies #249 #253)
-#255 := (and #254 #249)
-#256 := (implies #245 #255)
-#257 := (and #256 #245)
-#258 := (implies true #257)
-#259 := (implies #234 #258)
-#231 := (= uf_22 uf_14)
-#260 := (implies #231 #259)
-#261 := (implies #229 #260)
-#226 := (= uf_19 uf_15)
-#262 := (implies #226 #261)
-#263 := (implies true #262)
-#264 := (implies true #263)
-#117 := (= #116 uf_8)
-#118 := (not #117)
-#129 := (< #110 uf_9)
-#138 := (and #129 #118)
-#139 := (exists (vars (?x41 T2)) #138)
-#224 := (not #139)
-#265 := (implies #224 #264)
-#266 := (implies true #265)
-#267 := (implies true #266)
-#166 := (<= #158 #110)
-#167 := (forall (vars (?x45 T2)) #166)
-#163 := (= #158 #110)
-#169 := (= #168 uf_8)
-#170 := (implies #169 #163)
-#171 := (forall (vars (?x46 T2)) #170)
-#174 := (<= 0::int #158)
-#175 := (forall (vars (?x47 T2)) #174)
-#181 := (<= #180 #158)
-#178 := (not #169)
-#177 := (= #176 uf_8)
-#179 := (and #177 #178)
-#182 := (implies #179 #181)
-#183 := (forall (vars (?x48 T2) (?x49 T2)) #182)
-#185 := (+ #158 #91)
-#186 := (<= #180 #185)
-#184 := (and #92 #169)
-#187 := (implies #184 #186)
-#188 := (forall (vars (?x50 T2) (?x51 T2)) #187)
-#192 := (< #158 #180)
-#193 := (and #169 #192)
-#191 := (= #180 #185)
-#194 := (and #191 #193)
-#195 := (exists (vars (?x53 T2)) #194)
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-#1680 := [monotonicity #1677]: #1679
-#1701 := [monotonicity #1680 #1698]: #1700
-#1706 := [trans #1701 #1704]: #1705
-#1803 := [monotonicity #1706 #1800]: #1802
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-#1441 := (iff #571 #1440)
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-#1421 := [rewrite]: #1420
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-#1431 := [monotonicity #1425 #1428]: #1430
-#1436 := [trans #1431 #1434]: #1435
-#1439 := [quant-intro #1436]: #1438
-#1414 := (iff #570 #1413)
-#1411 := (iff #547 #1410)
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-#1415 := [monotonicity #1412]: #1414
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-#1445 := [quant-intro #1442]: #1444
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-#1825 := (iff #1129 #1824)
-#1822 := (iff #544 #1821)
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-#1817 := [rewrite]: #1816
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-#1810 := (iff #526 #1807)
-#1804 := (and #1348 #505)
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-#1809 := [rewrite]: #1808
-#1805 := (iff #526 #1804)
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-#1811 := [trans #1806 #1809]: #1810
-#1814 := [monotonicity #1811]: #1813
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-#1823 := [quant-intro #1820]: #1822
-#1826 := [monotonicity #1823]: #1825
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-#1829 := (or #1416 #517)
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-#1834 := [rewrite]: #1833
-#1830 := (iff #518 #1829)
-#1827 := (iff #121 #1416)
-#1828 := [rewrite]: #1827
-#1831 := [monotonicity #1828]: #1830
-#1836 := [trans #1831 #1834]: #1835
-#1839 := [quant-intro #1836]: #1838
-#1842 := [monotonicity #1839]: #1841
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-#1850 := (iff #1147 #1849)
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-#1845 := [rewrite]: #1844
-#1848 := [quant-intro #1845]: #1847
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-#1856 := [monotonicity #1853]: #1855
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-#1399 := (iff #491 #1398)
-#1396 := (iff #490 #1395)
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-#1394 := [monotonicity #1391]: #1393
-#1397 := [monotonicity #1394]: #1396
-#1384 := (iff #104 #1383)
-#1381 := (iff #103 #1378)
-#1372 := (and #77 #1366)
-#1375 := (and #1370 #1372)
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-#1380 := [rewrite]: #1379
-#1376 := (iff #103 #1375)
-#1373 := (iff #102 #1372)
-#1367 := (iff #101 #1366)
-#1368 := [rewrite]: #1367
-#1374 := [monotonicity #1368]: #1373
-#1369 := (iff #100 #1370)
-#1371 := [rewrite]: #1369
-#1377 := [monotonicity #1371 #1374]: #1376
-#1382 := [trans #1377 #1380]: #1381
-#1385 := [quant-intro #1382]: #1384
-#1400 := [monotonicity #1385 #1397]: #1399
-#1403 := [quant-intro #1400]: #1402
-#1859 := [monotonicity #1403]: #1858
-#1877 := [monotonicity #1859 #1874]: #1876
-#1882 := [trans #1877 #1880]: #1881
-#1885 := [monotonicity #1403 #1882]: #1884
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-#1361 := (iff #481 #1360)
-#1358 := (iff #476 #1357)
-#1355 := (iff #475 #1354)
-#1352 := (iff #469 #1351)
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-#1340 := [rewrite]: #1341
-#1359 := [monotonicity #1340 #1356]: #1358
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-#1365 := [monotonicity #1362]: #1364
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-#1891 := [monotonicity #1362 #1888]: #1890
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-#1331 := [rewrite]: #1330
-#1327 := (iff #461 #1326)
-#1321 := (iff #87 #1322)
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-#1328 := [monotonicity #1325]: #1327
-#1333 := [trans #1328 #1331]: #1332
-#1336 := [quant-intro #1333]: #1335
-#1339 := [monotonicity #1336]: #1338
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-#1897 := [monotonicity #1336 #1894]: #1896
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-#1315 := (iff #83 #1314)
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-#1312 := [rewrite]: #1311
-#1316 := [quant-intro #1312]: #1315
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-#1910 := (iff #423 #70)
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-#1914 := [monotonicity #1911]: #1913
-#1917 := [quant-intro #1914]: #1916
-#1920 := [monotonicity #1917]: #1919
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-#1937 := [monotonicity #1934]: #1936
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-#1247 := [rewrite]: #1246
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-#462 := (iff #457 #461)
-#463 := [rewrite]: #462
-#458 := (iff #88 #457)
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-#456 := [rewrite]: #455
-#459 := [monotonicity #456]: #458
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-#477 := (iff #472 #476)
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-#488 := (iff #105 #487)
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-#486 := [rewrite]: #485
-#489 := [monotonicity #486]: #488
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