--- a/Admin/components/components.sha1 Thu Mar 13 16:28:25 2014 +0100
+++ b/Admin/components/components.sha1 Thu Mar 13 16:39:08 2014 +0100
@@ -80,3 +80,4 @@
3a8f77822278fe9250890e357248bc678d8fac95 z3-3.2-1.tar.gz
12ae71acde43bd7bed1e005c43034b208c0cba4c z3-3.2.tar.gz
d94a716502c8503d63952bcb4d4176fac8b28704 z3-4.0.tar.gz
+86e721296c400ada440e4a9ce11b9e845eec9e25 z3-4.3.0.tar.gz
--- a/Admin/components/main Thu Mar 13 16:28:25 2014 +0100
+++ b/Admin/components/main Thu Mar 13 16:39:08 2014 +0100
@@ -11,5 +11,6 @@
scala-2.10.3
spass-3.8ds
z3-3.2-1
+z3-4.3.0
xz-java-1.2-1
-ProofGeneral-4.2-1
\ No newline at end of file
+ProofGeneral-4.2-1
--- a/etc/isar-keywords.el Thu Mar 13 16:28:25 2014 +0100
+++ b/etc/isar-keywords.el Thu Mar 13 16:39:08 2014 +0100
@@ -244,6 +244,7 @@
"sledgehammer"
"sledgehammer_params"
"smt_status"
+ "smt2_status"
"solve_direct"
"sorry"
"spark_end"
@@ -447,6 +448,7 @@
"refute"
"sledgehammer"
"smt_status"
+ "smt2_status"
"solve_direct"
"spark_status"
"term"
--- a/src/HOL/Lifting_Option.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Lifting_Option.thy Thu Mar 13 16:39:08 2014 +0100
@@ -17,8 +17,8 @@
| _ \<Rightarrow> False)"
by (auto split: prod.split option.split)
-abbreviation (input) option_pred :: "('a \<Rightarrow> bool) \<Rightarrow> 'a option \<Rightarrow> bool" where
- "option_pred \<equiv> case_option True"
+abbreviation (input) pred_option :: "('a \<Rightarrow> bool) \<Rightarrow> 'a option \<Rightarrow> bool" where
+ "pred_option \<equiv> case_option True"
lemma rel_option_eq [relator_eq]:
"rel_option (op =) = (op =)"
@@ -35,7 +35,7 @@
lemma Domainp_option[relator_domain]:
assumes "Domainp A = P"
- shows "Domainp (rel_option A) = (option_pred P)"
+ shows "Domainp (rel_option A) = (pred_option P)"
using assms unfolding Domainp_iff[abs_def] rel_option_iff[abs_def]
by (auto iff: fun_eq_iff split: option.split)
@@ -64,7 +64,7 @@
unfolding bi_unique_def split_option_all by simp
lemma option_invariant_commute [invariant_commute]:
- "rel_option (Lifting.invariant P) = Lifting.invariant (option_pred P)"
+ "rel_option (Lifting.invariant P) = Lifting.invariant (pred_option P)"
by (auto simp add: fun_eq_iff Lifting.invariant_def split_option_all)
subsection {* Quotient theorem for the Lifting package *}
--- a/src/HOL/Lifting_Product.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Lifting_Product.thy Thu Mar 13 16:39:08 2014 +0100
@@ -10,12 +10,12 @@
subsection {* Relator and predicator properties *}
-definition prod_pred :: "('a \<Rightarrow> bool) \<Rightarrow> ('b \<Rightarrow> bool) \<Rightarrow> 'a \<times> 'b \<Rightarrow> bool"
-where "prod_pred R1 R2 = (\<lambda>(a, b). R1 a \<and> R2 b)"
+definition pred_prod :: "('a \<Rightarrow> bool) \<Rightarrow> ('b \<Rightarrow> bool) \<Rightarrow> 'a \<times> 'b \<Rightarrow> bool"
+where "pred_prod R1 R2 = (\<lambda>(a, b). R1 a \<and> R2 b)"
-lemma prod_pred_apply [simp]:
- "prod_pred P1 P2 (a, b) \<longleftrightarrow> P1 a \<and> P2 b"
- by (simp add: prod_pred_def)
+lemma pred_prod_apply [simp]:
+ "pred_prod P1 P2 (a, b) \<longleftrightarrow> P1 a \<and> P2 b"
+ by (simp add: pred_prod_def)
lemmas rel_prod_eq[relator_eq] = prod.rel_eq
lemmas rel_prod_mono[relator_mono] = prod.rel_mono
@@ -27,8 +27,8 @@
lemma Domainp_prod[relator_domain]:
assumes "Domainp T1 = P1"
assumes "Domainp T2 = P2"
- shows "Domainp (rel_prod T1 T2) = (prod_pred P1 P2)"
-using assms unfolding rel_prod_def prod_pred_def by blast
+ shows "Domainp (rel_prod T1 T2) = (pred_prod P1 P2)"
+using assms unfolding rel_prod_def pred_prod_def by blast
lemma left_total_rel_prod [reflexivity_rule]:
assumes "left_total R1"
@@ -62,8 +62,8 @@
using assms unfolding bi_unique_def rel_prod_def by auto
lemma prod_invariant_commute [invariant_commute]:
- "rel_prod (Lifting.invariant P1) (Lifting.invariant P2) = Lifting.invariant (prod_pred P1 P2)"
- by (simp add: fun_eq_iff rel_prod_def prod_pred_def Lifting.invariant_def) blast
+ "rel_prod (Lifting.invariant P1) (Lifting.invariant P2) = Lifting.invariant (pred_prod P1 P2)"
+ by (simp add: fun_eq_iff rel_prod_def pred_prod_def Lifting.invariant_def) blast
subsection {* Quotient theorem for the Lifting package *}
@@ -109,4 +109,3 @@
end
end
-
--- a/src/HOL/List.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/List.thy Thu Mar 13 16:39:08 2014 +0100
@@ -1299,7 +1299,7 @@
case (snoc a xs)
show ?case
proof cases
- assume "x = a" thus ?case using snoc by (metis set_simps(1) emptyE)
+ assume "x = a" thus ?case using snoc by (auto intro!: exI)
next
assume "x \<noteq> a" thus ?case using snoc by fastforce
qed
@@ -1332,7 +1332,8 @@
show ?case
proof cases
assume "P x"
- thus ?thesis by simp (metis Un_upper1 contra_subsetD in_set_conv_decomp_first self_append_conv2 set_append)
+ hence "x # xs = [] @ x # xs \<and> P x \<and> (\<forall>y\<in>set []. \<not> P y)" by simp
+ thus ?thesis by fast
next
assume "\<not> P x"
hence "\<exists>x\<in>set xs. P x" using Cons(2) by simp
@@ -1359,7 +1360,7 @@
case (snoc x xs)
show ?case
proof cases
- assume "P x" thus ?thesis by (metis emptyE set_empty)
+ assume "P x" thus ?thesis by (auto intro!: exI)
next
assume "\<not> P x"
hence "\<exists>x\<in>set xs. P x" using snoc(2) by simp
@@ -1375,7 +1376,8 @@
lemma split_list_last_prop_iff:
"(\<exists>x \<in> set xs. P x) \<longleftrightarrow>
(\<exists>ys x zs. xs = ys@x#zs \<and> P x \<and> (\<forall>z \<in> set zs. \<not> P z))"
-by (metis split_list_last_prop [where P=P] in_set_conv_decomp)
+ by rule (erule split_list_last_prop, auto)
+
lemma finite_list: "finite A ==> EX xs. set xs = A"
by (erule finite_induct) (auto simp add: set_simps(2) [symmetric] simp del: set_simps(2))
@@ -1773,7 +1775,7 @@
done
lemma list_update_nonempty[simp]: "xs[k:=x] = [] \<longleftrightarrow> xs=[]"
-by(metis length_0_conv length_list_update)
+by (simp only: length_0_conv[symmetric] length_list_update)
lemma list_update_same_conv:
"i < length xs ==> (xs[i := x] = xs) = (xs!i = x)"
@@ -1936,7 +1938,7 @@
lemma snoc_eq_iff_butlast:
"xs @ [x] = ys \<longleftrightarrow> (ys \<noteq> [] & butlast ys = xs & last ys = x)"
-by (metis append_butlast_last_id append_is_Nil_conv butlast_snoc last_snoc not_Cons_self)
+by fastforce
subsubsection {* @{const take} and @{const drop} *}
@@ -2121,8 +2123,7 @@
"m >= n \<Longrightarrow> set(drop m xs) <= set(drop n xs)"
apply(induct xs arbitrary: m n)
apply(auto simp:drop_Cons split:nat.split)
-apply (metis set_drop_subset subset_iff)
-done
+by (metis set_drop_subset subset_iff)
lemma in_set_takeD: "x : set(take n xs) \<Longrightarrow> x : set xs"
using set_take_subset by fast
@@ -3250,15 +3251,9 @@
apply (case_tac j)
apply (clarsimp simp add: set_conv_nth, simp)
apply (rule conjI)
-(*TOO SLOW
-apply (metis Zero_neq_Suc gr0_conv_Suc in_set_conv_nth lessI less_trans_Suc nth_Cons' nth_Cons_Suc)
-*)
apply (clarsimp simp add: set_conv_nth)
apply (erule_tac x = 0 in allE, simp)
apply (erule_tac x = "Suc i" in allE, simp, clarsimp)
-(*TOO SLOW
-apply (metis Suc_Suc_eq lessI less_trans_Suc nth_Cons_Suc)
-*)
apply (erule_tac x = "Suc i" in allE, simp)
apply (erule_tac x = "Suc j" in allE, simp)
done
@@ -3403,8 +3398,7 @@
lemma distinct_length_2_or_more:
"distinct (a # b # xs) \<longleftrightarrow> (a \<noteq> b \<and> distinct (a # xs) \<and> distinct (b # xs))"
-by (metis distinct.simps(2) list.sel(1) hd_in_set list.simps(2) set_ConsD set_rev_mp
- set_subset_Cons)
+by force
lemma remdups_adj_Cons: "remdups_adj (x # xs) =
(case remdups_adj xs of [] \<Rightarrow> [x] | y # xs \<Rightarrow> if x = y then y # xs else x # y # xs)"
@@ -3636,8 +3630,8 @@
case Nil thus ?case by simp
next
case (Cons x xs) thus ?case
- by(auto simp: nth_Cons' split: if_splits)
- (metis One_nat_def diff_Suc_1 less_Suc_eq_0_disj)
+ apply(auto simp: nth_Cons' split: if_splits)
+ using diff_Suc_1[unfolded One_nat_def] less_Suc_eq_0_disj by fastforce
qed
lemma find_cong[fundef_cong]:
@@ -3683,8 +3677,8 @@
(case List.extract P xs of
None \<Rightarrow> None |
Some (ys, y, zs) \<Rightarrow> Some (x#ys, y, zs)))"
-by(auto simp add: extract_def split: list.splits)
- (metis comp_def dropWhile_eq_Nil_conv list.distinct(1))
+by(auto simp add: extract_def comp_def split: list.splits)
+ (metis dropWhile_eq_Nil_conv list.distinct(1))
subsubsection {* @{const remove1} *}
@@ -3792,7 +3786,7 @@
lemma map_removeAll_inj: "inj f \<Longrightarrow>
map f (removeAll x xs) = removeAll (f x) (map f xs)"
-by(metis map_removeAll_inj_on subset_inj_on subset_UNIV)
+by (rule map_removeAll_inj_on, erule subset_inj_on, rule subset_UNIV)
subsubsection {* @{const replicate} *}
@@ -3962,7 +3956,7 @@
with * show ?thesis by blast
qed
then show ?case
- using xs'_def ys'_def by metis
+ using xs'_def ys'_def by meson
qed
lemma comm_append_is_replicate:
@@ -3974,7 +3968,7 @@
proof -
obtain m n zs where "concat (replicate m zs) = xs"
and "concat (replicate n zs) = ys"
- using assms by (metis comm_append_are_replicate)
+ using comm_append_are_replicate[of xs ys, OF assms] by blast
then have "m + n > 1" and "concat (replicate (m+n) zs) = xs @ ys"
using `xs \<noteq> []` and `ys \<noteq> []`
by (auto simp: replicate_add)
@@ -4511,10 +4505,11 @@
qed
lemma infinite_UNIV_listI: "~ finite(UNIV::'a list set)"
-apply(rule notI)
-apply(drule finite_maxlen)
-apply (metis UNIV_I length_replicate less_not_refl)
-done
+apply (rule notI)
+apply (drule finite_maxlen)
+apply clarsimp
+apply (erule_tac x = "replicate n undefined" in allE)
+by simp
subsection {* Sorting *}
@@ -4726,7 +4721,7 @@
proof(induct rule:list_induct2[OF 1])
case 1 show ?case by simp
next
- case 2 thus ?case by (simp add:sorted_Cons)
+ case 2 thus ?case by (simp add: sorted_Cons)
(metis Diff_insert_absorb antisym insertE insert_iff)
qed
qed
@@ -5660,10 +5655,10 @@
by (simp add: listrel1_def Cons_eq_append_conv) (blast)
lemma listrel1I1: "(x,y) \<in> r \<Longrightarrow> (x # xs, y # xs) \<in> listrel1 r"
-by (metis Cons_listrel1_Cons)
+by fast
lemma listrel1I2: "(xs, ys) \<in> listrel1 r \<Longrightarrow> (x # xs, x # ys) \<in> listrel1 r"
-by (metis Cons_listrel1_Cons)
+by fast
lemma append_listrel1I:
"(xs, ys) \<in> listrel1 r \<and> us = vs \<or> xs = ys \<and> (us, vs) \<in> listrel1 r
@@ -5757,8 +5752,8 @@
done
lemma wf_listrel1_iff[simp]: "wf(listrel1 r) = wf r"
-by(metis wf_acc_iff in_lists_conv_set lists_accI lists_accD Cons_in_lists_iff)
-
+by (auto simp: wf_acc_iff
+ intro: lists_accD lists_accI[THEN Cons_in_lists_iff[THEN iffD1, THEN conjunct1]])
subsubsection {* Lifting Relations to Lists: all elements *}
@@ -5901,7 +5896,7 @@
case base show ?case by(auto simp add: listrel_iff_zip set_zip)
next
case (step ys zs)
- thus ?case by (metis listrel_reflcl_if_listrel1 listrel_rtrancl_trans)
+ thus ?case by (metis listrel_reflcl_if_listrel1 listrel_rtrancl_trans)
qed
qed
qed
--- a/src/HOL/ROOT Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/ROOT Thu Mar 13 16:39:08 2014 +0100
@@ -777,7 +777,8 @@
"Boogie_Dijkstra.certs"
"Boogie_Max.certs"
"SMT_Examples.certs"
- "SMT_Word_Examples.certs"
+ "SMT_Examples.certs2"
+ "SMT_Word_Examples.certs2"
"VCC_Max.certs"
session "HOL-SPARK" (main) in "SPARK" = "HOL-Word" +
--- a/src/HOL/Real.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Real.thy Thu Mar 13 16:39:08 2014 +0100
@@ -2197,7 +2197,20 @@
times_real_inst.times_real uminus_real_inst.uminus_real
zero_real_inst.zero_real
+
+subsection {* Setup for SMT *}
+
ML_file "Tools/SMT/smt_real.ML"
setup SMT_Real.setup
+ML_file "Tools/SMT2/smt2_real.ML"
+ML_file "Tools/SMT2/z3_new_real.ML"
+
+lemma [z3_new_rule]:
+ "0 + (x::real) = x"
+ "x + 0 = x"
+ "0 * x = 0"
+ "1 * x = x"
+ "x + y = y + x"
+ by auto
end
--- a/src/HOL/Relation.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Relation.thy Thu Mar 13 16:39:08 2014 +0100
@@ -1135,7 +1135,4 @@
(auto simp: comp_fun_commute.fold_insert comp_fun_commute_relcomp_fold insert_relcomp_fold
cong: if_cong)
-
-
end
-
--- a/src/HOL/SMT.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/SMT.thy Thu Mar 13 16:39:08 2014 +0100
@@ -31,14 +31,13 @@
quantifier block.
*}
-datatype pattern = Pattern
+typedecl pattern
-definition pat :: "'a \<Rightarrow> pattern" where "pat _ = Pattern"
-definition nopat :: "'a \<Rightarrow> pattern" where "nopat _ = Pattern"
+consts
+ pat :: "'a \<Rightarrow> pattern"
+ nopat :: "'a \<Rightarrow> pattern"
-definition trigger :: "pattern list list \<Rightarrow> bool \<Rightarrow> bool"
-where "trigger _ P = P"
-
+definition trigger :: "pattern list list \<Rightarrow> bool \<Rightarrow> bool" where "trigger _ P = P"
subsection {* Quantifier weights *}
@@ -67,7 +66,6 @@
*}
-
subsection {* Higher-order encoding *}
text {*
@@ -88,7 +86,6 @@
fun_upd_upd fun_app_def
-
subsection {* First-order logic *}
text {*
@@ -107,7 +104,6 @@
definition term_false where "term_false = False"
-
subsection {* Integer division and modulo for Z3 *}
definition z3div :: "int \<Rightarrow> int \<Rightarrow> int" where
@@ -117,7 +113,6 @@
"z3mod k l = (if 0 \<le> l then k mod l else k mod (-l))"
-
subsection {* Setup *}
ML_file "Tools/SMT/smt_builtin.ML"
@@ -426,7 +421,7 @@
hide_type (open) pattern
-hide_const Pattern fun_app term_true term_false z3div z3mod
+hide_const fun_app term_true term_false z3div z3mod
hide_const (open) trigger pat nopat weight
end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT2.thy Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,445 @@
+(* Title: HOL/SMT2.thy
+ Author: Sascha Boehme, TU Muenchen
+*)
+
+header {* Bindings to Satisfiability Modulo Theories (SMT) solvers based on SMT-LIB 2 *}
+
+theory SMT2
+imports Record
+keywords "smt2_status" :: diag
+begin
+
+ML_file "Tools/SMT2/smt2_util.ML"
+ML_file "Tools/SMT2/smt2_failure.ML"
+ML_file "Tools/SMT2/smt2_config.ML"
+
+
+subsection {* Triggers for quantifier instantiation *}
+
+text {*
+Some SMT solvers support patterns as a quantifier instantiation
+heuristics. Patterns may either be positive terms (tagged by "pat")
+triggering quantifier instantiations -- when the solver finds a
+term matching a positive pattern, it instantiates the corresponding
+quantifier accordingly -- or negative terms (tagged by "nopat")
+inhibiting quantifier instantiations. A list of patterns
+of the same kind is called a multipattern, and all patterns in a
+multipattern are considered conjunctively for quantifier instantiation.
+A list of multipatterns is called a trigger, and their multipatterns
+act disjunctively during quantifier instantiation. Each multipattern
+should mention at least all quantified variables of the preceding
+quantifier block.
+*}
+
+typedecl pattern
+
+consts
+ pat :: "'a \<Rightarrow> pattern"
+ nopat :: "'a \<Rightarrow> pattern"
+
+definition trigger :: "pattern list list \<Rightarrow> bool \<Rightarrow> bool" where "trigger _ P = P"
+
+
+subsection {* Quantifier weights *}
+
+text {*
+Weight annotations to quantifiers influence the priority of quantifier
+instantiations. They should be handled with care for solvers, which support
+them, because incorrect choices of weights might render a problem unsolvable.
+*}
+
+definition weight :: "int \<Rightarrow> bool \<Rightarrow> bool" where "weight _ P = P"
+
+text {*
+Weights must be nonnegative. The value @{text 0} is equivalent to providing
+no weight at all.
+
+Weights should only be used at quantifiers and only inside triggers (if the
+quantifier has triggers). Valid usages of weights are as follows:
+
+\begin{itemize}
+\item
+@{term "\<forall>x. trigger [[pat (P x)]] (weight 2 (P x))"}
+\item
+@{term "\<forall>x. weight 3 (P x)"}
+\end{itemize}
+*}
+
+
+subsection {* Higher-order encoding *}
+
+text {*
+Application is made explicit for constants occurring with varying
+numbers of arguments. This is achieved by the introduction of the
+following constant.
+*}
+
+definition fun_app :: "'a \<Rightarrow> 'a" where "fun_app f = f"
+
+text {*
+Some solvers support a theory of arrays which can be used to encode
+higher-order functions. The following set of lemmas specifies the
+properties of such (extensional) arrays.
+*}
+
+lemmas array_rules = ext fun_upd_apply fun_upd_same fun_upd_other fun_upd_upd fun_app_def
+
+
+subsection {* Normalization *}
+
+lemma case_bool_if[abs_def]: "case_bool x y P = (if P then x else y)"
+ by simp
+
+lemma nat_int': "\<forall>n. nat (int n) = n" by simp
+lemma int_nat_nneg: "\<forall>i. i \<ge> 0 \<longrightarrow> int (nat i) = i" by simp
+lemma int_nat_neg: "\<forall>i. i < 0 \<longrightarrow> int (nat i) = 0" by simp
+
+lemma nat_zero_as_int: "0 = nat 0" by (rule transfer_nat_int_numerals(1))
+lemma nat_one_as_int: "1 = nat 1" by (rule transfer_nat_int_numerals(2))
+lemma nat_numeral_as_int: "numeral = (\<lambda>i. nat (numeral i))" by simp
+lemma nat_less_as_int: "op < = (\<lambda>a b. int a < int b)" by simp
+lemma nat_leq_as_int: "op \<le> = (\<lambda>a b. int a <= int b)" by simp
+lemma Suc_as_int: "Suc = (\<lambda>a. nat (int a + 1))" by (rule ext) simp
+lemma nat_plus_as_int: "op + = (\<lambda>a b. nat (int a + int b))" by (rule ext)+ simp
+lemma nat_minus_as_int: "op - = (\<lambda>a b. nat (int a - int b))" by (rule ext)+ simp
+lemma nat_times_as_int: "op * = (\<lambda>a b. nat (int a * int b))" by (simp add: nat_mult_distrib)
+lemma nat_div_as_int: "op div = (\<lambda>a b. nat (int a div int b))" by (simp add: nat_div_distrib)
+lemma nat_mod_as_int: "op mod = (\<lambda>a b. nat (int a mod int b))" by (simp add: nat_mod_distrib)
+
+lemma int_Suc: "int (Suc n) = int n + 1" by simp
+lemma int_plus: "int (n + m) = int n + int m" by (rule of_nat_add)
+lemma int_minus: "int (n - m) = int (nat (int n - int m))" by auto
+
+lemmas Ex1_def_raw = Ex1_def[abs_def]
+lemmas Ball_def_raw = Ball_def[abs_def]
+lemmas Bex_def_raw = Bex_def[abs_def]
+lemmas abs_if_raw = abs_if[abs_def]
+lemmas min_def_raw = min_def[abs_def]
+lemmas max_def_raw = max_def[abs_def]
+
+
+subsection {* Integer division and modulo for Z3 *}
+
+text {*
+The following Z3-inspired definitions are overspecified for the case where @{text "l = 0"}. This
+Schönheitsfehler is corrected in the @{text div_as_z3div} and @{text mod_as_z3mod} theorems.
+*}
+
+definition z3div :: "int \<Rightarrow> int \<Rightarrow> int" where
+ "z3div k l = (if l \<ge> 0 then k div l else - (k div - l))"
+
+definition z3mod :: "int \<Rightarrow> int \<Rightarrow> int" where
+ "z3mod k l = k mod (if l \<ge> 0 then l else - l)"
+
+lemma div_as_z3div:
+ "\<forall>k l. k div l = (if l = 0 then 0 else if l > 0 then z3div k l else z3div (- k) (- l))"
+ by (simp add: z3div_def)
+
+lemma mod_as_z3mod:
+ "\<forall>k l. k mod l = (if l = 0 then k else if l > 0 then z3mod k l else - z3mod (- k) (- l))"
+ by (simp add: z3mod_def)
+
+
+subsection {* Setup *}
+
+ML_file "Tools/SMT2/smt2_builtin.ML"
+ML_file "Tools/SMT2/smt2_datatypes.ML"
+ML_file "Tools/SMT2/smt2_normalize.ML"
+ML_file "Tools/SMT2/smt2_translate.ML"
+ML_file "Tools/SMT2/smtlib2.ML"
+ML_file "Tools/SMT2/smtlib2_interface.ML"
+ML_file "Tools/SMT2/z3_new_model.ML"
+ML_file "Tools/SMT2/z3_new_proof.ML"
+ML_file "Tools/SMT2/smt2_solver.ML"
+ML_file "Tools/SMT2/z3_new_isar.ML"
+ML_file "Tools/SMT2/z3_new_interface.ML"
+ML_file "Tools/SMT2/z3_new_replay_util.ML"
+ML_file "Tools/SMT2/z3_new_replay_literals.ML"
+ML_file "Tools/SMT2/z3_new_replay_rules.ML"
+ML_file "Tools/SMT2/z3_new_replay_methods.ML"
+ML_file "Tools/SMT2/z3_new_replay.ML"
+ML_file "Tools/SMT2/smt2_systems.ML"
+
+method_setup smt2 = {*
+ Scan.optional Attrib.thms [] >>
+ (fn thms => fn ctxt =>
+ METHOD (fn facts => HEADGOAL (SMT2_Solver.smt2_tac ctxt (thms @ facts))))
+*} "apply an SMT solver to the current goal (based on SMT-LIB 2)"
+
+
+subsection {* Configuration *}
+
+text {*
+The current configuration can be printed by the command
+@{text smt2_status}, which shows the values of most options.
+*}
+
+
+
+subsection {* General configuration options *}
+
+text {*
+The option @{text smt2_solver} can be used to change the target SMT
+solver. The possible values can be obtained from the @{text smt2_status}
+command.
+
+Due to licensing restrictions, Yices and Z3 are not installed/enabled
+by default. Z3 is free for non-commercial applications and can be enabled
+by setting Isabelle system option @{text z3_non_commercial} to @{text yes}.
+*}
+
+declare [[ smt2_solver = z3_new ]]
+
+text {*
+Since SMT solvers are potentially non-terminating, there is a timeout
+(given in seconds) to restrict their runtime. A value greater than
+120 (seconds) is in most cases not advisable.
+*}
+
+declare [[ smt2_timeout = 20 ]]
+
+text {*
+SMT solvers apply randomized heuristics. In case a problem is not
+solvable by an SMT solver, changing the following option might help.
+*}
+
+declare [[ smt2_random_seed = 1 ]]
+
+text {*
+In general, the binding to SMT solvers runs as an oracle, i.e, the SMT
+solvers are fully trusted without additional checks. The following
+option can cause the SMT solver to run in proof-producing mode, giving
+a checkable certificate. This is currently only implemented for Z3.
+*}
+
+declare [[ smt2_oracle = false ]]
+
+text {*
+Each SMT solver provides several commandline options to tweak its
+behaviour. They can be passed to the solver by setting the following
+options.
+*}
+
+(* declare [[ cvc3_options = "" ]] TODO *)
+(* declare [[ yices_options = "" ]] TODO *)
+(* declare [[ z3_options = "" ]] TODO *)
+
+text {*
+The SMT method provides an inference mechanism to detect simple triggers
+in quantified formulas, which might increase the number of problems
+solvable by SMT solvers (note: triggers guide quantifier instantiations
+in the SMT solver). To turn it on, set the following option.
+*}
+
+declare [[ smt2_infer_triggers = false ]]
+
+text {*
+Enable the following option to use built-in support for div/mod, datatypes,
+and records in Z3. Currently, this is implemented only in oracle mode.
+*}
+
+declare [[ z3_new_extensions = false ]]
+
+text {*
+The SMT method monomorphizes the given facts, that is, it tries to
+instantiate all schematic type variables with fixed types occurring
+in the problem. This is a (possibly nonterminating) fixed-point
+construction whose cycles are limited by the following option.
+*}
+
+declare [[ monomorph_max_rounds = 5 ]]
+
+text {*
+In addition, the number of generated monomorphic instances is limited
+by the following option.
+*}
+
+declare [[ monomorph_max_new_instances = 500 ]]
+
+
+
+subsection {* Certificates *}
+
+text {*
+By setting the option @{text smt2_certificates} to the name of a file,
+all following applications of an SMT solver a cached in that file.
+Any further application of the same SMT solver (using the very same
+configuration) re-uses the cached certificate instead of invoking the
+solver. An empty string disables caching certificates.
+
+The filename should be given as an explicit path. It is good
+practice to use the name of the current theory (with ending
+@{text ".certs"} instead of @{text ".thy"}) as the certificates file.
+Certificate files should be used at most once in a certain theory context,
+to avoid race conditions with other concurrent accesses.
+*}
+
+declare [[ smt2_certificates = "" ]]
+
+text {*
+The option @{text smt2_read_only_certificates} controls whether only
+stored certificates are should be used or invocation of an SMT solver
+is allowed. When set to @{text true}, no SMT solver will ever be
+invoked and only the existing certificates found in the configured
+cache are used; when set to @{text false} and there is no cached
+certificate for some proposition, then the configured SMT solver is
+invoked.
+*}
+
+declare [[ smt2_read_only_certificates = false ]]
+
+
+
+subsection {* Tracing *}
+
+text {*
+The SMT method, when applied, traces important information. To
+make it entirely silent, set the following option to @{text false}.
+*}
+
+declare [[ smt2_verbose = true ]]
+
+text {*
+For tracing the generated problem file given to the SMT solver as
+well as the returned result of the solver, the option
+@{text smt2_trace} should be set to @{text true}.
+*}
+
+declare [[ smt2_trace = false ]]
+
+text {*
+From the set of assumptions given to the SMT solver, those assumptions
+used in the proof are traced when the following option is set to
+@{term true}. This only works for Z3 when it runs in non-oracle mode
+(see options @{text smt2_solver} and @{text smt2_oracle} above).
+*}
+
+declare [[ smt2_trace_used_facts = false ]]
+
+
+subsection {* Schematic rules for Z3 proof reconstruction *}
+
+text {*
+Several prof rules of Z3 are not very well documented. There are two
+lemma groups which can turn failing Z3 proof reconstruction attempts
+into succeeding ones: the facts in @{text z3_rule} are tried prior to
+any implemented reconstruction procedure for all uncertain Z3 proof
+rules; the facts in @{text z3_simp} are only fed to invocations of
+the simplifier when reconstructing theory-specific proof steps.
+*}
+
+lemmas [z3_new_rule] =
+ refl eq_commute conj_commute disj_commute simp_thms nnf_simps
+ ring_distribs field_simps times_divide_eq_right times_divide_eq_left
+ if_True if_False not_not
+
+lemma [z3_new_rule]:
+ "(P \<and> Q) = (\<not>(\<not>P \<or> \<not>Q))"
+ "(P \<and> Q) = (\<not>(\<not>Q \<or> \<not>P))"
+ "(\<not>P \<and> Q) = (\<not>(P \<or> \<not>Q))"
+ "(\<not>P \<and> Q) = (\<not>(\<not>Q \<or> P))"
+ "(P \<and> \<not>Q) = (\<not>(\<not>P \<or> Q))"
+ "(P \<and> \<not>Q) = (\<not>(Q \<or> \<not>P))"
+ "(\<not>P \<and> \<not>Q) = (\<not>(P \<or> Q))"
+ "(\<not>P \<and> \<not>Q) = (\<not>(Q \<or> P))"
+ by auto
+
+lemma [z3_new_rule]:
+ "(P \<longrightarrow> Q) = (Q \<or> \<not>P)"
+ "(\<not>P \<longrightarrow> Q) = (P \<or> Q)"
+ "(\<not>P \<longrightarrow> Q) = (Q \<or> P)"
+ "(True \<longrightarrow> P) = P"
+ "(P \<longrightarrow> True) = True"
+ "(False \<longrightarrow> P) = True"
+ "(P \<longrightarrow> P) = True"
+ by auto
+
+lemma [z3_new_rule]:
+ "((P = Q) \<longrightarrow> R) = (R | (Q = (\<not>P)))"
+ by auto
+
+lemma [z3_new_rule]:
+ "(\<not>True) = False"
+ "(\<not>False) = True"
+ "(x = x) = True"
+ "(P = True) = P"
+ "(True = P) = P"
+ "(P = False) = (\<not>P)"
+ "(False = P) = (\<not>P)"
+ "((\<not>P) = P) = False"
+ "(P = (\<not>P)) = False"
+ "((\<not>P) = (\<not>Q)) = (P = Q)"
+ "\<not>(P = (\<not>Q)) = (P = Q)"
+ "\<not>((\<not>P) = Q) = (P = Q)"
+ "(P \<noteq> Q) = (Q = (\<not>P))"
+ "(P = Q) = ((\<not>P \<or> Q) \<and> (P \<or> \<not>Q))"
+ "(P \<noteq> Q) = ((\<not>P \<or> \<not>Q) \<and> (P \<or> Q))"
+ by auto
+
+lemma [z3_new_rule]:
+ "(if P then P else \<not>P) = True"
+ "(if \<not>P then \<not>P else P) = True"
+ "(if P then True else False) = P"
+ "(if P then False else True) = (\<not>P)"
+ "(if P then Q else True) = ((\<not>P) \<or> Q)"
+ "(if P then Q else True) = (Q \<or> (\<not>P))"
+ "(if P then Q else \<not>Q) = (P = Q)"
+ "(if P then Q else \<not>Q) = (Q = P)"
+ "(if P then \<not>Q else Q) = (P = (\<not>Q))"
+ "(if P then \<not>Q else Q) = ((\<not>Q) = P)"
+ "(if \<not>P then x else y) = (if P then y else x)"
+ "(if P then (if Q then x else y) else x) = (if P \<and> (\<not>Q) then y else x)"
+ "(if P then (if Q then x else y) else x) = (if (\<not>Q) \<and> P then y else x)"
+ "(if P then (if Q then x else y) else y) = (if P \<and> Q then x else y)"
+ "(if P then (if Q then x else y) else y) = (if Q \<and> P then x else y)"
+ "(if P then x else if P then y else z) = (if P then x else z)"
+ "(if P then x else if Q then x else y) = (if P \<or> Q then x else y)"
+ "(if P then x else if Q then x else y) = (if Q \<or> P then x else y)"
+ "(if P then x = y else x = z) = (x = (if P then y else z))"
+ "(if P then x = y else y = z) = (y = (if P then x else z))"
+ "(if P then x = y else z = y) = (y = (if P then x else z))"
+ by auto
+
+lemma [z3_new_rule]:
+ "0 + (x::int) = x"
+ "x + 0 = x"
+ "x + x = 2 * x"
+ "0 * x = 0"
+ "1 * x = x"
+ "x + y = y + x"
+ by auto
+
+lemma [z3_new_rule]: (* for def-axiom *)
+ "P = Q \<or> P \<or> Q"
+ "P = Q \<or> \<not>P \<or> \<not>Q"
+ "(\<not>P) = Q \<or> \<not>P \<or> Q"
+ "(\<not>P) = Q \<or> P \<or> \<not>Q"
+ "P = (\<not>Q) \<or> \<not>P \<or> Q"
+ "P = (\<not>Q) \<or> P \<or> \<not>Q"
+ "P \<noteq> Q \<or> P \<or> \<not>Q"
+ "P \<noteq> Q \<or> \<not>P \<or> Q"
+ "P \<noteq> (\<not>Q) \<or> P \<or> Q"
+ "(\<not>P) \<noteq> Q \<or> P \<or> Q"
+ "P \<or> Q \<or> P \<noteq> (\<not>Q)"
+ "P \<or> Q \<or> (\<not>P) \<noteq> Q"
+ "P \<or> \<not>Q \<or> P \<noteq> Q"
+ "\<not>P \<or> Q \<or> P \<noteq> Q"
+ "P \<or> y = (if P then x else y)"
+ "P \<or> (if P then x else y) = y"
+ "\<not>P \<or> x = (if P then x else y)"
+ "\<not>P \<or> (if P then x else y) = x"
+ "P \<or> R \<or> \<not>(if P then Q else R)"
+ "\<not>P \<or> Q \<or> \<not>(if P then Q else R)"
+ "\<not>(if P then Q else R) \<or> \<not>P \<or> Q"
+ "\<not>(if P then Q else R) \<or> P \<or> R"
+ "(if P then Q else R) \<or> \<not>P \<or> \<not>Q"
+ "(if P then Q else R) \<or> P \<or> \<not>R"
+ "(if P then \<not>Q else R) \<or> \<not>P \<or> Q"
+ "(if P then Q else \<not>R) \<or> P \<or> R"
+ by auto
+
+hide_type (open) pattern
+hide_const fun_app z3div z3mod
+hide_const (open) trigger pat nopat weight
+
+end
--- a/src/HOL/SMT_Examples/SMT_Examples.certs Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs Thu Mar 13 16:39:08 2014 +0100
@@ -1,669 +1,3 @@
-23d01cdabb599769b54210e40617eea3d6c91e30 8 0
-#2 := false
-#1 := true
-#7 := (not true)
-#29 := (iff #7 false)
-#30 := [rewrite]: #29
-#28 := [asserted]: #7
-[mp #28 #30]: false
-unsat
-22e23526a38d50ce23abbe4dbfb697891cbcd840 22 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (not #8)
-#10 := (or #8 #9)
-#11 := (not #10)
-#40 := (iff #11 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#33 := (iff #10 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#32 := [asserted]: #11
-[mp #32 #41]: false
-unsat
-121552dd328e0993a2c6099c592d9c3db7fff190 28 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#1 := true
-#9 := (and #8 true)
-#10 := (iff #9 #8)
-#11 := (not #10)
-#46 := (iff #11 false)
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (iff #8 #8)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#33 := [rewrite]: #10
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #11
-[mp #32 #47]: false
-unsat
-263480c8c5909524c36f6198f60c623fbcfc953d 41 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (or #8 #10)
-#64 := (iff #11 false)
-#59 := (or false false)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #11 #59)
-#57 := (iff #10 false)
-#48 := (not #10)
-#12 := (not #8)
-#13 := (and #11 #12)
-#37 := (not #13)
-#38 := (or #37 #10)
-#41 := (not #38)
-#14 := (implies #13 #10)
-#15 := (not #14)
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#36 := [asserted]: #15
-#46 := [mp #36 #43]: #41
-#49 := [not-or-elim #46]: #48
-#58 := [iff-false #49]: #57
-#55 := (iff #8 false)
-#44 := [not-or-elim #46]: #13
-#47 := [and-elim #44]: #12
-#56 := [iff-false #47]: #55
-#61 := [monotonicity #56 #58]: #60
-#65 := [trans #61 #63]: #64
-#45 := [and-elim #44]: #11
-[mp #45 #65]: false
-unsat
-79d9d246dd9d27e03e8f1ea895e790f3a4420bfd 55 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-#16 := (and #8 #13)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-#15 := (and #13 #10)
-#17 := (or #15 #16)
-#18 := (implies #8 #17)
-#19 := (or #18 #8)
-#11 := (and #8 #10)
-#14 := (or #11 #13)
-#20 := (implies #14 #19)
-#21 := (not #20)
-#71 := (iff #21 false)
-#43 := (not #8)
-#44 := (or #43 #17)
-#47 := (or #44 #8)
-#53 := (not #14)
-#54 := (or #53 #47)
-#59 := (not #54)
-#69 := (iff #59 false)
-#1 := true
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #59 #64)
-#62 := (iff #54 true)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#60 := (iff #21 #59)
-#57 := (iff #20 #54)
-#50 := (implies #14 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #20 #50)
-#48 := (iff #19 #47)
-#45 := (iff #18 #44)
-#46 := [rewrite]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [monotonicity #58]: #60
-#72 := [trans #61 #70]: #71
-#42 := [asserted]: #21
-[mp #42 #72]: false
-unsat
-050883983ebe99dc3b7f24a011b1724b1b2c4dd9 33 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f6 :: S1
-#14 := f6
-#15 := (= f6 f1)
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-#16 := (and #13 #15)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#11 := (and #8 #10)
-#17 := (or #11 #16)
-#18 := (implies #17 #17)
-#19 := (not #18)
-#48 := (iff #19 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #19 #43)
-#41 := (iff #18 true)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#40 := [asserted]: #19
-[mp #40 #49]: false
-unsat
-8575241c64c02491d277f6598ca57e576f5a6b45 60 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#9 := (iff #8 #8)
-#10 := (iff #9 #8)
-#11 := (iff #10 #8)
-#12 := (iff #11 #8)
-#13 := (iff #12 #8)
-#14 := (iff #13 #8)
-#15 := (iff #14 #8)
-#16 := (iff #15 #8)
-#17 := (iff #16 #8)
-#18 := (not #17)
-#78 := (iff #18 false)
-#1 := true
-#73 := (not true)
-#76 := (iff #73 false)
-#77 := [rewrite]: #76
-#74 := (iff #18 #73)
-#71 := (iff #17 true)
-#40 := (iff #9 true)
-#41 := [rewrite]: #40
-#69 := (iff #17 #9)
-#42 := (iff true #8)
-#45 := (iff #42 #8)
-#46 := [rewrite]: #45
-#66 := (iff #16 #42)
-#64 := (iff #15 true)
-#62 := (iff #15 #9)
-#59 := (iff #14 #42)
-#57 := (iff #13 true)
-#55 := (iff #13 #9)
-#52 := (iff #12 #42)
-#50 := (iff #11 true)
-#48 := (iff #11 #9)
-#43 := (iff #10 #42)
-#44 := [monotonicity #41]: #43
-#47 := [trans #44 #46]: #11
-#49 := [monotonicity #47]: #48
-#51 := [trans #49 #41]: #50
-#53 := [monotonicity #51]: #52
-#54 := [trans #53 #46]: #13
-#56 := [monotonicity #54]: #55
-#58 := [trans #56 #41]: #57
-#60 := [monotonicity #58]: #59
-#61 := [trans #60 #46]: #15
-#63 := [monotonicity #61]: #62
-#65 := [trans #63 #41]: #64
-#67 := [monotonicity #65]: #66
-#68 := [trans #67 #46]: #17
-#70 := [monotonicity #68]: #69
-#72 := [trans #70 #41]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#39 := [asserted]: #18
-[mp #39 #79]: false
-unsat
-8434421285df70a7e1728b19173d86303151090b 165 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f6 :: S1
-#13 := f6
-#14 := (= f6 f1)
-decl f5 :: S1
-#11 := f5
-#12 := (= f5 f1)
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#75 := (or #8 #10 #12 #14)
-#215 := (iff #75 false)
-#210 := (or false false false false)
-#213 := (iff #210 false)
-#214 := [rewrite]: #213
-#211 := (iff #75 #210)
-#167 := (iff #14 false)
-#119 := (not #14)
-#122 := (or #119 #12)
-#175 := (iff #122 #119)
-#170 := (or #119 false)
-#173 := (iff #170 #119)
-#174 := [rewrite]: #173
-#171 := (iff #122 #170)
-#168 := (iff #12 false)
-#25 := (not #12)
-decl f11 :: S1
-#43 := f11
-#44 := (= f11 f1)
-#45 := (not #44)
-#46 := (and #44 #45)
-decl f10 :: S1
-#40 := f10
-#41 := (= f10 f1)
-#47 := (or #41 #46)
-#42 := (not #41)
-#48 := (and #42 #47)
-#49 := (or #12 #48)
-#50 := (not #49)
-#150 := (iff #50 #25)
-#148 := (iff #49 #12)
-#143 := (or #12 false)
-#146 := (iff #143 #12)
-#147 := [rewrite]: #146
-#144 := (iff #49 #143)
-#141 := (iff #48 false)
-#136 := (and #42 #41)
-#139 := (iff #136 false)
-#140 := [rewrite]: #139
-#137 := (iff #48 #136)
-#134 := (iff #47 #41)
-#129 := (or #41 false)
-#132 := (iff #129 #41)
-#133 := [rewrite]: #132
-#130 := (iff #47 #129)
-#126 := (iff #46 false)
-#128 := [rewrite]: #126
-#131 := [monotonicity #128]: #130
-#135 := [trans #131 #133]: #134
-#138 := [monotonicity #135]: #137
-#142 := [trans #138 #140]: #141
-#145 := [monotonicity #142]: #144
-#149 := [trans #145 #147]: #148
-#151 := [monotonicity #149]: #150
-#125 := [asserted]: #50
-#154 := [mp #125 #151]: #25
-#169 := [iff-false #154]: #168
-#172 := [monotonicity #169]: #171
-#176 := [trans #172 #174]: #175
-#37 := (or #14 false)
-#38 := (not #37)
-#39 := (or #38 #12)
-#123 := (iff #39 #122)
-#120 := (iff #38 #119)
-#116 := (iff #37 #14)
-#118 := [rewrite]: #116
-#121 := [monotonicity #118]: #120
-#124 := [monotonicity #121]: #123
-#115 := [asserted]: #39
-#127 := [mp #115 #124]: #122
-#166 := [mp #127 #176]: #119
-#177 := [iff-false #166]: #167
-#165 := (iff #10 false)
-#109 := (not #10)
-#112 := (or #109 #12)
-#183 := (iff #112 #109)
-#178 := (or #109 false)
-#181 := (iff #178 #109)
-#182 := [rewrite]: #181
-#179 := (iff #112 #178)
-#180 := [monotonicity #169]: #179
-#184 := [trans #180 #182]: #183
-decl f9 :: S1
-#30 := f9
-#31 := (= f9 f1)
-#32 := (not #31)
-#33 := (or #31 #32)
-#34 := (and #10 #33)
-#35 := (not #34)
-#36 := (or #35 #12)
-#113 := (iff #36 #112)
-#110 := (iff #35 #109)
-#107 := (iff #34 #10)
-#1 := true
-#102 := (and #10 true)
-#105 := (iff #102 #10)
-#106 := [rewrite]: #105
-#103 := (iff #34 #102)
-#99 := (iff #33 true)
-#101 := [rewrite]: #99
-#104 := [monotonicity #101]: #103
-#108 := [trans #104 #106]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#98 := [asserted]: #36
-#117 := [mp #98 #114]: #112
-#164 := [mp #117 #184]: #109
-#185 := [iff-false #164]: #165
-#163 := (iff #8 false)
-#92 := (not #8)
-#95 := (or #92 #10)
-#191 := (iff #95 #92)
-#186 := (or #92 false)
-#189 := (iff #186 #92)
-#190 := [rewrite]: #189
-#187 := (iff #95 #186)
-#188 := [monotonicity #185]: #187
-#192 := [trans #188 #190]: #191
-#26 := (and #12 #25)
-#27 := (or #8 #26)
-#28 := (not #27)
-#29 := (or #28 #10)
-#96 := (iff #29 #95)
-#93 := (iff #28 #92)
-#90 := (iff #27 #8)
-#85 := (or #8 false)
-#88 := (iff #85 #8)
-#89 := [rewrite]: #88
-#86 := (iff #27 #85)
-#79 := (iff #26 false)
-#84 := [rewrite]: #79
-#87 := [monotonicity #84]: #86
-#91 := [trans #87 #89]: #90
-#94 := [monotonicity #91]: #93
-#97 := [monotonicity #94]: #96
-#74 := [asserted]: #29
-#100 := [mp #74 #97]: #95
-#162 := [mp #100 #192]: #92
-#193 := [iff-false #162]: #163
-#212 := [monotonicity #193 #185 #169 #177]: #211
-#216 := [trans #212 #214]: #215
-#15 := (or #12 #14)
-#16 := (or #10 #15)
-#17 := (or #8 #16)
-#76 := (iff #17 #75)
-#77 := [rewrite]: #76
-#72 := [asserted]: #17
-#78 := [mp #72 #77]: #75
-[mp #78 #216]: false
-unsat
-2571c5d0e3c2bb55fd62ced2ec0c2fd2a4870074 59 0
-#2 := false
-decl f3 :: (-> S3 S2 S2)
-decl f6 :: S2
-#16 := f6
-decl f4 :: (-> S4 S2 S3)
-decl f7 :: S2
-#19 := f7
-decl f5 :: S4
-#7 := f5
-#21 := (f4 f5 f7)
-#22 := (f3 #21 f6)
-#18 := (f4 f5 f6)
-#20 := (f3 #18 f7)
-#23 := (= #20 #22)
-#57 := (not #23)
-#17 := (= f6 f6)
-#24 := (and #17 #23)
-#25 := (not #24)
-#58 := (iff #25 #57)
-#55 := (iff #24 #23)
-#1 := true
-#50 := (and true #23)
-#53 := (iff #50 #23)
-#54 := [rewrite]: #53
-#51 := (iff #24 #50)
-#48 := (iff #17 true)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#59 := [monotonicity #56]: #58
-#47 := [asserted]: #25
-#62 := [mp #47 #59]: #57
-#8 := (:var 1 S2)
-#10 := (:var 0 S2)
-#12 := (f4 f5 #10)
-#13 := (f3 #12 #8)
-#546 := (pattern #13)
-#9 := (f4 f5 #8)
-#11 := (f3 #9 #10)
-#545 := (pattern #11)
-#14 := (= #11 #13)
-#547 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #545 #546) #14)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#550 := (iff #15 #547)
-#548 := (iff #14 #14)
-#549 := [refl]: #548
-#551 := [quant-intro #549]: #550
-#70 := (~ #15 #15)
-#68 := (~ #14 #14)
-#69 := [refl]: #68
-#71 := [nnf-pos #69]: #70
-#46 := [asserted]: #15
-#61 := [mp~ #46 #71]: #15
-#552 := [mp #61 #551]: #547
-#130 := (not #547)
-#216 := (or #130 #23)
-#131 := [quant-inst #16 #19]: #216
-[unit-resolution #131 #552 #62]: false
-unsat
-53042978396971446eabf6039172bd47071e3fd3 67 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> Int S1)
-decl ?v0!0 :: Int
-#55 := ?v0!0
-#56 := (f3 ?v0!0)
-#57 := (= #56 f1)
-#58 := (not #57)
-decl ?v1!1 :: Int
-#66 := ?v1!1
-#67 := (f3 ?v1!1)
-#68 := (= #67 f1)
-#69 := (or #57 #68)
-#70 := (not #69)
-#86 := (and #57 #70)
-#63 := (not #58)
-#76 := (and #63 #70)
-#87 := (iff #76 #86)
-#84 := (iff #63 #57)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#7 := (:var 0 Int)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#10 := (:var 1 Int)
-#11 := (f3 #10)
-#12 := (= #11 f1)
-#13 := (or #12 #9)
-#14 := (forall (vars (?v1 Int)) #13)
-#39 := (not #9)
-#40 := (or #39 #14)
-#43 := (forall (vars (?v0 Int)) #40)
-#46 := (not #43)
-#79 := (~ #46 #76)
-#50 := (or #57 #9)
-#52 := (forall (vars (?v1 Int)) #50)
-#59 := (or #58 #52)
-#60 := (not #59)
-#77 := (~ #60 #76)
-#71 := (not #52)
-#72 := (~ #71 #70)
-#73 := [sk]: #72
-#64 := (~ #63 #63)
-#65 := [refl]: #64
-#78 := [nnf-neg #65 #73]: #77
-#61 := (~ #46 #60)
-#62 := [sk]: #61
-#80 := [trans #62 #78]: #79
-#15 := (implies #9 #14)
-#16 := (forall (vars (?v0 Int)) #15)
-#17 := (not #16)
-#47 := (iff #17 #46)
-#44 := (iff #16 #43)
-#41 := (iff #15 #40)
-#42 := [rewrite]: #41
-#45 := [quant-intro #42]: #44
-#48 := [monotonicity #45]: #47
-#38 := [asserted]: #17
-#51 := [mp #38 #48]: #46
-#81 := [mp~ #51 #80]: #76
-#82 := [mp #81 #88]: #86
-#89 := [and-elim #82]: #70
-#90 := [not-or-elim #89]: #58
-#83 := [and-elim #82]: #57
-[unit-resolution #83 #90]: false
-unsat
-a69a9e8c5e31ec6b9da4cf96f47b52cf6b9404d9 117 0
-#2 := false
-decl f3 :: (-> S3 S2 S1)
-#10 := (:var 0 S2)
-decl f4 :: (-> S4 S1 S3)
-decl f6 :: S1
-#16 := f6
-decl f5 :: S4
-#7 := f5
-#17 := (f4 f5 f6)
-#18 := (f3 #17 #10)
-#573 := (pattern #18)
-decl f1 :: S1
-#3 := f1
-#19 := (= #18 f1)
-#76 := (not #19)
-#574 := (forall (vars (?v0 S2)) (:pat #573) #76)
-decl f7 :: S2
-#21 := f7
-#22 := (f3 #17 f7)
-#23 := (= #22 f1)
-#150 := (= f6 f1)
-#151 := (iff #23 #150)
-#8 := (:var 1 S1)
-#9 := (f4 f5 #8)
-#11 := (f3 #9 #10)
-#566 := (pattern #11)
-#13 := (= #8 f1)
-#12 := (= #11 f1)
-#14 := (iff #12 #13)
-#567 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #566) #14)
-#15 := (forall (vars (?v0 S1) (?v1 S2)) #14)
-#570 := (iff #15 #567)
-#568 := (iff #14 #14)
-#569 := [refl]: #568
-#571 := [quant-intro #569]: #570
-#62 := (~ #15 #15)
-#60 := (~ #14 #14)
-#61 := [refl]: #60
-#63 := [nnf-pos #61]: #62
-#46 := [asserted]: #15
-#53 := [mp~ #46 #63]: #15
-#572 := [mp #53 #571]: #567
-#152 := (not #567)
-#228 := (or #152 #151)
-#561 := [quant-inst #16 #21]: #228
-#237 := [unit-resolution #561 #572]: #151
-decl ?v0!0 :: S2
-#66 := ?v0!0
-#67 := (f3 #17 ?v0!0)
-#68 := (= #67 f1)
-#236 := (iff #68 #150)
-#238 := (or #152 #236)
-#229 := [quant-inst #16 #66]: #238
-#227 := [unit-resolution #229 #572]: #236
-#240 := (not #236)
-#199 := (or #240 #150)
-#55 := (not #23)
-#215 := [hypothesis]: #55
-#83 := (or #68 #23)
-#79 := (forall (vars (?v0 S2)) #76)
-#82 := (or #79 #55)
-#84 := (and #83 #82)
-#20 := (exists (vars (?v0 S2)) #19)
-#48 := (not #20)
-#49 := (iff #48 #23)
-#85 := (~ #49 #84)
-#57 := (~ #23 #23)
-#65 := [refl]: #57
-#64 := (~ #55 #55)
-#56 := [refl]: #64
-#80 := (~ #48 #79)
-#77 := (~ #76 #76)
-#78 := [refl]: #77
-#81 := [nnf-neg #78]: #80
-#73 := (not #48)
-#74 := (~ #73 #68)
-#69 := (~ #20 #68)
-#70 := [sk]: #69
-#75 := [nnf-neg #70]: #74
-#86 := [nnf-pos #75 #81 #56 #65]: #85
-#24 := (iff #20 #23)
-#25 := (not #24)
-#50 := (iff #25 #49)
-#51 := [rewrite]: #50
-#47 := [asserted]: #25
-#54 := [mp #47 #51]: #49
-#87 := [mp~ #54 #86]: #84
-#90 := [and-elim #87]: #83
-#557 := [unit-resolution #90 #215]: #68
-#243 := (not #68)
-#222 := (or #240 #243 #150)
-#558 := [def-axiom]: #222
-#541 := [unit-resolution #558 #557]: #199
-#203 := [unit-resolution #541 #227]: #150
-#241 := (not #150)
-#562 := (not #151)
-#204 := (or #562 #241)
-#563 := (or #562 #23 #241)
-#564 := [def-axiom]: #563
-#205 := [unit-resolution #564 #215]: #204
-#206 := [unit-resolution #205 #203 #237]: false
-#543 := [lemma #206]: #23
-#579 := (or #574 #55)
-#580 := (iff #82 #579)
-#577 := (iff #79 #574)
-#575 := (iff #76 #76)
-#576 := [refl]: #575
-#578 := [quant-intro #576]: #577
-#581 := [monotonicity #578]: #580
-#91 := [and-elim #87]: #82
-#582 := [mp #91 #581]: #579
-#242 := [unit-resolution #582 #543]: #574
-#555 := (not #574)
-#214 := (or #555 #55)
-#219 := [quant-inst #21]: #214
-[unit-resolution #219 #543 #242]: false
-unsat
d97439af6f5bc7794ab403d0f6cc318d103016a1 1288 0
#2 := false
decl f1 :: S1
@@ -1953,6 +1287,124 @@
#1532 := [unit-resolution #769 #1531]: #20
[unit-resolution #606 #1532 #1528]: false
unsat
+a69a9e8c5e31ec6b9da4cf96f47b52cf6b9404d9 117 0
+#2 := false
+decl f3 :: (-> S3 S2 S1)
+#10 := (:var 0 S2)
+decl f4 :: (-> S4 S1 S3)
+decl f6 :: S1
+#16 := f6
+decl f5 :: S4
+#7 := f5
+#17 := (f4 f5 f6)
+#18 := (f3 #17 #10)
+#573 := (pattern #18)
+decl f1 :: S1
+#3 := f1
+#19 := (= #18 f1)
+#76 := (not #19)
+#574 := (forall (vars (?v0 S2)) (:pat #573) #76)
+decl f7 :: S2
+#21 := f7
+#22 := (f3 #17 f7)
+#23 := (= #22 f1)
+#150 := (= f6 f1)
+#151 := (iff #23 #150)
+#8 := (:var 1 S1)
+#9 := (f4 f5 #8)
+#11 := (f3 #9 #10)
+#566 := (pattern #11)
+#13 := (= #8 f1)
+#12 := (= #11 f1)
+#14 := (iff #12 #13)
+#567 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #566) #14)
+#15 := (forall (vars (?v0 S1) (?v1 S2)) #14)
+#570 := (iff #15 #567)
+#568 := (iff #14 #14)
+#569 := [refl]: #568
+#571 := [quant-intro #569]: #570
+#62 := (~ #15 #15)
+#60 := (~ #14 #14)
+#61 := [refl]: #60
+#63 := [nnf-pos #61]: #62
+#46 := [asserted]: #15
+#53 := [mp~ #46 #63]: #15
+#572 := [mp #53 #571]: #567
+#152 := (not #567)
+#228 := (or #152 #151)
+#561 := [quant-inst #16 #21]: #228
+#237 := [unit-resolution #561 #572]: #151
+decl ?v0!0 :: S2
+#66 := ?v0!0
+#67 := (f3 #17 ?v0!0)
+#68 := (= #67 f1)
+#236 := (iff #68 #150)
+#238 := (or #152 #236)
+#229 := [quant-inst #16 #66]: #238
+#227 := [unit-resolution #229 #572]: #236
+#240 := (not #236)
+#199 := (or #240 #150)
+#55 := (not #23)
+#215 := [hypothesis]: #55
+#83 := (or #68 #23)
+#79 := (forall (vars (?v0 S2)) #76)
+#82 := (or #79 #55)
+#84 := (and #83 #82)
+#20 := (exists (vars (?v0 S2)) #19)
+#48 := (not #20)
+#49 := (iff #48 #23)
+#85 := (~ #49 #84)
+#57 := (~ #23 #23)
+#65 := [refl]: #57
+#64 := (~ #55 #55)
+#56 := [refl]: #64
+#80 := (~ #48 #79)
+#77 := (~ #76 #76)
+#78 := [refl]: #77
+#81 := [nnf-neg #78]: #80
+#73 := (not #48)
+#74 := (~ #73 #68)
+#69 := (~ #20 #68)
+#70 := [sk]: #69
+#75 := [nnf-neg #70]: #74
+#86 := [nnf-pos #75 #81 #56 #65]: #85
+#24 := (iff #20 #23)
+#25 := (not #24)
+#50 := (iff #25 #49)
+#51 := [rewrite]: #50
+#47 := [asserted]: #25
+#54 := [mp #47 #51]: #49
+#87 := [mp~ #54 #86]: #84
+#90 := [and-elim #87]: #83
+#557 := [unit-resolution #90 #215]: #68
+#243 := (not #68)
+#222 := (or #240 #243 #150)
+#558 := [def-axiom]: #222
+#541 := [unit-resolution #558 #557]: #199
+#203 := [unit-resolution #541 #227]: #150
+#241 := (not #150)
+#562 := (not #151)
+#204 := (or #562 #241)
+#563 := (or #562 #23 #241)
+#564 := [def-axiom]: #563
+#205 := [unit-resolution #564 #215]: #204
+#206 := [unit-resolution #205 #203 #237]: false
+#543 := [lemma #206]: #23
+#579 := (or #574 #55)
+#580 := (iff #82 #579)
+#577 := (iff #79 #574)
+#575 := (iff #76 #76)
+#576 := [refl]: #575
+#578 := [quant-intro #576]: #577
+#581 := [monotonicity #578]: #580
+#91 := [and-elim #87]: #82
+#582 := [mp #91 #581]: #579
+#242 := [unit-resolution #582 #543]: #574
+#555 := (not #574)
+#214 := (or #555 #55)
+#219 := [quant-inst #21]: #214
+[unit-resolution #219 #543 #242]: false
+unsat
fdf61e060f49731790f4d6c8f9b26c21349c60b3 117 0
#2 := false
decl f1 :: S1
@@ -2071,6716 +1523,6 @@
#603 := [unit-resolution #271 #618]: #602
[unit-resolution #603 #601 #297]: false
unsat
-5c792581e65682628e5c59ca9f3f8801e6aeba72 61 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#7 := f4
-#8 := (f3 f4)
-#9 := (= #8 f1)
-decl f5 :: S2
-#18 := f5
-#19 := (f3 f5)
-#20 := (= #19 f1)
-#45 := (not #9)
-#46 := (or #45 #20)
-#49 := (not #46)
-#21 := (implies #9 #20)
-#22 := (not #21)
-#50 := (iff #22 #49)
-#47 := (iff #21 #46)
-#48 := [rewrite]: #47
-#51 := [monotonicity #48]: #50
-#44 := [asserted]: #22
-#54 := [mp #44 #51]: #49
-#52 := [not-or-elim #54]: #9
-#10 := (:var 0 S2)
-#11 := (f3 #10)
-#550 := (pattern #11)
-#12 := (= #11 f1)
-#15 := (not #12)
-#551 := (forall (vars (?v0 S2)) (:pat #550) #15)
-#16 := (forall (vars (?v0 S2)) #15)
-#554 := (iff #16 #551)
-#552 := (iff #15 #15)
-#553 := [refl]: #552
-#555 := [quant-intro #553]: #554
-#13 := (exists (vars (?v0 S2)) #12)
-#14 := (not #13)
-#60 := (~ #14 #16)
-#63 := (~ #15 #15)
-#64 := [refl]: #63
-#72 := [nnf-neg #64]: #60
-#17 := (if #9 #14 #16)
-#70 := (iff #17 #14)
-#1 := true
-#65 := (if true #14 #16)
-#68 := (iff #65 #14)
-#69 := [rewrite]: #68
-#66 := (iff #17 #65)
-#61 := (iff #9 true)
-#62 := [iff-true #52]: #61
-#67 := [monotonicity #62]: #66
-#71 := [trans #67 #69]: #70
-#43 := [asserted]: #17
-#59 := [mp #43 #71]: #14
-#57 := [mp~ #59 #72]: #16
-#556 := [mp #57 #555]: #551
-#135 := (not #551)
-#221 := (or #135 #45)
-#136 := [quant-inst #7]: #221
-[unit-resolution #136 #556 #52]: false
-unsat
-0ce3a745d60cdbf0fe26b07c5e76de09d459dd25 17 0
-#2 := false
-#7 := 3::Int
-#8 := (= 3::Int 3::Int)
-#9 := (not #8)
-#38 := (iff #9 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (iff #8 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #9
-[mp #30 #39]: false
-unsat
-1532b1dde71eb42ca0a012bb62d9bbadf37fa326 17 0
-#2 := false
-#7 := 3::Real
-#8 := (= 3::Real 3::Real)
-#9 := (not #8)
-#38 := (iff #9 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (iff #8 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #9
-[mp #30 #39]: false
-unsat
-94425abeeb45b838fcb1ab9c8323796e36a681e5 26 0
-#2 := false
-#10 := 4::Int
-#8 := 1::Int
-#7 := 3::Int
-#9 := (+ 3::Int 1::Int)
-#11 := (= #9 4::Int)
-#12 := (not #11)
-#47 := (iff #12 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #12 #42)
-#40 := (iff #11 true)
-#35 := (= 4::Int 4::Int)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#34 := [rewrite]: #11
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#33 := [asserted]: #12
-[mp #33 #48]: false
-unsat
-673f00f23a414ea8ab1557752d859ea787c89c1b 41 0
-#2 := false
-decl f3 :: Int
-#7 := f3
-decl f5 :: Int
-#9 := f5
-#12 := (+ f5 f3)
-decl f4 :: Int
-#8 := f4
-#13 := (+ f4 #12)
-#10 := (+ f4 f5)
-#11 := (+ f3 #10)
-#14 := (= #11 #13)
-#15 := (not #14)
-#59 := (iff #15 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #15 #54)
-#52 := (iff #14 true)
-#47 := (= #11 #11)
-#50 := (iff #47 true)
-#51 := [rewrite]: #50
-#48 := (iff #14 #47)
-#45 := (= #13 #11)
-#37 := (+ f3 f5)
-#40 := (+ f4 #37)
-#43 := (= #40 #11)
-#44 := [rewrite]: #43
-#41 := (= #13 #40)
-#38 := (= #12 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#36 := [asserted]: #15
-[mp #36 #60]: false
-unsat
-1f5e59fc26e6d68939e39d2fe658ebc1a264f509 35 0
-#2 := false
-#8 := 3::Int
-#9 := 8::Int
-#10 := (<= 3::Int 8::Int)
-#11 := (if #10 8::Int 3::Int)
-#7 := 5::Int
-#12 := (< 5::Int #11)
-#13 := (not #12)
-#58 := (iff #13 false)
-#1 := true
-#53 := (not true)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #13 #53)
-#51 := (iff #12 true)
-#46 := (< 5::Int 8::Int)
-#49 := (iff #46 true)
-#50 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (= #11 8::Int)
-#39 := (if true 8::Int 3::Int)
-#42 := (= #39 8::Int)
-#43 := [rewrite]: #42
-#40 := (= #11 #39)
-#37 := (iff #10 true)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#55 := [monotonicity #52]: #54
-#59 := [trans #55 #57]: #58
-#34 := [asserted]: #13
-[mp #34 #59]: false
-unsat
-e7f019160a38d08774f8a2e816f96aa54c924fba 216 0
-#2 := false
-#10 := 0::Real
-decl f4 :: Real
-#8 := f4
-#43 := -1::Real
-#45 := (* -1::Real f4)
-decl f3 :: Real
-#7 := f3
-#44 := (* -1::Real f3)
-#46 := (+ #44 #45)
-#9 := (+ f3 f4)
-#71 := (>= #9 0::Real)
-#78 := (if #71 #9 #46)
-#153 := (* -1::Real #78)
-#181 := (+ #46 #153)
-#183 := (>= #181 0::Real)
-#134 := (= #46 #78)
-#72 := (not #71)
-#95 := (>= f4 0::Real)
-#96 := (not #95)
-#154 := (+ #9 #153)
-#156 := (>= #154 0::Real)
-#133 := (= #9 #78)
-#197 := (not #134)
-#192 := (not #183)
-#163 := [hypothesis]: #95
-#193 := (or #192 #96)
-#184 := [hypothesis]: #183
-#102 := (if #95 f4 #45)
-#114 := (* -1::Real #102)
-#83 := (>= f3 0::Real)
-#90 := (if #83 f3 #44)
-#113 := (* -1::Real #90)
-#115 := (+ #113 #114)
-#116 := (+ #78 #115)
-#117 := (<= #116 0::Real)
-#122 := (not #117)
-#18 := (- f4)
-#17 := (< f4 0::Real)
-#19 := (if #17 #18 f4)
-#15 := (- f3)
-#14 := (< f3 0::Real)
-#16 := (if #14 #15 f3)
-#20 := (+ #16 #19)
-#12 := (- #9)
-#11 := (< #9 0::Real)
-#13 := (if #11 #12 #9)
-#21 := (<= #13 #20)
-#22 := (not #21)
-#125 := (iff #22 #122)
-#59 := (if #17 #45 f4)
-#54 := (if #14 #44 f3)
-#62 := (+ #54 #59)
-#49 := (if #11 #46 #9)
-#65 := (<= #49 #62)
-#68 := (not #65)
-#123 := (iff #68 #122)
-#120 := (iff #65 #117)
-#107 := (+ #90 #102)
-#110 := (<= #78 #107)
-#118 := (iff #110 #117)
-#119 := [rewrite]: #118
-#111 := (iff #65 #110)
-#108 := (= #62 #107)
-#105 := (= #59 #102)
-#99 := (if #96 #45 f4)
-#103 := (= #99 #102)
-#104 := [rewrite]: #103
-#100 := (= #59 #99)
-#97 := (iff #17 #96)
-#98 := [rewrite]: #97
-#101 := [monotonicity #98]: #100
-#106 := [trans #101 #104]: #105
-#93 := (= #54 #90)
-#84 := (not #83)
-#87 := (if #84 #44 f3)
-#91 := (= #87 #90)
-#92 := [rewrite]: #91
-#88 := (= #54 #87)
-#85 := (iff #14 #84)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#94 := [trans #89 #92]: #93
-#109 := [monotonicity #94 #106]: #108
-#81 := (= #49 #78)
-#75 := (if #72 #46 #9)
-#79 := (= #75 #78)
-#80 := [rewrite]: #79
-#76 := (= #49 #75)
-#73 := (iff #11 #72)
-#74 := [rewrite]: #73
-#77 := [monotonicity #74]: #76
-#82 := [trans #77 #80]: #81
-#112 := [monotonicity #82 #109]: #111
-#121 := [trans #112 #119]: #120
-#124 := [monotonicity #121]: #123
-#69 := (iff #22 #68)
-#66 := (iff #21 #65)
-#63 := (= #20 #62)
-#60 := (= #19 #59)
-#57 := (= #18 #45)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#55 := (= #16 #54)
-#52 := (= #15 #44)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#64 := [monotonicity #56 #61]: #63
-#50 := (= #13 #49)
-#47 := (= #12 #46)
-#48 := [rewrite]: #47
-#51 := [monotonicity #48]: #50
-#67 := [monotonicity #51 #64]: #66
-#70 := [monotonicity #67]: #69
-#126 := [trans #70 #124]: #125
-#42 := [asserted]: #22
-#127 := [mp #42 #126]: #122
-#147 := (+ f4 #114)
-#148 := (<= #147 0::Real)
-#141 := (= f4 #102)
-#143 := (or #96 #141)
-#144 := [def-axiom]: #143
-#172 := [unit-resolution #144 #163]: #141
-#173 := (not #141)
-#174 := (or #173 #148)
-#175 := [th-lemma arith triangle-eq]: #174
-#176 := [unit-resolution #175 #172]: #148
-#152 := (+ #44 #113)
-#155 := (<= #152 0::Real)
-#130 := (= #44 #90)
-#178 := (or #84 #96)
-#150 := (+ f3 #113)
-#151 := (<= #150 0::Real)
-#129 := (= f3 #90)
-#157 := [hypothesis]: #83
-#137 := (or #84 #129)
-#138 := [def-axiom]: #137
-#158 := [unit-resolution #138 #157]: #129
-#159 := (not #129)
-#160 := (or #159 #151)
-#161 := [th-lemma arith triangle-eq]: #160
-#162 := [unit-resolution #161 #158]: #151
-#164 := (or #71 #84 #96)
-#165 := [th-lemma arith assign-bounds -1 -1]: #164
-#166 := [unit-resolution #165 #157 #163]: #71
-#135 := (or #72 #133)
-#136 := [def-axiom]: #135
-#167 := [unit-resolution #136 #166]: #133
-#168 := (not #133)
-#169 := (or #168 #156)
-#170 := [th-lemma arith triangle-eq]: #169
-#171 := [unit-resolution #170 #167]: #156
-#177 := [th-lemma arith farkas 1 -1 -1 1 #176 #171 #127 #162]: false
-#179 := [lemma #177]: #178
-#185 := [unit-resolution #179 #163]: #84
-#139 := (or #83 #130)
-#140 := [def-axiom]: #139
-#186 := [unit-resolution #140 #185]: #130
-#187 := (not #130)
-#188 := (or #187 #155)
-#189 := [th-lemma arith triangle-eq]: #188
-#190 := [unit-resolution #189 #186]: #155
-#191 := [th-lemma arith farkas 2 -1 -1 1 1 #163 #190 #176 #127 #184]: false
-#194 := [lemma #191]: #193
-#202 := [unit-resolution #194 #163]: #192
-#198 := (or #197 #183)
-#195 := [hypothesis]: #192
-#196 := [hypothesis]: #134
-#199 := [th-lemma arith triangle-eq]: #198
-#200 := [unit-resolution #199 #196 #195]: false
-#201 := [lemma #200]: #198
-#203 := [unit-resolution #201 #202]: #197
-#131 := (or #71 #134)
-#132 := [def-axiom]: #131
-#204 := [unit-resolution #132 #203]: #71
-#205 := [unit-resolution #136 #204]: #133
-#206 := [unit-resolution #170 #205]: #156
-#207 := [th-lemma arith farkas 2 1 1 1 1 #185 #190 #176 #127 #206]: false
-#208 := [lemma #207]: #96
-#149 := (+ #45 #114)
-#180 := (<= #149 0::Real)
-#142 := (= #45 #102)
-#145 := (or #95 #142)
-#146 := [def-axiom]: #145
-#213 := [unit-resolution #146 #208]: #142
-#214 := (not #142)
-#215 := (or #214 #180)
-#216 := [th-lemma arith triangle-eq]: #215
-#217 := [unit-resolution #216 #213]: #180
-#219 := (not #156)
-#220 := (not #151)
-#221 := (or #219 #220)
-#211 := [hypothesis]: #151
-#212 := [hypothesis]: #156
-#218 := [th-lemma arith farkas 2 1 1 1 1 #208 #217 #127 #212 #211]: false
-#222 := [lemma #218]: #221
-#227 := [unit-resolution #222 #162]: #219
-#223 := [hypothesis]: #219
-#224 := [hypothesis]: #133
-#225 := [unit-resolution #170 #224 #223]: false
-#226 := [lemma #225]: #169
-#228 := [unit-resolution #226 #227]: #168
-#229 := [unit-resolution #136 #228]: #72
-#230 := [unit-resolution #132 #229]: #134
-#231 := [unit-resolution #201 #230]: #183
-#232 := [th-lemma arith farkas 1/2 -1/2 -1/2 1/2 1 #231 #162 #217 #127 #157]: false
-#233 := [lemma #232]: #84
-#234 := (or #72 #83 #95)
-#235 := [th-lemma arith assign-bounds 1 1]: #234
-#236 := [unit-resolution #235 #233 #208]: #72
-#237 := [unit-resolution #132 #236]: #134
-#238 := [unit-resolution #201 #237]: #183
-#239 := [unit-resolution #140 #233]: #130
-#240 := [unit-resolution #189 #239]: #155
-[th-lemma arith farkas -1 -1 1 1 #240 #217 #127 #238]: false
-unsat
-9e5f324cc33eb4abf1be11d977dfdec45557ae46 42 0
-#2 := false
-decl f3 :: (-> S1 S2)
-decl f1 :: S1
-#3 := f1
-#12 := (f3 f1)
-decl f2 :: S1
-#4 := f2
-#8 := 3::Int
-#7 := 2::Int
-#9 := (< 2::Int 3::Int)
-#10 := (if #9 f1 f2)
-#11 := (f3 #10)
-#13 := (= #11 #12)
-#14 := (not #13)
-#60 := (iff #14 false)
-#1 := true
-#55 := (not true)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #14 #55)
-#53 := (iff #13 true)
-#48 := (= #12 #12)
-#51 := (iff #48 true)
-#52 := [rewrite]: #51
-#49 := (iff #13 #48)
-#45 := (= #10 f1)
-#40 := (if true f1 f2)
-#43 := (= #40 f1)
-#44 := [rewrite]: #43
-#41 := (= #10 #40)
-#38 := (iff #9 true)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#47 := [monotonicity #46]: #13
-#50 := [monotonicity #47]: #49
-#54 := [trans #50 #52]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#35 := [asserted]: #14
-[mp #35 #61]: false
-unsat
-cc322c3513bba37f77e905b379b26c79239b69a4 49 0
-#2 := false
-#12 := 1::Int
-decl f3 :: Int
-#8 := f3
-#13 := (< f3 1::Int)
-#9 := 3::Int
-#10 := (+ f3 3::Int)
-#7 := 4::Int
-#11 := (<= 4::Int #10)
-#14 := (or #11 #13)
-#15 := (not #14)
-#69 := (iff #15 false)
-#37 := (+ 3::Int f3)
-#40 := (<= 4::Int #37)
-#43 := (or #40 #13)
-#46 := (not #43)
-#67 := (iff #46 false)
-#1 := true
-#62 := (not true)
-#65 := (iff #62 false)
-#66 := [rewrite]: #65
-#63 := (iff #46 #62)
-#60 := (iff #43 true)
-#51 := (>= f3 1::Int)
-#52 := (not #51)
-#55 := (or #51 #52)
-#58 := (iff #55 true)
-#59 := [rewrite]: #58
-#56 := (iff #43 #55)
-#53 := (iff #13 #52)
-#54 := [rewrite]: #53
-#49 := (iff #40 #51)
-#50 := [rewrite]: #49
-#57 := [monotonicity #50 #54]: #56
-#61 := [trans #57 #59]: #60
-#64 := [monotonicity #61]: #63
-#68 := [trans #64 #66]: #67
-#47 := (iff #15 #46)
-#44 := (iff #14 #43)
-#41 := (iff #11 #40)
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#70 := [trans #48 #68]: #69
-#36 := [asserted]: #15
-[mp #36 #70]: false
-unsat
-75c4589e7d7ab0bf262babccc302883b71f9a923 63 0
-#2 := false
-#14 := 0::Int
-decl f4 :: Int
-#10 := f4
-#49 := -1::Int
-#52 := (* -1::Int f4)
-decl f3 :: Int
-#8 := f3
-#53 := (+ f3 #52)
-#70 := (>= #53 0::Int)
-#94 := (iff #70 false)
-#51 := -4::Int
-#87 := (>= -4::Int 0::Int)
-#86 := (iff #87 false)
-#93 := [rewrite]: #86
-#88 := (iff #70 #87)
-#54 := (= #53 -4::Int)
-#11 := 4::Int
-#12 := (+ f3 4::Int)
-#13 := (= f4 #12)
-#56 := (iff #13 #54)
-#39 := (+ 4::Int f3)
-#46 := (= f4 #39)
-#50 := (iff #46 #54)
-#55 := [rewrite]: #50
-#47 := (iff #13 #46)
-#44 := (= #12 #39)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45]: #47
-#57 := [trans #48 #55]: #56
-#38 := [asserted]: #13
-#58 := [mp #38 #57]: #54
-#85 := [monotonicity #58]: #88
-#95 := [trans #85 #93]: #94
-#15 := (- f4 f3)
-#16 := (< 0::Int #15)
-#17 := (not #16)
-#81 := (iff #17 #70)
-#60 := (* -1::Int f3)
-#61 := (+ #60 f4)
-#64 := (< 0::Int #61)
-#67 := (not #64)
-#79 := (iff #67 #70)
-#71 := (not #70)
-#74 := (not #71)
-#77 := (iff #74 #70)
-#78 := [rewrite]: #77
-#75 := (iff #67 #74)
-#72 := (iff #64 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#68 := (iff #17 #67)
-#65 := (iff #16 #64)
-#62 := (= #15 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#82 := [trans #69 #80]: #81
-#59 := [asserted]: #17
-#83 := [mp #59 #82]: #70
-[mp #83 #95]: false
-unsat
-31769d5312feac1587c3f744c5c881fb2d86e85f 35 0
-#2 := false
-#9 := 5::Int
-#7 := 2::Int
-#8 := (+ 2::Int 2::Int)
-#10 := (= #8 5::Int)
-#11 := (not #10)
-#12 := (not #11)
-#56 := (iff #12 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #12 #51)
-#49 := (iff #11 true)
-#44 := (not false)
-#47 := (iff #44 true)
-#48 := [rewrite]: #47
-#45 := (iff #11 #44)
-#42 := (iff #10 false)
-#34 := 4::Int
-#37 := (= 4::Int 5::Int)
-#40 := (iff #37 false)
-#41 := [rewrite]: #40
-#38 := (iff #10 #37)
-#35 := (= #8 4::Int)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#33 := [asserted]: #12
-[mp #33 #57]: false
-unsat
-f8ba8c3ed7f7c7d5e49139b62e145fc6eee338f1 45 0
-#2 := false
-#14 := 4::Real
-decl f4 :: Real
-#11 := f4
-#10 := 7::Real
-#12 := (* 7::Real f4)
-decl f3 :: Real
-#8 := f3
-#7 := 3::Real
-#9 := (* 3::Real f3)
-#13 := (+ #9 #12)
-#48 := (>= #13 4::Real)
-#46 := (not #48)
-#15 := (< #13 4::Real)
-#47 := (iff #15 #46)
-#44 := [rewrite]: #47
-#41 := [asserted]: #15
-#45 := [mp #41 #44]: #46
-#16 := 2::Real
-#17 := (* 2::Real f3)
-#50 := (<= #17 3::Real)
-#51 := (not #50)
-#18 := (< 3::Real #17)
-#52 := (iff #18 #51)
-#53 := [rewrite]: #52
-#42 := [asserted]: #18
-#54 := [mp #42 #53]: #51
-#19 := 0::Real
-#58 := (>= f4 0::Real)
-#20 := (< f4 0::Real)
-#21 := (not #20)
-#65 := (iff #21 #58)
-#56 := (not #58)
-#60 := (not #56)
-#63 := (iff #60 #58)
-#64 := [rewrite]: #63
-#61 := (iff #21 #60)
-#57 := (iff #20 #56)
-#59 := [rewrite]: #57
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#43 := [asserted]: #21
-#67 := [mp #43 #66]: #58
-[th-lemma arith farkas 7 3/2 1 #67 #54 #45]: false
-unsat
-c61600e5a5dab4b2c2864caededa0b50f81df696 59 0
-#2 := false
-#19 := (not false)
-decl f4 :: Int
-#11 := f4
-#7 := 0::Int
-#15 := (<= 0::Int f4)
-#16 := (not #15)
-#17 := (or #16 #15)
-#9 := 1::Int
-#10 := (- 1::Int)
-#12 := (* #10 f4)
-decl f3 :: Int
-#8 := f3
-#13 := (+ f3 #12)
-#14 := (<= 0::Int #13)
-#18 := (or #14 #17)
-#20 := (iff #18 #19)
-#21 := (not #20)
-#77 := (iff #21 false)
-#1 := true
-#72 := (not true)
-#75 := (iff #72 false)
-#76 := [rewrite]: #75
-#73 := (iff #21 #72)
-#70 := (iff #20 true)
-#65 := (iff true true)
-#68 := (iff #65 true)
-#69 := [rewrite]: #68
-#66 := (iff #20 #65)
-#63 := (iff #19 true)
-#64 := [rewrite]: #63
-#61 := (iff #18 true)
-#42 := -1::Int
-#45 := (* -1::Int f4)
-#48 := (+ f3 #45)
-#51 := (<= 0::Int #48)
-#56 := (or #51 true)
-#59 := (iff #56 true)
-#60 := [rewrite]: #59
-#57 := (iff #18 #56)
-#54 := (iff #17 true)
-#55 := [rewrite]: #54
-#52 := (iff #14 #51)
-#49 := (= #13 #48)
-#46 := (= #12 #45)
-#43 := (= #10 -1::Int)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#50 := [monotonicity #47]: #49
-#53 := [monotonicity #50]: #52
-#58 := [monotonicity #53 #55]: #57
-#62 := [trans #58 #60]: #61
-#67 := [monotonicity #62 #64]: #66
-#71 := [trans #67 #69]: #70
-#74 := [monotonicity #71]: #73
-#78 := [trans #74 #76]: #77
-#41 := [asserted]: #21
-[mp #41 #78]: false
-unsat
-7f98d11cd70eeb0eb4aea9722e1648cd3cfdbe2c 439 0
-#2 := false
-decl f4 :: Int
-#8 := f4
-decl f3 :: Int
-#7 := f3
-#20 := (= f3 f4)
-#287 := (not #20)
-#24 := (= f4 f3)
-#312 := (not #24)
-#499 := (iff #312 #287)
-#458 := (iff #24 #20)
-#459 := [commutativity]: #458
-#500 := [monotonicity #459]: #499
-decl f5 :: Int
-#10 := f5
-#30 := (= f5 f4)
-#13 := (= f4 f5)
-#493 := (iff #13 #30)
-#491 := (iff #30 #13)
-#492 := [commutativity]: #491
-#494 := [symm #492]: #493
-#18 := (= f3 f5)
-#238 := (not #18)
-#28 := (= f5 f3)
-#337 := (not #28)
-#485 := (iff #337 #238)
-#483 := (iff #28 #18)
-#484 := [commutativity]: #483
-#486 := [monotonicity #484]: #485
-#55 := 0::Int
-#77 := -1::Int
-#102 := (* -1::Int f4)
-#103 := (+ f3 #102)
-#104 := (<= #103 0::Int)
-#105 := (not #104)
-#118 := (>= #103 0::Int)
-#78 := (* -1::Int f5)
-#96 := (+ f4 #78)
-#95 := (>= #96 0::Int)
-#94 := (not #95)
-#261 := (not #13)
-#435 := [hypothesis]: #261
-#127 := (<= #96 0::Int)
-#474 := (or #18 #13)
-#441 := [hypothesis]: #238
-#447 := (or #104 #18 #13)
-#436 := [hypothesis]: #105
-#300 := (or #127 #104)
-#128 := (not #127)
-#134 := (and #128 #105)
-#216 := (not #134)
-#309 := (iff #216 #300)
-#301 := (not #300)
-#304 := (not #301)
-#307 := (iff #304 #300)
-#308 := [rewrite]: #307
-#305 := (iff #216 #304)
-#302 := (iff #134 #301)
-#303 := [rewrite]: #302
-#306 := [monotonicity #303]: #305
-#310 := [trans #306 #308]: #309
-#37 := (and #30 #24)
-#79 := (+ f3 #78)
-#80 := (<= #79 0::Int)
-#81 := (not #80)
-#84 := (and #13 #81)
-#88 := (>= #79 0::Int)
-#87 := (not #88)
-#91 := (and #24 #87)
-#99 := (and #94 #81)
-#108 := (and #105 #28)
-#111 := (and #105 #87)
-#114 := (and #30 #105)
-#117 := (not #118)
-#121 := (and #28 #117)
-#124 := (and #81 #117)
-#131 := (and #128 #24)
-#137 := (and #20 #94)
-#140 := (and #18 #128)
-#143 := (and #87 #128)
-#146 := (and #117 #13)
-#149 := (and #117 #94)
-#197 := (or #149 #146 #143 #140 #137 #134 #131 #124 #121 #114 #111 #108 #99 #91 #84 #37)
-#202 := (not #197)
-#26 := (< f5 f3)
-#36 := (and #13 #26)
-#38 := (or #36 #37)
-#15 := (< f3 f5)
-#35 := (and #24 #15)
-#39 := (or #35 #38)
-#11 := (< f4 f5)
-#34 := (and #11 #26)
-#40 := (or #34 #39)
-#22 := (< f4 f3)
-#33 := (and #22 #28)
-#41 := (or #33 #40)
-#32 := (and #22 #15)
-#42 := (or #32 #41)
-#31 := (and #30 #22)
-#43 := (or #31 #42)
-#9 := (< f3 f4)
-#29 := (and #28 #9)
-#44 := (or #29 #43)
-#27 := (and #26 #9)
-#45 := (or #27 #44)
-#16 := (< f5 f4)
-#25 := (and #16 #24)
-#46 := (or #25 #45)
-#23 := (and #16 #22)
-#47 := (or #23 #46)
-#21 := (and #20 #11)
-#48 := (or #21 #47)
-#19 := (and #18 #16)
-#49 := (or #19 #48)
-#17 := (and #15 #16)
-#50 := (or #17 #49)
-#14 := (and #9 #13)
-#51 := (or #14 #50)
-#12 := (and #9 #11)
-#52 := (or #12 #51)
-#53 := (not #52)
-#203 := (iff #53 #202)
-#200 := (iff #52 #197)
-#152 := (or #84 #37)
-#155 := (or #91 #152)
-#158 := (or #99 #155)
-#161 := (or #108 #158)
-#164 := (or #111 #161)
-#167 := (or #114 #164)
-#170 := (or #121 #167)
-#173 := (or #124 #170)
-#176 := (or #131 #173)
-#179 := (or #134 #176)
-#182 := (or #137 #179)
-#185 := (or #140 #182)
-#188 := (or #143 #185)
-#191 := (or #146 #188)
-#194 := (or #149 #191)
-#198 := (iff #194 #197)
-#199 := [rewrite]: #198
-#195 := (iff #52 #194)
-#192 := (iff #51 #191)
-#189 := (iff #50 #188)
-#186 := (iff #49 #185)
-#183 := (iff #48 #182)
-#180 := (iff #47 #179)
-#177 := (iff #46 #176)
-#174 := (iff #45 #173)
-#171 := (iff #44 #170)
-#168 := (iff #43 #167)
-#165 := (iff #42 #164)
-#162 := (iff #41 #161)
-#159 := (iff #40 #158)
-#156 := (iff #39 #155)
-#153 := (iff #38 #152)
-#85 := (iff #36 #84)
-#82 := (iff #26 #81)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#154 := [monotonicity #86]: #153
-#92 := (iff #35 #91)
-#89 := (iff #15 #87)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#157 := [monotonicity #93 #154]: #156
-#100 := (iff #34 #99)
-#97 := (iff #11 #94)
-#98 := [rewrite]: #97
-#101 := [monotonicity #98 #83]: #100
-#160 := [monotonicity #101 #157]: #159
-#109 := (iff #33 #108)
-#106 := (iff #22 #105)
-#107 := [rewrite]: #106
-#110 := [monotonicity #107]: #109
-#163 := [monotonicity #110 #160]: #162
-#112 := (iff #32 #111)
-#113 := [monotonicity #107 #90]: #112
-#166 := [monotonicity #113 #163]: #165
-#115 := (iff #31 #114)
-#116 := [monotonicity #107]: #115
-#169 := [monotonicity #116 #166]: #168
-#122 := (iff #29 #121)
-#119 := (iff #9 #117)
-#120 := [rewrite]: #119
-#123 := [monotonicity #120]: #122
-#172 := [monotonicity #123 #169]: #171
-#125 := (iff #27 #124)
-#126 := [monotonicity #83 #120]: #125
-#175 := [monotonicity #126 #172]: #174
-#132 := (iff #25 #131)
-#129 := (iff #16 #128)
-#130 := [rewrite]: #129
-#133 := [monotonicity #130]: #132
-#178 := [monotonicity #133 #175]: #177
-#135 := (iff #23 #134)
-#136 := [monotonicity #130 #107]: #135
-#181 := [monotonicity #136 #178]: #180
-#138 := (iff #21 #137)
-#139 := [monotonicity #98]: #138
-#184 := [monotonicity #139 #181]: #183
-#141 := (iff #19 #140)
-#142 := [monotonicity #130]: #141
-#187 := [monotonicity #142 #184]: #186
-#144 := (iff #17 #143)
-#145 := [monotonicity #90 #130]: #144
-#190 := [monotonicity #145 #187]: #189
-#147 := (iff #14 #146)
-#148 := [monotonicity #120]: #147
-#193 := [monotonicity #148 #190]: #192
-#150 := (iff #12 #149)
-#151 := [monotonicity #120 #98]: #150
-#196 := [monotonicity #151 #193]: #195
-#201 := [trans #196 #199]: #200
-#204 := [monotonicity #201]: #203
-#74 := [asserted]: #53
-#205 := [mp #74 #204]: #202
-#217 := [not-or-elim #205]: #216
-#311 := [mp #217 #310]: #300
-#437 := [unit-resolution #311 #436]: #127
-#438 := (or #13 #128 #94)
-#439 := [th-lemma arith triangle-eq]: #438
-#440 := [unit-resolution #439 #437 #435]: #94
-#363 := (or #104 #88)
-#226 := (not #111)
-#372 := (iff #226 #363)
-#364 := (not #363)
-#367 := (not #364)
-#370 := (iff #367 #363)
-#371 := [rewrite]: #370
-#368 := (iff #226 #367)
-#365 := (iff #111 #364)
-#366 := [rewrite]: #365
-#369 := [monotonicity #366]: #368
-#373 := [trans #369 #371]: #372
-#227 := [not-or-elim #205]: #226
-#374 := [mp #227 #373]: #363
-#442 := [unit-resolution #374 #436]: #88
-#443 := (or #18 #81 #87)
-#444 := [th-lemma arith triangle-eq]: #443
-#445 := [unit-resolution #444 #442 #441]: #81
-#387 := (or #95 #80)
-#230 := (not #99)
-#396 := (iff #230 #387)
-#388 := (not #387)
-#391 := (not #388)
-#394 := (iff #391 #387)
-#395 := [rewrite]: #394
-#392 := (iff #230 #391)
-#389 := (iff #99 #388)
-#390 := [rewrite]: #389
-#393 := [monotonicity #390]: #392
-#397 := [trans #393 #395]: #396
-#231 := [not-or-elim #205]: #230
-#398 := [mp #231 #397]: #387
-#446 := [unit-resolution #398 #445 #440]: false
-#448 := [lemma #446]: #447
-#466 := [unit-resolution #448 #441 #435]: #104
-#464 := (or #80 #13 #105)
-#460 := (iff #20 #24)
-#461 := [symm #459]: #460
-#453 := [hypothesis]: #104
-#449 := [hypothesis]: #81
-#325 := (or #80 #118)
-#220 := (not #124)
-#334 := (iff #220 #325)
-#326 := (not #325)
-#329 := (not #326)
-#332 := (iff #329 #325)
-#333 := [rewrite]: #332
-#330 := (iff #220 #329)
-#327 := (iff #124 #326)
-#328 := [rewrite]: #327
-#331 := [monotonicity #328]: #330
-#335 := [trans #331 #333]: #334
-#221 := [not-or-elim #205]: #220
-#336 := [mp #221 #335]: #325
-#454 := [unit-resolution #336 #449]: #118
-#455 := (or #20 #105 #117)
-#456 := [th-lemma arith triangle-eq]: #455
-#457 := [unit-resolution #456 #454 #453]: #20
-#462 := [mp #457 #461]: #24
-#450 := [unit-resolution #398 #449]: #95
-#451 := [unit-resolution #439 #450 #435]: #128
-#313 := (or #127 #312)
-#218 := (not #131)
-#322 := (iff #218 #313)
-#314 := (not #313)
-#317 := (not #314)
-#320 := (iff #317 #313)
-#321 := [rewrite]: #320
-#318 := (iff #218 #317)
-#315 := (iff #131 #314)
-#316 := [rewrite]: #315
-#319 := [monotonicity #316]: #318
-#323 := [trans #319 #321]: #322
-#219 := [not-or-elim #205]: #218
-#324 := [mp #219 #323]: #313
-#452 := [unit-resolution #324 #451]: #312
-#463 := [unit-resolution #452 #462]: false
-#465 := [lemma #463]: #464
-#467 := [unit-resolution #465 #466 #435]: #80
-#468 := [unit-resolution #444 #467 #441]: #87
-#250 := (or #88 #127)
-#210 := (not #143)
-#239 := (iff #210 #250)
-#247 := (not #250)
-#246 := (not #247)
-#241 := (iff #246 #250)
-#242 := [rewrite]: #241
-#243 := (iff #210 #246)
-#248 := (iff #143 #247)
-#245 := [rewrite]: #248
-#244 := [monotonicity #245]: #243
-#240 := [trans #244 #242]: #239
-#211 := [not-or-elim #205]: #210
-#76 := [mp #211 #240]: #250
-#469 := [unit-resolution #76 #468]: #127
-#470 := [unit-resolution #439 #469 #435]: #94
-#271 := (or #118 #95)
-#206 := (not #149)
-#266 := (iff #206 #271)
-#272 := (not #271)
-#269 := (not #272)
-#268 := (iff #269 #271)
-#265 := [rewrite]: #268
-#270 := (iff #206 #269)
-#273 := (iff #149 #272)
-#274 := [rewrite]: #273
-#267 := [monotonicity #274]: #270
-#263 := [trans #267 #265]: #266
-#207 := [not-or-elim #205]: #206
-#264 := [mp #207 #263]: #271
-#471 := [unit-resolution #264 #470]: #118
-#288 := (or #287 #95)
-#214 := (not #137)
-#297 := (iff #214 #288)
-#289 := (not #288)
-#292 := (not #289)
-#295 := (iff #292 #288)
-#296 := [rewrite]: #295
-#293 := (iff #214 #292)
-#290 := (iff #137 #289)
-#291 := [rewrite]: #290
-#294 := [monotonicity #291]: #293
-#298 := [trans #294 #296]: #297
-#215 := [not-or-elim #205]: #214
-#299 := [mp #215 #298]: #288
-#472 := [unit-resolution #299 #470]: #287
-#473 := [unit-resolution #456 #472 #471 #466]: false
-#475 := [lemma #473]: #474
-#476 := [unit-resolution #475 #435]: #18
-#275 := (or #238 #127)
-#212 := (not #140)
-#284 := (iff #212 #275)
-#276 := (not #275)
-#279 := (not #276)
-#282 := (iff #279 #275)
-#283 := [rewrite]: #282
-#280 := (iff #212 #279)
-#277 := (iff #140 #276)
-#278 := [rewrite]: #277
-#281 := [monotonicity #278]: #280
-#285 := [trans #281 #283]: #284
-#213 := [not-or-elim #205]: #212
-#286 := [mp #213 #285]: #275
-#477 := [unit-resolution #286 #476]: #127
-#478 := [unit-resolution #439 #477 #435]: #94
-#479 := [unit-resolution #264 #478]: #118
-#480 := [unit-resolution #299 #478]: #287
-#481 := [unit-resolution #456 #480 #479]: #105
-#375 := (or #104 #337)
-#228 := (not #108)
-#384 := (iff #228 #375)
-#376 := (not #375)
-#379 := (not #376)
-#382 := (iff #379 #375)
-#383 := [rewrite]: #382
-#380 := (iff #228 #379)
-#377 := (iff #108 #376)
-#378 := [rewrite]: #377
-#381 := [monotonicity #378]: #380
-#385 := [trans #381 #383]: #384
-#229 := [not-or-elim #205]: #228
-#386 := [mp #229 #385]: #375
-#482 := [unit-resolution #386 #481]: #337
-#487 := [mp #482 #486]: #238
-#488 := [unit-resolution #476 #487]: false
-#489 := [lemma #488]: #13
-#495 := [mp #489 #494]: #30
-#350 := (not #30)
-#423 := (or #350 #312)
-#236 := (not #37)
-#432 := (iff #236 #423)
-#424 := (not #423)
-#427 := (not #424)
-#430 := (iff #427 #423)
-#431 := [rewrite]: #430
-#428 := (iff #236 #427)
-#425 := (iff #37 #424)
-#426 := [rewrite]: #425
-#429 := [monotonicity #426]: #428
-#433 := [trans #429 #431]: #432
-#237 := [not-or-elim #205]: #236
-#434 := [mp #237 #433]: #423
-#498 := [unit-resolution #434 #495]: #312
-#501 := [mp #498 #500]: #287
-#262 := (or #118 #261)
-#208 := (not #146)
-#251 := (iff #208 #262)
-#259 := (not #262)
-#258 := (not #259)
-#253 := (iff #258 #262)
-#254 := [rewrite]: #253
-#255 := (iff #208 #258)
-#260 := (iff #146 #259)
-#257 := [rewrite]: #260
-#256 := [monotonicity #257]: #255
-#252 := [trans #256 #254]: #251
-#209 := [not-or-elim #205]: #208
-#249 := [mp #209 #252]: #262
-#490 := [unit-resolution #249 #489]: #118
-#351 := (or #350 #104)
-#224 := (not #114)
-#360 := (iff #224 #351)
-#352 := (not #351)
-#355 := (not #352)
-#358 := (iff #355 #351)
-#359 := [rewrite]: #358
-#356 := (iff #224 #355)
-#353 := (iff #114 #352)
-#354 := [rewrite]: #353
-#357 := [monotonicity #354]: #356
-#361 := [trans #357 #359]: #360
-#225 := [not-or-elim #205]: #224
-#362 := [mp #225 #361]: #351
-#496 := [unit-resolution #362 #495]: #104
-#497 := [unit-resolution #456 #496 #490]: #20
-[unit-resolution #497 #501]: false
-unsat
-70bd6436662c1fd4b8c8a6f696914593051990e6 52 0
-#2 := false
-#11 := 1::Real
-decl f3 :: Real
-#7 := f3
-#9 := 2::Real
-#10 := (* 2::Real f3)
-#12 := (+ #10 1::Real)
-#8 := (+ f3 f3)
-#13 := (< #8 #12)
-#14 := (or false #13)
-#15 := (or #13 #14)
-#16 := (not #15)
-#72 := (iff #16 false)
-#40 := (+ 1::Real #10)
-#43 := (< #10 #40)
-#60 := (not #43)
-#70 := (iff #60 false)
-#1 := true
-#65 := (not true)
-#68 := (iff #65 false)
-#69 := [rewrite]: #68
-#66 := (iff #60 #65)
-#63 := (iff #43 true)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#71 := [trans #67 #69]: #70
-#61 := (iff #16 #60)
-#58 := (iff #15 #43)
-#53 := (or #43 #43)
-#56 := (iff #53 #43)
-#57 := [rewrite]: #56
-#54 := (iff #15 #53)
-#51 := (iff #14 #43)
-#46 := (or false #43)
-#49 := (iff #46 #43)
-#50 := [rewrite]: #49
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#41 := (= #12 #40)
-#42 := [rewrite]: #41
-#38 := (= #8 #10)
-#39 := [rewrite]: #38
-#45 := [monotonicity #39 #42]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#55 := [monotonicity #45 #52]: #54
-#59 := [trans #55 #57]: #58
-#62 := [monotonicity #59]: #61
-#73 := [trans #62 #71]: #72
-#37 := [asserted]: #16
-[mp #37 #73]: false
-unsat
-6e7ef563e385e00340c905e5fb44172a278ff733 2215 0
-#2 := false
-decl f12 :: Int
-#52 := f12
-decl f5 :: Int
-#13 := f5
-#64 := (= f5 f12)
-#9 := 0::Int
-#97 := -1::Int
-#235 := (* -1::Int f12)
-#733 := (+ f5 #235)
-#735 := (>= #733 0::Int)
-decl f10 :: Int
-#40 := f10
-#201 := (* -1::Int f10)
-#394 := (>= f10 0::Int)
-#401 := (if #394 f10 #201)
-#412 := (* -1::Int #401)
-#746 := (+ f10 #412)
-#748 := (>= #746 0::Int)
-#916 := (not #748)
-decl f11 :: Int
-#46 := f11
-#218 := (* -1::Int f11)
-#365 := (>= f11 0::Int)
-#372 := (if #365 f11 #218)
-#383 := (* -1::Int #372)
-#743 := (+ f11 #383)
-#745 := (>= #743 0::Int)
-#717 := (= f11 #372)
-#899 := (not #735)
-#900 := [hypothesis]: #899
-#1902 := (or #365 #735)
-decl f4 :: Int
-#8 := f4
-#98 := (* -1::Int f4)
-#568 := (>= f4 0::Int)
-#575 := (if #568 f4 #98)
-#586 := (* -1::Int #575)
-#985 := (+ f4 #586)
-#986 := (<= #985 0::Int)
-#1269 := (not #986)
-#888 := (<= #746 0::Int)
-#709 := (= f10 #401)
-#366 := (not #365)
-#1202 := [hypothesis]: #366
-#1880 := (or #394 #735 #365)
-#655 := (= f4 #575)
-decl f3 :: Int
-#7 := f3
-#116 := (* -1::Int f3)
-#539 := (>= f3 0::Int)
-#546 := (if #539 f3 #116)
-#557 := (* -1::Int #546)
-#761 := (+ f3 #557)
-#762 := (<= #761 0::Int)
-#669 := (= f3 #546)
-#1863 := (or #539 #365 #735)
-#395 := (not #394)
-decl f6 :: Int
-#16 := f6
-#510 := (>= f6 0::Int)
-#511 := (not #510)
-decl f9 :: Int
-#34 := f9
-#184 := (* -1::Int f9)
-#423 := (>= f9 0::Int)
-#430 := (if #423 f9 #184)
-#441 := (* -1::Int #430)
-#749 := (+ f9 #441)
-#751 := (>= #749 0::Int)
-#701 := (= f9 #430)
-#1430 := (>= #985 0::Int)
-#1498 := (not #1430)
-#587 := (+ f5 #586)
-#588 := (+ f3 #587)
-#649 := (<= #588 0::Int)
-#589 := (= #588 0::Int)
-decl f13 :: Int
-#58 := f13
-#65 := (= f4 f13)
-#66 := (and #64 #65)
-#336 := (>= f12 0::Int)
-#343 := (if #336 f12 #235)
-#354 := (* -1::Int #343)
-#355 := (+ f13 #354)
-#356 := (+ f11 #355)
-#357 := (= #356 0::Int)
-#362 := (not #357)
-#384 := (+ f12 #383)
-#385 := (+ f10 #384)
-#386 := (= #385 0::Int)
-#391 := (not #386)
-#413 := (+ f11 #412)
-#414 := (+ f9 #413)
-#415 := (= #414 0::Int)
-#420 := (not #415)
-#442 := (+ f10 #441)
-decl f8 :: Int
-#28 := f8
-#443 := (+ f8 #442)
-#444 := (= #443 0::Int)
-#449 := (not #444)
-#167 := (* -1::Int f8)
-#452 := (>= f8 0::Int)
-#459 := (if #452 f8 #167)
-#470 := (* -1::Int #459)
-#471 := (+ f9 #470)
-decl f7 :: Int
-#22 := f7
-#472 := (+ f7 #471)
-#473 := (= #472 0::Int)
-#478 := (not #473)
-#150 := (* -1::Int f7)
-#481 := (>= f7 0::Int)
-#488 := (if #481 f7 #150)
-#499 := (* -1::Int #488)
-#500 := (+ f8 #499)
-#501 := (+ f6 #500)
-#502 := (= #501 0::Int)
-#507 := (not #502)
-#133 := (* -1::Int f6)
-#517 := (if #510 f6 #133)
-#528 := (* -1::Int #517)
-#529 := (+ f7 #528)
-#530 := (+ f3 #529)
-#531 := (= #530 0::Int)
-#536 := (not #531)
-#558 := (+ f6 #557)
-#559 := (+ f4 #558)
-#560 := (= #559 0::Int)
-#565 := (not #560)
-#594 := (not #589)
-#624 := (or #594 #565 #536 #507 #478 #449 #420 #391 #362 #66)
-#629 := (not #624)
-#60 := (- f12)
-#59 := (< f12 0::Int)
-#61 := (if #59 #60 f12)
-#62 := (- #61 f11)
-#63 := (= f13 #62)
-#67 := (implies #63 #66)
-#54 := (- f11)
-#53 := (< f11 0::Int)
-#55 := (if #53 #54 f11)
-#56 := (- #55 f10)
-#57 := (= f12 #56)
-#68 := (implies #57 #67)
-#48 := (- f10)
-#47 := (< f10 0::Int)
-#49 := (if #47 #48 f10)
-#50 := (- #49 f9)
-#51 := (= f11 #50)
-#69 := (implies #51 #68)
-#42 := (- f9)
-#41 := (< f9 0::Int)
-#43 := (if #41 #42 f9)
-#44 := (- #43 f8)
-#45 := (= f10 #44)
-#70 := (implies #45 #69)
-#36 := (- f8)
-#35 := (< f8 0::Int)
-#37 := (if #35 #36 f8)
-#38 := (- #37 f7)
-#39 := (= f9 #38)
-#71 := (implies #39 #70)
-#30 := (- f7)
-#29 := (< f7 0::Int)
-#31 := (if #29 #30 f7)
-#32 := (- #31 f6)
-#33 := (= f8 #32)
-#72 := (implies #33 #71)
-#24 := (- f6)
-#23 := (< f6 0::Int)
-#25 := (if #23 #24 f6)
-#26 := (- #25 f3)
-#27 := (= f7 #26)
-#73 := (implies #27 #72)
-#18 := (- f3)
-#17 := (< f3 0::Int)
-#19 := (if #17 #18 f3)
-#20 := (- #19 f4)
-#21 := (= f6 #20)
-#74 := (implies #21 #73)
-#11 := (- f4)
-#10 := (< f4 0::Int)
-#12 := (if #10 #11 f4)
-#14 := (- #12 f5)
-#15 := (= f3 #14)
-#75 := (implies #15 #74)
-#76 := (not #75)
-#632 := (iff #76 #629)
-#238 := (if #59 #235 f12)
-#244 := (+ #218 #238)
-#249 := (= f13 #244)
-#255 := (not #249)
-#256 := (or #255 #66)
-#221 := (if #53 #218 f11)
-#227 := (+ #201 #221)
-#232 := (= f12 #227)
-#264 := (not #232)
-#265 := (or #264 #256)
-#204 := (if #47 #201 f10)
-#210 := (+ #184 #204)
-#215 := (= f11 #210)
-#273 := (not #215)
-#274 := (or #273 #265)
-#187 := (if #41 #184 f9)
-#193 := (+ #167 #187)
-#198 := (= f10 #193)
-#282 := (not #198)
-#283 := (or #282 #274)
-#170 := (if #35 #167 f8)
-#176 := (+ #150 #170)
-#181 := (= f9 #176)
-#291 := (not #181)
-#292 := (or #291 #283)
-#153 := (if #29 #150 f7)
-#159 := (+ #133 #153)
-#164 := (= f8 #159)
-#300 := (not #164)
-#301 := (or #300 #292)
-#136 := (if #23 #133 f6)
-#142 := (+ #116 #136)
-#147 := (= f7 #142)
-#309 := (not #147)
-#310 := (or #309 #301)
-#119 := (if #17 #116 f3)
-#125 := (+ #98 #119)
-#130 := (= f6 #125)
-#318 := (not #130)
-#319 := (or #318 #310)
-#101 := (if #10 #98 f4)
-#107 := (* -1::Int f5)
-#108 := (+ #107 #101)
-#113 := (= f3 #108)
-#327 := (not #113)
-#328 := (or #327 #319)
-#333 := (not #328)
-#630 := (iff #333 #629)
-#627 := (iff #328 #624)
-#597 := (or #362 #66)
-#600 := (or #391 #597)
-#603 := (or #420 #600)
-#606 := (or #449 #603)
-#609 := (or #478 #606)
-#612 := (or #507 #609)
-#615 := (or #536 #612)
-#618 := (or #565 #615)
-#621 := (or #594 #618)
-#625 := (iff #621 #624)
-#626 := [rewrite]: #625
-#622 := (iff #328 #621)
-#619 := (iff #319 #618)
-#616 := (iff #310 #615)
-#613 := (iff #301 #612)
-#610 := (iff #292 #609)
-#607 := (iff #283 #606)
-#604 := (iff #274 #603)
-#601 := (iff #265 #600)
-#598 := (iff #256 #597)
-#363 := (iff #255 #362)
-#360 := (iff #249 #357)
-#348 := (+ #218 #343)
-#351 := (= f13 #348)
-#358 := (iff #351 #357)
-#359 := [rewrite]: #358
-#352 := (iff #249 #351)
-#349 := (= #244 #348)
-#346 := (= #238 #343)
-#337 := (not #336)
-#340 := (if #337 #235 f12)
-#344 := (= #340 #343)
-#345 := [rewrite]: #344
-#341 := (= #238 #340)
-#338 := (iff #59 #337)
-#339 := [rewrite]: #338
-#342 := [monotonicity #339]: #341
-#347 := [trans #342 #345]: #346
-#350 := [monotonicity #347]: #349
-#353 := [monotonicity #350]: #352
-#361 := [trans #353 #359]: #360
-#364 := [monotonicity #361]: #363
-#599 := [monotonicity #364]: #598
-#392 := (iff #264 #391)
-#389 := (iff #232 #386)
-#377 := (+ #201 #372)
-#380 := (= f12 #377)
-#387 := (iff #380 #386)
-#388 := [rewrite]: #387
-#381 := (iff #232 #380)
-#378 := (= #227 #377)
-#375 := (= #221 #372)
-#369 := (if #366 #218 f11)
-#373 := (= #369 #372)
-#374 := [rewrite]: #373
-#370 := (= #221 #369)
-#367 := (iff #53 #366)
-#368 := [rewrite]: #367
-#371 := [monotonicity #368]: #370
-#376 := [trans #371 #374]: #375
-#379 := [monotonicity #376]: #378
-#382 := [monotonicity #379]: #381
-#390 := [trans #382 #388]: #389
-#393 := [monotonicity #390]: #392
-#602 := [monotonicity #393 #599]: #601
-#421 := (iff #273 #420)
-#418 := (iff #215 #415)
-#406 := (+ #184 #401)
-#409 := (= f11 #406)
-#416 := (iff #409 #415)
-#417 := [rewrite]: #416
-#410 := (iff #215 #409)
-#407 := (= #210 #406)
-#404 := (= #204 #401)
-#398 := (if #395 #201 f10)
-#402 := (= #398 #401)
-#403 := [rewrite]: #402
-#399 := (= #204 #398)
-#396 := (iff #47 #395)
-#397 := [rewrite]: #396
-#400 := [monotonicity #397]: #399
-#405 := [trans #400 #403]: #404
-#408 := [monotonicity #405]: #407
-#411 := [monotonicity #408]: #410
-#419 := [trans #411 #417]: #418
-#422 := [monotonicity #419]: #421
-#605 := [monotonicity #422 #602]: #604
-#450 := (iff #282 #449)
-#447 := (iff #198 #444)
-#435 := (+ #167 #430)
-#438 := (= f10 #435)
-#445 := (iff #438 #444)
-#446 := [rewrite]: #445
-#439 := (iff #198 #438)
-#436 := (= #193 #435)
-#433 := (= #187 #430)
-#424 := (not #423)
-#427 := (if #424 #184 f9)
-#431 := (= #427 #430)
-#432 := [rewrite]: #431
-#428 := (= #187 #427)
-#425 := (iff #41 #424)
-#426 := [rewrite]: #425
-#429 := [monotonicity #426]: #428
-#434 := [trans #429 #432]: #433
-#437 := [monotonicity #434]: #436
-#440 := [monotonicity #437]: #439
-#448 := [trans #440 #446]: #447
-#451 := [monotonicity #448]: #450
-#608 := [monotonicity #451 #605]: #607
-#479 := (iff #291 #478)
-#476 := (iff #181 #473)
-#464 := (+ #150 #459)
-#467 := (= f9 #464)
-#474 := (iff #467 #473)
-#475 := [rewrite]: #474
-#468 := (iff #181 #467)
-#465 := (= #176 #464)
-#462 := (= #170 #459)
-#453 := (not #452)
-#456 := (if #453 #167 f8)
-#460 := (= #456 #459)
-#461 := [rewrite]: #460
-#457 := (= #170 #456)
-#454 := (iff #35 #453)
-#455 := [rewrite]: #454
-#458 := [monotonicity #455]: #457
-#463 := [trans #458 #461]: #462
-#466 := [monotonicity #463]: #465
-#469 := [monotonicity #466]: #468
-#477 := [trans #469 #475]: #476
-#480 := [monotonicity #477]: #479
-#611 := [monotonicity #480 #608]: #610
-#508 := (iff #300 #507)
-#505 := (iff #164 #502)
-#493 := (+ #133 #488)
-#496 := (= f8 #493)
-#503 := (iff #496 #502)
-#504 := [rewrite]: #503
-#497 := (iff #164 #496)
-#494 := (= #159 #493)
-#491 := (= #153 #488)
-#482 := (not #481)
-#485 := (if #482 #150 f7)
-#489 := (= #485 #488)
-#490 := [rewrite]: #489
-#486 := (= #153 #485)
-#483 := (iff #29 #482)
-#484 := [rewrite]: #483
-#487 := [monotonicity #484]: #486
-#492 := [trans #487 #490]: #491
-#495 := [monotonicity #492]: #494
-#498 := [monotonicity #495]: #497
-#506 := [trans #498 #504]: #505
-#509 := [monotonicity #506]: #508
-#614 := [monotonicity #509 #611]: #613
-#537 := (iff #309 #536)
-#534 := (iff #147 #531)
-#522 := (+ #116 #517)
-#525 := (= f7 #522)
-#532 := (iff #525 #531)
-#533 := [rewrite]: #532
-#526 := (iff #147 #525)
-#523 := (= #142 #522)
-#520 := (= #136 #517)
-#514 := (if #511 #133 f6)
-#518 := (= #514 #517)
-#519 := [rewrite]: #518
-#515 := (= #136 #514)
-#512 := (iff #23 #511)
-#513 := [rewrite]: #512
-#516 := [monotonicity #513]: #515
-#521 := [trans #516 #519]: #520
-#524 := [monotonicity #521]: #523
-#527 := [monotonicity #524]: #526
-#535 := [trans #527 #533]: #534
-#538 := [monotonicity #535]: #537
-#617 := [monotonicity #538 #614]: #616
-#566 := (iff #318 #565)
-#563 := (iff #130 #560)
-#551 := (+ #98 #546)
-#554 := (= f6 #551)
-#561 := (iff #554 #560)
-#562 := [rewrite]: #561
-#555 := (iff #130 #554)
-#552 := (= #125 #551)
-#549 := (= #119 #546)
-#540 := (not #539)
-#543 := (if #540 #116 f3)
-#547 := (= #543 #546)
-#548 := [rewrite]: #547
-#544 := (= #119 #543)
-#541 := (iff #17 #540)
-#542 := [rewrite]: #541
-#545 := [monotonicity #542]: #544
-#550 := [trans #545 #548]: #549
-#553 := [monotonicity #550]: #552
-#556 := [monotonicity #553]: #555
-#564 := [trans #556 #562]: #563
-#567 := [monotonicity #564]: #566
-#620 := [monotonicity #567 #617]: #619
-#595 := (iff #327 #594)
-#592 := (iff #113 #589)
-#580 := (+ #107 #575)
-#583 := (= f3 #580)
-#590 := (iff #583 #589)
-#591 := [rewrite]: #590
-#584 := (iff #113 #583)
-#581 := (= #108 #580)
-#578 := (= #101 #575)
-#569 := (not #568)
-#572 := (if #569 #98 f4)
-#576 := (= #572 #575)
-#577 := [rewrite]: #576
-#573 := (= #101 #572)
-#570 := (iff #10 #569)
-#571 := [rewrite]: #570
-#574 := [monotonicity #571]: #573
-#579 := [trans #574 #577]: #578
-#582 := [monotonicity #579]: #581
-#585 := [monotonicity #582]: #584
-#593 := [trans #585 #591]: #592
-#596 := [monotonicity #593]: #595
-#623 := [monotonicity #596 #620]: #622
-#628 := [trans #623 #626]: #627
-#631 := [monotonicity #628]: #630
-#334 := (iff #76 #333)
-#331 := (iff #75 #328)
-#324 := (implies #113 #319)
-#329 := (iff #324 #328)
-#330 := [rewrite]: #329
-#325 := (iff #75 #324)
-#322 := (iff #74 #319)
-#315 := (implies #130 #310)
-#320 := (iff #315 #319)
-#321 := [rewrite]: #320
-#316 := (iff #74 #315)
-#313 := (iff #73 #310)
-#306 := (implies #147 #301)
-#311 := (iff #306 #310)
-#312 := [rewrite]: #311
-#307 := (iff #73 #306)
-#304 := (iff #72 #301)
-#297 := (implies #164 #292)
-#302 := (iff #297 #301)
-#303 := [rewrite]: #302
-#298 := (iff #72 #297)
-#295 := (iff #71 #292)
-#288 := (implies #181 #283)
-#293 := (iff #288 #292)
-#294 := [rewrite]: #293
-#289 := (iff #71 #288)
-#286 := (iff #70 #283)
-#279 := (implies #198 #274)
-#284 := (iff #279 #283)
-#285 := [rewrite]: #284
-#280 := (iff #70 #279)
-#277 := (iff #69 #274)
-#270 := (implies #215 #265)
-#275 := (iff #270 #274)
-#276 := [rewrite]: #275
-#271 := (iff #69 #270)
-#268 := (iff #68 #265)
-#261 := (implies #232 #256)
-#266 := (iff #261 #265)
-#267 := [rewrite]: #266
-#262 := (iff #68 #261)
-#259 := (iff #67 #256)
-#252 := (implies #249 #66)
-#257 := (iff #252 #256)
-#258 := [rewrite]: #257
-#253 := (iff #67 #252)
-#250 := (iff #63 #249)
-#247 := (= #62 #244)
-#241 := (- #238 f11)
-#245 := (= #241 #244)
-#246 := [rewrite]: #245
-#242 := (= #62 #241)
-#239 := (= #61 #238)
-#236 := (= #60 #235)
-#237 := [rewrite]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#248 := [trans #243 #246]: #247
-#251 := [monotonicity #248]: #250
-#254 := [monotonicity #251]: #253
-#260 := [trans #254 #258]: #259
-#233 := (iff #57 #232)
-#230 := (= #56 #227)
-#224 := (- #221 f10)
-#228 := (= #224 #227)
-#229 := [rewrite]: #228
-#225 := (= #56 #224)
-#222 := (= #55 #221)
-#219 := (= #54 #218)
-#220 := [rewrite]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#231 := [trans #226 #229]: #230
-#234 := [monotonicity #231]: #233
-#263 := [monotonicity #234 #260]: #262
-#269 := [trans #263 #267]: #268
-#216 := (iff #51 #215)
-#213 := (= #50 #210)
-#207 := (- #204 f9)
-#211 := (= #207 #210)
-#212 := [rewrite]: #211
-#208 := (= #50 #207)
-#205 := (= #49 #204)
-#202 := (= #48 #201)
-#203 := [rewrite]: #202
-#206 := [monotonicity #203]: #205
-#209 := [monotonicity #206]: #208
-#214 := [trans #209 #212]: #213
-#217 := [monotonicity #214]: #216
-#272 := [monotonicity #217 #269]: #271
-#278 := [trans #272 #276]: #277
-#199 := (iff #45 #198)
-#196 := (= #44 #193)
-#190 := (- #187 f8)
-#194 := (= #190 #193)
-#195 := [rewrite]: #194
-#191 := (= #44 #190)
-#188 := (= #43 #187)
-#185 := (= #42 #184)
-#186 := [rewrite]: #185
-#189 := [monotonicity #186]: #188
-#192 := [monotonicity #189]: #191
-#197 := [trans #192 #195]: #196
-#200 := [monotonicity #197]: #199
-#281 := [monotonicity #200 #278]: #280
-#287 := [trans #281 #285]: #286
-#182 := (iff #39 #181)
-#179 := (= #38 #176)
-#173 := (- #170 f7)
-#177 := (= #173 #176)
-#178 := [rewrite]: #177
-#174 := (= #38 #173)
-#171 := (= #37 #170)
-#168 := (= #36 #167)
-#169 := [rewrite]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#180 := [trans #175 #178]: #179
-#183 := [monotonicity #180]: #182
-#290 := [monotonicity #183 #287]: #289
-#296 := [trans #290 #294]: #295
-#165 := (iff #33 #164)
-#162 := (= #32 #159)
-#156 := (- #153 f6)
-#160 := (= #156 #159)
-#161 := [rewrite]: #160
-#157 := (= #32 #156)
-#154 := (= #31 #153)
-#151 := (= #30 #150)
-#152 := [rewrite]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#163 := [trans #158 #161]: #162
-#166 := [monotonicity #163]: #165
-#299 := [monotonicity #166 #296]: #298
-#305 := [trans #299 #303]: #304
-#148 := (iff #27 #147)
-#145 := (= #26 #142)
-#139 := (- #136 f3)
-#143 := (= #139 #142)
-#144 := [rewrite]: #143
-#140 := (= #26 #139)
-#137 := (= #25 #136)
-#134 := (= #24 #133)
-#135 := [rewrite]: #134
-#138 := [monotonicity #135]: #137
-#141 := [monotonicity #138]: #140
-#146 := [trans #141 #144]: #145
-#149 := [monotonicity #146]: #148
-#308 := [monotonicity #149 #305]: #307
-#314 := [trans #308 #312]: #313
-#131 := (iff #21 #130)
-#128 := (= #20 #125)
-#122 := (- #119 f4)
-#126 := (= #122 #125)
-#127 := [rewrite]: #126
-#123 := (= #20 #122)
-#120 := (= #19 #119)
-#117 := (= #18 #116)
-#118 := [rewrite]: #117
-#121 := [monotonicity #118]: #120
-#124 := [monotonicity #121]: #123
-#129 := [trans #124 #127]: #128
-#132 := [monotonicity #129]: #131
-#317 := [monotonicity #132 #314]: #316
-#323 := [trans #317 #321]: #322
-#114 := (iff #15 #113)
-#111 := (= #14 #108)
-#104 := (- #101 f5)
-#109 := (= #104 #108)
-#110 := [rewrite]: #109
-#105 := (= #14 #104)
-#102 := (= #12 #101)
-#99 := (= #11 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#106 := [monotonicity #103]: #105
-#112 := [trans #106 #110]: #111
-#115 := [monotonicity #112]: #114
-#326 := [monotonicity #115 #323]: #325
-#332 := [trans #326 #330]: #331
-#335 := [monotonicity #332]: #334
-#633 := [trans #335 #631]: #632
-#96 := [asserted]: #76
-#634 := [mp #96 #633]: #629
-#635 := [not-or-elim #634]: #589
-#1489 := (or #594 #649)
-#1490 := [th-lemma arith triangle-eq]: #1489
-#1491 := [unit-resolution #1490 #635]: #649
-#675 := (<= #559 0::Int)
-#636 := [not-or-elim #634]: #560
-#1486 := (or #565 #675)
-#1487 := [th-lemma arith triangle-eq]: #1486
-#1488 := [unit-resolution #1487 #636]: #675
-#1251 := (+ #167 #470)
-#741 := (>= #1251 0::Int)
-#1066 := [hypothesis]: #424
-#1804 := (or #539 #423)
-#818 := [hypothesis]: #540
-#1760 := (or #394 #539 #423)
-#747 := (+ #201 #412)
-#1708 := (>= #747 0::Int)
-#710 := (= #201 #401)
-#1122 := [hypothesis]: #395
-#713 := (or #394 #710)
-#714 := [def-axiom]: #713
-#1709 := [unit-resolution #714 #1122]: #710
-#1230 := (not #710)
-#1710 := (or #1230 #1708)
-#1711 := [th-lemma arith triangle-eq]: #1710
-#1712 := [unit-resolution #1711 #1709]: #1708
-#683 := (<= #530 0::Int)
-#637 := [not-or-elim #634]: #531
-#895 := (or #536 #683)
-#896 := [th-lemma arith triangle-eq]: #895
-#897 := [unit-resolution #896 #637]: #683
-#760 := (+ f6 #528)
-#756 := (>= #760 0::Int)
-#677 := (= f6 #517)
-#1197 := (or #510 #423)
-#989 := [hypothesis]: #511
-#1188 := (or #481 #510 #423)
-#752 := (+ f8 #470)
-#988 := (<= #752 0::Int)
-#1014 := (not #988)
-#1062 := (+ #150 #499)
-#1161 := (<= #1062 0::Int)
-#686 := (= #150 #488)
-#891 := [hypothesis]: #482
-#689 := (or #481 #686)
-#690 := [def-axiom]: #689
-#1169 := [unit-resolution #690 #891]: #686
-#1094 := (not #686)
-#1170 := (or #1094 #1161)
-#1171 := [th-lemma arith triangle-eq]: #1170
-#1172 := [unit-resolution #1171 #1169]: #1161
-#927 := (+ #184 #441)
-#744 := (>= #927 0::Int)
-#702 := (= #184 #430)
-#705 := (or #423 #702)
-#706 := [def-axiom]: #705
-#1071 := [unit-resolution #706 #1066]: #702
-#954 := (not #702)
-#1173 := (or #954 #744)
-#1174 := [th-lemma arith triangle-eq]: #1173
-#1175 := [unit-resolution #1174 #1071]: #744
-#1166 := (or #394 #423 #481)
-#700 := (>= #472 0::Int)
-#639 := [not-or-elim #634]: #473
-#1011 := (or #478 #700)
-#1012 := [th-lemma arith triangle-eq]: #1011
-#1013 := [unit-resolution #1012 #639]: #700
-#928 := (<= #927 0::Int)
-#955 := (or #954 #928)
-#1027 := (not #928)
-#1028 := [hypothesis]: #1027
-#1029 := [hypothesis]: #702
-#956 := [th-lemma arith triangle-eq]: #955
-#1030 := [unit-resolution #956 #1029 #1028]: false
-#1031 := [lemma #1030]: #955
-#1072 := [unit-resolution #1031 #1071]: #928
-#708 := (>= #443 0::Int)
-#640 := [not-or-elim #634]: #444
-#905 := (or #449 #708)
-#906 := [th-lemma arith triangle-eq]: #905
-#907 := [unit-resolution #906 #640]: #708
-#1015 := (not #700)
-#1048 := (not #708)
-#1130 := (or #481 #394 #1048 #1014 #1015 #423 #1027)
-#1131 := [th-lemma arith assign-bounds 1 1 1 1 2 1]: #1130
-#1162 := [unit-resolution #1131 #1122 #1066 #907 #891 #1072 #1013]: #1014
-#693 := (= f8 #459)
-#1123 := (or #452 #423 #394 #1048 #1027)
-#1124 := [th-lemma arith assign-bounds 1 1 1 1]: #1123
-#1163 := [unit-resolution #1124 #1122 #907 #1072 #1066]: #452
-#695 := (or #453 #693)
-#696 := [def-axiom]: #695
-#1164 := [unit-resolution #696 #1163]: #693
-#1007 := (not #693)
-#1008 := (or #1007 #988)
-#1067 := [hypothesis]: #1014
-#1068 := [hypothesis]: #693
-#1009 := [th-lemma arith triangle-eq]: #1008
-#1069 := [unit-resolution #1009 #1068 #1067]: false
-#1070 := [lemma #1069]: #1008
-#1165 := [unit-resolution #1070 #1164 #1162]: false
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-#1593 := [unit-resolution #1592 #1590]: #1570
-#1599 := [unit-resolution #778 #1578]: #762
-#1602 := (or #365 #1267 #1027 #423 #452)
-#1600 := (or #365 #1267 #1240 #1027 #1048 #423 #452)
-#1601 := [th-lemma arith assign-bounds 1 1 1 1 2 1]: #1600
-#1603 := [unit-resolution #1601 #907 #1217]: #1602
-#1604 := [unit-resolution #1603 #1066 #1557 #1362 #1598]: #365
-#1605 := [unit-resolution #720 #1604]: #717
-#1606 := [unit-resolution #1476 #1605]: #1200
-#1607 := (not #1570)
-#1608 := (or #734 #1499 #1500 #1501 #1502 #1050 #823 #1267 #1240 #1001 #1002 #844 #1607 #870 #871)
-#1609 := [th-lemma arith assign-bounds -1 -1 1 1 -1 1 -1 1 -1 1 -1 1 -2 2]: #1608
-#1610 := [unit-resolution #1609 #1606 #816 #869 #791 #1217 #1494 #1491 #1599 #1566 #1574 #1598 #773 #1480 #1593]: #734
-#1611 := [unit-resolution #856 #1597]: #748
-#887 := (<= #886 0::Int)
-#923 := (or #922 #887)
-#915 := (not #887)
-#920 := [hypothesis]: #915
-#921 := [hypothesis]: #656
-#924 := [th-lemma arith triangle-eq]: #923
-#925 := [unit-resolution #924 #921 #920]: false
-#926 := [lemma #925]: #923
-#1612 := [unit-resolution #926 #1590]: #887
-#940 := (or #876 #757)
-#941 := [th-lemma arith triangle-eq]: #940
-#1613 := [unit-resolution #941 #1573]: #757
-#1614 := [unit-resolution #1207 #1605]: #745
-#794 := (not #757)
-#1615 := (or #735 #948 #795 #822 #1439 #1015 #1504 #916 #947 #794 #1049 #1503 #915 #917 #1051)
-#1616 := [th-lemma arith assign-bounds -1 -1 1 1 -1 1 -1 1 -1 1 -1 1 -2 2]: #1615
-#1617 := [unit-resolution #1616 #1614 #897 #787 #1013 #882 #782 #903 #1488 #1613 #1612 #1611 #1586 #1579 #1467]: #735
-#1618 := [unit-resolution #1515 #1617 #1610]: #64
-#1619 := [unit-resolution #658 #1618]: #668
-#740 := (+ f12 #354)
-#1571 := (<= #740 0::Int)
-#725 := (= f12 #343)
-#1620 := (or #336 #1500 #1501 #1267 #1240 #423)
-#1621 := [th-lemma arith assign-bounds 1 1 1 1 1]: #1620
-#1622 := [unit-resolution #1621 #1066 #1494 #1217 #1598 #1606]: #336
-#727 := (or #337 #725)
-#728 := [def-axiom]: #727
-#1623 := [unit-resolution #728 #1622]: #725
-#1394 := (not #725)
-#1624 := (or #1394 #1571)
-#1625 := [th-lemma arith triangle-eq]: #1624
-#1626 := [unit-resolution #1625 #1623]: #1571
-#1627 := (not #1571)
-#1628 := (or #738 #1627 #1500 #1501 #1539 #1504 #917 #1051 #1503 #1439 #1015 #1177 #1178)
-#1629 := [th-lemma arith assign-bounds 1 1 -1 -1 1 -1 1 -1 1 -1 -1 1]: #1628
-#1630 := [unit-resolution #1629 #1175 #1013 #836 #1494 #1537 #1488 #1586 #1579 #897 #1467 #1606 #1626]: #738
-#742 := (>= #740 0::Int)
-#1395 := (or #1394 #742)
-#1396 := [th-lemma arith triangle-eq]: #1395
-#1631 := [unit-resolution #1396 #1623]: #742
-#796 := (not #742)
-#1632 := (or #739 #796 #795 #822 #824 #823 #870 #871 #844 #1502 #1050 #1027 #1048)
-#1633 := [th-lemma arith assign-bounds 1 1 -1 -1 1 -1 1 -1 1 -1 -1 1]: #1632
-#1634 := [unit-resolution #1633 #1614 #791 #907 #782 #769 #773 #816 #1631 #1599 #1566 #1557 #1480]: #739
-#1635 := [unit-resolution #1544 #1634 #1630 #1619]: false
-#1637 := [lemma #1635]: #1636
-#1683 := [unit-resolution #1637 #1362]: #423
-#1684 := [unit-resolution #704 #1683]: #701
-#1685 := [unit-resolution #911 #1684]: #750
-#1686 := [unit-resolution #1377 #1685 #1362]: #365
-#1687 := [unit-resolution #720 #1686]: #717
-#1688 := [unit-resolution #1476 #1687]: #1200
-#1689 := [unit-resolution #1207 #1687]: #745
-#1663 := (or #735 #844 #916 #795 #1439 #794 #917 #1503)
-#1652 := [hypothesis]: #1356
-#784 := [hypothesis]: #745
-#913 := [hypothesis]: #748
-#889 := [hypothesis]: #762
-#1653 := [hypothesis]: #933
-#898 := [hypothesis]: #756
-#788 := [hypothesis]: #757
-#1654 := [unit-resolution #1616 #900 #897 #787 #1013 #882 #782 #903 #1488 #788 #784 #913 #898 #1653 #1652]: #915
-#1655 := [unit-resolution #926 #1654]: #922
-#1656 := [unit-resolution #652 #1655]: #568
-#1657 := [unit-resolution #654 #1656]: #655
-#1658 := [unit-resolution #1265 #1657]: #986
-#1659 := (or #1064 #794 #1504 #569 #917 #1051 #1503)
-#1660 := [th-lemma arith assign-bounds -1 2 -2 -2 2 -2]: #1659
-#1661 := [unit-resolution #1660 #1656 #897 #788 #898 #1488 #1653]: #1064
-#1662 := [unit-resolution #1512 #1661 #1658 #787 #1013 #882 #782 #903 #773 #889 #913 #784 #900 #1652]: false
-#1664 := [lemma #1662]: #1663
-#1690 := [unit-resolution #1664 #1599 #1611 #1689 #1467 #1613 #1586 #1579]: #735
-#1650 := (or #739 #795 #844 #1502 #1500 #1268 #1267)
-#1642 := [hypothesis]: #741
-#766 := [hypothesis]: #765
-#1643 := [unit-resolution #1633 #766 #791 #907 #782 #769 #773 #816 #784 #889 #1566 #1557 #1642]: #796
-#1385 := [hypothesis]: #888
-#1644 := [hypothesis]: #1200
-#1645 := [unit-resolution #1528 #766 #791 #907 #1217 #1494 #769 #1644 #889 #1566 #1252 #1385 #1642 #816 #773]: #1526
-#1638 := [hypothesis]: #1526
-#1639 := [hypothesis]: #726
-#1640 := [unit-resolution #1524 #1639 #1638]: false
-#1641 := [lemma #1640]: #1523
-#1646 := [unit-resolution #1641 #1645]: #1522
-#1647 := [unit-resolution #730 #1646]: #336
-#1648 := [unit-resolution #728 #1647]: #725
-#1649 := [unit-resolution #1396 #1648 #1643]: false
-#1651 := [lemma #1649]: #1650
-#1691 := [unit-resolution #1651 #1689 #1599 #1480 #1688 #1685 #1598]: #739
-#1692 := [unit-resolution #1408 #1684]: #751
-#1675 := (or #738 #795 #916 #917 #1503 #1439 #838)
-#813 := [hypothesis]: #751
-#1668 := [hypothesis]: #825
-#1669 := [unit-resolution #1541 #1668 #1013 #836 #882 #782 #1537 #1652 #784 #813 #913 #898 #1653 #897 #1488]: #1538
-#1665 := [hypothesis]: #1538
-#1666 := [unit-resolution #1531 #1639 #1665]: false
-#1667 := [lemma #1666]: #1530
-#1670 := [unit-resolution #1667 #1669]: #1522
-#1671 := [unit-resolution #730 #1670]: #336
-#1672 := [unit-resolution #728 #1671]: #725
-#1673 := [unit-resolution #1625 #1672]: #1571
-#1674 := [th-lemma arith farkas 1/2 -1/2 1 -1 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 1/2 -1/2 1 #784 #782 #913 #882 #1488 #898 #897 #1653 #1652 #1013 #1673 #1537 #1668 #813 #836 #1671]: false
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-#1695 := [unit-resolution #658 #1694]: #667
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-#1697 := [unit-resolution #1506 #1696 #869 #791 #1217 #1494 #1688 #1579 #1682 #1598 #1480 #1488 #1491]: #1498
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-#1677 := [hypothesis]: #1607
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-#1701 := [unit-resolution #654 #1700]: #655
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-#1714 := [unit-resolution #1706 #1066]: #481
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-#1716 := [unit-resolution #941 #1715]: #757
-#1717 := [unit-resolution #696 #1703]: #693
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-#1045 := [th-lemma arith triangle-eq]: #1044
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-#1077 := [th-lemma arith assign-bounds 2 1]: #1076
-#1719 := [unit-resolution #1077 #1066 #1557]: #838
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-#1721 := [th-lemma arith farkas 1 1]: #1720
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-#1724 := (or #1177 #1268 #394 #365 #1227 #1240)
-#1725 := [th-lemma arith assign-bounds 1 2 2 2 2]: #1724
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-#1729 := [unit-resolution #720 #1728]: #717
-#1730 := [unit-resolution #1207 #1729]: #745
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-#1732 := [th-lemma arith assign-bounds 1 1 1 2 2 1 1 1 1 1 1]: #1731
-#1733 := [unit-resolution #1732 #1122 #897 #787 #791 #907 #773 #1716 #1718 #820 #1713 #1557]: #568
-#1734 := [unit-resolution #654 #1733]: #655
-#1735 := [unit-resolution #1265 #1734]: #986
-#1736 := [th-lemma arith assign-bounds 1 -1 -1 -1 1 1 -1 1 -3 3 1 -2 2 -2 2 -1 #1735 #903 #773 #1730 #782 #882 #1718 #791 #1716 #787 #820 #907 #1557 #1713 #897 #1712]: #735
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-#1740 := [unit-resolution #878 #1715]: #812
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-#1750 := [unit-resolution #728 #1749]: #725
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-#1025 := (or #510 #795 #796 #739 #539)
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-#1046 := [unit-resolution #1045 #1043]: #754
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-#1052 := (or #1027 #1048 #796 #824 #739 #794 #1049 #797 #1050 #795 #822 #821 #823 #917 #1051)
-#1053 := [th-lemma arith assign-bounds -1 -1 1 1 -2 2 -1 1 -1 1 1 -1 -1 1]: #1052
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-#1781 := [unit-resolution #1780 #1776 #1722 #1774 #1175]: #365
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-#1772 := (or #735 #795 #1001 #1754 #916)
-#1284 := [hypothesis]: #812
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-#904 := [hypothesis]: #887
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-#1765 := [lemma #1763]: #1764
-#1766 := [unit-resolution #1765 #900 #1762 #1284 #784 #913]: #915
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-#1771 := [th-lemma arith farkas -1 1 1 -1 1 1 1 -1 1 -1 -1 -1 -2 1 #903 #900 #1488 #784 #782 #882 #1448 #1013 #1284 #869 #1762 #913 #1768 #1770]: false
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-#1796 := (or #1607 #823 #797 #1050 #794 #1049 #821 #1499 #734 #1500 #1501 #1240 #1267)
-#1797 := [th-lemma arith assign-bounds 1 1 -1 1 -1 -1 -1 1 -1 1 1 -1]: #1796
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-#1801 := [unit-resolution #654 #1800]: #655
-#1802 := [unit-resolution #1464 #1801]: #1430
-#1803 := [th-lemma arith farkas -1/2 -1/2 1/2 -3/2 3/2 1/2 -1 1 -1 1 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 1 #1488 #1448 #1013 #1740 #869 #1739 #836 #1175 #1566 #816 #1802 #1491 #1795 #1783 #1494 #1217 #1776 #1774]: false
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-#1807 := (or #741 #797 #794 #1049 #917 #1051 #540)
-#1808 := [th-lemma arith assign-bounds -1 -2 2 -2 2 -2]: #1807
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-#1813 := [unit-resolution #712 #1812]: #709
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-#1815 := (or #1161 #1049 #453 #482 #511)
-#1816 := [th-lemma arith assign-bounds -1 1 1 1]: #1815
-#1817 := [unit-resolution #1816 #1714 #787 #1703 #1203]: #1161
-#1818 := [unit-resolution #1780 #1814 #1722 #1812 #1175]: #365
-#1819 := [unit-resolution #720 #1818]: #717
-#1820 := [unit-resolution #1476 #1819]: #1200
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-#1822 := [unit-resolution #1496 #1821]: #933
-#1823 := [unit-resolution #1207 #1819]: #745
-#1826 := (or #1356 #453)
-#1824 := (or #1356 #453 #1014)
-#1825 := [th-lemma arith assign-bounds 2 -1]: #1824
-#1827 := [unit-resolution #1825 #1448]: #1826
-#1828 := [unit-resolution #1827 #1703]: #1356
-#1829 := [unit-resolution #778 #1821]: #762
-#1830 := [unit-resolution #856 #1813]: #748
-#1831 := [unit-resolution #1664 #1830 #1829 #1822 #1828 #1716 #1713 #1823]: #735
-#1832 := [unit-resolution #1651 #1820 #1829 #1809 #1823 #1722 #1814]: #739
-#1833 := [unit-resolution #1621 #1820 #1494 #1217 #1066 #1814]: #336
-#1834 := [unit-resolution #728 #1833]: #725
-#1835 := [unit-resolution #1625 #1834]: #1571
-#1836 := [unit-resolution #1629 #1835 #1013 #836 #1494 #1537 #1822 #1713 #1820 #1175 #1828 #897 #1488]: #738
-#1837 := [unit-resolution #1544 #1836 #1832]: #65
-#1838 := [unit-resolution #658 #1837]: #667
-#1839 := [unit-resolution #1515 #1838 #1831]: #949
-#1840 := [unit-resolution #1506 #1839 #869 #791 #1217 #1494 #1822 #1820 #1817 #1814 #1809 #1488 #1491]: #1498
-#1073 := (or #759 #540 #844)
-#1074 := [th-lemma arith assign-bounds 2 -1]: #1073
-#1841 := [unit-resolution #1074 #1829 #1806]: #759
-#1842 := [unit-resolution #1797 #1839 #787 #791 #1217 #1494 #773 #1716 #1718 #1841 #1814 #1820 #1491]: #1607
-#1843 := [unit-resolution #1679 #1842]: #922
-#1844 := [unit-resolution #652 #1843]: #568
-#1845 := [unit-resolution #654 #1844]: #655
-#1846 := [unit-resolution #1464 #1845 #1840]: false
-#1847 := [lemma #1846]: #423
-#1849 := [unit-resolution #704 #1847]: #701
-#1850 := [unit-resolution #1408 #1849]: #751
-#1354 := (or #539 #511 #365 #838)
-#1335 := [hypothesis]: #510
-#1336 := [unit-resolution #680 #1335]: #677
-#1337 := [unit-resolution #832 #1336]: #811
-#1338 := [unit-resolution #1036 #818 #816 #1335 #1337]: #481
-#1339 := [unit-resolution #688 #1338]: #685
-#1340 := [unit-resolution #878 #1339]: #812
-#1341 := [unit-resolution #1041 #1340 #869 #818 #1337 #816]: #452
-#1342 := [unit-resolution #696 #1341]: #693
-#1343 := [unit-resolution #1045 #1342]: #754
-#1344 := (or #983 #511 #870)
-#1345 := [th-lemma arith assign-bounds 2 -1]: #1344
-#1346 := [unit-resolution #1345 #1337 #1335]: #983
-#1347 := [unit-resolution #941 #1339]: #757
-#1289 := (or #539 #794 #1227 #995 #838 #365 #1001 #870)
-#1282 := [hypothesis]: #983
-#1283 := [hypothesis]: #753
-#890 := [hypothesis]: #811
-#1285 := [unit-resolution #1041 #818 #869 #1284 #890 #816]: #452
-#1286 := [unit-resolution #696 #1285]: #693
-#1287 := [unit-resolution #1045 #1286]: #754
-#1288 := [th-lemma arith farkas 2 2 1 1 1 1 1 1 1 1 1 1 #1287 #791 #788 #1283 #1217 #787 #816 #818 #1282 #813 #836 #1202]: false
-#1290 := [lemma #1288]: #1289
-#1348 := [unit-resolution #1290 #1347 #818 #1346 #813 #1202 #1340 #1337]: #1227
-#1349 := [unit-resolution #1234 #1348]: #1230
-#1350 := [unit-resolution #714 #1349]: #394
-#1351 := [unit-resolution #712 #1350]: #709
-#1352 := [unit-resolution #1220 #1351]: #888
-#1353 := [th-lemma arith farkas 1 -1 -1 1 -1 -1 -1 1 1 #1352 #1347 #1217 #787 #1335 #1350 #1343 #791 #1202]: false
-#1355 := [lemma #1353]: #1354
-#1851 := [unit-resolution #1355 #818 #1850 #1202]: #511
-#1852 := [unit-resolution #911 #1849]: #750
-#1199 := (+ #218 #383)
-#1201 := (>= #1199 0::Int)
-#718 := (= #218 #372)
-#721 := (or #365 #718)
-#722 := [def-axiom]: #721
-#1226 := [unit-resolution #722 #1202]: #718
-#1235 := (not #718)
-#1236 := (or #1235 #1201)
-#1237 := [th-lemma arith triangle-eq]: #1236
-#1238 := [unit-resolution #1237 #1226]: #1201
-#1223 := (not #1201)
-#1278 := (or #481 #1268 #735 #1223 #510)
-#1214 := [hypothesis]: #1201
-#1253 := [unit-resolution #1184 #1172 #869 #989 #891]: #452
-#1254 := [unit-resolution #696 #1253]: #693
-#1255 := [unit-resolution #1070 #1254]: #988
-#1256 := [unit-resolution #997 #891 #816 #989 #994]: #539
-#1257 := [unit-resolution #672 #1256]: #669
-#1258 := [unit-resolution #778 #1257]: #762
-#1259 := (or #568 #540 #844 #823 #510)
-#1260 := [th-lemma arith assign-bounds 1 1 1 1]: #1259
-#1261 := [unit-resolution #1260 #1258 #773 #989 #1256]: #568
-#1262 := [unit-resolution #654 #1261]: #655
-#1266 := [unit-resolution #1265 #1262]: #986
-#1270 := (or #1267 #1240 #1268 #1048 #844 #1049 #823 #1090 #1014 #1015 #1223 #822 #1269 #948 #735)
-#1271 := [th-lemma arith assign-bounds -1 2 -2 1 1 -1 -1 1 -1 -1 1 1 -1 1]: #1270
-#1272 := [unit-resolution #1271 #1258 #787 #1013 #907 #1217 #782 #900 #773 #1266 #1255 #1252 #1208 #903 #1214]: #1267
-#1275 := [unit-resolution #1274 #891 #907 #1013 #1255 #1252]: #394
-#1276 := [unit-resolution #712 #1275]: #709
-#1277 := [unit-resolution #1220 #1276 #1272]: false
-#1279 := [lemma #1277]: #1278
-#1853 := [unit-resolution #1279 #1851 #900 #1238 #1852]: #481
-#1854 := [unit-resolution #688 #1853]: #685
-#1855 := [unit-resolution #878 #1854]: #812
-#1311 := (or #539 #510 #395 #838 #1001)
-#1306 := [unit-resolution #1305 #994 #989]: #811
-#1307 := [unit-resolution #1041 #818 #869 #1284 #1306 #816]: #452
-#1308 := [unit-resolution #696 #1307]: #693
-#1309 := [unit-resolution #1045 #1308]: #754
-#783 := [hypothesis]: #394
-#1310 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 1 #989 #783 #791 #816 #818 #994 #813 #836 #1309]: false
-#1312 := [lemma #1310]: #1311
-#1856 := [unit-resolution #1312 #1855 #1850 #818 #1851]: #395
-#1857 := [unit-resolution #941 #1854]: #757
-#1858 := [unit-resolution #682 #1851]: #678
-#1859 := [unit-resolution #993 #1858]: #983
-#1860 := [unit-resolution #1290 #1859 #1566 #1850 #818 #1202 #1855 #1857]: #1227
-#1861 := [unit-resolution #1234 #1860]: #1230
-#1862 := [unit-resolution #714 #1861 #1856]: false
-#1864 := [lemma #1862]: #1863
-#1865 := [unit-resolution #1864 #1202 #900]: #539
-#1866 := [unit-resolution #672 #1865]: #669
-#1867 := [unit-resolution #778 #1866]: #762
-#1868 := [unit-resolution #1482 #1122 #1852]: #481
-#1869 := [unit-resolution #688 #1868]: #685
-#1870 := [unit-resolution #941 #1869]: #757
-#1871 := (or #511 #797 #1050 #794 #1049 #1227 #365 #1240 #394)
-#1872 := [th-lemma arith assign-bounds 1 1 1 1 1 1 1 1]: #1871
-#1873 := [unit-resolution #1872 #1122 #791 #787 #1217 #1202 #1870 #1718 #1723]: #511
-#1874 := (or #568 #540 #844 #510)
-#1875 := [unit-resolution #1260 #773]: #1874
-#1876 := [unit-resolution #1875 #1873 #1865 #1867]: #568
-#1877 := [unit-resolution #654 #1876]: #655
-#1878 := [unit-resolution #1265 #1877]: #986
-#1879 := [th-lemma arith farkas -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 #903 #900 #1867 #773 #782 #1238 #1718 #791 #1870 #787 #1723 #1217 #1878]: false
-#1881 := [lemma #1879]: #1880
-#1882 := [unit-resolution #1881 #1202 #900]: #394
-#1883 := [unit-resolution #712 #1882]: #709
-#1884 := [unit-resolution #1361 #1883]: #888
-#1885 := (or #481 #735 #844 #1267 #1268 #1223 #870)
-#1392 := (or #481 #735 #844 #1267 #1014 #1268 #1223 #870)
-#1378 := [hypothesis]: #988
-#1386 := [unit-resolution #1271 #1208 #787 #1013 #907 #1217 #782 #900 #889 #1385 #1378 #1252 #773 #903 #1214]: #1269
-#1389 := [unit-resolution #1388 #891 #816 #890 #889 #773]: #568
-#1390 := [unit-resolution #654 #1389]: #655
-#1391 := [unit-resolution #1265 #1390 #1386]: false
-#1393 := [lemma #1391]: #1392
-#1886 := [unit-resolution #1393 #1448]: #1885
-#1887 := [unit-resolution #1886 #1884 #900 #1566 #1852 #1238 #1867]: #481
-#1888 := [unit-resolution #688 #1887]: #685
-#1889 := [unit-resolution #941 #1888]: #757
-#1890 := (or #1064 #797 #1050 #838 #395 #1178 #794)
-#1891 := [th-lemma arith assign-bounds -2 2 -2 -2 2 -1]: #1890
-#1892 := [unit-resolution #1891 #1882 #836 #1889 #1718 #1850 #791]: #1064
-#1893 := (or #1267 #1268 #844 #1090 #1223 #1269 #735)
-#1894 := [unit-resolution #1271 #787 #1013 #907 #1217 #782 #1448 #773 #903]: #1893
-#1895 := [unit-resolution #1894 #1892 #900 #1238 #1867 #1852 #1884]: #1269
-#1896 := [unit-resolution #878 #1888]: #812
-#1897 := (or #1090 #1001 #823 #568 #870 #871 #844)
-#1898 := [th-lemma arith assign-bounds 1 2 2 2 2 2]: #1897
-#1899 := [unit-resolution #1898 #1892 #816 #1867 #1566 #1896 #773]: #568
-#1900 := [unit-resolution #654 #1899]: #655
-#1901 := [unit-resolution #1265 #1900 #1895]: false
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-#1924 := [unit-resolution #1903 #900]: #365
-#1925 := [unit-resolution #720 #1924]: #717
-#2127 := [unit-resolution #1207 #1925]: #745
-#1967 := (or #394 #481)
-#1968 := [unit-resolution #1482 #1852]: #1967
-#2032 := [unit-resolution #1968 #891]: #394
-#2033 := [unit-resolution #712 #2032]: #709
-#2034 := [unit-resolution #856 #2033]: #748
-#1998 := (or #394 #539)
-#1969 := [unit-resolution #1968 #1122]: #481
-#1970 := [unit-resolution #688 #1969]: #685
-#1971 := [unit-resolution #941 #1970]: #757
-#1225 := (or #365 #539 #1227 #794)
-#1218 := (or #539 #794 #1227 #995 #365)
-#1931 := [hypothesis]: #1001
-#1935 := (or #812 #757)
-#1936 := [th-lemma arith farkas 1 1]: #1935
-#1937 := [unit-resolution #1936 #1931]: #757
-#1932 := [hypothesis]: #685
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-#1934 := [lemma #1933]: #877
-#1938 := [unit-resolution #1934 #1931]: #876
-#1939 := [unit-resolution #688 #1938]: #482
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-#1941 := [th-lemma arith assign-bounds 2 1]: #1940
-#1942 := [unit-resolution #1941 #1939 #1937]: #1179
-#1943 := [unit-resolution #690 #1939]: #686
-#1944 := [unit-resolution #1171 #1943 #1942]: false
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-#1210 := [unit-resolution #1221 #1202 #818 #1283 #788]: #995
-#1211 := (or #539 #511 #365)
-#1212 := [unit-resolution #1355 #1850]: #1211
-#1213 := [unit-resolution #1212 #1202 #818]: #511
-#1222 := [unit-resolution #682 #1213]: #678
-#1224 := [unit-resolution #993 #1222 #1210]: false
-#1946 := [lemma #1224]: #1225
-#1972 := [unit-resolution #1946 #1723 #818 #1971]: #365
-#1973 := [unit-resolution #720 #1972]: #717
-#1974 := [unit-resolution #1476 #1973]: #1200
-#1913 := (or #568 #394 #539)
-#1904 := [hypothesis]: #569
-#1905 := [unit-resolution #1732 #1904 #897 #787 #791 #907 #773 #1122 #1718 #820 #1870 #1557]: #917
-#1908 := (or #568 #821 #539 #510)
-#1906 := (or #568 #821 #539 #823 #510)
-#1907 := [th-lemma arith assign-bounds 1 1 1 1]: #1906
-#1909 := [unit-resolution #1907 #773]: #1908
-#1910 := [unit-resolution #1909 #1904 #818 #820]: #510
-#1911 := [unit-resolution #680 #1910]: #677
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-#1914 := [lemma #1912]: #1913
-#1915 := [unit-resolution #1914 #1122 #818]: #568
-#1916 := [unit-resolution #654 #1915]: #655
-#1975 := [unit-resolution #1464 #1916]: #1430
-#1929 := (or #394 #735 #539)
-#1917 := [unit-resolution #1265 #1916]: #986
-#934 := (or #735 #734)
-#964 := [th-lemma arith farkas 1 1]: #934
-#965 := [unit-resolution #964 #900]: #734
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-#1919 := [th-lemma arith assign-bounds 1 1 1 2 1 1 1 1 1 1 1]: #1918
-#1920 := [unit-resolution #1919 #1870 #773 #787 #791 #1847 #903 #965 #818 #1718 #820 #1917]: #336
-#1921 := [unit-resolution #728 #1920]: #725
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-#1923 := [unit-resolution #878 #1869]: #812
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-#1150 := (or #795 #796 #739 #735)
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-#853 := [unit-resolution #712 #783]: #709
-#857 := [unit-resolution #856 #853]: #748
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-#826 := (or #510 #821 #539 #795 #395 #822 #823 #796 #824 #825)
-#827 := [th-lemma arith assign-bounds 1 1 1 1 1 1 1 1 1]: #826
-#935 := [unit-resolution #827 #820 #818 #783 #782 #769 #801 #770 #784 #773]: #510
-#936 := [unit-resolution #680 #935]: #677
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-#872 := (or #481 #870 #539 #871 #821 #795 #395 #822 #823 #796 #824 #825)
-#873 := [th-lemma arith assign-bounds 1 2 1 1 1 1 1 1 1 1 1]: #872
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-#931 := (or #569 #795 #395 #796 #739)
-#929 := [hypothesis]: #568
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-#845 := (or #510 #540 #844 #795 #395 #822 #823 #796 #824 #825)
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-#969 := [unit-resolution #846 #968 #966 #783 #782 #769 #801 #770 #784 #773]: #510
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-#792 := [hypothesis]: #423
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-#1092 := [lemma #1089]: #1091
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-#1138 := [unit-resolution #832 #1120]: #811
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-#1145 := [unit-resolution #688 #1144]: #685
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-#1249 := (or #423 #365 #337)
-#1241 := (or #1227 #1240 #337 #1223 #423 #822)
-#1242 := [th-lemma arith assign-bounds -1 -1 -1 1 1]: #1241
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-#1245 := [unit-resolution #714 #1244]: #394
-#1246 := [unit-resolution #712 #1245]: #709
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-#1403 := [unit-resolution #911 #1402]: #750
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-#1333 := (or #510 #796 #838 #739 #735 #1268)
-#1280 := [unit-resolution #1151 #770 #766 #900]: #795
-#1313 := [unit-resolution #1207 #1280]: #860
-#1314 := [unit-resolution #720 #1313]: #366
-#1315 := [unit-resolution #722 #1314]: #718
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-#1317 := [unit-resolution #1279 #989 #900 #1316 #1252]: #481
-#1318 := [unit-resolution #688 #1317]: #685
-#1319 := [unit-resolution #878 #1318]: #812
-#1302 := (or #1227 #796 #995 #838 #739 #1079 #482 #365 #870)
-#1281 := [hypothesis]: #481
-#1291 := [unit-resolution #688 #1281]: #685
-#1292 := [unit-resolution #878 #1291]: #812
-#1293 := [hypothesis]: #984
-#1294 := [unit-resolution #941 #1291]: #757
-#1295 := [unit-resolution #1290 #1283 #1294 #1282 #813 #1202 #1292 #890]: #539
-#1296 := [unit-resolution #1109 #1295 #1293 #869 #1281 #1292 #897]: #452
-#1297 := [unit-resolution #696 #1296]: #693
-#1298 := [unit-resolution #1045 #1297]: #754
-#1299 := [unit-resolution #672 #1295]: #669
-#1300 := [unit-resolution #778 #1299]: #762
-#1301 := [th-lemma arith farkas -1 1 -1 1 1 -1 -2 2 -2 2 -1 1 -1 1 -3 3 1 #770 #769 #1238 #782 #1300 #773 #1294 #1283 #1217 #787 #816 #1282 #813 #836 #1298 #791 #766]: false
-#1303 := [lemma #1301]: #1302
-#1320 := [unit-resolution #1303 #994 #770 #813 #766 #1023 #1317 #1314 #1306]: #1227
-#1321 := [unit-resolution #1234 #1320]: #1230
-#1322 := [unit-resolution #714 #1321]: #394
-#1323 := [unit-resolution #1312 #989 #1322 #813 #1319]: #539
-#1324 := [unit-resolution #672 #1323]: #669
-#1325 := [unit-resolution #778 #1324]: #762
-#1326 := [unit-resolution #1109 #1323 #1023 #869 #1317 #1319 #897]: #452
-#1327 := [unit-resolution #696 #1326]: #693
-#1328 := [unit-resolution #1045 #1327]: #754
-#1329 := [unit-resolution #941 #1318]: #757
-#1330 := [unit-resolution #712 #1322]: #709
-#1331 := [unit-resolution #1220 #1330]: #888
-#1332 := [th-lemma arith farkas -1 1 -1 1 -4 2 -2 -2 2 -3 3 1 -1 -1 1 -1 1 1 #770 #769 #1316 #782 #1322 #1331 #1329 #1217 #787 #1328 #791 #1325 #773 #816 #994 #813 #836 #766]: false
-#1334 := [lemma #1332]: #1333
-#1410 := [unit-resolution #1334 #1397 #1409 #766 #900 #1403]: #510
-#1411 := [unit-resolution #1355 #1410 #1400 #1409]: #539
-#1412 := [unit-resolution #680 #1410]: #677
-#1413 := [unit-resolution #959 #1412]: #756
-#1383 := (or #394 #917 #540 #424 #1014)
-#1379 := [unit-resolution #1274 #1122 #907 #1378 #1013 #912]: #481
-#1380 := [unit-resolution #688 #1379]: #685
-#1381 := [unit-resolution #941 #1380]: #757
-#1382 := [th-lemma arith farkas -1 1 -1 1 1 -1 -1 1 1 #787 #898 #897 #774 #792 #1122 #912 #907 #1381]: false
-#1384 := [lemma #1382]: #1383
-#1414 := [unit-resolution #1384 #1413 #1411 #1401 #1406]: #394
-#1415 := [unit-resolution #712 #1414]: #709
-#1416 := [unit-resolution #1361 #1415]: #888
-#1417 := (or #794 #1049 #917 #1051 #540 #1268 #1048 #1267 #1240 #365)
-#1418 := [th-lemma arith assign-bounds -1 1 -1 1 -1 1 -1 1 -1]: #1417
-#1419 := [unit-resolution #1418 #1400 #787 #907 #1217 #897 #1411 #1413 #1403 #1416]: #794
-#1420 := [unit-resolution #832 #1412]: #811
-#1421 := [unit-resolution #722 #1400]: #718
-#1422 := [unit-resolution #1237 #1421]: #1201
-#1423 := [unit-resolution #672 #1411]: #669
-#1424 := [unit-resolution #778 #1423]: #762
-#1425 := [unit-resolution #1393 #1424 #900 #1416 #1406 #1403 #1422 #1420]: #481
-#1426 := [unit-resolution #688 #1425]: #685
-#1427 := [unit-resolution #941 #1426 #1419]: false
-#1429 := [lemma #1427]: #1428
-#1927 := [unit-resolution #1429 #1920 #900]: #739
-#1928 := [th-lemma arith farkas -1 -1 1/2 -1/2 1/2 1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 -1/2 1/2 1 #1537 #1927 #1917 #903 #900 #1926 #1488 #1494 #1739 #1448 #1013 #1923 #869 #1712 #882 #1922]: false
-#1930 := [lemma #1928]: #1929
-#1976 := [unit-resolution #1930 #1122 #818]: #735
-#1965 := (or #510 #539 #899 #794 #1227 #1498)
-#1947 := [unit-resolution #1946 #1283 #818 #788]: #365
-#1948 := [unit-resolution #720 #1947]: #717
-#1949 := [unit-resolution #1476 #1948]: #1200
-#1950 := (or #336 #1240 #1500 #1501 #1227 #510 #797 #1050 #794 #1049 #995 #871 #838 #1178 #539)
-#1951 := [th-lemma arith assign-bounds 1 1 1 1 1 3 3 1 1 2 2 2 2 2]: #1950
-#1952 := [unit-resolution #1951 #989 #816 #787 #791 #836 #1217 #1494 #818 #788 #1718 #1850 #1283 #994 #1949]: #336
-#1953 := [unit-resolution #728 #1952]: #725
-#1954 := [unit-resolution #1625 #1953]: #1571
-#1955 := [hypothesis]: #735
-#1956 := [hypothesis]: #1430
-#1957 := [th-lemma arith assign-bounds 1 -1 1 -1 -1 1 1 3 -3 1 -1 -1 -2 2 2 -2 #1217 #1949 #1956 #1491 #1488 #1494 #1739 #1718 #791 #788 #787 #1283 #994 #816 #1850 #836]: #734
-#1958 := [unit-resolution #1515 #1957 #1955]: #64
-#1959 := [unit-resolution #658 #1958]: #668
-#1960 := [unit-resolution #1207 #1948]: #745
-#1961 := [unit-resolution #1396 #1953]: #742
-#1962 := [unit-resolution #1061 #1961 #818 #1960]: #739
-#1963 := [unit-resolution #1544 #1962 #1959]: #825
-#1964 := [th-lemma arith farkas -1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 1 #1537 #1963 #1949 #1488 #1494 #1739 #994 #816 #1718 #791 #1850 #836 #1954]: false
-#1966 := [lemma #1964]: #1965
-#1977 := [unit-resolution #1966 #1976 #818 #1971 #1723 #1975]: #510
-#1978 := (or #744 #838 #511 #797 #1050 #794 #1049)
-#1979 := [th-lemma arith assign-bounds -1 -2 -2 2 -2 2]: #1978
-#1980 := [unit-resolution #1979 #1971 #791 #787 #1718 #1850 #1977]: #744
-#1983 := (or #1177 #1500 #336 #1267)
-#1981 := (or #1177 #1268 #1500 #336 #1501 #1267 #1240)
-#1982 := [th-lemma arith assign-bounds 1 2 2 2 2 2]: #1981
-#1984 := [unit-resolution #1982 #1494 #1852 #1217]: #1983
-#1985 := [unit-resolution #1984 #1980 #1974 #1748]: #336
-#1986 := [unit-resolution #728 #1985]: #725
-#1987 := [unit-resolution #1396 #1986]: #742
-#1988 := [unit-resolution #1625 #1986]: #1571
-#1989 := (or #738 #1627 #1500 #1177 #1754)
-#1990 := [unit-resolution #1756 #869 #1013 #836 #1494 #1537 #1566 #1945 #1448 #816 #1488]: #1989
-#1991 := [unit-resolution #1990 #1988 #1739 #1980 #1974]: #738
-#1992 := [unit-resolution #1207 #1973]: #745
-#1993 := [unit-resolution #1061 #1987 #818 #1992]: #739
-#1994 := [unit-resolution #1544 #1993 #1991]: #65
-#1995 := [unit-resolution #658 #1994]: #667
-#1996 := [unit-resolution #1515 #1995 #1976]: #949
-#1997 := [th-lemma arith farkas -1 -1 1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 1 #769 #1991 #1992 #773 #782 #820 #1718 #791 #1217 #1975 #1491 #1996 #1971 #787 #1723 #1987]: false
-#1999 := [lemma #1997]: #1998
-#2000 := [unit-resolution #1999 #818]: #394
-#2001 := (or #539 #510 #395)
-#2002 := [unit-resolution #1312 #1850 #1945]: #2001
-#2003 := [unit-resolution #2002 #2000 #818]: #510
-#2008 := (or #1090 #511 #539)
-#2006 := (or #1090 #1001 #870 #511 #539)
-#2004 := (or #1090 #1001 #870 #871 #511 #539)
-#2005 := [th-lemma arith assign-bounds 1 2 2 2 2]: #2004
-#2007 := [unit-resolution #2005 #816]: #2006
-#2009 := [unit-resolution #2007 #1566 #1945]: #2008
-#2010 := [unit-resolution #2009 #2003 #818]: #1090
-#2011 := (or #1064 #395 #794)
-#2012 := [unit-resolution #1891 #836 #1718 #1850 #791]: #2011
-#2013 := [unit-resolution #2012 #2010 #2000]: #794
-#2014 := (or #481 #511 #539)
-#2015 := [unit-resolution #1455 #1566]: #2014
-#2016 := [unit-resolution #2015 #2003 #818]: #481
-#2017 := [unit-resolution #688 #2016]: #685
-#2018 := [unit-resolution #941 #2017 #2013]: false
-#2019 := [lemma #2018]: #539
-#2023 := [unit-resolution #672 #2019]: #669
-#2024 := [unit-resolution #778 #2023]: #762
-#2035 := (or #568 #844 #481)
-#2036 := [unit-resolution #1460 #1566]: #2035
-#2037 := [unit-resolution #2036 #891 #2024]: #568
-#2038 := [unit-resolution #654 #2037]: #655
-#2039 := [unit-resolution #1265 #2038]: #986
-#2030 := (or #735 #1090 #1269 #916)
-#2025 := [hypothesis]: #986
-#2026 := (or #735 #1269 #1090 #795 #844 #916)
-#2027 := [unit-resolution #1512 #787 #1013 #882 #782 #903 #773 #1828]: #2026
-#2028 := [unit-resolution #2027 #900 #1088 #2025 #2024 #913]: #795
-#2029 := [unit-resolution #1207 #1925 #2028]: false
-#2031 := [lemma #2029]: #2030
-#2040 := [unit-resolution #2031 #1208 #2039 #2034]: #735
-#2041 := [unit-resolution #1464 #2038]: #1430
-#2068 := (or #510 #481)
-#2042 := [unit-resolution #1496 #2023]: #933
-#1848 := (<= #1199 0::Int)
-#2043 := (or #366 #947 #838 #1178 #916 #1179 #481 #510 #1002)
-#2044 := [th-lemma arith assign-bounds 1 1 1 1 1 1 1 1]: #2043
-#2045 := [unit-resolution #2044 #989 #869 #836 #882 #891 #1850 #2034 #1172]: #366
-#2046 := [unit-resolution #722 #2045]: #718
-#2047 := (or #1235 #1848)
-#2048 := [th-lemma arith triangle-eq]: #2047
-#2049 := [unit-resolution #2048 #2046]: #1848
-#2050 := (not #1848)
-#2051 := (or #734 #1503 #797 #1050 #947 #1498 #1499 #1504 #1501 #916 #1179 #1002 #2050 #838 #1178)
-#2052 := [th-lemma arith assign-bounds 1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 2 -2]: #2051
-#2053 := [unit-resolution #2052 #2049 #869 #791 #836 #882 #1494 #1491 #1718 #1850 #2034 #2042 #1172 #2041 #1488]: #734
-#2054 := [unit-resolution #1515 #2053 #2040]: #64
-#2055 := [unit-resolution #658 #2054]: #668
-#2056 := [unit-resolution #1569 #990]: #984
-#2057 := (or #336 #797 #1050 #947 #1501 #916 #1179 #510 #1002 #2050 #838 #1178)
-#2058 := [th-lemma arith assign-bounds 1 1 1 1 1 1 1 1 1 2 2]: #2057
-#2059 := [unit-resolution #2058 #989 #791 #836 #882 #1494 #869 #1718 #1850 #2034 #1172 #2049]: #336
-#2060 := [unit-resolution #728 #2059]: #725
-#2061 := [unit-resolution #1625 #2060]: #1571
-#2062 := [th-lemma arith assign-bounds 1 -1 -1 -1 1 -3 3 -1 1 -1 1 1 2 -2 2 -2 #2061 #1537 #1494 #1718 #791 #1850 #836 #2042 #1488 #2056 #897 #2049 #882 #2034 #1172 #869]: #738
-#2063 := [unit-resolution #1361 #2033]: #888
-#2064 := [unit-resolution #1237 #2046]: #1201
-#2065 := [unit-resolution #1396 #2060]: #742
-#2066 := [th-lemma arith assign-bounds 1 -1 -1 -1 1 -3 3 -1 1 -1 1 1 2 -2 2 -2 #2065 #769 #782 #1448 #1013 #1852 #907 #2024 #773 #994 #816 #2064 #1217 #2063 #1208 #787]: #739
-#2067 := [unit-resolution #1544 #2066 #2062 #2055]: false
-#2069 := [lemma #2067]: #2068
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-#2101 := (or #1235 #1090 #1267 #511 #899 #916 #1179 #1498)
-#2083 := [hypothesis]: #718
-#2084 := [unit-resolution #1237 #2083]: #1201
-#2085 := [unit-resolution #959 #1336]: #756
-#2086 := [hypothesis]: #1161
-#2087 := [unit-resolution #2048 #2083]: #1848
-#2088 := [unit-resolution #2052 #2087 #869 #791 #836 #882 #1494 #1491 #1718 #1850 #913 #2042 #2086 #1956 #1488]: #734
-#2089 := [unit-resolution #1515 #2088 #1955]: #64
-#2090 := [unit-resolution #658 #2089]: #668
-#2081 := (or #739 #1267 #1090 #1223 #511 #2050)
-#2071 := [hypothesis]: #1848
-#2073 := (or #1526 #739 #2050)
-#2070 := [hypothesis]: #1433
-#2072 := [th-lemma arith farkas -1 -1 -1 -1 1 1 1 -1 1 -1 1 -1 1 #769 #766 #1566 #2024 #773 #816 #1850 #836 #1718 #791 #1494 #2071 #2070]: false
-#2074 := [lemma #2072]: #2073
-#2075 := [unit-resolution #2074 #766 #2071]: #1526
-#2076 := [unit-resolution #1641 #2075]: #1522
-#2077 := [unit-resolution #730 #2076]: #336
-#2078 := [unit-resolution #728 #2077]: #725
-#2079 := [unit-resolution #1396 #2078]: #742
-#2080 := [th-lemma arith farkas -1/2 1/2 1 -1/2 -1 1 -1 1/2 -3/2 3/2 1/2 -1/2 -1/2 -1/2 -1/2 1/2 1/2 1 #1448 #1013 #1217 #782 #1385 #1088 #787 #1214 #1852 #907 #2079 #769 #766 #1566 #2024 #773 #816 #1335]: false
-#2082 := [lemma #2080]: #2081
-#2091 := [unit-resolution #2082 #2084 #1088 #1385 #1335 #2087]: #739
-#2092 := [unit-resolution #1544 #2091 #2090]: #825
-#2093 := (or #1538 #1539 #738 #917 #1503 #1504 #1051 #1268 #1048 #1014 #1015 #822 #1223)
-#2094 := [th-lemma arith assign-bounds -1 -1 -1 -1 1 1 1 -1 1 -1 1 -1]: #2093
-#2095 := [unit-resolution #2094 #2092 #1013 #907 #782 #1537 #897 #2085 #1448 #1852 #2042 #2084 #1488]: #1538
-#2096 := [unit-resolution #1667 #2095]: #1522
-#2097 := [unit-resolution #730 #2096]: #336
-#2098 := [unit-resolution #728 #2097]: #725
-#2099 := [unit-resolution #1625 #2098]: #1571
-#2100 := [th-lemma arith farkas -1 -1 -2 -1 -1 1 1 1 -1 1 -1 1 -1 1 #1537 #2092 #2097 #2085 #2042 #1488 #897 #1852 #907 #1448 #1013 #782 #2084 #2099]: false
-#2102 := [lemma #2100]: #2101
-#2104 := [unit-resolution #2102 #1208 #2063 #2103 #2040 #2034 #1172 #2041]: #1235
-#2105 := [unit-resolution #722 #2104]: #365
-#2106 := (or #741 #797 #947 #916 #838 #1178 #366)
-#2107 := [th-lemma arith assign-bounds -1 2 -2 -2 2 -2]: #2106
-#2108 := [unit-resolution #2107 #2105 #882 #1718 #1850 #2034 #836]: #741
-#2109 := [unit-resolution #720 #2105]: #717
-#2110 := [unit-resolution #1476 #2109]: #1200
-#2111 := (or #734 #1498 #1179 #1500 #1502 #1503 #1267)
-#2112 := [unit-resolution #1506 #869 #791 #1217 #1494 #1488 #1491]: #2111
-#2113 := [unit-resolution #2112 #2110 #2042 #2041 #1172 #2063 #2108]: #734
-#2114 := [unit-resolution #1515 #2113 #2040]: #64
-#2115 := [unit-resolution #680 #2103]: #677
-#2116 := [unit-resolution #959 #2115]: #756
-#2117 := [unit-resolution #1207 #2109]: #745
-#2118 := (or #738 #795 #916 #917 #1503)
-#2119 := [unit-resolution #1676 #1850 #1828]: #2118
-#2120 := [unit-resolution #2119 #2117 #2042 #2116 #2034]: #738
-#2121 := (or #739 #795 #844 #1502 #1500 #1267)
-#2122 := [unit-resolution #1651 #1852]: #2121
-#2123 := [unit-resolution #2122 #2108 #2117 #2024 #2110 #2063]: #739
-#2124 := [unit-resolution #1544 #2123 #2120]: #65
-#2125 := [unit-resolution #658 #2124 #2114]: false
-#2126 := [lemma #2125]: #481
-#2149 := [unit-resolution #688 #2126]: #685
-#2020 := [hypothesis]: #794
-#2021 := [unit-resolution #941 #1932 #2020]: false
-#2022 := [lemma #2021]: #940
-#2150 := [unit-resolution #2022 #2149]: #757
-#2147 := (or #510 #735)
-#2136 := (or #916 #1001 #482 #947 #510 #1002 #838 #1178 #366)
-#2137 := [th-lemma arith assign-bounds -1 1 -1 -1 1 1 -1 1]: #2136
-#2138 := [unit-resolution #2137 #989 #869 #836 #882 #1924 #1850 #2126 #1945]: #916
-#2130 := (not #1708)
-#2139 := [unit-resolution #1875 #989 #2019 #2024]: #568
-#2140 := [unit-resolution #654 #2139]: #655
-#2141 := [unit-resolution #1265 #2140]: #986
-#2131 := (or #2130 #1079 #1269 #735)
-#2128 := [hypothesis]: #1708
-#2129 := [th-lemma arith farkas 1 -1 -1 1 -3/2 3/2 1/2 -1/2 -1/2 1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1 #1293 #897 #1852 #907 #1448 #1013 #2128 #1945 #882 #869 #2127 #2024 #2025 #903 #900 #773 #782 #2019]: false
-#2132 := [lemma #2129]: #2131
-#2142 := [unit-resolution #2132 #2056 #2141 #900]: #2130
-#2133 := [hypothesis]: #2130
-#2134 := [unit-resolution #1711 #1229 #2133]: false
-#2135 := [lemma #2134]: #1710
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-#2144 := [unit-resolution #714 #2143]: #394
-#2145 := [unit-resolution #712 #2144]: #709
-#2146 := [unit-resolution #856 #2145 #2138]: false
-#2148 := [lemma #2146]: #2147
-#2151 := [unit-resolution #2148 #900]: #510
-#2152 := [unit-resolution #680 #2151]: #677
-#2153 := [unit-resolution #959 #2152]: #756
-#2154 := (or #735 #844 #916 #795 #794 #917 #1503)
-#2155 := [unit-resolution #1664 #1828]: #2154
-#2156 := [unit-resolution #2155 #2153 #2042 #2024 #2150 #900 #2127]: #916
-#2159 := (or #394 #917 #540)
-#2157 := (or #394 #917 #540 #424)
-#2158 := [unit-resolution #1384 #1448]: #2157
-#2160 := [unit-resolution #2158 #1847]: #2159
-#2161 := [unit-resolution #2160 #2153 #2019]: #394
-#2162 := [unit-resolution #712 #2161]: #709
-#2163 := [unit-resolution #856 #2162 #2156]: false
-#2164 := [lemma #2163]: #735
-#2208 := (or #365 #510)
-#2187 := [unit-resolution #1464 #2140]: #1430
-#2188 := (or #1161 #482)
-#2189 := [unit-resolution #1681 #1945]: #2188
-#2190 := [unit-resolution #2189 #2126]: #1161
-#2165 := [unit-resolution #2048 #1226]: #1848
-#2185 := (or #394 #1079 #1269 #1498 #365 #995)
-#2168 := (or #336 #365 #2050 #394)
-#2166 := (or #336 #1501 #365 #2050 #394)
-#2167 := [th-lemma arith assign-bounds 1 1 1 1]: #2166
-#2169 := [unit-resolution #2167 #1494]: #2168
-#2170 := [unit-resolution #2169 #1122 #1202 #2165]: #336
-#2171 := [unit-resolution #728 #2170]: #725
-#2172 := [unit-resolution #1396 #2171]: #742
-#2173 := (or #1227 #796 #995 #739 #1079 #482 #365)
-#2174 := [unit-resolution #1303 #1566 #1850]: #2173
-#2175 := [unit-resolution #2174 #2172 #2126 #1293 #1202 #1282 #1723]: #739
-#2176 := [unit-resolution #2135 #1709]: #1708
-#2177 := (or #734 #2130 #1014 #1015 #1001 #947 #1002 #1503 #1498 #1499 #1504 #1501 #2050)
-#2178 := [th-lemma arith assign-bounds 1 -1 1 -1 -1 1 1 1 -1 -1 1 -1]: #2177
-#2179 := [unit-resolution #2178 #2176 #869 #1013 #882 #1494 #1491 #1945 #1448 #2042 #1956 #2165 #1488]: #734
-#2180 := [unit-resolution #1515 #2179 #2164]: #64
-#2181 := [unit-resolution #658 #2180]: #668
-#2182 := [unit-resolution #1544 #2181 #2175]: #825
-#2183 := [unit-resolution #1625 #2171]: #1571
-#2184 := [th-lemma arith farkas -1 1 1 -1 -2 2 -2 -1 1 -1 1 -1 1 -1 1 1 #2183 #1537 #1293 #897 #2025 #903 #2179 #1448 #1013 #1852 #907 #2024 #773 #782 #1238 #2182]: false
-#2186 := [lemma #2184]: #2185
-#2191 := [unit-resolution #2186 #1202 #2141 #2187 #2056 #994]: #394
-#2192 := [unit-resolution #712 #2191]: #709
-#2193 := [unit-resolution #856 #2192]: #748
-#2194 := [unit-resolution #2052 #2193 #869 #791 #836 #882 #1494 #1491 #1718 #1850 #2165 #2042 #2190 #2187 #1488]: #734
-#2195 := [unit-resolution #1515 #2194 #2164]: #64
-#2196 := [unit-resolution #658 #2195]: #668
-#2197 := [unit-resolution #1361 #2192]: #888
-#2198 := (or #753 #395 #1267)
-#2199 := [th-lemma arith assign-bounds 2 -1]: #2198
-#2200 := [unit-resolution #2199 #2197 #2191]: #753
-#2201 := [unit-resolution #2058 #2193 #791 #836 #882 #1494 #869 #1718 #1850 #989 #2190 #2165]: #336
-#2202 := [unit-resolution #728 #2201]: #725
-#2203 := [unit-resolution #1396 #2202]: #742
-#2204 := [unit-resolution #2174 #2203 #2126 #2056 #1202 #994 #2200]: #739
-#2205 := [unit-resolution #1544 #2204 #2196]: #825
-#2206 := [unit-resolution #1625 #2202]: #1571
-#2207 := [th-lemma arith farkas -1 1 1 -1 -2 2 -2 -1 1 -1 1 -1 1 -1 1 1 #2206 #1537 #2056 #897 #2141 #903 #2194 #1448 #1013 #1852 #907 #2024 #773 #782 #1238 #2205]: false
-#2209 := [lemma #2207]: #2208
-#2210 := [unit-resolution #2209 #989]: #365
-#2231 := [unit-resolution #2137 #2210 #869 #836 #882 #989 #1850 #2126 #1945]: #916
-#2229 := (or #2130 #510)
-#2211 := [unit-resolution #720 #2210]: #717
-#2212 := [unit-resolution #1476 #2211]: #1200
-#2213 := (or #1848 #1500 #366)
-#2214 := [th-lemma arith assign-bounds 1 -2]: #2213
-#2215 := [unit-resolution #2214 #2212 #2210]: #1848
-#2216 := [unit-resolution #2178 #2128 #869 #1013 #882 #1494 #1491 #1945 #1448 #2042 #2187 #2215 #1488]: #734
-#2217 := [unit-resolution #1515 #2216 #2164]: #64
-#2218 := [unit-resolution #658 #2217]: #668
-#2219 := [unit-resolution #1207 #2211]: #745
-#2220 := (or #336 #844 #1269 #948 #949 #823 #510)
-#2221 := [th-lemma arith assign-bounds 1 1 1 1 1 1]: #2220
-#2222 := [unit-resolution #2221 #2216 #773 #903 #989 #2024 #2141]: #336
-#2223 := [unit-resolution #728 #2222]: #725
-#2224 := [unit-resolution #1396 #2223]: #742
-#2225 := [unit-resolution #1117 #2224 #2219 #989]: #739
-#2226 := [unit-resolution #1544 #2225 #2218]: #825
-#2227 := [unit-resolution #1625 #2223]: #1571
-#2228 := [th-lemma arith farkas -2 2 -1 -1 1 -1 1 -1 -1 1 1 1 -1 -1 1 1 #1448 #1013 #1945 #882 #869 #2141 #903 #2216 #2227 #1537 #2226 #2056 #897 #1852 #907 #2128]: false
-#2230 := [lemma #2228]: #2229
-#2232 := [unit-resolution #2230 #989]: #2130
-#2233 := [unit-resolution #2135 #2232]: #1230
-#2234 := [unit-resolution #714 #2233]: #394
-#2235 := [unit-resolution #712 #2234]: #709
-#2236 := [unit-resolution #856 #2235 #2231]: false
-#2237 := [lemma #2236]: #510
-#2238 := [unit-resolution #680 #2237]: #677
-#2239 := [unit-resolution #959 #2238]: #756
-#2240 := [unit-resolution #2160 #2239 #2019]: #394
-#2241 := [unit-resolution #1979 #2237 #791 #787 #1718 #1850 #2150]: #744
-#2242 := [unit-resolution #712 #2240]: #709
-#2243 := [unit-resolution #1361 #2242]: #888
-#2244 := (or #1177 #1267 #365 #395)
-#2245 := [unit-resolution #1780 #1852]: #2244
-#2246 := [unit-resolution #2245 #2243 #2241 #2240]: #365
-#2247 := [unit-resolution #720 #2246]: #717
-#2248 := [unit-resolution #1476 #2247]: #1200
-#2249 := (or #741 #794 #917 #540)
-#2250 := [unit-resolution #1808 #787 #897 #1718]: #2249
-#2251 := [unit-resolution #2250 #2239 #2019 #2150]: #741
-#2252 := [unit-resolution #2012 #2240 #2150]: #1064
-#2253 := (or #1090 #568 #844)
-#2254 := [unit-resolution #1898 #816 #1945 #1566 #773]: #2253
-#2255 := [unit-resolution #2254 #2252 #2024]: #568
-#2256 := [unit-resolution #654 #2255]: #655
-#2257 := [unit-resolution #1464 #2256]: #1430
-#2258 := [unit-resolution #2112 #2257 #2042 #2251 #2190 #2243 #2248]: #734
-#2259 := [unit-resolution #1515 #2258 #2164]: #64
-#2260 := [unit-resolution #1207 #2247]: #745
-#2261 := [unit-resolution #856 #2242]: #748
-#2262 := [unit-resolution #2119 #2261 #2042 #2260 #2239]: #738
-#2263 := [unit-resolution #2122 #2248 #2251 #2024 #2260 #2243]: #739
-#2264 := [unit-resolution #1544 #2263 #2262]: #65
-[unit-resolution #658 #2264 #2259]: false
-unsat
-68356683e9cf34e34d65674fa3c8a62835e193a4 341 0
-#2 := false
-#24 := 0::Int
-decl f3 :: Int
-#7 := f3
-#433 := (<= f3 0::Int)
-#443 := (>= f3 0::Int)
-#754 := (not #443)
-#410 := (not #433)
-#755 := (or #410 #754)
-#716 := (not #755)
-#10 := 2::Int
-#763 := (mod f3 2::Int)
-#111 := -1::Int
-#420 := (* -1::Int #763)
-decl f4 :: (-> S2 Int Int)
-decl f5 :: (-> S3 Int S2)
-decl f6 :: S3
-#11 := f6
-#12 := (f5 f6 f3)
-#13 := (f4 #12 2::Int)
-#550 := (+ #13 #420)
-#757 := (= #550 0::Int)
-#706 := (not #757)
-#718 := (>= #550 0::Int)
-#663 := (not #718)
-#658 := [hypothesis]: #718
-#696 := (>= #763 0::Int)
-#1 := true
-#69 := [true-axiom]: true
-#659 := (or false #696)
-#660 := [th-lemma arith]: #659
-#661 := [unit-resolution #660 #69]: #696
-#99 := (>= #13 0::Int)
-#102 := (not #99)
-#8 := 1::Int
-#14 := (* 2::Int #13)
-#15 := (+ #14 1::Int)
-#16 := (+ f3 #15)
-#9 := (+ f3 1::Int)
-#17 := (<= #9 #16)
-#18 := (not #17)
-#107 := (iff #18 #102)
-#81 := (+ f3 #14)
-#82 := (+ 1::Int #81)
-#72 := (+ 1::Int f3)
-#87 := (<= #72 #82)
-#90 := (not #87)
-#105 := (iff #90 #102)
-#97 := (>= #14 0::Int)
-#93 := (not #97)
-#103 := (iff #93 #102)
-#100 := (iff #97 #99)
-#101 := [rewrite]: #100
-#104 := [monotonicity #101]: #103
-#94 := (iff #90 #93)
-#95 := (iff #87 #97)
-#96 := [rewrite]: #95
-#98 := [monotonicity #96]: #94
-#106 := [trans #98 #104]: #105
-#91 := (iff #18 #90)
-#88 := (iff #17 #87)
-#85 := (= #16 #82)
-#75 := (+ 1::Int #14)
-#78 := (+ f3 #75)
-#83 := (= #78 #82)
-#84 := [rewrite]: #83
-#79 := (= #16 #78)
-#76 := (= #15 #75)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#86 := [trans #80 #84]: #85
-#73 := (= #9 #72)
-#74 := [rewrite]: #73
-#89 := [monotonicity #74 #86]: #88
-#92 := [monotonicity #89]: #91
-#108 := [trans #92 #106]: #107
-#71 := [asserted]: #18
-#109 := [mp #71 #108]: #102
-#662 := [th-lemma arith farkas -1 1 1 #109 #661 #658]: false
-#664 := [lemma #662]: #663
-#673 := (or #706 #718)
-#653 := [th-lemma arith triangle-eq]: #673
-#654 := [unit-resolution #653 #664]: #706
-#645 := (or #716 #757)
-#742 := -2::Int
-#431 := (* -1::Int f3)
-#466 := (mod #431 -2::Int)
-#362 := (+ #13 #466)
-#461 := (= #362 0::Int)
-#740 := (if #755 #757 #461)
-#442 := (= #13 0::Int)
-#441 := (= f3 0::Int)
-#451 := (if #441 #442 #740)
-#22 := (:var 0 Int)
-#20 := (:var 1 Int)
-#42 := (f5 f6 #20)
-#43 := (f4 #42 #22)
-#776 := (pattern #43)
-#115 := (* -1::Int #22)
-#112 := (* -1::Int #20)
-#170 := (mod #112 #115)
-#285 := (+ #43 #170)
-#286 := (= #285 0::Int)
-#44 := (mod #20 #22)
-#282 := (* -1::Int #44)
-#283 := (+ #43 #282)
-#284 := (= #283 0::Int)
-#137 := (<= #22 0::Int)
-#144 := (>= #20 0::Int)
-#229 := (or #144 #137)
-#230 := (not #229)
-#133 := (<= #20 0::Int)
-#227 := (or #133 #137)
-#228 := (not #227)
-#233 := (or #228 #230)
-#287 := (if #233 #284 #286)
-#281 := (= #43 0::Int)
-#25 := (= #20 0::Int)
-#288 := (if #25 #281 #287)
-#280 := (= #43 #20)
-#26 := (= #22 0::Int)
-#289 := (if #26 #280 #288)
-#777 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #776) #289)
-#292 := (forall (vars (?v0 Int) (?v1 Int)) #289)
-#780 := (iff #292 #777)
-#778 := (iff #289 #289)
-#779 := [refl]: #778
-#781 := [quant-intro #779]: #780
-#176 := (* -1::Int #170)
-#249 := (if #233 #44 #176)
-#252 := (if #25 0::Int #249)
-#255 := (if #26 #20 #252)
-#258 := (= #43 #255)
-#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
-#293 := (iff #261 #292)
-#290 := (iff #258 #289)
-#291 := [rewrite]: #290
-#294 := [quant-intro #291]: #293
-#138 := (not #137)
-#145 := (not #144)
-#148 := (and #145 #138)
-#134 := (not #133)
-#141 := (and #134 #138)
-#151 := (or #141 #148)
-#196 := (if #151 #44 #176)
-#199 := (if #25 0::Int #196)
-#202 := (if #26 #20 #199)
-#205 := (= #43 #202)
-#208 := (forall (vars (?v0 Int) (?v1 Int)) #205)
-#262 := (iff #208 #261)
-#259 := (iff #205 #258)
-#256 := (= #202 #255)
-#253 := (= #199 #252)
-#250 := (= #196 #249)
-#234 := (iff #151 #233)
-#231 := (iff #148 #230)
-#232 := [rewrite]: #231
-#221 := (iff #141 #228)
-#222 := [rewrite]: #221
-#235 := [monotonicity #222 #232]: #234
-#251 := [monotonicity #235]: #250
-#254 := [monotonicity #251]: #253
-#257 := [monotonicity #254]: #256
-#260 := [monotonicity #257]: #259
-#263 := [quant-intro #260]: #262
-#219 := (~ #208 #208)
-#218 := (~ #205 #205)
-#215 := [refl]: #218
-#220 := [nnf-pos #215]: #219
-#36 := (- #22)
-#35 := (- #20)
-#45 := (mod #35 #36)
-#46 := (- #45)
-#29 := (< 0::Int #22)
-#31 := (< #20 0::Int)
-#32 := (and #31 #29)
-#28 := (< 0::Int #20)
-#30 := (and #28 #29)
-#33 := (or #30 #32)
-#47 := (if #33 #44 #46)
-#48 := (if #25 0::Int #47)
-#49 := (if #26 #20 #48)
-#50 := (= #43 #49)
-#51 := (forall (vars (?v0 Int) (?v1 Int)) #50)
-#211 := (iff #51 #208)
-#181 := (if #33 #44 #176)
-#184 := (if #25 0::Int #181)
-#187 := (if #26 #20 #184)
-#190 := (= #43 #187)
-#193 := (forall (vars (?v0 Int) (?v1 Int)) #190)
-#209 := (iff #193 #208)
-#206 := (iff #190 #205)
-#203 := (= #187 #202)
-#200 := (= #184 #199)
-#197 := (= #181 #196)
-#152 := (iff #33 #151)
-#149 := (iff #32 #148)
-#139 := (iff #29 #138)
-#140 := [rewrite]: #139
-#146 := (iff #31 #145)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147 #140]: #149
-#142 := (iff #30 #141)
-#135 := (iff #28 #134)
-#136 := [rewrite]: #135
-#143 := [monotonicity #136 #140]: #142
-#153 := [monotonicity #143 #150]: #152
-#198 := [monotonicity #153]: #197
-#201 := [monotonicity #198]: #200
-#204 := [monotonicity #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [quant-intro #207]: #209
-#194 := (iff #51 #193)
-#191 := (iff #50 #190)
-#188 := (= #49 #187)
-#185 := (= #48 #184)
-#182 := (= #47 #181)
-#179 := (= #46 #176)
-#173 := (- #170)
-#177 := (= #173 #176)
-#178 := [rewrite]: #177
-#174 := (= #46 #173)
-#171 := (= #45 #170)
-#116 := (= #36 #115)
-#117 := [rewrite]: #116
-#113 := (= #35 #112)
-#114 := [rewrite]: #113
-#172 := [monotonicity #114 #117]: #171
-#175 := [monotonicity #172]: #174
-#180 := [trans #175 #178]: #179
-#183 := [monotonicity #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [monotonicity #186]: #188
-#192 := [monotonicity #189]: #191
-#195 := [quant-intro #192]: #194
-#212 := [trans #195 #210]: #211
-#169 := [asserted]: #51
-#213 := [mp #169 #212]: #208
-#216 := [mp~ #213 #220]: #208
-#264 := [mp #216 #263]: #261
-#295 := [mp #264 #294]: #292
-#782 := [mp #295 #781]: #777
-#735 := (not #777)
-#724 := (or #735 #451)
-#432 := (* -1::Int 2::Int)
-#764 := (mod #431 #432)
-#765 := (+ #13 #764)
-#766 := (= #765 0::Int)
-#444 := (<= 2::Int 0::Int)
-#447 := (or #443 #444)
-#426 := (not #447)
-#445 := (or #433 #444)
-#446 := (not #445)
-#761 := (or #446 #426)
-#767 := (if #761 #757 #766)
-#762 := (if #441 #442 #767)
-#440 := (= #13 f3)
-#356 := (= 2::Int 0::Int)
-#768 := (if #356 #440 #762)
-#725 := (or #735 #768)
-#721 := (iff #725 #724)
-#727 := (iff #724 #724)
-#728 := [rewrite]: #727
-#734 := (iff #768 #451)
-#454 := (if false #440 #451)
-#448 := (iff #454 #451)
-#730 := [rewrite]: #448
-#732 := (iff #768 #454)
-#452 := (iff #762 #451)
-#737 := (iff #767 #740)
-#462 := (iff #766 #461)
-#738 := (= #765 #362)
-#467 := (= #764 #466)
-#743 := (= #432 -2::Int)
-#465 := [rewrite]: #743
-#468 := [monotonicity #465]: #467
-#739 := [monotonicity #468]: #738
-#736 := [monotonicity #739]: #462
-#753 := (iff #761 #755)
-#394 := (iff #426 #754)
-#389 := (iff #447 #443)
-#748 := (or #443 false)
-#745 := (iff #748 #443)
-#751 := [rewrite]: #745
-#749 := (iff #447 #748)
-#423 := (iff #444 false)
-#759 := [rewrite]: #423
-#750 := [monotonicity #759]: #749
-#752 := [trans #750 #751]: #389
-#395 := [monotonicity #752]: #394
-#746 := (iff #446 #410)
-#408 := (iff #445 #433)
-#419 := (or #433 false)
-#744 := (iff #419 #433)
-#407 := [rewrite]: #744
-#760 := (iff #445 #419)
-#403 := [monotonicity #759]: #760
-#409 := [trans #403 #407]: #408
-#747 := [monotonicity #409]: #746
-#756 := [monotonicity #747 #395]: #753
-#741 := [monotonicity #756 #736]: #737
-#453 := [monotonicity #741]: #452
-#758 := (iff #356 false)
-#418 := [rewrite]: #758
-#733 := [monotonicity #418 #453]: #732
-#731 := [trans #733 #730]: #734
-#722 := [monotonicity #731]: #721
-#723 := [trans #722 #728]: #721
-#726 := [quant-inst #7 #10]: #725
-#729 := [mp #726 #723]: #724
-#656 := [unit-resolution #729 #782]: #451
-#594 := (not #441)
-#593 := (not #451)
-#665 := (or #593 #594)
-#699 := (not #442)
-#657 := (or #699 #99)
-#694 := [th-lemma arith triangle-eq]: #657
-#695 := [unit-resolution #694 #109]: #699
-#553 := (or #593 #594 #442)
-#701 := [def-axiom]: #553
-#655 := [unit-resolution #701 #695]: #665
-#666 := [unit-resolution #655 #656]: #594
-#603 := (or #593 #441 #740)
-#698 := [def-axiom]: #603
-#644 := [unit-resolution #698 #666 #656]: #740
-#720 := (not #740)
-#549 := (or #720 #716 #757)
-#551 := [def-axiom]: #549
-#647 := [unit-resolution #551 #644]: #645
-#648 := [unit-resolution #647 #654]: #716
-#571 := (or #755 #433)
-#572 := [def-axiom]: #571
-#649 := [unit-resolution #572 #648]: #433
-#714 := (or #755 #443)
-#715 := [def-axiom]: #714
-#650 := [unit-resolution #715 #648]: #443
-#651 := (or #441 #410 #754)
-#646 := [th-lemma arith triangle-eq]: #651
-#652 := [unit-resolution #646 #666]: #755
-[unit-resolution #652 #650 #649]: false
-unsat
-1432b33c6328a1ffc0a07c49f1ba0f71ab4e0de0 343 0
-#2 := false
-#23 := 0::Int
-decl f3 :: Int
-#7 := f3
-#428 := (<= f3 0::Int)
-#438 := (>= f3 0::Int)
-#749 := (not #438)
-#405 := (not #428)
-#750 := (or #405 #749)
-#712 := (not #750)
-#10 := 2::Int
-#758 := (mod f3 2::Int)
-#106 := -1::Int
-#415 := (* -1::Int #758)
-decl f4 :: (-> S2 Int Int)
-decl f5 :: (-> S3 Int S2)
-decl f6 :: S3
-#8 := f6
-#9 := (f5 f6 f3)
-#11 := (f4 #9 2::Int)
-#545 := (+ #11 #415)
-#752 := (= #545 0::Int)
-#703 := (not #752)
-#713 := (<= #545 0::Int)
-#659 := (not #713)
-#663 := (>= #758 2::Int)
-#665 := (not #663)
-#1 := true
-#68 := [true-axiom]: true
-#654 := (or false #665)
-#655 := [th-lemma arith]: #654
-#656 := [unit-resolution #655 #68]: #665
-#657 := [hypothesis]: #713
-#97 := (>= #11 2::Int)
-#14 := 3::Int
-#15 := (+ f3 3::Int)
-#12 := (+ #11 #11)
-#13 := (+ f3 #12)
-#16 := (< #13 #15)
-#17 := (not #16)
-#102 := (iff #17 #97)
-#77 := (+ 3::Int f3)
-#71 := (* 2::Int #11)
-#74 := (+ f3 #71)
-#80 := (< #74 #77)
-#83 := (not #80)
-#100 := (iff #83 #97)
-#90 := (>= #71 3::Int)
-#98 := (iff #90 #97)
-#99 := [rewrite]: #98
-#95 := (iff #83 #90)
-#88 := (not #90)
-#87 := (not #88)
-#93 := (iff #87 #90)
-#94 := [rewrite]: #93
-#91 := (iff #83 #87)
-#89 := (iff #80 #88)
-#86 := [rewrite]: #89
-#92 := [monotonicity #86]: #91
-#96 := [trans #92 #94]: #95
-#101 := [trans #96 #99]: #100
-#84 := (iff #17 #83)
-#81 := (iff #16 #80)
-#78 := (= #15 #77)
-#79 := [rewrite]: #78
-#75 := (= #13 #74)
-#72 := (= #12 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [monotonicity #76 #79]: #81
-#85 := [monotonicity #82]: #84
-#103 := [trans #85 #101]: #102
-#70 := [asserted]: #17
-#104 := [mp #70 #103]: #97
-#658 := [th-lemma arith farkas -1 1 1 #104 #657 #656]: false
-#660 := [lemma #658]: #659
-#648 := (or #703 #713)
-#649 := [th-lemma arith triangle-eq]: #648
-#651 := [unit-resolution #649 #660]: #703
-#641 := (or #712 #752)
-#737 := -2::Int
-#426 := (* -1::Int f3)
-#461 := (mod #426 -2::Int)
-#357 := (+ #11 #461)
-#456 := (= #357 0::Int)
-#735 := (if #750 #752 #456)
-#437 := (= #11 0::Int)
-#436 := (= f3 0::Int)
-#446 := (if #436 #437 #735)
-#21 := (:var 0 Int)
-#19 := (:var 1 Int)
-#41 := (f5 f6 #19)
-#42 := (f4 #41 #21)
-#771 := (pattern #42)
-#110 := (* -1::Int #21)
-#107 := (* -1::Int #19)
-#165 := (mod #107 #110)
-#280 := (+ #42 #165)
-#281 := (= #280 0::Int)
-#43 := (mod #19 #21)
-#277 := (* -1::Int #43)
-#278 := (+ #42 #277)
-#279 := (= #278 0::Int)
-#132 := (<= #21 0::Int)
-#139 := (>= #19 0::Int)
-#224 := (or #139 #132)
-#225 := (not #224)
-#128 := (<= #19 0::Int)
-#222 := (or #128 #132)
-#223 := (not #222)
-#228 := (or #223 #225)
-#282 := (if #228 #279 #281)
-#276 := (= #42 0::Int)
-#24 := (= #19 0::Int)
-#283 := (if #24 #276 #282)
-#275 := (= #42 #19)
-#25 := (= #21 0::Int)
-#284 := (if #25 #275 #283)
-#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #284)
-#287 := (forall (vars (?v0 Int) (?v1 Int)) #284)
-#775 := (iff #287 #772)
-#773 := (iff #284 #284)
-#774 := [refl]: #773
-#776 := [quant-intro #774]: #775
-#171 := (* -1::Int #165)
-#244 := (if #228 #43 #171)
-#247 := (if #24 0::Int #244)
-#250 := (if #25 #19 #247)
-#253 := (= #42 #250)
-#256 := (forall (vars (?v0 Int) (?v1 Int)) #253)
-#288 := (iff #256 #287)
-#285 := (iff #253 #284)
-#286 := [rewrite]: #285
-#289 := [quant-intro #286]: #288
-#133 := (not #132)
-#140 := (not #139)
-#143 := (and #140 #133)
-#129 := (not #128)
-#136 := (and #129 #133)
-#146 := (or #136 #143)
-#191 := (if #146 #43 #171)
-#194 := (if #24 0::Int #191)
-#197 := (if #25 #19 #194)
-#200 := (= #42 #197)
-#203 := (forall (vars (?v0 Int) (?v1 Int)) #200)
-#257 := (iff #203 #256)
-#254 := (iff #200 #253)
-#251 := (= #197 #250)
-#248 := (= #194 #247)
-#245 := (= #191 #244)
-#229 := (iff #146 #228)
-#226 := (iff #143 #225)
-#227 := [rewrite]: #226
-#216 := (iff #136 #223)
-#217 := [rewrite]: #216
-#230 := [monotonicity #217 #227]: #229
-#246 := [monotonicity #230]: #245
-#249 := [monotonicity #246]: #248
-#252 := [monotonicity #249]: #251
-#255 := [monotonicity #252]: #254
-#258 := [quant-intro #255]: #257
-#214 := (~ #203 #203)
-#213 := (~ #200 #200)
-#210 := [refl]: #213
-#215 := [nnf-pos #210]: #214
-#35 := (- #21)
-#34 := (- #19)
-#44 := (mod #34 #35)
-#45 := (- #44)
-#28 := (< 0::Int #21)
-#30 := (< #19 0::Int)
-#31 := (and #30 #28)
-#27 := (< 0::Int #19)
-#29 := (and #27 #28)
-#32 := (or #29 #31)
-#46 := (if #32 #43 #45)
-#47 := (if #24 0::Int #46)
-#48 := (if #25 #19 #47)
-#49 := (= #42 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#206 := (iff #50 #203)
-#176 := (if #32 #43 #171)
-#179 := (if #24 0::Int #176)
-#182 := (if #25 #19 #179)
-#185 := (= #42 #182)
-#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
-#204 := (iff #188 #203)
-#201 := (iff #185 #200)
-#198 := (= #182 #197)
-#195 := (= #179 #194)
-#192 := (= #176 #191)
-#147 := (iff #32 #146)
-#144 := (iff #31 #143)
-#134 := (iff #28 #133)
-#135 := [rewrite]: #134
-#141 := (iff #30 #140)
-#142 := [rewrite]: #141
-#145 := [monotonicity #142 #135]: #144
-#137 := (iff #29 #136)
-#130 := (iff #27 #129)
-#131 := [rewrite]: #130
-#138 := [monotonicity #131 #135]: #137
-#148 := [monotonicity #138 #145]: #147
-#193 := [monotonicity #148]: #192
-#196 := [monotonicity #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [monotonicity #199]: #201
-#205 := [quant-intro #202]: #204
-#189 := (iff #50 #188)
-#186 := (iff #49 #185)
-#183 := (= #48 #182)
-#180 := (= #47 #179)
-#177 := (= #46 #176)
-#174 := (= #45 #171)
-#168 := (- #165)
-#172 := (= #168 #171)
-#173 := [rewrite]: #172
-#169 := (= #45 #168)
-#166 := (= #44 #165)
-#111 := (= #35 #110)
-#112 := [rewrite]: #111
-#108 := (= #34 #107)
-#109 := [rewrite]: #108
-#167 := [monotonicity #109 #112]: #166
-#170 := [monotonicity #167]: #169
-#175 := [trans #170 #173]: #174
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [monotonicity #181]: #183
-#187 := [monotonicity #184]: #186
-#190 := [quant-intro #187]: #189
-#207 := [trans #190 #205]: #206
-#164 := [asserted]: #50
-#208 := [mp #164 #207]: #203
-#211 := [mp~ #208 #215]: #203
-#259 := [mp #211 #258]: #256
-#290 := [mp #259 #289]: #287
-#777 := [mp #290 #776]: #772
-#730 := (not #772)
-#719 := (or #730 #446)
-#427 := (* -1::Int 2::Int)
-#759 := (mod #426 #427)
-#760 := (+ #11 #759)
-#761 := (= #760 0::Int)
-#439 := (<= 2::Int 0::Int)
-#442 := (or #438 #439)
-#421 := (not #442)
-#440 := (or #428 #439)
-#441 := (not #440)
-#756 := (or #441 #421)
-#762 := (if #756 #752 #761)
-#757 := (if #436 #437 #762)
-#435 := (= #11 f3)
-#351 := (= 2::Int 0::Int)
-#763 := (if #351 #435 #757)
-#720 := (or #730 #763)
-#716 := (iff #720 #719)
-#722 := (iff #719 #719)
-#723 := [rewrite]: #722
-#729 := (iff #763 #446)
-#449 := (if false #435 #446)
-#443 := (iff #449 #446)
-#725 := [rewrite]: #443
-#727 := (iff #763 #449)
-#447 := (iff #757 #446)
-#732 := (iff #762 #735)
-#457 := (iff #761 #456)
-#733 := (= #760 #357)
-#462 := (= #759 #461)
-#738 := (= #427 -2::Int)
-#460 := [rewrite]: #738
-#463 := [monotonicity #460]: #462
-#734 := [monotonicity #463]: #733
-#731 := [monotonicity #734]: #457
-#748 := (iff #756 #750)
-#389 := (iff #421 #749)
-#384 := (iff #442 #438)
-#743 := (or #438 false)
-#740 := (iff #743 #438)
-#746 := [rewrite]: #740
-#744 := (iff #442 #743)
-#418 := (iff #439 false)
-#754 := [rewrite]: #418
-#745 := [monotonicity #754]: #744
-#747 := [trans #745 #746]: #384
-#390 := [monotonicity #747]: #389
-#741 := (iff #441 #405)
-#403 := (iff #440 #428)
-#414 := (or #428 false)
-#739 := (iff #414 #428)
-#402 := [rewrite]: #739
-#755 := (iff #440 #414)
-#398 := [monotonicity #754]: #755
-#404 := [trans #398 #402]: #403
-#742 := [monotonicity #404]: #741
-#751 := [monotonicity #742 #390]: #748
-#736 := [monotonicity #751 #731]: #732
-#448 := [monotonicity #736]: #447
-#753 := (iff #351 false)
-#413 := [rewrite]: #753
-#728 := [monotonicity #413 #448]: #727
-#726 := [trans #728 #725]: #729
-#717 := [monotonicity #726]: #716
-#718 := [trans #717 #723]: #716
-#721 := [quant-inst #7 #10]: #720
-#724 := [mp #721 #718]: #719
-#652 := [unit-resolution #724 #777]: #446
-#548 := (not #436)
-#589 := (not #446)
-#643 := (or #589 #548)
-#697 := (not #437)
-#565 := (<= #11 0::Int)
-#653 := (not #565)
-#690 := (not #97)
-#691 := (or #653 #690)
-#650 := [th-lemma arith farkas 1 1]: #691
-#661 := [unit-resolution #650 #104]: #653
-#639 := (or #697 #565)
-#640 := [th-lemma arith triangle-eq]: #639
-#642 := [unit-resolution #640 #661]: #697
-#696 := (or #589 #548 #437)
-#598 := [def-axiom]: #696
-#644 := [unit-resolution #598 #642]: #643
-#645 := [unit-resolution #644 #652]: #548
-#693 := (or #589 #436 #735)
-#694 := [def-axiom]: #693
-#646 := [unit-resolution #694 #645 #652]: #735
-#544 := (not #735)
-#546 := (or #544 #712 #752)
-#547 := [def-axiom]: #546
-#647 := [unit-resolution #547 #646]: #641
-#633 := [unit-resolution #647 #651]: #712
-#567 := (or #750 #428)
-#709 := [def-axiom]: #567
-#629 := [unit-resolution #709 #633]: #428
-#710 := (or #750 #438)
-#711 := [def-axiom]: #710
-#630 := [unit-resolution #711 #633]: #438
-#631 := (or #436 #405 #749)
-#634 := [th-lemma arith triangle-eq]: #631
-#635 := [unit-resolution #634 #645]: #750
-[unit-resolution #635 #630 #629]: false
-unsat
-6c2df05479a46eb0dc1434ea9ed59f4fae72c26e 101 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#7 := f3
-#9 := (= f3 0::Real)
-#10 := (not #9)
-#45 := [asserted]: #10
-#100 := (<= f3 0::Real)
-#20 := 2::Real
-#47 := (* 2::Real f3)
-#102 := (<= #47 0::Real)
-#95 := (= #47 0::Real)
-#19 := 4::Real
-#14 := (- f3)
-#13 := (< f3 0::Real)
-#15 := (if #13 #14 f3)
-#12 := 1::Real
-#16 := (< 1::Real #15)
-#17 := (not #16)
-#18 := (or #16 #17)
-#21 := (if #18 4::Real 2::Real)
-#22 := (* #21 f3)
-#11 := (+ f3 f3)
-#23 := (= #11 #22)
-#24 := (not #23)
-#25 := (not #24)
-#96 := (iff #25 #95)
-#77 := (* 4::Real f3)
-#80 := (= #47 #77)
-#93 := (iff #80 #95)
-#94 := [rewrite]: #93
-#91 := (iff #25 #80)
-#83 := (not #80)
-#86 := (not #83)
-#89 := (iff #86 #80)
-#90 := [rewrite]: #89
-#87 := (iff #25 #86)
-#84 := (iff #24 #83)
-#81 := (iff #23 #80)
-#78 := (= #22 #77)
-#75 := (= #21 4::Real)
-#1 := true
-#70 := (if true 4::Real 2::Real)
-#73 := (= #70 4::Real)
-#74 := [rewrite]: #73
-#71 := (= #21 #70)
-#68 := (iff #18 true)
-#50 := -1::Real
-#51 := (* -1::Real f3)
-#54 := (if #13 #51 f3)
-#57 := (< 1::Real #54)
-#60 := (not #57)
-#63 := (or #57 #60)
-#66 := (iff #63 true)
-#67 := [rewrite]: #66
-#64 := (iff #18 #63)
-#61 := (iff #17 #60)
-#58 := (iff #16 #57)
-#55 := (= #15 #54)
-#52 := (= #14 #51)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#59 := [monotonicity #56]: #58
-#62 := [monotonicity #59]: #61
-#65 := [monotonicity #59 #62]: #64
-#69 := [trans #65 #67]: #68
-#72 := [monotonicity #69]: #71
-#76 := [trans #72 #74]: #75
-#79 := [monotonicity #76]: #78
-#48 := (= #11 #47)
-#49 := [rewrite]: #48
-#82 := [monotonicity #49 #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [monotonicity #85]: #87
-#92 := [trans #88 #90]: #91
-#97 := [trans #92 #94]: #96
-#46 := [asserted]: #25
-#98 := [mp #46 #97]: #95
-#104 := (not #95)
-#105 := (or #104 #102)
-#106 := [th-lemma arith triangle-eq]: #105
-#107 := [unit-resolution #106 #98]: #102
-#108 := (not #102)
-#109 := (or #100 #108)
-#110 := [th-lemma arith assign-bounds 1]: #109
-#111 := [unit-resolution #110 #107]: #100
-#101 := (>= f3 0::Real)
-#103 := (>= #47 0::Real)
-#112 := (or #104 #103)
-#113 := [th-lemma arith triangle-eq]: #112
-#114 := [unit-resolution #113 #98]: #103
-#115 := (not #103)
-#116 := (or #101 #115)
-#117 := [th-lemma arith assign-bounds 1]: #116
-#118 := [unit-resolution #117 #114]: #101
-#120 := (not #101)
-#119 := (not #100)
-#121 := (or #9 #119 #120)
-#122 := [th-lemma arith triangle-eq]: #121
-[unit-resolution #122 #118 #111 #45]: false
-unsat
-0eb09039097aac0255a0090f04ca5df53ea2d10a 24 0
-#2 := false
-#7 := (exists (vars (?v0 Int)) false)
-#8 := (not #7)
-#9 := (not #8)
-#45 := (iff #9 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #9 #40)
-#38 := (iff #8 true)
-#33 := (not false)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #8 #33)
-#31 := (iff #7 false)
-#32 := [elim-unused]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #9
-[mp #30 #46]: false
-unsat
-9f8072a1ad3de2c920c120b81de67bceefc50c87 916 0
-#2 := false
-#22 := 1::Int
-decl f3 :: (-> S2 Int Int)
-#12 := 2::Int
-decl f4 :: (-> S3 Int S2)
-decl f7 :: Int
-#9 := f7
-decl f5 :: S3
-#7 := f5
-#24 := (f4 f5 f7)
-#25 := (f3 #24 2::Int)
-#1265 := (<= #25 1::Int)
-#14 := 0::Int
-#551 := (mod f7 2::Int)
-#84 := -1::Int
-#521 := (* -1::Int #551)
-#522 := (+ #25 #521)
-#920 := (<= #522 0::Int)
-#523 := (= #522 0::Int)
-decl f6 :: Int
-#8 := f6
-#10 := (+ f6 f7)
-#431 := (>= #10 0::Int)
-#426 := (= #10 0::Int)
-#746 := (mod #10 2::Int)
-#748 := (* -1::Int #746)
-#11 := (f4 f5 #10)
-#13 := (f3 #11 2::Int)
-#405 := (+ #13 #748)
-#535 := (= #405 0::Int)
-#686 := (not #535)
-#691 := (<= #405 0::Int)
-#1269 := [hypothesis]: #535
-#1270 := (or #686 #691)
-#1271 := [th-lemma arith triangle-eq]: #1270
-#1272 := [unit-resolution #1271 #1269]: #691
-#693 := (>= #405 0::Int)
-#1273 := (or #686 #693)
-#1626 := [th-lemma arith triangle-eq]: #1273
-#1627 := [unit-resolution #1626 #1269]: #693
-#1371 := (not #691)
-#1437 := (not #693)
-#1647 := (or #1437 #1371)
-#1274 := (div f7 2::Int)
-#447 := -2::Int
-#1287 := (* -2::Int #1274)
-#1288 := (+ #521 #1287)
-#1289 := (+ f7 #1288)
-#1286 := (= #1289 0::Int)
-#1349 := (not #1286)
-#1474 := [hypothesis]: #1349
-#1 := true
-#78 := [true-axiom]: true
-#1346 := (or false #1286)
-#1347 := [th-lemma arith]: #1346
-#1475 := [unit-resolution #1347 #78 #1474]: false
-#1476 := [lemma #1475]: #1286
-#1472 := (or #1349 #1437 #1371)
-#1296 := (>= #551 0::Int)
-#1398 := (or false #1296)
-#1399 := [th-lemma arith]: #1398
-#1400 := [unit-resolution #1399 #78]: #1296
-#1422 := (>= #1289 0::Int)
-#1444 := [hypothesis]: #1286
-#1445 := (or #1349 #1422)
-#1446 := [th-lemma arith triangle-eq]: #1445
-#1447 := [unit-resolution #1446 #1444]: #1422
-#19 := 3::Int
-#17 := 4::Int
-#16 := (f4 f5 f6)
-#18 := (f3 #16 4::Int)
-#539 := (>= #18 3::Int)
-#20 := (= #18 3::Int)
-#81 := [asserted]: #20
-#989 := (not #20)
-#1010 := (or #989 #539)
-#1011 := [th-lemma arith triangle-eq]: #1010
-#1012 := [unit-resolution #1011 #81]: #539
-#831 := (div f6 4::Int)
-#634 := -4::Int
-#847 := (* -4::Int #831)
-#672 := (mod f6 4::Int)
-#673 := (* -1::Int #672)
-#848 := (+ #673 #847)
-#849 := (+ f6 #848)
-#855 := (>= #849 0::Int)
-#846 := (= #849 0::Int)
-#993 := (or false #846)
-#994 := [th-lemma arith]: #993
-#995 := [unit-resolution #994 #78]: #846
-#996 := (not #846)
-#1013 := (or #996 #855)
-#1014 := [th-lemma arith triangle-eq]: #1013
-#1015 := [unit-resolution #1014 #995]: #855
-#531 := (>= #13 0::Int)
-#15 := (= #13 0::Int)
-#80 := [asserted]: #15
-#593 := (not #15)
-#1428 := (or #593 #531)
-#1429 := [th-lemma arith triangle-eq]: #1428
-#1430 := [unit-resolution #1429 #80]: #531
-#777 := (div #10 2::Int)
-#794 := (* -2::Int #777)
-#795 := (+ #748 #794)
-#796 := (+ f7 #795)
-#797 := (+ f6 #796)
-#1268 := (>= #797 0::Int)
-#792 := (= #797 0::Int)
-#1355 := (or false #792)
-#1356 := [th-lemma arith]: #1355
-#1357 := [unit-resolution #1356 #78]: #792
-#1358 := (not #792)
-#1431 := (or #1358 #1268)
-#1432 := [th-lemma arith triangle-eq]: #1431
-#1433 := [unit-resolution #1432 #1357]: #1268
-#1434 := [hypothesis]: #693
-#674 := (+ #18 #673)
-#571 := (>= #674 0::Int)
-#668 := (= #674 0::Int)
-#453 := (* -1::Int f6)
-#631 := (mod #453 -4::Int)
-#619 := (+ #18 #631)
-#624 := (= #619 0::Int)
-#681 := (>= f6 0::Int)
-#640 := (not #681)
-#667 := (<= f6 0::Int)
-#641 := (not #667)
-#630 := (or #641 #640)
-#627 := (if #630 #668 #624)
-#678 := (= f6 0::Int)
-#561 := (not #678)
-#670 := (= #18 0::Int)
-#566 := (not #670)
-#389 := (= 3::Int 0::Int)
-#396 := (iff #389 false)
-#397 := [rewrite]: #396
-#407 := [hypothesis]: #670
-#409 := (= 3::Int #18)
-#410 := [symm #81]: #409
-#391 := [trans #410 #407]: #389
-#398 := [mp #391 #397]: false
-#399 := [lemma #398]: #566
-#1204 := (or #561 #670)
-#601 := (if #678 #670 #627)
-#32 := (:var 0 Int)
-#30 := (:var 1 Int)
-#51 := (f4 f5 #30)
-#52 := (f3 #51 #32)
-#761 := (pattern #52)
-#88 := (* -1::Int #32)
-#85 := (* -1::Int #30)
-#143 := (mod #85 #88)
-#272 := (+ #52 #143)
-#273 := (= #272 0::Int)
-#53 := (mod #30 #32)
-#269 := (* -1::Int #53)
-#270 := (+ #52 #269)
-#271 := (= #270 0::Int)
-#110 := (<= #32 0::Int)
-#117 := (>= #30 0::Int)
-#216 := (or #117 #110)
-#217 := (not #216)
-#106 := (<= #30 0::Int)
-#212 := (or #106 #110)
-#213 := (not #212)
-#220 := (or #213 #217)
-#274 := (if #220 #271 #273)
-#268 := (= #52 0::Int)
-#34 := (= #30 0::Int)
-#275 := (if #34 #268 #274)
-#267 := (= #52 #30)
-#35 := (= #32 0::Int)
-#276 := (if #35 #267 #275)
-#762 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #761) #276)
-#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
-#765 := (iff #279 #762)
-#763 := (iff #276 #276)
-#764 := [refl]: #763
-#766 := [quant-intro #764]: #765
-#149 := (* -1::Int #143)
-#236 := (if #220 #53 #149)
-#239 := (if #34 0::Int #236)
-#242 := (if #35 #30 #239)
-#245 := (= #52 #242)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#280 := (iff #248 #279)
-#277 := (iff #245 #276)
-#278 := [rewrite]: #277
-#281 := [quant-intro #278]: #280
-#111 := (not #110)
-#118 := (not #117)
-#121 := (and #118 #111)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (if #124 #53 #149)
-#172 := (if #34 0::Int #169)
-#175 := (if #35 #30 #172)
-#178 := (= #52 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#249 := (iff #181 #248)
-#246 := (iff #178 #245)
-#243 := (= #175 #242)
-#240 := (= #172 #239)
-#237 := (= #169 #236)
-#221 := (iff #124 #220)
-#218 := (iff #121 #217)
-#219 := [rewrite]: #218
-#214 := (iff #114 #213)
-#215 := [rewrite]: #214
-#222 := [monotonicity #215 #219]: #221
-#238 := [monotonicity #222]: #237
-#241 := [monotonicity #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [monotonicity #244]: #246
-#250 := [quant-intro #247]: #249
-#191 := (~ #181 #181)
-#193 := (~ #178 #178)
-#190 := [refl]: #193
-#194 := [nnf-pos #190]: #191
-#45 := (- #32)
-#44 := (- #30)
-#54 := (mod #44 #45)
-#55 := (- #54)
-#38 := (< 0::Int #32)
-#40 := (< #30 0::Int)
-#41 := (and #40 #38)
-#37 := (< 0::Int #30)
-#39 := (and #37 #38)
-#42 := (or #39 #41)
-#56 := (if #42 #53 #55)
-#57 := (if #34 0::Int #56)
-#58 := (if #35 #30 #57)
-#59 := (= #52 #58)
-#60 := (forall (vars (?v0 Int) (?v1 Int)) #59)
-#184 := (iff #60 #181)
-#154 := (if #42 #53 #149)
-#157 := (if #34 0::Int #154)
-#160 := (if #35 #30 #157)
-#163 := (= #52 #160)
-#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #42 #124)
-#122 := (iff #41 #121)
-#112 := (iff #38 #111)
-#113 := [rewrite]: #112
-#119 := (iff #40 #118)
-#120 := [rewrite]: #119
-#123 := [monotonicity #120 #113]: #122
-#115 := (iff #39 #114)
-#108 := (iff #37 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #60 #166)
-#164 := (iff #59 #163)
-#161 := (= #58 #160)
-#158 := (= #57 #157)
-#155 := (= #56 #154)
-#152 := (= #55 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #55 #146)
-#144 := (= #54 #143)
-#89 := (= #45 #88)
-#90 := [rewrite]: #89
-#86 := (= #44 #85)
-#87 := [rewrite]: #86
-#145 := [monotonicity #87 #90]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #60
-#186 := [mp #142 #185]: #181
-#195 := [mp~ #186 #194]: #181
-#251 := [mp #195 #250]: #248
-#282 := [mp #251 #281]: #279
-#767 := [mp #282 #766]: #762
-#555 := (not #762)
-#612 := (or #555 #601)
-#675 := (* -1::Int 4::Int)
-#659 := (mod #453 #675)
-#660 := (+ #18 #659)
-#662 := (= #660 0::Int)
-#669 := (<= 4::Int 0::Int)
-#677 := (or #681 #669)
-#682 := (not #677)
-#679 := (or #667 #669)
-#680 := (not #679)
-#671 := (or #680 #682)
-#663 := (if #671 #668 #662)
-#664 := (if #678 #670 #663)
-#676 := (= #18 f6)
-#689 := (= 4::Int 0::Int)
-#665 := (if #689 #676 #664)
-#615 := (or #555 #665)
-#617 := (iff #615 #612)
-#618 := (iff #612 #612)
-#598 := [rewrite]: #618
-#610 := (iff #665 #601)
-#496 := (if false #676 #601)
-#609 := (iff #496 #601)
-#614 := [rewrite]: #609
-#607 := (iff #665 #496)
-#602 := (iff #664 #601)
-#622 := (iff #663 #627)
-#625 := (iff #662 #624)
-#620 := (= #660 #619)
-#637 := (= #659 #631)
-#635 := (= #675 -4::Int)
-#636 := [rewrite]: #635
-#623 := [monotonicity #636]: #637
-#621 := [monotonicity #623]: #620
-#626 := [monotonicity #621]: #625
-#632 := (iff #671 #630)
-#651 := (iff #682 #640)
-#649 := (iff #677 #681)
-#644 := (or #681 false)
-#647 := (iff #644 #681)
-#648 := [rewrite]: #647
-#645 := (iff #677 #644)
-#652 := (iff #669 false)
-#653 := [rewrite]: #652
-#646 := [monotonicity #653]: #645
-#650 := [trans #646 #648]: #649
-#629 := [monotonicity #650]: #651
-#642 := (iff #680 #641)
-#638 := (iff #679 #667)
-#655 := (or #667 false)
-#654 := (iff #655 #667)
-#658 := [rewrite]: #654
-#656 := (iff #679 #655)
-#657 := [monotonicity #653]: #656
-#639 := [trans #657 #658]: #638
-#643 := [monotonicity #639]: #642
-#633 := [monotonicity #643 #629]: #632
-#628 := [monotonicity #633 #626]: #622
-#603 := [monotonicity #628]: #602
-#661 := (iff #689 false)
-#666 := [rewrite]: #661
-#608 := [monotonicity #666 #603]: #607
-#611 := [trans #608 #614]: #610
-#613 := [monotonicity #611]: #617
-#544 := [trans #613 #598]: #617
-#616 := [quant-inst #8 #17]: #615
-#599 := [mp #616 #544]: #612
-#1203 := [unit-resolution #599 #767]: #601
-#560 := (not #601)
-#562 := (or #560 #561 #670)
-#563 := [def-axiom]: #562
-#1205 := [unit-resolution #563 #1203]: #1204
-#1206 := [unit-resolution #1205 #399]: #561
-#1207 := (or #678 #627)
-#564 := (or #560 #678 #627)
-#565 := [def-axiom]: #564
-#1208 := [unit-resolution #565 #1203]: #1207
-#1209 := [unit-resolution #1208 #1206]: #627
-#606 := (not #630)
-#826 := [hypothesis]: #606
-#580 := (or #630 #667)
-#604 := [def-axiom]: #580
-#827 := [unit-resolution #604 #826]: #667
-#605 := (or #630 #681)
-#600 := [def-axiom]: #605
-#828 := [unit-resolution #600 #826]: #681
-#829 := (or #678 #641 #640)
-#830 := [th-lemma arith triangle-eq]: #829
-#879 := [unit-resolution #830 #828 #827 #1206]: false
-#880 := [lemma #879]: #630
-#582 := (not #627)
-#584 := (or #582 #606 #668)
-#585 := [def-axiom]: #584
-#1353 := [unit-resolution #585 #880 #1209]: #668
-#576 := (not #668)
-#1216 := (or #576 #571)
-#1217 := [th-lemma arith triangle-eq]: #1216
-#1435 := [unit-resolution #1217 #1353]: #571
-#1330 := (* -1::Int #1274)
-#1051 := (* -2::Int #831)
-#1331 := (+ #1051 #1330)
-#940 := (* -1::Int #777)
-#1332 := (+ #940 #1331)
-#1333 := (+ #748 #1332)
-#1334 := (+ #673 #1333)
-#1335 := (+ #18 #1334)
-#1336 := (+ #13 #1335)
-#1337 := (+ f7 #1336)
-#1338 := (+ f6 #1337)
-#1339 := (>= #1338 2::Int)
-#1369 := (not #1339)
-#921 := (>= #522 0::Int)
-#1362 := [hypothesis]: #691
-#1438 := (or #523 #1437 #1371)
-#532 := (<= #18 3::Int)
-#990 := (or #989 #532)
-#991 := [th-lemma arith triangle-eq]: #990
-#992 := [unit-resolution #991 #81]: #532
-#854 := (<= #849 0::Int)
-#997 := (or #996 #854)
-#998 := [th-lemma arith triangle-eq]: #997
-#999 := [unit-resolution #998 #995]: #854
-#545 := (<= f7 0::Int)
-#542 := (= f7 0::Int)
-#1190 := (not #523)
-#1308 := [hypothesis]: #1190
-#1420 := (or #542 #523)
-#347 := (* -1::Int f7)
-#507 := (mod #347 -2::Int)
-#504 := (+ #25 #507)
-#493 := (= #504 0::Int)
-#548 := (>= f7 0::Int)
-#497 := (not #548)
-#517 := (not #545)
-#502 := (or #517 #497)
-#476 := (if #502 #523 #493)
-#1255 := (not #542)
-#1412 := [hypothesis]: #1255
-#1406 := (or #542 #476)
-#543 := (= #25 0::Int)
-#480 := (if #542 #543 #476)
-#366 := (or #555 #480)
-#416 := (* -1::Int 2::Int)
-#524 := (mod #347 #416)
-#526 := (+ #25 #524)
-#527 := (= #526 0::Int)
-#418 := (<= 2::Int 0::Int)
-#549 := (or #548 #418)
-#550 := (not #549)
-#546 := (or #545 #418)
-#547 := (not #546)
-#533 := (or #547 #550)
-#528 := (if #533 #523 #527)
-#371 := (if #542 #543 #528)
-#541 := (= #25 f7)
-#341 := (= 2::Int 0::Int)
-#529 := (if #341 #541 #371)
-#351 := (or #555 #529)
-#352 := (iff #351 #366)
-#355 := (iff #366 #366)
-#342 := [rewrite]: #355
-#488 := (iff #529 #480)
-#483 := (if false #541 #480)
-#486 := (iff #483 #480)
-#487 := [rewrite]: #486
-#484 := (iff #529 #483)
-#481 := (iff #371 #480)
-#478 := (iff #528 #476)
-#491 := (iff #527 #493)
-#490 := (= #526 #504)
-#500 := (= #524 #507)
-#721 := (= #416 -2::Int)
-#725 := [rewrite]: #721
-#503 := [monotonicity #725]: #500
-#492 := [monotonicity #503]: #490
-#494 := [monotonicity #492]: #491
-#506 := (iff #533 #502)
-#498 := (iff #550 #497)
-#505 := (iff #549 #548)
-#511 := (or #548 false)
-#510 := (iff #511 #548)
-#515 := [rewrite]: #510
-#513 := (iff #549 #511)
-#404 := (iff #418 false)
-#392 := [rewrite]: #404
-#514 := [monotonicity #392]: #513
-#495 := [trans #514 #515]: #505
-#501 := [monotonicity #495]: #498
-#520 := (iff #547 #517)
-#518 := (iff #546 #545)
-#525 := (or #545 false)
-#512 := (iff #525 #545)
-#516 := [rewrite]: #512
-#530 := (iff #546 #525)
-#509 := [monotonicity #392]: #530
-#519 := [trans #509 #516]: #518
-#508 := [monotonicity #519]: #520
-#499 := [monotonicity #508 #501]: #506
-#479 := [monotonicity #499 #494]: #478
-#482 := [monotonicity #479]: #481
-#753 := (iff #341 false)
-#743 := [rewrite]: #753
-#485 := [monotonicity #743 #482]: #484
-#477 := [trans #485 #487]: #488
-#350 := [monotonicity #477]: #352
-#344 := [trans #350 #342]: #352
-#349 := [quant-inst #9 #12]: #351
-#345 := [mp #349 #344]: #366
-#1313 := [unit-resolution #345 #767]: #480
-#1254 := (not #480)
-#1258 := (or #1254 #542 #476)
-#1259 := [def-axiom]: #1258
-#1407 := [unit-resolution #1259 #1313]: #1406
-#1413 := [unit-resolution #1407 #1412]: #476
-#1410 := (or #548 #523)
-#1309 := [hypothesis]: #497
-#881 := (or #502 #548)
-#882 := [def-axiom]: #881
-#1310 := [unit-resolution #882 #1309]: #502
-#1311 := (or #1255 #548)
-#1312 := [th-lemma arith triangle-eq]: #1311
-#1295 := [unit-resolution #1312 #1309]: #1255
-#1408 := [unit-resolution #1407 #1295]: #476
-#883 := (not #502)
-#802 := (not #476)
-#1102 := (or #802 #883 #523)
-#1103 := [def-axiom]: #1102
-#1409 := [unit-resolution #1103 #1408 #1310 #1308]: false
-#1411 := [lemma #1409]: #1410
-#1414 := [unit-resolution #1411 #1308]: #548
-#1415 := (or #542 #517 #497)
-#1416 := [th-lemma arith triangle-eq]: #1415
-#1417 := [unit-resolution #1416 #1412 #1414]: #517
-#370 := (or #502 #545)
-#372 := [def-axiom]: #370
-#1418 := [unit-resolution #372 #1417]: #502
-#1419 := [unit-resolution #1103 #1418 #1413 #1308]: false
-#1421 := [lemma #1419]: #1420
-#1424 := [unit-resolution #1421 #1308]: #542
-#1425 := (or #1255 #545)
-#1426 := [th-lemma arith triangle-eq]: #1425
-#1427 := [unit-resolution #1426 #1424]: #545
-#570 := (<= #13 0::Int)
-#1364 := (or #593 #570)
-#1365 := [th-lemma arith triangle-eq]: #1364
-#1366 := [unit-resolution #1365 #80]: #570
-#1267 := (<= #797 0::Int)
-#1359 := (or #1358 #1267)
-#1360 := [th-lemma arith triangle-eq]: #1359
-#1361 := [unit-resolution #1360 #1357]: #1267
-#540 := (<= #674 0::Int)
-#1212 := (or #576 #540)
-#1213 := [th-lemma arith triangle-eq]: #1212
-#1354 := [unit-resolution #1213 #1353]: #540
-#1436 := [th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 #1435 #1354 #1434 #1362 #1433 #1361 #1430 #1366 #1414 #1427 #1015 #999 #1012 #992]: false
-#1439 := [lemma #1436]: #1438
-#1448 := [unit-resolution #1439 #1434 #1362]: #523
-#1449 := (or #1190 #921)
-#1450 := [th-lemma arith triangle-eq]: #1449
-#1451 := [unit-resolution #1450 #1448]: #921
-#1266 := (>= #25 1::Int)
-#1344 := (not #1266)
-#1452 := (or #1190 #920)
-#1453 := [th-lemma arith triangle-eq]: #1452
-#1454 := [unit-resolution #1453 #1448]: #920
-#1302 := (>= #551 2::Int)
-#1303 := (not #1302)
-#1455 := (or false #1303)
-#1456 := [th-lemma arith]: #1455
-#1457 := [unit-resolution #1456 #78]: #1303
-#1458 := (not #920)
-#1459 := (or #1265 #1302 #1458)
-#1460 := [th-lemma arith assign-bounds 1 1]: #1459
-#1461 := [unit-resolution #1460 #1457 #1454]: #1265
-#1464 := (not #1265)
-#1467 := (or #1464 #1344)
-#26 := (= #25 1::Int)
-#189 := (not #26)
-#21 := (f3 #16 2::Int)
-#23 := (= #21 1::Int)
-#1248 := (or #606 #23)
-#884 := (div f6 2::Int)
-#1118 := (* -1::Int #884)
-#1119 := (+ #1051 #1118)
-#1120 := (+ #673 #1119)
-#448 := (mod f6 2::Int)
-#457 := (* -1::Int #448)
-#1121 := (+ #457 #1120)
-#1122 := (+ #18 #1121)
-#1123 := (+ f6 #1122)
-#1124 := (>= #1123 2::Int)
-#1134 := (not #1124)
-#1210 := [hypothesis]: #630
-#1211 := [unit-resolution #585 #1210 #1209]: #668
-#1214 := [unit-resolution #1213 #1211]: #540
-#1005 := (not #540)
-#1135 := (or #1134 #1005)
-#906 := (>= #448 0::Int)
-#1129 := (or false #906)
-#1130 := [th-lemma arith]: #1129
-#1131 := [unit-resolution #1130 #78]: #906
-#1000 := [hypothesis]: #540
-#897 := (* -2::Int #884)
-#898 := (+ #457 #897)
-#899 := (+ f6 #898)
-#904 := (<= #899 0::Int)
-#896 := (= #899 0::Int)
-#1076 := (or false #896)
-#1077 := [th-lemma arith]: #1076
-#1078 := [unit-resolution #1077 #78]: #896
-#1079 := (not #896)
-#1080 := (or #1079 #904)
-#1081 := [th-lemma arith triangle-eq]: #1080
-#1082 := [unit-resolution #1081 #1078]: #904
-#1132 := [hypothesis]: #1124
-#1133 := [th-lemma arith farkas -1 2 -1 -1 -1 1 #992 #1132 #999 #1082 #1000 #1131]: false
-#1136 := [lemma #1133]: #1135
-#1215 := [unit-resolution #1136 #1214]: #1134
-#1218 := [unit-resolution #1217 #1211]: #571
-#905 := (>= #899 0::Int)
-#1219 := (or #1079 #905)
-#1220 := [th-lemma arith triangle-eq]: #1219
-#1221 := [unit-resolution #1220 #1078]: #905
-#458 := (+ #21 #457)
-#369 := (>= #458 0::Int)
-#449 := (= #458 0::Int)
-#489 := (mod #453 -2::Int)
-#471 := (+ #21 #489)
-#474 := (= #471 0::Int)
-#455 := (if #630 #449 #474)
-#475 := (= #21 0::Int)
-#424 := (if #678 #475 #455)
-#375 := (or #555 #424)
-#459 := (mod #453 #416)
-#440 := (+ #21 #459)
-#441 := (= #440 0::Int)
-#462 := (or #681 #418)
-#464 := (not #462)
-#460 := (or #667 #418)
-#461 := (not #460)
-#463 := (or #461 #464)
-#442 := (if #463 #449 #441)
-#434 := (if #678 #475 #442)
-#467 := (= #21 f6)
-#443 := (if #341 #467 #434)
-#377 := (or #555 #443)
-#381 := (iff #377 #375)
-#382 := (iff #375 #375)
-#357 := [rewrite]: #382
-#384 := (iff #443 #424)
-#390 := (if false #467 #424)
-#385 := (iff #390 #424)
-#386 := [rewrite]: #385
-#402 := (iff #443 #390)
-#400 := (iff #434 #424)
-#456 := (iff #442 #455)
-#465 := (iff #441 #474)
-#472 := (= #440 #471)
-#469 := (= #459 #489)
-#470 := [monotonicity #725]: #469
-#473 := [monotonicity #470]: #472
-#454 := [monotonicity #473]: #465
-#466 := (iff #463 #630)
-#422 := (iff #464 #640)
-#420 := (iff #462 #681)
-#406 := (iff #462 #644)
-#419 := [monotonicity #392]: #406
-#421 := [trans #419 #648]: #420
-#423 := [monotonicity #421]: #422
-#414 := (iff #461 #641)
-#445 := (iff #460 #667)
-#444 := (iff #460 #655)
-#435 := [monotonicity #392]: #444
-#412 := [trans #435 #658]: #445
-#415 := [monotonicity #412]: #414
-#468 := [monotonicity #415 #423]: #466
-#413 := [monotonicity #468 #454]: #456
-#401 := [monotonicity #413]: #400
-#383 := [monotonicity #743 #401]: #402
-#387 := [trans #383 #386]: #384
-#376 := [monotonicity #387]: #381
-#361 := [trans #376 #357]: #381
-#378 := [quant-inst #8 #12]: #377
-#362 := [mp #378 #361]: #375
-#1222 := [unit-resolution #362 #767]: #424
-#348 := (not #424)
-#1223 := (or #348 #455)
-#353 := (or #348 #678 #455)
-#354 := [def-axiom]: #353
-#1224 := [unit-resolution #354 #1206]: #1223
-#1225 := [unit-resolution #1224 #1222]: #455
-#368 := (not #455)
-#373 := (or #368 #606 #449)
-#356 := [def-axiom]: #373
-#1226 := [unit-resolution #356 #1210 #1225]: #449
-#363 := (not #449)
-#1227 := (or #363 #369)
-#1228 := [th-lemma arith triangle-eq]: #1227
-#1229 := [unit-resolution #1228 #1226]: #369
-#346 := (>= #21 1::Int)
-#1084 := (not #346)
-#343 := (<= #21 1::Int)
-#912 := (>= #448 2::Int)
-#913 := (not #912)
-#1230 := (or false #913)
-#1231 := [th-lemma arith]: #1230
-#1232 := [unit-resolution #1231 #78]: #913
-#367 := (<= #458 0::Int)
-#1233 := (or #363 #367)
-#1234 := [th-lemma arith triangle-eq]: #1233
-#1235 := [unit-resolution #1234 #1226]: #367
-#1236 := (not #367)
-#1237 := (or #343 #912 #1236)
-#1238 := [th-lemma arith assign-bounds 1 1]: #1237
-#1239 := [unit-resolution #1238 #1235 #1232]: #343
-#1241 := (not #343)
-#1244 := (or #1241 #1084)
-#188 := (not #23)
-#1240 := [hypothesis]: #188
-#1242 := (or #23 #1241 #1084)
-#1243 := [th-lemma arith triangle-eq]: #1242
-#1245 := [unit-resolution #1243 #1240]: #1244
-#1246 := [unit-resolution #1245 #1239]: #1084
-#1247 := [th-lemma arith farkas -1/2 -1/2 1/2 -1/2 -1/2 -1/2 1 #1012 #1015 #1246 #1229 #1221 #1218 #1215]: false
-#1249 := [lemma #1247]: #1248
-#1462 := [unit-resolution #1249 #880]: #23
-#200 := (or #188 #189)
-#27 := (and #23 #26)
-#28 := (not #27)
-#209 := (iff #28 #200)
-#201 := (not #200)
-#204 := (not #201)
-#207 := (iff #204 #200)
-#208 := [rewrite]: #207
-#205 := (iff #28 #204)
-#202 := (iff #27 #201)
-#203 := [rewrite]: #202
-#206 := [monotonicity #203]: #205
-#210 := [trans #206 #208]: #209
-#82 := [asserted]: #28
-#211 := [mp #82 #210]: #200
-#1463 := [unit-resolution #211 #1462]: #189
-#1465 := (or #26 #1464 #1344)
-#1466 := [th-lemma arith triangle-eq]: #1465
-#1468 := [unit-resolution #1466 #1463]: #1467
-#1469 := [unit-resolution #1468 #1461]: #1344
-#1370 := (not #921)
-#1372 := (or #1369 #1370 #1371 #1266)
-#1345 := [hypothesis]: #1344
-#1294 := (<= #1289 0::Int)
-#1348 := [unit-resolution #1347 #78]: #1286
-#1350 := (or #1349 #1294)
-#1351 := [th-lemma arith triangle-eq]: #1350
-#1352 := [unit-resolution #1351 #1348]: #1294
-#1363 := [hypothesis]: #1339
-#1367 := [hypothesis]: #921
-#1368 := [th-lemma arith farkas -1 1 -2 1 1 1 1 1 1 1 #1367 #1366 #1363 #1362 #1361 #1354 #1352 #999 #992 #1345]: false
-#1373 := [lemma #1368]: #1372
-#1470 := [unit-resolution #1373 #1469 #1362 #1451]: #1369
-#1471 := [th-lemma arith farkas -2 1 1 1 1 1 1 1 1 #1470 #1435 #1434 #1433 #1430 #1015 #1012 #1447 #1400]: false
-#1473 := [lemma #1471]: #1472
-#1648 := [unit-resolution #1473 #1476]: #1647
-#1649 := [unit-resolution #1648 #1627 #1272]: false
-#1650 := [lemma #1649]: #686
-#1479 := (or #426 #535)
-#1423 := [hypothesis]: #686
-#723 := (+ #453 #347)
-#722 := (mod #723 -2::Int)
-#437 := (+ #13 #722)
-#717 := (= #437 0::Int)
-#741 := (not #431)
-#427 := (<= #10 0::Int)
-#735 := (not #427)
-#450 := (or #735 #741)
-#715 := (if #450 #535 #717)
-#589 := (not #426)
-#768 := [hypothesis]: #589
-#1441 := (or #426 #715)
-#720 := (if #426 #15 #715)
-#556 := (or #555 #720)
-#742 := (* -1::Int #10)
-#417 := (mod #742 #416)
-#749 := (+ #13 #417)
-#750 := (= #749 0::Int)
-#428 := (or #431 #418)
-#432 := (not #428)
-#429 := (or #427 #418)
-#430 := (not #429)
-#411 := (or #430 #432)
-#751 := (if #411 #535 #750)
-#752 := (if #426 #15 #751)
-#425 := (= #13 #10)
-#747 := (if #341 #425 #752)
-#557 := (or #555 #747)
-#700 := (iff #557 #556)
-#702 := (iff #556 #556)
-#696 := [rewrite]: #702
-#708 := (iff #747 #720)
-#745 := (* -1::Int #13)
-#388 := (+ f7 #745)
-#729 := (+ f6 #388)
-#744 := (= #729 0::Int)
-#711 := (if false #744 #720)
-#712 := (iff #711 #720)
-#713 := [rewrite]: #712
-#706 := (iff #747 #711)
-#709 := (iff #752 #720)
-#719 := (iff #751 #715)
-#718 := (iff #750 #717)
-#438 := (= #749 #437)
-#726 := (= #417 #722)
-#724 := (= #742 #723)
-#446 := [rewrite]: #724
-#436 := [monotonicity #446 #725]: #726
-#439 := [monotonicity #436]: #438
-#433 := [monotonicity #439]: #718
-#451 := (iff #411 #450)
-#727 := (iff #432 #741)
-#740 := (iff #428 #431)
-#374 := (or #431 false)
-#379 := (iff #374 #431)
-#380 := [rewrite]: #379
-#737 := (iff #428 #374)
-#739 := [monotonicity #392]: #737
-#738 := [trans #739 #380]: #740
-#728 := [monotonicity #738]: #727
-#730 := (iff #430 #735)
-#733 := (iff #429 #427)
-#393 := (or #427 false)
-#731 := (iff #393 #427)
-#732 := [rewrite]: #731
-#394 := (iff #429 #393)
-#395 := [monotonicity #392]: #394
-#734 := [trans #395 #732]: #733
-#736 := [monotonicity #734]: #730
-#452 := [monotonicity #736 #728]: #451
-#716 := [monotonicity #452 #433]: #719
-#710 := [monotonicity #716]: #709
-#408 := (iff #425 #744)
-#403 := [rewrite]: #408
-#707 := [monotonicity #743 #403 #710]: #706
-#714 := [trans #707 #713]: #708
-#701 := [monotonicity #714]: #700
-#697 := [trans #701 #696]: #700
-#699 := [quant-inst #10 #12]: #557
-#703 := [mp #699 #697]: #556
-#1440 := [unit-resolution #703 #767]: #720
-#587 := (not #720)
-#591 := (or #587 #426 #715)
-#592 := [def-axiom]: #591
-#1442 := [unit-resolution #592 #1440]: #1441
-#1443 := [unit-resolution #1442 #768]: #715
-#775 := (or #450 #426)
-#536 := (not #450)
-#769 := [hypothesis]: #536
-#704 := (or #450 #427)
-#698 := [def-axiom]: #704
-#770 := [unit-resolution #698 #769]: #427
-#705 := (or #450 #431)
-#534 := [def-axiom]: #705
-#771 := [unit-resolution #534 #769]: #431
-#772 := (or #426 #735 #741)
-#773 := [th-lemma arith triangle-eq]: #772
-#774 := [unit-resolution #773 #771 #770 #768]: false
-#776 := [lemma #774]: #775
-#1477 := [unit-resolution #776 #768]: #450
-#695 := (not #715)
-#577 := (or #695 #536 #535)
-#578 := [def-axiom]: #577
-#1478 := [unit-resolution #578 #1477 #1443 #1423]: false
-#1480 := [lemma #1478]: #1479
-#1651 := [unit-resolution #1480 #1650]: #426
-#1652 := (or #589 #431)
-#1653 := [th-lemma arith triangle-eq]: #1652
-#1654 := [unit-resolution #1653 #1651]: #431
-#1655 := (or #589 #427)
-#1656 := [th-lemma arith triangle-eq]: #1655
-#1657 := [unit-resolution #1656 #1651]: #427
-#1645 := (or #523 #741 #735)
-#1513 := [hypothesis]: #427
-#1580 := (or #497 #735 #667)
-#1022 := [hypothesis]: #641
-#1487 := [hypothesis]: #548
-#1579 := [th-lemma arith farkas -1 1 1 #1513 #1487 #1022]: false
-#1581 := [lemma #1579]: #1580
-#1641 := [unit-resolution #1581 #1414 #1513]: #667
-#1642 := [unit-resolution #830 #1206]: #630
-#1643 := [unit-resolution #1642 #1641]: #640
-#1573 := [hypothesis]: #431
-#1644 := [th-lemma arith farkas -1 1 1 #1573 #1643 #1427]: false
-#1646 := [lemma #1644]: #1645
-#1658 := [unit-resolution #1646 #1657 #1654]: #523
-#1659 := [unit-resolution #1453 #1658]: #920
-#1660 := (or #1265 #1458)
-#1623 := [hypothesis]: #1302
-#1624 := [unit-resolution #1456 #78 #1623]: false
-#1625 := [lemma #1624]: #1303
-#1661 := [unit-resolution #1460 #1625]: #1660
-#1662 := [unit-resolution #1661 #1659]: #1265
-#1503 := (+ #673 #1331)
-#1609 := (+ #521 #1503)
-#1610 := (+ #18 #1609)
-#1611 := (+ f7 #1610)
-#1612 := (+ f6 #1611)
-#1613 := (>= #1612 2::Int)
-#1620 := (not #1613)
-#1621 := (or #1620 #735)
-#1512 := [unit-resolution #1351 #1476]: #1294
-#1618 := [hypothesis]: #1613
-#1619 := [th-lemma arith farkas 2 -1 -1 -1 -1 -1 1 #1618 #1513 #1354 #999 #992 #1512 #1400]: false
-#1622 := [lemma #1619]: #1621
-#1663 := [unit-resolution #1622 #1657]: #1620
-#1664 := [unit-resolution #1450 #1658]: #921
-#1639 := (or #1370 #1613 #741 #1266)
-#1597 := [unit-resolution #1446 #1476]: #1422
-#1637 := [th-lemma arith #1573 #1345 #1367 #1435 #1015 #1012 #1597]: #1613
-#1636 := [hypothesis]: #1620
-#1638 := [unit-resolution #1636 #1637]: false
-#1640 := [lemma #1638]: #1639
-#1665 := [unit-resolution #1640 #1664 #1654 #1663]: #1266
-[unit-resolution #1468 #1665 #1662]: false
-unsat
-f966ee970dc5619d71e606afb53aade7fa8a1452 24 0
-#2 := false
-#7 := (exists (vars (?v0 Real)) false)
-#8 := (not #7)
-#9 := (not #8)
-#45 := (iff #9 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #9 #40)
-#38 := (iff #8 true)
-#33 := (not false)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #8 #33)
-#31 := (iff #7 false)
-#32 := [elim-unused]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #9
-[mp #30 #46]: false
-unsat
-c4f4c8220660d1979009b33a643f0927bee816b1 1 0
-unsat
-e7ef76d73ccb9bc09d2b5368495a7a59d1bae3dc 1 0
-unsat
-db6426d59fdd57da8ca5d11de399761d1f1443de 1 0
-unsat
-a2da5fa16f268876e3dcbc1874e34212d0a36218 54 0
-#2 := false
-#11 := 1::Int
-#8 := 0::Int
-#135 := (= 0::Int 1::Int)
-#137 := (iff #135 false)
-#138 := [rewrite]: #137
-decl ?v1!0 :: Int
-#55 := ?v1!0
-#58 := (= ?v1!0 1::Int)
-decl ?v0!1 :: Int
-#56 := ?v0!1
-#57 := (= ?v0!1 0::Int)
-#50 := (and #57 #58)
-#59 := (= ?v0!1 ?v1!0)
-#60 := (not #59)
-#52 := (not #50)
-#61 := (or #52 #60)
-#62 := (not #61)
-#10 := (:var 0 Int)
-#7 := (:var 1 Int)
-#14 := (= #7 #10)
-#15 := (not #14)
-#12 := (= #10 1::Int)
-#9 := (= #7 0::Int)
-#13 := (and #9 #12)
-#39 := (not #13)
-#40 := (or #39 #15)
-#43 := (forall (vars (?v0 Int) (?v1 Int)) #40)
-#46 := (not #43)
-#63 := (~ #46 #62)
-#64 := [sk]: #63
-#16 := (implies #13 #15)
-#17 := (forall (vars (?v0 Int) (?v1 Int)) #16)
-#18 := (not #17)
-#47 := (iff #18 #46)
-#44 := (iff #17 #43)
-#41 := (iff #16 #40)
-#42 := [rewrite]: #41
-#45 := [quant-intro #42]: #44
-#48 := [monotonicity #45]: #47
-#38 := [asserted]: #18
-#51 := [mp #38 #48]: #46
-#67 := [mp~ #51 #64]: #62
-#70 := [not-or-elim #67]: #50
-#72 := [and-elim #70]: #58
-#133 := (= 0::Int ?v1!0)
-#73 := [not-or-elim #67]: #59
-#131 := (= 0::Int ?v0!1)
-#71 := [and-elim #70]: #57
-#132 := [symm #71]: #131
-#134 := [trans #132 #73]: #133
-#136 := [trans #134 #72]: #135
-[mp #136 #138]: false
-unsat
-46597b09986e0d4d045609318eeba242d6132e5c 82 0
-#2 := false
-#8 := (:var 0 Int)
-#10 := 0::Int
-#12 := (<= 0::Int #8)
-#11 := (< #8 0::Int)
-#13 := (or #11 #12)
-#7 := (:var 1 Int)
-#9 := (< #7 #8)
-#14 := (implies #9 #13)
-#15 := (forall (vars (?v1 Int)) #14)
-#16 := (exists (vars (?v0 Int)) #15)
-#17 := (not #16)
-#102 := (iff #17 false)
-#38 := (not #9)
-#39 := (or #38 #13)
-#42 := (forall (vars (?v1 Int)) #39)
-#45 := (exists (vars (?v0 Int)) #42)
-#48 := (not #45)
-#100 := (iff #48 false)
-#1 := true
-#95 := (not true)
-#98 := (iff #95 false)
-#99 := [rewrite]: #98
-#96 := (iff #48 #95)
-#93 := (iff #45 true)
-#88 := (exists (vars (?v0 Int)) true)
-#91 := (iff #88 true)
-#92 := [elim-unused]: #91
-#89 := (iff #45 #88)
-#86 := (iff #42 true)
-#81 := (forall (vars (?v1 Int)) true)
-#84 := (iff #81 true)
-#85 := [elim-unused]: #84
-#82 := (iff #42 #81)
-#79 := (iff #39 true)
-#53 := (>= #8 0::Int)
-#51 := (not #53)
-#71 := (or #51 #53)
-#57 := -1::Int
-#60 := (* -1::Int #8)
-#61 := (+ #7 #60)
-#59 := (>= #61 0::Int)
-#74 := (or #59 #71)
-#77 := (iff #74 true)
-#78 := [rewrite]: #77
-#75 := (iff #39 #74)
-#72 := (iff #13 #71)
-#55 := (iff #12 #53)
-#56 := [rewrite]: #55
-#52 := (iff #11 #51)
-#54 := [rewrite]: #52
-#73 := [monotonicity #54 #56]: #72
-#69 := (iff #38 #59)
-#58 := (not #59)
-#64 := (not #58)
-#67 := (iff #64 #59)
-#68 := [rewrite]: #67
-#65 := (iff #38 #64)
-#62 := (iff #9 #58)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#76 := [monotonicity #70 #73]: #75
-#80 := [trans #76 #78]: #79
-#83 := [quant-intro #80]: #82
-#87 := [trans #83 #85]: #86
-#90 := [quant-intro #87]: #89
-#94 := [trans #90 #92]: #93
-#97 := [monotonicity #94]: #96
-#101 := [trans #97 #99]: #100
-#49 := (iff #17 #48)
-#46 := (iff #16 #45)
-#43 := (iff #15 #42)
-#40 := (iff #14 #39)
-#41 := [rewrite]: #40
-#44 := [quant-intro #41]: #43
-#47 := [quant-intro #44]: #46
-#50 := [monotonicity #47]: #49
-#103 := [trans #50 #101]: #102
-#37 := [asserted]: #17
-[mp #37 #103]: false
-unsat
-aea13e787f95ed97feac7bd1dfc69160a5b8be70 78 0
-#2 := false
-#8 := (:var 0 Int)
-#10 := 2::Int
-#14 := (* 2::Int #8)
-#12 := 1::Int
-#7 := (:var 1 Int)
-#11 := (* 2::Int #7)
-#13 := (+ #11 1::Int)
-#15 := (< #13 #14)
-#9 := (< #7 #8)
-#16 := (implies #9 #15)
-#17 := (forall (vars (?v0 Int) (?v1 Int)) #16)
-#18 := (not #17)
-#98 := (iff #18 false)
-#40 := (+ 1::Int #11)
-#43 := (< #40 #14)
-#49 := (not #9)
-#50 := (or #49 #43)
-#55 := (forall (vars (?v0 Int) (?v1 Int)) #50)
-#58 := (not #55)
-#96 := (iff #58 false)
-#1 := true
-#91 := (not true)
-#94 := (iff #91 false)
-#95 := [rewrite]: #94
-#92 := (iff #58 #91)
-#89 := (iff #55 true)
-#84 := (forall (vars (?v0 Int) (?v1 Int)) true)
-#87 := (iff #84 true)
-#88 := [elim-unused]: #87
-#85 := (iff #55 #84)
-#82 := (iff #50 true)
-#20 := 0::Int
-#61 := -1::Int
-#64 := (* -1::Int #8)
-#65 := (+ #7 #64)
-#63 := (>= #65 0::Int)
-#62 := (not #63)
-#76 := (or #63 #62)
-#80 := (iff #76 true)
-#81 := [rewrite]: #80
-#78 := (iff #50 #76)
-#77 := (iff #43 #62)
-#75 := [rewrite]: #77
-#73 := (iff #49 #63)
-#68 := (not #62)
-#71 := (iff #68 #63)
-#72 := [rewrite]: #71
-#69 := (iff #49 #68)
-#66 := (iff #9 #62)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#74 := [trans #70 #72]: #73
-#79 := [monotonicity #74 #75]: #78
-#83 := [trans #79 #81]: #82
-#86 := [quant-intro #83]: #85
-#90 := [trans #86 #88]: #89
-#93 := [monotonicity #90]: #92
-#97 := [trans #93 #95]: #96
-#59 := (iff #18 #58)
-#56 := (iff #17 #55)
-#53 := (iff #16 #50)
-#46 := (implies #9 #43)
-#51 := (iff #46 #50)
-#52 := [rewrite]: #51
-#47 := (iff #16 #46)
-#44 := (iff #15 #43)
-#41 := (= #13 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#54 := [trans #48 #52]: #53
-#57 := [quant-intro #54]: #56
-#60 := [monotonicity #57]: #59
-#99 := [trans #60 #97]: #98
-#39 := [asserted]: #18
-[mp #39 #99]: false
-unsat
-e6703a33319f0e5148dba82e8205956f98cd7b63 56 0
-#2 := false
-#12 := (:var 0 Int)
-#7 := 2::Int
-#13 := (* 2::Int #12)
-#10 := 1::Int
-#8 := (:var 1 Int)
-#9 := (* 2::Int #8)
-#11 := (+ #9 1::Int)
-#14 := (= #11 #13)
-#15 := (not #14)
-#16 := (forall (vars (?v0 Int) (?v1 Int)) #15)
-#17 := (not #16)
-#77 := (iff #17 false)
-#39 := (+ 1::Int #9)
-#42 := (= #39 #13)
-#45 := (not #42)
-#48 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#51 := (not #48)
-#75 := (iff #51 false)
-#1 := true
-#70 := (not true)
-#73 := (iff #70 false)
-#74 := [rewrite]: #73
-#71 := (iff #51 #70)
-#68 := (iff #48 true)
-#63 := (forall (vars (?v0 Int) (?v1 Int)) true)
-#66 := (iff #63 true)
-#67 := [elim-unused]: #66
-#64 := (iff #48 #63)
-#61 := (iff #45 true)
-#54 := (not false)
-#59 := (iff #54 true)
-#60 := [rewrite]: #59
-#55 := (iff #45 #54)
-#56 := (iff #42 false)
-#57 := [rewrite]: #56
-#58 := [monotonicity #57]: #55
-#62 := [trans #58 #60]: #61
-#65 := [quant-intro #62]: #64
-#69 := [trans #65 #67]: #68
-#72 := [monotonicity #69]: #71
-#76 := [trans #72 #74]: #75
-#52 := (iff #17 #51)
-#49 := (iff #16 #48)
-#46 := (iff #15 #45)
-#43 := (iff #14 #42)
-#40 := (= #11 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#50 := [quant-intro #47]: #49
-#53 := [monotonicity #50]: #52
-#78 := [trans #53 #76]: #77
-#38 := [asserted]: #17
-[mp #38 #78]: false
-unsat
-8a770e2a15f5bbced47daef21d1d322e18a383fb 89 0
-#2 := false
-#7 := 2::Int
-decl ?v0!1 :: Int
-#71 := ?v0!1
-decl ?v1!0 :: Int
-#70 := ?v1!0
-#85 := (+ ?v1!0 ?v0!1)
-#94 := (= #85 2::Int)
-#109 := (not #94)
-#97 := (>= #85 2::Int)
-#100 := (not #97)
-#88 := (<= #85 2::Int)
-#91 := (not #88)
-#103 := (or #91 #94 #100)
-#106 := (not #103)
-#72 := (+ ?v0!1 ?v1!0)
-#74 := (>= #72 2::Int)
-#75 := (not #74)
-#67 := (= #72 2::Int)
-#73 := (<= #72 2::Int)
-#40 := (not #73)
-#76 := (or #40 #67 #75)
-#77 := (not #76)
-#107 := (iff #77 #106)
-#104 := (iff #76 #103)
-#101 := (iff #75 #100)
-#98 := (iff #74 #97)
-#86 := (= #72 #85)
-#87 := [rewrite]: #86
-#99 := [monotonicity #87]: #98
-#102 := [monotonicity #99]: #101
-#95 := (iff #67 #94)
-#96 := [monotonicity #87]: #95
-#92 := (iff #40 #91)
-#89 := (iff #73 #88)
-#90 := [monotonicity #87]: #89
-#93 := [monotonicity #90]: #92
-#105 := [monotonicity #93 #96 #102]: #104
-#108 := [monotonicity #105]: #107
-#9 := (:var 0 Int)
-#8 := (:var 1 Int)
-#10 := (+ #8 #9)
-#44 := (>= #10 2::Int)
-#41 := (not #44)
-#12 := (= #10 2::Int)
-#45 := (<= #10 2::Int)
-#46 := (not #45)
-#55 := (or #46 #12 #41)
-#60 := (forall (vars (?v0 Int) (?v1 Int)) #55)
-#63 := (not #60)
-#78 := (~ #63 #77)
-#79 := [sk]: #78
-#13 := (< #10 2::Int)
-#14 := (or #12 #13)
-#11 := (< 2::Int #10)
-#15 := (or #11 #14)
-#16 := (forall (vars (?v0 Int) (?v1 Int)) #15)
-#17 := (not #16)
-#64 := (iff #17 #63)
-#61 := (iff #16 #60)
-#58 := (iff #15 #55)
-#49 := (or #12 #41)
-#52 := (or #46 #49)
-#56 := (iff #52 #55)
-#57 := [rewrite]: #56
-#53 := (iff #15 #52)
-#50 := (iff #14 #49)
-#43 := (iff #13 #41)
-#42 := [rewrite]: #43
-#51 := [monotonicity #42]: #50
-#47 := (iff #11 #46)
-#48 := [rewrite]: #47
-#54 := [monotonicity #48 #51]: #53
-#59 := [trans #54 #57]: #58
-#62 := [quant-intro #59]: #61
-#65 := [monotonicity #62]: #64
-#38 := [asserted]: #17
-#66 := [mp #38 #65]: #63
-#82 := [mp~ #66 #79]: #77
-#83 := [mp #82 #108]: #106
-#110 := [not-or-elim #83]: #109
-#111 := [not-or-elim #83]: #97
-#173 := (or #94 #100)
-#84 := [not-or-elim #83]: #88
-#171 := (or #94 #91 #100)
-#172 := [th-lemma arith triangle-eq]: #171
-#174 := [unit-resolution #172 #84]: #173
-[unit-resolution #174 #111 #110]: false
-unsat
-c93368b1109e5b13c7d8bc3c33d69c60ba539127 89 0
-#2 := false
-#7 := 0::Int
-decl ?v0!0 :: Int
-#87 := ?v0!0
-#88 := (<= ?v0!0 0::Int)
-#157 := (not #88)
-#166 := [hypothesis]: #88
-#10 := 1::Int
-#89 := (>= ?v0!0 1::Int)
-#90 := (not #89)
-#167 := (or #90 #157)
-#168 := [th-lemma arith farkas 1 1]: #167
-#169 := [unit-resolution #168 #166]: #90
-#170 := (or #157 #89)
-#56 := -1::Int
-#83 := (<= ?v0!0 -1::Int)
-#84 := (not #83)
-#91 := (if #88 #90 #84)
-#92 := (not #91)
-#8 := (:var 0 Int)
-#57 := (<= #8 -1::Int)
-#58 := (not #57)
-#62 := (>= #8 1::Int)
-#61 := (not #62)
-#52 := (<= #8 0::Int)
-#68 := (if #52 #61 #58)
-#73 := (forall (vars (?v0 Int)) #68)
-#76 := (not #73)
-#93 := (~ #76 #92)
-#94 := [sk]: #93
-#13 := (< #8 1::Int)
-#11 := (+ #8 1::Int)
-#12 := (< 0::Int #11)
-#9 := (< 0::Int #8)
-#14 := (if #9 #12 #13)
-#15 := (forall (vars (?v0 Int)) #14)
-#16 := (not #15)
-#79 := (iff #16 #76)
-#37 := (+ 1::Int #8)
-#40 := (< 0::Int #37)
-#43 := (if #9 #40 #13)
-#46 := (forall (vars (?v0 Int)) #43)
-#49 := (not #46)
-#77 := (iff #49 #76)
-#74 := (iff #46 #73)
-#71 := (iff #43 #68)
-#53 := (not #52)
-#65 := (if #53 #58 #61)
-#69 := (iff #65 #68)
-#70 := [rewrite]: #69
-#66 := (iff #43 #65)
-#63 := (iff #13 #61)
-#64 := [rewrite]: #63
-#59 := (iff #40 #58)
-#60 := [rewrite]: #59
-#54 := (iff #9 #53)
-#55 := [rewrite]: #54
-#67 := [monotonicity #55 #60 #64]: #66
-#72 := [trans #67 #70]: #71
-#75 := [quant-intro #72]: #74
-#78 := [monotonicity #75]: #77
-#50 := (iff #16 #49)
-#47 := (iff #15 #46)
-#44 := (iff #14 #43)
-#41 := (iff #12 #40)
-#38 := (= #11 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [quant-intro #45]: #47
-#51 := [monotonicity #48]: #50
-#80 := [trans #51 #78]: #79
-#36 := [asserted]: #16
-#81 := [mp #36 #80]: #76
-#97 := [mp~ #81 #94]: #92
-#162 := (or #91 #157 #89)
-#163 := [def-axiom]: #162
-#171 := [unit-resolution #163 #97]: #170
-#172 := [unit-resolution #171 #169 #166]: false
-#173 := [lemma #172]: #157
-#174 := (or #84 #88)
-#175 := [th-lemma arith farkas 1 1]: #174
-#176 := [unit-resolution #175 #173]: #84
-#177 := (or #88 #83)
-#164 := (or #91 #88 #83)
-#165 := [def-axiom]: #164
-#178 := [unit-resolution #165 #97]: #177
-[unit-resolution #178 #176 #173]: false
-unsat
-8578dab7bf88c7d119f9af2e5f7eaf948f1bdb87 84 0
-WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
-#2 := false
-#8 := 0::Int
-#7 := (:var 0 Int)
-#49 := (<= #7 0::Int)
-#50 := (not #49)
-#47 := (>= #7 0::Int)
-#45 := (not #47)
-#53 := (or #45 #50)
-#56 := (forall (vars (?v0 Int)) #53)
-#525 := (not #56)
-#218 := (<= 0::Int 0::Int)
-#539 := (not #218)
-#207 := (>= 0::Int 0::Int)
-#201 := (not #207)
-#537 := (or #201 #539)
-#526 := (or #525 #537)
-#170 := (iff #526 #525)
-#527 := (or #525 false)
-#530 := (iff #527 #525)
-#169 := [rewrite]: #530
-#164 := (iff #526 #527)
-#523 := (iff #537 false)
-#182 := (or false false)
-#185 := (iff #182 false)
-#522 := [rewrite]: #185
-#183 := (iff #537 #182)
-#178 := (iff #539 false)
-#1 := true
-#543 := (not true)
-#222 := (iff #543 false)
-#544 := [rewrite]: #222
-#194 := (iff #539 #543)
-#198 := (iff #218 true)
-#535 := [rewrite]: #198
-#536 := [monotonicity #535]: #194
-#520 := [trans #536 #544]: #178
-#534 := (iff #201 false)
-#538 := (iff #201 #543)
-#541 := (iff #207 true)
-#542 := [rewrite]: #541
-#326 := [monotonicity #542]: #538
-#193 := [trans #326 #544]: #534
-#184 := [monotonicity #193 #520]: #183
-#524 := [trans #184 #522]: #523
-#528 := [monotonicity #524]: #164
-#531 := [trans #528 #169]: #170
-#521 := [quant-inst #8]: #526
-#529 := [mp #521 #531]: #525
-#69 := (~ #56 #56)
-#67 := (~ #53 #53)
-#68 := [refl]: #67
-#70 := [nnf-pos #68]: #69
-#10 := (< 0::Int #7)
-#9 := (< #7 0::Int)
-#11 := (or #9 #10)
-#12 := (forall (vars (?v0 Int)) #11)
-#13 := (if #12 false true)
-#14 := (not #13)
-#59 := (iff #14 #56)
-#57 := (iff #12 #56)
-#54 := (iff #11 #53)
-#51 := (iff #10 #50)
-#52 := [rewrite]: #51
-#46 := (iff #9 #45)
-#48 := [rewrite]: #46
-#55 := [monotonicity #48 #52]: #54
-#58 := [quant-intro #55]: #57
-#43 := (iff #14 #12)
-#35 := (not #12)
-#38 := (not #35)
-#41 := (iff #38 #12)
-#42 := [rewrite]: #41
-#39 := (iff #14 #38)
-#36 := (iff #13 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#60 := [trans #44 #58]: #59
-#34 := [asserted]: #14
-#61 := [mp #34 #60]: #56
-#63 := [mp~ #61 #70]: #56
-[unit-resolution #63 #529]: false
-unsat
-f6f0c702e5caae5d1fc0a3e7862c44d261de6d47 63 0
-#2 := false
-#15 := 1::Int
-#12 := (:var 1 Int)
-#10 := 6::Int
-#11 := (- 6::Int)
-#13 := (* #11 #12)
-#8 := (:var 2 Int)
-#7 := 4::Int
-#9 := (* 4::Int #8)
-#14 := (+ #9 #13)
-#16 := (= #14 1::Int)
-#17 := (exists (vars (?v0 Int) (?v1 Int) (?v2 Int)) #16)
-#18 := (not #17)
-#19 := (not #18)
-#86 := (iff #19 false)
-#56 := (:var 0 Int)
-#41 := -6::Int
-#58 := (* -6::Int #56)
-#57 := (* 4::Int #12)
-#59 := (+ #57 #58)
-#60 := (= #59 1::Int)
-#61 := (exists (vars (?v0 Int) (?v1 Int)) #60)
-#84 := (iff #61 false)
-#77 := (exists (vars (?v0 Int) (?v1 Int)) false)
-#82 := (iff #77 false)
-#83 := [elim-unused]: #82
-#80 := (iff #61 #77)
-#78 := (iff #60 false)
-#79 := [rewrite]: #78
-#81 := [quant-intro #79]: #80
-#85 := [trans #81 #83]: #84
-#74 := (iff #19 #61)
-#66 := (not #61)
-#69 := (not #66)
-#72 := (iff #69 #61)
-#73 := [rewrite]: #72
-#70 := (iff #19 #69)
-#67 := (iff #18 #66)
-#64 := (iff #17 #61)
-#44 := (* -6::Int #12)
-#47 := (+ #9 #44)
-#50 := (= #47 1::Int)
-#53 := (exists (vars (?v0 Int) (?v1 Int) (?v2 Int)) #50)
-#62 := (iff #53 #61)
-#63 := [elim-unused]: #62
-#54 := (iff #17 #53)
-#51 := (iff #16 #50)
-#48 := (= #14 #47)
-#45 := (= #13 #44)
-#42 := (= #11 -6::Int)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#55 := [quant-intro #52]: #54
-#65 := [trans #55 #63]: #64
-#68 := [monotonicity #65]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#87 := [trans #75 #85]: #86
-#40 := [asserted]: #19
-[mp #40 #87]: false
-unsat
-252d255c564463d916bc68156eea8dbe7fb0be0a 165 0
-WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
-#2 := false
-#7 := 0::Int
-#8 := (:var 0 Int)
-#55 := (<= #8 0::Int)
-#56 := (not #55)
-#52 := (>= #8 0::Int)
-#51 := (not #52)
-#59 := (or #51 #56)
-#62 := (forall (vars (?v0 Int)) #59)
-#95 := (not #62)
-#587 := (<= 0::Int 0::Int)
-#586 := (not #587)
-#585 := (>= 0::Int 0::Int)
-#248 := (not #585)
-#593 := (or #248 #586)
-#290 := (or #95 #593)
-#569 := (iff #290 #95)
-#292 := (or #95 false)
-#572 := (iff #292 #95)
-#287 := [rewrite]: #572
-#293 := (iff #290 #292)
-#576 := (iff #593 false)
-#578 := (or false false)
-#575 := (iff #578 false)
-#579 := [rewrite]: #575
-#300 := (iff #593 #578)
-#201 := (iff #586 false)
-#1 := true
-#594 := (not true)
-#592 := (iff #594 false)
-#595 := [rewrite]: #592
-#306 := (iff #586 #594)
-#304 := (iff #587 true)
-#305 := [rewrite]: #304
-#307 := [monotonicity #305]: #306
-#577 := [trans #307 #595]: #201
-#581 := (iff #248 false)
-#589 := (iff #248 #594)
-#233 := (iff #585 true)
-#234 := [rewrite]: #233
-#249 := [monotonicity #234]: #589
-#582 := [trans #249 #595]: #581
-#301 := [monotonicity #582 #577]: #300
-#580 := [trans #301 #579]: #576
-#571 := [monotonicity #580]: #293
-#573 := [trans #571 #287]: #569
-#291 := [quant-inst #7]: #290
-#570 := [mp #291 #573]: #95
-decl z3name!0 :: bool
-#92 := z3name!0
-#15 := 3::Int
-#39 := -1::Int
-#99 := (if z3name!0 -1::Int 3::Int)
-#284 := (= #99 3::Int)
-#604 := (not #284)
-#602 := (>= #99 3::Int)
-#259 := (not #602)
-#102 := (<= #99 0::Int)
-#65 := (if #62 -1::Int 3::Int)
-#71 := (<= #65 0::Int)
-#103 := (~ #71 #102)
-#100 := (= #65 #99)
-#97 := (~ #62 z3name!0)
-#88 := (or z3name!0 #95)
-#93 := (not z3name!0)
-#94 := (or #93 #62)
-#89 := (and #94 #88)
-#96 := [intro-def]: #89
-#98 := [apply-def #96]: #97
-#101 := [monotonicity #98]: #100
-#104 := [monotonicity #101]: #103
-#13 := 1::Int
-#14 := (- 1::Int)
-#10 := (< 0::Int #8)
-#9 := (< #8 0::Int)
-#11 := (or #9 #10)
-#12 := (forall (vars (?v0 Int)) #11)
-#16 := (if #12 #14 3::Int)
-#17 := (< 0::Int #16)
-#18 := (not #17)
-#84 := (iff #18 #71)
-#42 := (if #12 -1::Int 3::Int)
-#45 := (< 0::Int #42)
-#48 := (not #45)
-#82 := (iff #48 #71)
-#72 := (not #71)
-#77 := (not #72)
-#80 := (iff #77 #71)
-#81 := [rewrite]: #80
-#78 := (iff #48 #77)
-#75 := (iff #45 #72)
-#68 := (< 0::Int #65)
-#73 := (iff #68 #72)
-#74 := [rewrite]: #73
-#69 := (iff #45 #68)
-#66 := (= #42 #65)
-#63 := (iff #12 #62)
-#60 := (iff #11 #59)
-#57 := (iff #10 #56)
-#58 := [rewrite]: #57
-#53 := (iff #9 #51)
-#54 := [rewrite]: #53
-#61 := [monotonicity #54 #58]: #60
-#64 := [quant-intro #61]: #63
-#67 := [monotonicity #64]: #66
-#70 := [monotonicity #67]: #69
-#76 := [trans #70 #74]: #75
-#79 := [monotonicity #76]: #78
-#83 := [trans #79 #81]: #82
-#49 := (iff #18 #48)
-#46 := (iff #17 #45)
-#43 := (= #16 #42)
-#40 := (= #14 -1::Int)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#50 := [monotonicity #47]: #49
-#85 := [trans #50 #83]: #84
-#38 := [asserted]: #18
-#86 := [mp #38 #85]: #71
-#133 := [mp~ #86 #104]: #102
-#389 := (not #102)
-#596 := (or #259 #389)
-#270 := [th-lemma arith farkas 1 1]: #596
-#271 := [unit-resolution #270 #133]: #259
-#603 := [hypothesis]: #284
-#605 := (or #604 #602)
-#606 := [th-lemma arith triangle-eq]: #605
-#601 := [unit-resolution #606 #603 #271]: false
-#607 := [lemma #601]: #604
-#286 := (or z3name!0 #284)
-#265 := [def-axiom]: #286
-#574 := [unit-resolution #265 #607]: z3name!0
-decl ?v0!1 :: Int
-#115 := ?v0!1
-#118 := (<= ?v0!1 0::Int)
-#119 := (not #118)
-#116 := (>= ?v0!1 0::Int)
-#117 := (not #116)
-#120 := (or #117 #119)
-#121 := (not #120)
-#126 := (or z3name!0 #121)
-#129 := (and #94 #126)
-#130 := (~ #89 #129)
-#127 := (~ #88 #126)
-#122 := (~ #95 #121)
-#123 := [sk]: #122
-#113 := (~ z3name!0 z3name!0)
-#114 := [refl]: #113
-#128 := [monotonicity #114 #123]: #127
-#111 := (~ #94 #94)
-#109 := (~ #62 #62)
-#107 := (~ #59 #59)
-#108 := [refl]: #107
-#110 := [nnf-pos #108]: #109
-#105 := (~ #93 #93)
-#106 := [refl]: #105
-#112 := [monotonicity #106 #110]: #111
-#131 := [monotonicity #112 #128]: #130
-#132 := [mp~ #96 #131]: #129
-#136 := [and-elim #132]: #94
-#563 := [unit-resolution #136 #574]: #62
-[unit-resolution #563 #570]: false
-unsat
-302156fb98e1f9b5657a3c89c418d5e1813f274a 101 0
-#2 := false
-#7 := 0::Int
-decl ?v1!1 :: Int
-#92 := ?v1!1
-decl ?v2!0 :: Int
-#91 := ?v2!0
-#109 := (+ ?v2!0 ?v1!1)
-#112 := (<= #109 0::Int)
-#115 := (not #112)
-#87 := (<= ?v2!0 0::Int)
-#88 := (not #87)
-#93 := (<= ?v1!1 0::Int)
-#94 := (not #93)
-#95 := (and #94 #88)
-#96 := (not #95)
-#118 := (or #96 #115)
-#121 := (not #118)
-#97 := (+ ?v1!1 ?v2!0)
-#98 := (<= #97 0::Int)
-#99 := (not #98)
-#100 := (or #96 #99)
-#101 := (not #100)
-#122 := (iff #101 #121)
-#119 := (iff #100 #118)
-#116 := (iff #99 #115)
-#113 := (iff #98 #112)
-#110 := (= #97 #109)
-#111 := [rewrite]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [monotonicity #120]: #122
-#10 := (:var 0 Int)
-#8 := (:var 1 Int)
-#13 := (+ #8 #10)
-#70 := (<= #13 0::Int)
-#71 := (not #70)
-#60 := (<= #10 0::Int)
-#61 := (not #60)
-#56 := (<= #8 0::Int)
-#57 := (not #56)
-#64 := (and #57 #61)
-#67 := (not #64)
-#74 := (or #67 #71)
-#77 := (forall (vars (?v1 Int) (?v2 Int)) #74)
-#80 := (not #77)
-#102 := (~ #80 #101)
-#103 := [sk]: #102
-#14 := (< 0::Int #13)
-#11 := (< 0::Int #10)
-#9 := (< 0::Int #8)
-#12 := (and #9 #11)
-#15 := (implies #12 #14)
-#16 := (forall (vars (?v1 Int) (?v2 Int)) #15)
-#17 := (exists (vars (?v0 Int)) #16)
-#18 := (not #17)
-#83 := (iff #18 #80)
-#39 := (not #12)
-#40 := (or #39 #14)
-#43 := (forall (vars (?v1 Int) (?v2 Int)) #40)
-#53 := (not #43)
-#81 := (iff #53 #80)
-#78 := (iff #43 #77)
-#75 := (iff #40 #74)
-#72 := (iff #14 #71)
-#73 := [rewrite]: #72
-#68 := (iff #39 #67)
-#65 := (iff #12 #64)
-#62 := (iff #11 #61)
-#63 := [rewrite]: #62
-#58 := (iff #9 #57)
-#59 := [rewrite]: #58
-#66 := [monotonicity #59 #63]: #65
-#69 := [monotonicity #66]: #68
-#76 := [monotonicity #69 #73]: #75
-#79 := [quant-intro #76]: #78
-#82 := [monotonicity #79]: #81
-#54 := (iff #18 #53)
-#51 := (iff #17 #43)
-#46 := (exists (vars (?v0 Int)) #43)
-#49 := (iff #46 #43)
-#50 := [elim-unused]: #49
-#47 := (iff #17 #46)
-#44 := (iff #16 #43)
-#41 := (iff #15 #40)
-#42 := [rewrite]: #41
-#45 := [quant-intro #42]: #44
-#48 := [quant-intro #45]: #47
-#52 := [trans #48 #50]: #51
-#55 := [monotonicity #52]: #54
-#84 := [trans #55 #82]: #83
-#38 := [asserted]: #18
-#85 := [mp #38 #84]: #80
-#106 := [mp~ #85 #103]: #101
-#107 := [mp #106 #123]: #121
-#126 := [not-or-elim #107]: #112
-#108 := [not-or-elim #107]: #95
-#124 := [and-elim #108]: #94
-#125 := [and-elim #108]: #88
-[th-lemma arith farkas 1 1 1 #125 #124 #126]: false
-unsat
-bcc217c52aea6d752e93b67733058589bedd0079 99 0
-#2 := false
-#39 := -1::Int
-decl ?v1!1 :: Int
-#101 := ?v1!1
-#106 := (<= ?v1!1 -1::Int)
-#107 := (not #106)
-#10 := 0::Real
-decl ?v2!0 :: Real
-#100 := ?v2!0
-#102 := (<= ?v2!0 0::Real)
-#103 := (not #102)
-#7 := 0::Int
-#98 := (<= ?v1!1 0::Int)
-#99 := (not #98)
-#104 := (and #99 #103)
-#105 := (not #104)
-#108 := (or #105 #107)
-#109 := (not #108)
-#8 := (:var 1 Int)
-#81 := (<= #8 -1::Int)
-#82 := (not #81)
-#11 := (:var 0 Real)
-#71 := (<= #11 0::Real)
-#72 := (not #71)
-#67 := (<= #8 0::Int)
-#68 := (not #67)
-#75 := (and #68 #72)
-#78 := (not #75)
-#85 := (or #78 #82)
-#88 := (forall (vars (?v1 Int) (?v2 Real)) #85)
-#91 := (not #88)
-#110 := (~ #91 #109)
-#111 := [sk]: #110
-#14 := 1::Int
-#15 := (- 1::Int)
-#16 := (< #15 #8)
-#12 := (< 0::Real #11)
-#9 := (< 0::Int #8)
-#13 := (and #9 #12)
-#17 := (implies #13 #16)
-#18 := (forall (vars (?v1 Int) (?v2 Real)) #17)
-#19 := (exists (vars (?v0 Int)) #18)
-#20 := (not #19)
-#94 := (iff #20 #91)
-#42 := (< -1::Int #8)
-#48 := (not #13)
-#49 := (or #48 #42)
-#54 := (forall (vars (?v1 Int) (?v2 Real)) #49)
-#64 := (not #54)
-#92 := (iff #64 #91)
-#89 := (iff #54 #88)
-#86 := (iff #49 #85)
-#83 := (iff #42 #82)
-#84 := [rewrite]: #83
-#79 := (iff #48 #78)
-#76 := (iff #13 #75)
-#73 := (iff #12 #72)
-#74 := [rewrite]: #73
-#69 := (iff #9 #68)
-#70 := [rewrite]: #69
-#77 := [monotonicity #70 #74]: #76
-#80 := [monotonicity #77]: #79
-#87 := [monotonicity #80 #84]: #86
-#90 := [quant-intro #87]: #89
-#93 := [monotonicity #90]: #92
-#65 := (iff #20 #64)
-#62 := (iff #19 #54)
-#57 := (exists (vars (?v0 Int)) #54)
-#60 := (iff #57 #54)
-#61 := [elim-unused]: #60
-#58 := (iff #19 #57)
-#55 := (iff #18 #54)
-#52 := (iff #17 #49)
-#45 := (implies #13 #42)
-#50 := (iff #45 #49)
-#51 := [rewrite]: #50
-#46 := (iff #17 #45)
-#43 := (iff #16 #42)
-#40 := (= #15 -1::Int)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#53 := [trans #47 #51]: #52
-#56 := [quant-intro #53]: #55
-#59 := [quant-intro #56]: #58
-#63 := [trans #59 #61]: #62
-#66 := [monotonicity #63]: #65
-#95 := [trans #66 #93]: #94
-#38 := [asserted]: #20
-#96 := [mp #38 #95]: #91
-#114 := [mp~ #96 #111]: #109
-#120 := [not-or-elim #114]: #106
-#117 := [not-or-elim #114]: #104
-#118 := [and-elim #117]: #99
-#178 := (or #107 #98)
-#179 := [th-lemma arith farkas 1 1]: #178
-#180 := [unit-resolution #179 #118]: #107
-[unit-resolution #180 #120]: false
-unsat
-8a78832884e41117489fba88c88de0b5cacb832a 143 0
-#2 := false
-#10 := 0::Int
-#8 := (:var 0 Int)
-#68 := (<= #8 0::Int)
-#69 := (not #68)
-#146 := (not false)
-#149 := (or #146 #69)
-#152 := (not #149)
-#155 := (forall (vars (?v0 Int)) #152)
-#182 := (iff #155 false)
-#177 := (forall (vars (?v0 Int)) false)
-#180 := (iff #177 false)
-#181 := [elim-unused]: #180
-#178 := (iff #155 #177)
-#175 := (iff #152 false)
-#1 := true
-#170 := (not true)
-#173 := (iff #170 false)
-#174 := [rewrite]: #173
-#171 := (iff #152 #170)
-#168 := (iff #149 true)
-#163 := (or true #69)
-#166 := (iff #163 true)
-#167 := [rewrite]: #166
-#164 := (iff #149 #163)
-#161 := (iff #146 true)
-#162 := [rewrite]: #161
-#165 := [monotonicity #162]: #164
-#169 := [trans #165 #167]: #168
-#172 := [monotonicity #169]: #171
-#176 := [trans #172 #174]: #175
-#179 := [quant-intro #176]: #178
-#183 := [trans #179 #181]: #182
-#59 := -1::Int
-#60 := (* -1::Int #8)
-#7 := (:var 1 Int)
-#61 := (+ #7 #60)
-#62 := (<= #61 0::Int)
-#65 := (not #62)
-#72 := (or #65 #69)
-#75 := (forall (vars (?v1 Int)) #72)
-#78 := (not #75)
-#81 := (or #78 #69)
-#107 := (not #81)
-#125 := (forall (vars (?v0 Int)) #107)
-#158 := (iff #125 #155)
-#129 := (forall (vars (?v1 Int)) #69)
-#132 := (not #129)
-#135 := (or #132 #69)
-#138 := (not #135)
-#141 := (forall (vars (?v0 Int)) #138)
-#156 := (iff #141 #155)
-#157 := [rewrite]: #156
-#142 := (iff #125 #141)
-#143 := [rewrite]: #142
-#159 := [trans #143 #157]: #158
-#118 := (and #75 #68)
-#121 := (forall (vars (?v0 Int)) #118)
-#126 := (iff #121 #125)
-#115 := (iff #118 #107)
-#124 := [rewrite]: #115
-#127 := [quant-intro #124]: #126
-#103 := (not #69)
-#106 := (and #75 #103)
-#110 := (forall (vars (?v0 Int)) #106)
-#122 := (iff #110 #121)
-#119 := (iff #106 #118)
-#116 := (iff #103 #68)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#84 := (exists (vars (?v0 Int)) #81)
-#87 := (not #84)
-#111 := (~ #87 #110)
-#108 := (~ #107 #106)
-#104 := (~ #103 #103)
-#105 := [refl]: #104
-#94 := (not #78)
-#95 := (~ #94 #75)
-#100 := (~ #75 #75)
-#98 := (~ #72 #72)
-#99 := [refl]: #98
-#101 := [nnf-pos #99]: #100
-#102 := [nnf-neg #101]: #95
-#109 := [nnf-neg #102 #105]: #108
-#112 := [nnf-neg #109]: #111
-#11 := (< 0::Int #8)
-#9 := (<= #7 #8)
-#12 := (implies #9 #11)
-#13 := (forall (vars (?v1 Int)) #12)
-#14 := (implies #13 #11)
-#15 := (exists (vars (?v0 Int)) #14)
-#16 := (not #15)
-#90 := (iff #16 #87)
-#37 := (not #9)
-#38 := (or #37 #11)
-#41 := (forall (vars (?v1 Int)) #38)
-#47 := (not #41)
-#48 := (or #47 #11)
-#53 := (exists (vars (?v0 Int)) #48)
-#56 := (not #53)
-#88 := (iff #56 #87)
-#85 := (iff #53 #84)
-#82 := (iff #48 #81)
-#70 := (iff #11 #69)
-#71 := [rewrite]: #70
-#79 := (iff #47 #78)
-#76 := (iff #41 #75)
-#73 := (iff #38 #72)
-#66 := (iff #37 #65)
-#63 := (iff #9 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#74 := [monotonicity #67 #71]: #73
-#77 := [quant-intro #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80 #71]: #82
-#86 := [quant-intro #83]: #85
-#89 := [monotonicity #86]: #88
-#57 := (iff #16 #56)
-#54 := (iff #15 #53)
-#51 := (iff #14 #48)
-#44 := (implies #41 #11)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #14 #44)
-#42 := (iff #13 #41)
-#39 := (iff #12 #38)
-#40 := [rewrite]: #39
-#43 := [quant-intro #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [quant-intro #52]: #54
-#58 := [monotonicity #55]: #57
-#91 := [trans #58 #89]: #90
-#36 := [asserted]: #16
-#92 := [mp #36 #91]: #87
-#113 := [mp~ #92 #112]: #110
-#114 := [mp #113 #123]: #121
-#128 := [mp #114 #127]: #125
-#160 := [mp #128 #159]: #155
-[mp #160 #183]: false
-unsat
-ea961570b37add45bc63c8f0e3f6ddc653b28f42 67 0
-ERROR: line 11 column 83: invalid pattern.
-#2 := false
-decl f3 :: Int
-#8 := f3
-#10 := 2::Int
-#12 := (* 2::Int f3)
-#7 := (:var 0 Int)
-#11 := (* 2::Int #7)
-#13 := (< #11 #12)
-#9 := (< #7 f3)
-#14 := (implies #9 #13)
-#15 := (forall (vars (?v0 Int)) #14)
-#16 := (not #15)
-#85 := (iff #16 false)
-#38 := (not #9)
-#39 := (or #38 #13)
-#42 := (forall (vars (?v0 Int)) #39)
-#45 := (not #42)
-#83 := (iff #45 false)
-#1 := true
-#78 := (not true)
-#81 := (iff #78 false)
-#82 := [rewrite]: #81
-#79 := (iff #45 #78)
-#76 := (iff #42 true)
-#71 := (forall (vars (?v0 Int)) true)
-#74 := (iff #71 true)
-#75 := [elim-unused]: #74
-#72 := (iff #42 #71)
-#69 := (iff #39 true)
-#18 := 0::Int
-#48 := -1::Int
-#51 := (* -1::Int f3)
-#52 := (+ #7 #51)
-#50 := (>= #52 0::Int)
-#49 := (not #50)
-#63 := (or #50 #49)
-#67 := (iff #63 true)
-#68 := [rewrite]: #67
-#65 := (iff #39 #63)
-#64 := (iff #13 #49)
-#62 := [rewrite]: #64
-#60 := (iff #38 #50)
-#55 := (not #49)
-#58 := (iff #55 #50)
-#59 := [rewrite]: #58
-#56 := (iff #38 #55)
-#53 := (iff #9 #49)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#66 := [monotonicity #61 #62]: #65
-#70 := [trans #66 #68]: #69
-#73 := [quant-intro #70]: #72
-#77 := [trans #73 #75]: #76
-#80 := [monotonicity #77]: #79
-#84 := [trans #80 #82]: #83
-#46 := (iff #16 #45)
-#43 := (iff #15 #42)
-#40 := (iff #14 #39)
-#41 := [rewrite]: #40
-#44 := [quant-intro #41]: #43
-#47 := [monotonicity #44]: #46
-#86 := [trans #47 #84]: #85
-#37 := [asserted]: #16
-[mp #37 #86]: false
-unsat
-cc87973002902704adc7d85df3fb8affa4a44929 54 0
-#2 := false
-#10 := 1::Int
-decl ?v1!0 :: Int
-#66 := ?v1!0
-#69 := (>= ?v1!0 1::Int)
-#62 := (not #69)
-#7 := 0::Int
-#67 := (<= ?v1!0 0::Int)
-#68 := (not #67)
-#63 := (or #68 #62)
-#70 := (not #63)
-#8 := (:var 0 Int)
-#47 := (>= #8 1::Int)
-#45 := (not #47)
-#41 := (<= #8 0::Int)
-#42 := (not #41)
-#49 := (or #42 #45)
-#52 := (forall (vars (?v1 Int)) #49)
-#55 := (not #52)
-#71 := (~ #55 #70)
-#72 := [sk]: #71
-#11 := (< #8 1::Int)
-#9 := (< 0::Int #8)
-#12 := (or #9 #11)
-#13 := (forall (vars (?v0 Int) (?v1 Int)) #12)
-#14 := (not #13)
-#58 := (iff #14 #55)
-#35 := (forall (vars (?v1 Int)) #12)
-#38 := (not #35)
-#56 := (iff #38 #55)
-#53 := (iff #35 #52)
-#50 := (iff #12 #49)
-#46 := (iff #11 #45)
-#48 := [rewrite]: #46
-#43 := (iff #9 #42)
-#44 := [rewrite]: #43
-#51 := [monotonicity #44 #48]: #50
-#54 := [quant-intro #51]: #53
-#57 := [monotonicity #54]: #56
-#39 := (iff #14 #38)
-#36 := (iff #13 #35)
-#37 := [elim-unused]: #36
-#40 := [monotonicity #37]: #39
-#59 := [trans #40 #57]: #58
-#34 := [asserted]: #14
-#60 := [mp #34 #59]: #55
-#75 := [mp~ #60 #72]: #70
-#79 := [not-or-elim #75]: #69
-#78 := [not-or-elim #75]: #67
-#137 := (or #62 #68)
-#138 := [th-lemma arith farkas 1 1]: #137
-#139 := [unit-resolution #138 #78]: #62
-[unit-resolution #139 #79]: false
-unsat
-1d9e76ccce459de8771731a1c234c6d9e2aa3527 1 0
-unsat
-e46d82e75c1853418f786555dbc1a12ba5d54f6e 75 0
-#2 := false
-#9 := 1::Int
-decl f5 :: Int
-#11 := f5
-#15 := (+ f5 1::Int)
-decl f3 :: Int
-#7 := f3
-#16 := (* f3 #15)
-decl f4 :: Int
-#8 := f4
-#14 := (* f3 f4)
-#17 := (+ #14 #16)
-#10 := (+ f4 1::Int)
-#12 := (+ #10 f5)
-#13 := (* f3 #12)
-#18 := (= #13 #17)
-#19 := (not #18)
-#93 := (iff #19 false)
-#1 := true
-#88 := (not true)
-#91 := (iff #88 false)
-#92 := [rewrite]: #91
-#89 := (iff #19 #88)
-#86 := (iff #18 true)
-#56 := (* f3 f5)
-#57 := (+ #14 #56)
-#58 := (+ f3 #57)
-#81 := (= #58 #58)
-#84 := (iff #81 true)
-#85 := [rewrite]: #84
-#82 := (iff #18 #81)
-#79 := (= #17 #58)
-#69 := (+ f3 #56)
-#74 := (+ #14 #69)
-#77 := (= #74 #58)
-#78 := [rewrite]: #77
-#75 := (= #17 #74)
-#72 := (= #16 #69)
-#63 := (+ 1::Int f5)
-#66 := (* f3 #63)
-#70 := (= #66 #69)
-#71 := [rewrite]: #70
-#67 := (= #16 #66)
-#64 := (= #15 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#73 := [trans #68 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#61 := (= #13 #58)
-#47 := (+ f4 f5)
-#48 := (+ 1::Int #47)
-#53 := (* f3 #48)
-#59 := (= #53 #58)
-#60 := [rewrite]: #59
-#54 := (= #13 #53)
-#51 := (= #12 #48)
-#41 := (+ 1::Int f4)
-#44 := (+ #41 f5)
-#49 := (= #44 #48)
-#50 := [rewrite]: #49
-#45 := (= #12 #44)
-#42 := (= #10 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52]: #54
-#62 := [trans #55 #60]: #61
-#83 := [monotonicity #62 #80]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #87]: #89
-#94 := [trans #90 #92]: #93
-#40 := [asserted]: #19
-[mp #40 #94]: false
-unsat
-60242f59c15f3933ccbd1d4ed5e4e07293c9dd72 62 0
-#2 := false
-decl f4 :: Real
-#9 := f4
-decl f3 :: Real
-#7 := f3
-#15 := 2::Real
-#16 := (* 2::Real f3)
-#17 := (* #16 f4)
-#8 := 1::Real
-#12 := (- 1::Real f4)
-#13 := (* f3 #12)
-#10 := (+ 1::Real f4)
-#11 := (* f3 #10)
-#14 := (- #11 #13)
-#18 := (= #14 #17)
-#19 := (not #18)
-#81 := (iff #19 false)
-#1 := true
-#76 := (not true)
-#79 := (iff #76 false)
-#80 := [rewrite]: #79
-#77 := (iff #19 #76)
-#74 := (iff #18 true)
-#41 := (* f3 f4)
-#63 := (* 2::Real #41)
-#69 := (= #63 #63)
-#72 := (iff #69 true)
-#73 := [rewrite]: #72
-#70 := (iff #18 #69)
-#67 := (= #17 #63)
-#68 := [rewrite]: #67
-#65 := (= #14 #63)
-#45 := -1::Real
-#53 := (* -1::Real #41)
-#54 := (+ f3 #53)
-#42 := (+ f3 #41)
-#59 := (- #42 #54)
-#62 := (= #59 #63)
-#64 := [rewrite]: #62
-#60 := (= #14 #59)
-#57 := (= #13 #54)
-#46 := (* -1::Real f4)
-#47 := (+ 1::Real #46)
-#50 := (* f3 #47)
-#55 := (= #50 #54)
-#56 := [rewrite]: #55
-#51 := (= #13 #50)
-#48 := (= #12 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#43 := (= #11 #42)
-#44 := [rewrite]: #43
-#61 := [monotonicity #44 #58]: #60
-#66 := [trans #61 #64]: #65
-#71 := [monotonicity #66 #68]: #70
-#75 := [trans #71 #73]: #74
-#78 := [monotonicity #75]: #77
-#82 := [trans #78 #80]: #81
-#40 := [asserted]: #19
-[mp #40 #82]: false
-unsat
-3ecab0bc7101d63e72b4fb9ac8a649c491da9533 141 0
-#2 := false
-decl f6 :: Int
-#12 := f6
-decl f7 :: Int
-#16 := f7
-decl f5 :: Int
-#11 := f5
-#27 := (+ f5 f7)
-#28 := (+ #27 f6)
-decl f4 :: Int
-#9 := f4
-#8 := 1::Int
-#10 := (+ 1::Int f4)
-#29 := (* #10 #28)
-#24 := (* f7 f4)
-#22 := (* #10 f7)
-#13 := (+ f5 f6)
-#19 := 2::Int
-#20 := (* 2::Int #10)
-#21 := (* #20 #13)
-#23 := (+ #21 #22)
-#25 := (+ #23 #24)
-decl f3 :: Int
-#7 := f3
-#26 := (+ f3 #25)
-#30 := (- #26 #29)
-#17 := (* f4 f7)
-#14 := (* #10 #13)
-#15 := (+ f3 #14)
-#18 := (+ #15 #17)
-#31 := (= #18 #30)
-#32 := (not #31)
-#157 := (iff #32 false)
-#1 := true
-#152 := (not true)
-#155 := (iff #152 false)
-#156 := [rewrite]: #155
-#153 := (iff #32 #152)
-#150 := (iff #31 true)
-#55 := (* f4 f6)
-#54 := (* f4 f5)
-#56 := (+ #54 #55)
-#67 := (+ #17 #56)
-#68 := (+ f6 #67)
-#69 := (+ f5 #68)
-#70 := (+ f3 #69)
-#144 := (= #70 #70)
-#148 := (iff #144 true)
-#149 := [rewrite]: #148
-#143 := (iff #31 #144)
-#146 := (= #30 #70)
-#131 := (+ f7 #67)
-#132 := (+ f6 #131)
-#133 := (+ f5 #132)
-#85 := (* 2::Int #55)
-#83 := (* 2::Int #54)
-#86 := (+ #83 #85)
-#112 := (* 2::Int #17)
-#113 := (+ #112 #86)
-#114 := (+ f7 #113)
-#84 := (* 2::Int f6)
-#115 := (+ #84 #114)
-#82 := (* 2::Int f5)
-#116 := (+ #82 #115)
-#121 := (+ f3 #116)
-#138 := (- #121 #133)
-#141 := (= #138 #70)
-#147 := [rewrite]: #141
-#139 := (= #30 #138)
-#136 := (= #29 #133)
-#124 := (+ f6 f7)
-#125 := (+ f5 #124)
-#128 := (* #10 #125)
-#134 := (= #128 #133)
-#135 := [rewrite]: #134
-#129 := (= #29 #128)
-#126 := (= #28 #125)
-#127 := [rewrite]: #126
-#130 := [monotonicity #127]: #129
-#137 := [trans #130 #135]: #136
-#122 := (= #26 #121)
-#119 := (= #25 #116)
-#99 := (+ #17 #86)
-#100 := (+ f7 #99)
-#101 := (+ #84 #100)
-#102 := (+ #82 #101)
-#109 := (+ #102 #17)
-#117 := (= #109 #116)
-#118 := [rewrite]: #117
-#110 := (= #25 #109)
-#107 := (= #24 #17)
-#108 := [rewrite]: #107
-#105 := (= #23 #102)
-#93 := (+ f7 #17)
-#87 := (+ #84 #86)
-#88 := (+ #82 #87)
-#96 := (+ #88 #93)
-#103 := (= #96 #102)
-#104 := [rewrite]: #103
-#97 := (= #23 #96)
-#94 := (= #22 #93)
-#95 := [rewrite]: #94
-#91 := (= #21 #88)
-#75 := (* 2::Int f4)
-#76 := (+ 2::Int #75)
-#79 := (* #76 #13)
-#89 := (= #79 #88)
-#90 := [rewrite]: #89
-#80 := (= #21 #79)
-#77 := (= #20 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#92 := [trans #81 #90]: #91
-#98 := [monotonicity #92 #95]: #97
-#106 := [trans #98 #104]: #105
-#111 := [monotonicity #106 #108]: #110
-#120 := [trans #111 #118]: #119
-#123 := [monotonicity #120]: #122
-#140 := [monotonicity #123 #137]: #139
-#145 := [trans #140 #147]: #146
-#73 := (= #18 #70)
-#57 := (+ f6 #56)
-#58 := (+ f5 #57)
-#61 := (+ f3 #58)
-#64 := (+ #61 #17)
-#71 := (= #64 #70)
-#72 := [rewrite]: #71
-#65 := (= #18 #64)
-#62 := (= #15 #61)
-#59 := (= #14 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#66 := [monotonicity #63]: #65
-#74 := [trans #66 #72]: #73
-#142 := [monotonicity #74 #145]: #143
-#151 := [trans #142 #149]: #150
-#154 := [monotonicity #151]: #153
-#158 := [trans #154 #156]: #157
-#53 := [asserted]: #32
-[mp #53 #158]: false
-unsat
43550507f510d81bc4fb9ef8c1fd14424eaa9070 37 0
#2 := false
#10 := 0::Int
@@ -8819,1764 +1561,6 @@
#53 := [not-or-elim #52]: #11
[th-lemma arith farkas 1 1 1 #53 #57 #55]: false
unsat
-f5067fa58c623377db978838e2294684a3fe7bb2 225 0
-#2 := false
-#24 := 0::Int
-decl f5 :: (-> S4 S3 Int)
-decl f3 :: (-> S2 Int S3)
-decl f7 :: S3
-#10 := f7
-decl f6 :: S4
-#9 := f6
-#11 := (f5 f6 f7)
-#8 := 2::Int
-#12 := (* 2::Int #11)
-decl f4 :: S2
-#7 := f4
-#13 := (f3 f4 #12)
-#276 := (f5 f6 #13)
-#185 := -1::Int
-#596 := (* -1::Int #276)
-#597 := (+ #12 #596)
-#577 := (<= #597 0::Int)
-#595 := (= #597 0::Int)
-#256 := (>= #11 0::Int)
-#579 := (= #276 0::Int)
-#436 := (not #579)
-#297 := (<= #276 0::Int)
-#533 := (not #297)
-#14 := 1::Int
-#544 := (>= #276 1::Int)
-#549 := (= #276 1::Int)
-#15 := (f3 f4 1::Int)
-#569 := (f5 f6 #15)
-#570 := (= #569 1::Int)
-#25 := (:var 0 Int)
-#27 := (f3 f4 #25)
-#607 := (pattern #27)
-#28 := (f5 f6 #27)
-#29 := (= #28 #25)
-#70 := (>= #25 0::Int)
-#71 := (not #70)
-#74 := (or #71 #29)
-#608 := (forall (vars (?v0 Int)) (:pat #607) #74)
-#77 := (forall (vars (?v0 Int)) #74)
-#611 := (iff #77 #608)
-#609 := (iff #74 #74)
-#610 := [refl]: #609
-#612 := [quant-intro #610]: #611
-#114 := (~ #77 #77)
-#113 := (~ #74 #74)
-#110 := [refl]: #113
-#115 := [nnf-pos #110]: #114
-#26 := (<= 0::Int #25)
-#30 := (implies #26 #29)
-#31 := (forall (vars (?v0 Int)) #30)
-#80 := (iff #31 #77)
-#61 := (not #26)
-#62 := (or #61 #29)
-#65 := (forall (vars (?v0 Int)) #62)
-#78 := (iff #65 #77)
-#75 := (iff #62 #74)
-#72 := (iff #61 #71)
-#68 := (iff #26 #70)
-#69 := [rewrite]: #68
-#73 := [monotonicity #69]: #72
-#76 := [monotonicity #73]: #75
-#79 := [quant-intro #76]: #78
-#66 := (iff #31 #65)
-#63 := (iff #30 #62)
-#64 := [rewrite]: #63
-#67 := [quant-intro #64]: #66
-#81 := [trans #67 #79]: #80
-#59 := [asserted]: #31
-#82 := [mp #59 #81]: #77
-#111 := [mp~ #82 #115]: #77
-#613 := [mp #111 #612]: #608
-#589 := (not #608)
-#555 := (or #589 #570)
-#299 := (>= 1::Int 0::Int)
-#192 := (not #299)
-#292 := (or #192 #570)
-#556 := (or #589 #292)
-#552 := (iff #556 #555)
-#558 := (iff #555 #555)
-#559 := [rewrite]: #558
-#562 := (iff #292 #570)
-#563 := (or false #570)
-#561 := (iff #563 #570)
-#565 := [rewrite]: #561
-#564 := (iff #292 #563)
-#284 := (iff #192 false)
-#1 := true
-#571 := (not true)
-#282 := (iff #571 false)
-#283 := [rewrite]: #282
-#568 := (iff #192 #571)
-#293 := (iff #299 true)
-#567 := [rewrite]: #293
-#572 := [monotonicity #567]: #568
-#285 := [trans #572 #283]: #284
-#278 := [monotonicity #285]: #564
-#566 := [trans #278 #565]: #562
-#553 := [monotonicity #566]: #552
-#554 := [trans #553 #559]: #552
-#557 := [quant-inst #14]: #556
-#560 := [mp #557 #554]: #555
-#383 := [unit-resolution #560 #613]: #570
-#536 := (= #276 #569)
-#16 := (= #13 #15)
-#17 := (not #16)
-#18 := (not #17)
-#56 := (iff #18 #16)
-#57 := [rewrite]: #56
-#55 := [asserted]: #18
-#60 := [mp #55 #57]: #16
-#424 := [monotonicity #60]: #536
-#425 := [trans #424 #383]: #549
-#384 := (not #549)
-#532 := (or #384 #544)
-#434 := [th-lemma arith triangle-eq]: #532
-#529 := [unit-resolution #434 #425]: #544
-#530 := (not #544)
-#418 := (or #530 #533)
-#433 := [th-lemma arith farkas 1 1]: #418
-#435 := [unit-resolution #433 #529]: #533
-#429 := (or #436 #297)
-#437 := [th-lemma arith triangle-eq]: #429
-#438 := [unit-resolution #437 #435]: #436
-#581 := (or #256 #579)
-#33 := (= #28 0::Int)
-#100 := (or #70 #33)
-#614 := (forall (vars (?v0 Int)) (:pat #607) #100)
-#103 := (forall (vars (?v0 Int)) #100)
-#617 := (iff #103 #614)
-#615 := (iff #100 #100)
-#616 := [refl]: #615
-#618 := [quant-intro #616]: #617
-#116 := (~ #103 #103)
-#124 := (~ #100 #100)
-#125 := [refl]: #124
-#117 := [nnf-pos #125]: #116
-#32 := (< #25 0::Int)
-#34 := (implies #32 #33)
-#35 := (forall (vars (?v0 Int)) #34)
-#106 := (iff #35 #103)
-#84 := (not #32)
-#85 := (or #84 #33)
-#88 := (forall (vars (?v0 Int)) #85)
-#104 := (iff #88 #103)
-#101 := (iff #85 #100)
-#98 := (iff #84 #70)
-#93 := (not #71)
-#96 := (iff #93 #70)
-#97 := [rewrite]: #96
-#94 := (iff #84 #93)
-#91 := (iff #32 #71)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#99 := [trans #95 #97]: #98
-#102 := [monotonicity #99]: #101
-#105 := [quant-intro #102]: #104
-#89 := (iff #35 #88)
-#86 := (iff #34 #85)
-#87 := [rewrite]: #86
-#90 := [quant-intro #87]: #89
-#107 := [trans #90 #105]: #106
-#83 := [asserted]: #35
-#108 := [mp #83 #107]: #103
-#126 := [mp~ #108 #117]: #103
-#619 := [mp #126 #618]: #614
-#219 := (not #614)
-#583 := (or #219 #256 #579)
-#271 := (>= #12 0::Int)
-#580 := (or #271 #579)
-#585 := (or #219 #580)
-#574 := (iff #585 #583)
-#225 := (or #219 #581)
-#587 := (iff #225 #583)
-#573 := [rewrite]: #587
-#586 := (iff #585 #225)
-#576 := (iff #580 #581)
-#592 := (iff #271 #256)
-#594 := [rewrite]: #592
-#582 := [monotonicity #594]: #576
-#584 := [monotonicity #582]: #586
-#281 := [trans #584 #573]: #574
-#224 := [quant-inst #12]: #585
-#296 := [mp #224 #281]: #583
-#439 := [unit-resolution #296 #619]: #581
-#440 := [unit-resolution #439 #438]: #256
-#250 := (not #256)
-#598 := (or #250 #595)
-#248 := (or #589 #250 #595)
-#273 := (= #276 #12)
-#272 := (not #271)
-#277 := (or #272 #273)
-#253 := (or #589 #277)
-#238 := (iff #253 #248)
-#249 := (or #589 #598)
-#575 := (iff #249 #248)
-#237 := [rewrite]: #575
-#591 := (iff #253 #249)
-#593 := (iff #277 #598)
-#261 := (iff #273 #595)
-#262 := [rewrite]: #261
-#381 := (iff #272 #250)
-#588 := [monotonicity #594]: #381
-#599 := [monotonicity #588 #262]: #593
-#233 := [monotonicity #599]: #591
-#239 := [trans #233 #237]: #238
-#590 := [quant-inst #12]: #253
-#240 := [mp #590 #239]: #248
-#441 := [unit-resolution #240 #613]: #598
-#534 := [unit-resolution #441 #440]: #595
-#531 := (not #595)
-#535 := (or #531 #577)
-#522 := [th-lemma arith triangle-eq]: #535
-#524 := [unit-resolution #522 #534]: #577
-#578 := (>= #597 0::Int)
-#516 := (or #531 #578)
-#513 := [th-lemma arith triangle-eq]: #516
-#515 := [unit-resolution #513 #534]: #578
-#550 := (<= #276 1::Int)
-#525 := (or #384 #550)
-#526 := [th-lemma arith triangle-eq]: #525
-#527 := [unit-resolution #526 #425]: #550
-[th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2 #529 #527 #515 #524]: false
-unsat
-4225ab6372dca8ebf6ba05ad5ea39526a6e2a129 55 0
-#2 := false
-#74 := 4::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#9 := (f3 f4 f5)
-#75 := (>= #9 4::Int)
-#76 := (not #75)
-#10 := 3::Int
-#65 := (>= #9 3::Int)
-#79 := (or #65 #76)
-#82 := (not #79)
-#14 := 7::Int
-#12 := 2::Int
-#13 := (* 2::Int #9)
-#15 := (< #13 7::Int)
-#11 := (< #9 3::Int)
-#16 := (implies #11 #15)
-#17 := (not #16)
-#85 := (iff #17 #82)
-#56 := (not #11)
-#57 := (or #56 #15)
-#60 := (not #57)
-#83 := (iff #60 #82)
-#80 := (iff #57 #79)
-#77 := (iff #15 #76)
-#78 := [rewrite]: #77
-#72 := (iff #56 #65)
-#63 := (not #65)
-#67 := (not #63)
-#70 := (iff #67 #65)
-#71 := [rewrite]: #70
-#68 := (iff #56 #67)
-#64 := (iff #11 #63)
-#66 := [rewrite]: #64
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#81 := [monotonicity #73 #78]: #80
-#84 := [monotonicity #81]: #83
-#61 := (iff #17 #60)
-#58 := (iff #16 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#86 := [trans #62 #84]: #85
-#55 := [asserted]: #17
-#87 := [mp #55 #86]: #82
-#89 := [not-or-elim #87]: #75
-#88 := [not-or-elim #87]: #63
-#300 := (or #76 #65)
-#216 := [th-lemma arith farkas 1 1]: #300
-#301 := [unit-resolution #216 #88]: #76
-[unit-resolution #301 #89]: false
-unsat
-6b3381ed26844d4b649300d18bdcc49988752527 270 0
-#2 := false
-#7 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: (-> S4 Int S3)
-decl f7 :: S3
-#11 := f7
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f7)
-#10 := 1::Int
-#13 := (+ 1::Int #12)
-decl f6 :: S4
-#9 := f6
-#14 := (f5 f6 #13)
-#15 := (f3 f4 #14)
-#60 := -1::Int
-#61 := (* -1::Int #12)
-#62 := (+ #61 #15)
-#65 := (f5 f6 #62)
-#68 := (f3 f4 #65)
-#625 := (* -1::Int #15)
-#593 := (+ #625 #68)
-#597 := (+ #12 #593)
-#574 := (>= #597 0::Int)
-#594 := (= #597 0::Int)
-#631 := (+ #12 #625)
-#315 := (<= #631 0::Int)
-#614 := (<= #631 -1::Int)
-#621 := (= #631 -1::Int)
-#294 := (>= #12 -1::Int)
-#416 := (>= #12 0::Int)
-#545 := (= #12 0::Int)
-#218 := (f5 f6 #12)
-#564 := (f3 f4 #218)
-#466 := (= #564 0::Int)
-#550 := (not #416)
-#551 := [hypothesis]: #550
-#561 := (or #416 #466)
-#27 := (:var 0 Int)
-#29 := (f5 f6 #27)
-#639 := (pattern #29)
-#30 := (f3 f4 #29)
-#35 := (= #30 0::Int)
-#101 := (>= #27 0::Int)
-#132 := (or #101 #35)
-#646 := (forall (vars (?v0 Int)) (:pat #639) #132)
-#135 := (forall (vars (?v0 Int)) #132)
-#649 := (iff #135 #646)
-#647 := (iff #132 #132)
-#648 := [refl]: #647
-#650 := [quant-intro #648]: #649
-#148 := (~ #135 #135)
-#156 := (~ #132 #132)
-#157 := [refl]: #156
-#149 := [nnf-pos #157]: #148
-#34 := (< #27 0::Int)
-#36 := (implies #34 #35)
-#37 := (forall (vars (?v0 Int)) #36)
-#138 := (iff #37 #135)
-#116 := (not #34)
-#117 := (or #116 #35)
-#120 := (forall (vars (?v0 Int)) #117)
-#136 := (iff #120 #135)
-#133 := (iff #117 #132)
-#130 := (iff #116 #101)
-#103 := (not #101)
-#125 := (not #103)
-#128 := (iff #125 #101)
-#129 := [rewrite]: #128
-#126 := (iff #116 #125)
-#123 := (iff #34 #103)
-#124 := [rewrite]: #123
-#127 := [monotonicity #124]: #126
-#131 := [trans #127 #129]: #130
-#134 := [monotonicity #131]: #133
-#137 := [quant-intro #134]: #136
-#121 := (iff #37 #120)
-#118 := (iff #36 #117)
-#119 := [rewrite]: #118
-#122 := [quant-intro #119]: #121
-#139 := [trans #122 #137]: #138
-#115 := [asserted]: #37
-#140 := [mp #115 #139]: #135
-#158 := [mp~ #140 #149]: #135
-#651 := [mp #158 #650]: #646
-#616 := (not #646)
-#450 := (or #616 #416 #466)
-#465 := (or #616 #561)
-#468 := (iff #465 #450)
-#461 := [rewrite]: #468
-#467 := [quant-inst #12]: #465
-#469 := [mp #467 #461]: #450
-#552 := [unit-resolution #469 #651]: #561
-#546 := [unit-resolution #552 #551]: #466
-#540 := (= #12 #564)
-#537 := (= f7 #218)
-#303 := (= #218 f7)
-#22 := (:var 0 S3)
-#23 := (f3 f4 #22)
-#632 := (pattern #23)
-#24 := (f5 f6 #23)
-#25 := (= #24 #22)
-#633 := (forall (vars (?v0 S3)) (:pat #632) #25)
-#26 := (forall (vars (?v0 S3)) #25)
-#636 := (iff #26 #633)
-#634 := (iff #25 #25)
-#635 := [refl]: #634
-#637 := [quant-intro #635]: #636
-#154 := (~ #26 #26)
-#152 := (~ #25 #25)
-#153 := [refl]: #152
-#155 := [nnf-pos #153]: #154
-#91 := [asserted]: #26
-#144 := [mp~ #91 #155]: #26
-#638 := [mp #144 #637]: #633
-#305 := (not #633)
-#296 := (or #305 #303)
-#307 := [quant-inst #11]: #296
-#553 := [unit-resolution #307 #638]: #303
-#538 := [symm #553]: #537
-#541 := [monotonicity #538]: #540
-#542 := [trans #541 #546]: #545
-#543 := (not #545)
-#539 := (or #543 #416)
-#544 := [th-lemma arith triangle-eq]: #539
-#530 := [unit-resolution #544 #551 #542]: false
-#531 := [lemma #530]: #416
-#547 := (or #550 #294)
-#533 := [th-lemma arith farkas 1 1]: #547
-#534 := [unit-resolution #533 #531]: #294
-#628 := (not #294)
-#622 := (or #628 #621)
-#31 := (= #30 #27)
-#106 := (or #103 #31)
-#640 := (forall (vars (?v0 Int)) (:pat #639) #106)
-#109 := (forall (vars (?v0 Int)) #106)
-#643 := (iff #109 #640)
-#641 := (iff #106 #106)
-#642 := [refl]: #641
-#644 := [quant-intro #642]: #643
-#146 := (~ #109 #109)
-#145 := (~ #106 #106)
-#142 := [refl]: #145
-#147 := [nnf-pos #142]: #146
-#28 := (<= 0::Int #27)
-#32 := (implies #28 #31)
-#33 := (forall (vars (?v0 Int)) #32)
-#112 := (iff #33 #109)
-#93 := (not #28)
-#94 := (or #93 #31)
-#97 := (forall (vars (?v0 Int)) #94)
-#110 := (iff #97 #109)
-#107 := (iff #94 #106)
-#104 := (iff #93 #103)
-#100 := (iff #28 #101)
-#102 := [rewrite]: #100
-#105 := [monotonicity #102]: #104
-#108 := [monotonicity #105]: #107
-#111 := [quant-intro #108]: #110
-#98 := (iff #33 #97)
-#95 := (iff #32 #94)
-#96 := [rewrite]: #95
-#99 := [quant-intro #96]: #98
-#113 := [trans #99 #111]: #112
-#92 := [asserted]: #33
-#114 := [mp #92 #113]: #109
-#143 := [mp~ #114 #147]: #109
-#645 := [mp #143 #644]: #640
-#266 := (not #640)
-#607 := (or #266 #628 #621)
-#413 := (= #15 #13)
-#289 := (>= #13 0::Int)
-#624 := (not #289)
-#620 := (or #624 #413)
-#270 := (or #266 #620)
-#612 := (iff #270 #607)
-#272 := (or #266 #622)
-#610 := (iff #272 #607)
-#611 := [rewrite]: #610
-#273 := (iff #270 #272)
-#282 := (iff #620 #622)
-#281 := (iff #413 #621)
-#286 := [rewrite]: #281
-#629 := (iff #624 #628)
-#295 := (iff #289 #294)
-#627 := [rewrite]: #295
-#630 := [monotonicity #627]: #629
-#623 := [monotonicity #630 #286]: #282
-#609 := [monotonicity #623]: #273
-#613 := [trans #609 #611]: #612
-#271 := [quant-inst #13]: #270
-#608 := [mp #271 #613]: #607
-#535 := [unit-resolution #608 #645]: #622
-#532 := [unit-resolution #535 #534]: #621
-#536 := (not #621)
-#516 := (or #536 #614)
-#517 := [th-lemma arith triangle-eq]: #516
-#519 := [unit-resolution #517 #532]: #614
-#520 := (not #614)
-#521 := (or #520 #315)
-#522 := [th-lemma arith farkas 1 1]: #521
-#523 := [unit-resolution #522 #519]: #315
-#595 := (not #315)
-#588 := (or #595 #594)
-#585 := (or #266 #595 #594)
-#604 := (= #68 #62)
-#603 := (>= #62 0::Int)
-#600 := (not #603)
-#314 := (or #600 #604)
-#590 := (or #266 #314)
-#577 := (iff #590 #585)
-#586 := (or #266 #588)
-#434 := (iff #586 #585)
-#435 := [rewrite]: #434
-#592 := (iff #590 #586)
-#589 := (iff #314 #588)
-#598 := (iff #604 #594)
-#587 := [rewrite]: #598
-#596 := (iff #600 #595)
-#316 := (iff #603 #315)
-#317 := [rewrite]: #316
-#311 := [monotonicity #317]: #596
-#584 := [monotonicity #311 #587]: #589
-#433 := [monotonicity #584]: #592
-#578 := [trans #433 #435]: #577
-#591 := [quant-inst #62]: #590
-#579 := [mp #591 #578]: #585
-#524 := [unit-resolution #579 #645]: #588
-#525 := [unit-resolution #524 #523]: #594
-#526 := (not #594)
-#527 := (or #526 #574)
-#528 := [th-lemma arith triangle-eq]: #527
-#518 := [unit-resolution #528 #525]: #574
-#77 := (<= #68 0::Int)
-#17 := (- #15 #12)
-#18 := (f5 f6 #17)
-#19 := (f3 f4 #18)
-#16 := (* 0::Int #15)
-#20 := (< #16 #19)
-#21 := (not #20)
-#88 := (iff #21 #77)
-#71 := (< 0::Int #68)
-#74 := (not #71)
-#86 := (iff #74 #77)
-#78 := (not #77)
-#81 := (not #78)
-#84 := (iff #81 #77)
-#85 := [rewrite]: #84
-#82 := (iff #74 #81)
-#79 := (iff #71 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#87 := [trans #83 #85]: #86
-#75 := (iff #21 #74)
-#72 := (iff #20 #71)
-#69 := (= #19 #68)
-#66 := (= #18 #65)
-#63 := (= #17 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#70 := [monotonicity #67]: #69
-#58 := (= #16 0::Int)
-#59 := [rewrite]: #58
-#73 := [monotonicity #59 #70]: #72
-#76 := [monotonicity #73]: #75
-#89 := [trans #76 #87]: #88
-#57 := [asserted]: #21
-#90 := [mp #57 #89]: #77
-[th-lemma arith farkas -1 -1 1 #90 #519 #518]: false
-unsat
-b3acce989065928cb3ce15ce4113a910c6fff5aa 269 0
-#2 := false
-#7 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: (-> S4 Int S3)
-decl f7 :: S3
-#11 := f7
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f7)
-#10 := 1::Int
-#13 := (+ 1::Int #12)
-decl f6 :: S4
-#9 := f6
-#14 := (f5 f6 #13)
-#15 := (f3 f4 #14)
-#65 := -1::Int
-#66 := (+ -1::Int #15)
-#69 := (f5 f6 #66)
-#367 := (f3 f4 #69)
-#638 := (* -1::Int #367)
-#499 := (+ #12 #638)
-#459 := (>= #499 0::Int)
-#498 := (= #12 #367)
-#605 := (= f7 #69)
-#72 := (= #69 f7)
-#101 := (<= #15 0::Int)
-#173 := (iff #101 #72)
-#192 := (iff #173 #72)
-#1 := true
-#187 := (iff true #72)
-#190 := (iff #187 #72)
-#191 := [rewrite]: #190
-#188 := (iff #173 #187)
-#179 := (iff #101 true)
-#102 := (not #101)
-#105 := (iff #102 #72)
-#108 := (or #105 #102)
-#111 := (not #108)
-#16 := (< 0::Int #15)
-#17 := (if #16 true false)
-#22 := (not #17)
-#23 := (implies #22 false)
-#18 := (- #15 1::Int)
-#19 := (f5 f6 #18)
-#20 := (= #19 f7)
-#21 := (iff #17 #20)
-#24 := (or #21 #23)
-#25 := (or false #24)
-#26 := (not #25)
-#114 := (iff #26 #111)
-#75 := (iff #16 #72)
-#88 := (or #75 #16)
-#98 := (not #88)
-#112 := (iff #98 #111)
-#109 := (iff #88 #108)
-#103 := (iff #16 #102)
-#104 := [rewrite]: #103
-#106 := (iff #75 #105)
-#107 := [monotonicity #104]: #106
-#110 := [monotonicity #107 #104]: #109
-#113 := [monotonicity #110]: #112
-#99 := (iff #26 #98)
-#96 := (iff #25 #88)
-#91 := (or false #88)
-#94 := (iff #91 #88)
-#95 := [rewrite]: #94
-#92 := (iff #25 #91)
-#89 := (iff #24 #88)
-#86 := (iff #23 #16)
-#78 := (not #16)
-#81 := (implies #78 false)
-#84 := (iff #81 #16)
-#85 := [rewrite]: #84
-#82 := (iff #23 #81)
-#79 := (iff #22 #78)
-#63 := (iff #17 #16)
-#64 := [rewrite]: #63
-#80 := [monotonicity #64]: #79
-#83 := [monotonicity #80]: #82
-#87 := [trans #83 #85]: #86
-#76 := (iff #21 #75)
-#73 := (iff #20 #72)
-#70 := (= #19 #69)
-#67 := (= #18 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #64 #74]: #76
-#90 := [monotonicity #77 #87]: #89
-#93 := [monotonicity #90]: #92
-#97 := [trans #93 #95]: #96
-#100 := [monotonicity #97]: #99
-#115 := [trans #100 #113]: #114
-#62 := [asserted]: #26
-#116 := [mp #62 #115]: #111
-#119 := [not-or-elim #116]: #101
-#180 := [iff-true #119]: #179
-#189 := [monotonicity #180]: #188
-#193 := [trans #189 #191]: #192
-#117 := (not #105)
-#174 := (iff #117 #173)
-#175 := [rewrite]: #174
-#118 := [not-or-elim #116]: #117
-#176 := [mp #118 #175]: #173
-#177 := [mp #176 #193]: #72
-#608 := [symm #177]: #605
-#513 := [monotonicity #608]: #498
-#514 := (not #498)
-#515 := (or #514 #459)
-#516 := [th-lemma arith triangle-eq]: #515
-#609 := [unit-resolution #516 #513]: #459
-#672 := (* -1::Int #15)
-#673 := (+ #12 #672)
-#654 := (<= #673 -1::Int)
-#671 := (= #673 -1::Int)
-#669 := (>= #12 -1::Int)
-#616 := (>= #367 0::Int)
-#621 := (= #367 0::Int)
-#646 := (>= #15 1::Int)
-#357 := (not #646)
-#606 := (or #357 #102)
-#610 := [th-lemma arith farkas 1 1]: #606
-#597 := [unit-resolution #610 #119]: #357
-#32 := (:var 0 Int)
-#34 := (f5 f6 #32)
-#682 := (pattern #34)
-#35 := (f3 f4 #34)
-#40 := (= #35 0::Int)
-#130 := (>= #32 0::Int)
-#161 := (or #130 #40)
-#689 := (forall (vars (?v0 Int)) (:pat #682) #161)
-#164 := (forall (vars (?v0 Int)) #161)
-#692 := (iff #164 #689)
-#690 := (iff #161 #161)
-#691 := [refl]: #690
-#693 := [quant-intro #691]: #692
-#197 := (~ #164 #164)
-#195 := (~ #161 #161)
-#196 := [refl]: #195
-#198 := [nnf-pos #196]: #197
-#39 := (< #32 0::Int)
-#41 := (implies #39 #40)
-#42 := (forall (vars (?v0 Int)) #41)
-#167 := (iff #42 #164)
-#145 := (not #39)
-#146 := (or #145 #40)
-#149 := (forall (vars (?v0 Int)) #146)
-#165 := (iff #149 #164)
-#162 := (iff #146 #161)
-#159 := (iff #145 #130)
-#132 := (not #130)
-#154 := (not #132)
-#157 := (iff #154 #130)
-#158 := [rewrite]: #157
-#155 := (iff #145 #154)
-#152 := (iff #39 #132)
-#153 := [rewrite]: #152
-#156 := [monotonicity #153]: #155
-#160 := [trans #156 #158]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#150 := (iff #42 #149)
-#147 := (iff #41 #146)
-#148 := [rewrite]: #147
-#151 := [quant-intro #148]: #150
-#168 := [trans #151 #166]: #167
-#144 := [asserted]: #42
-#169 := [mp #144 #168]: #164
-#199 := [mp~ #169 #198]: #164
-#694 := [mp #199 #693]: #689
-#660 := (not #689)
-#624 := (or #660 #646 #621)
-#644 := (>= #66 0::Int)
-#622 := (or #644 #621)
-#625 := (or #660 #622)
-#612 := (iff #625 #624)
-#623 := (or #646 #621)
-#626 := (or #660 #623)
-#458 := (iff #626 #624)
-#611 := [rewrite]: #458
-#455 := (iff #625 #626)
-#617 := (iff #622 #623)
-#643 := (iff #644 #646)
-#647 := [rewrite]: #643
-#618 := [monotonicity #647]: #617
-#457 := [monotonicity #618]: #455
-#614 := [trans #457 #611]: #612
-#619 := [quant-inst #66]: #625
-#615 := [mp #619 #614]: #624
-#599 := [unit-resolution #615 #694 #597]: #621
-#591 := (not #621)
-#588 := (or #591 #616)
-#590 := [th-lemma arith triangle-eq]: #588
-#600 := [unit-resolution #590 #599]: #616
-#602 := (not #459)
-#601 := (not #616)
-#598 := (or #669 #601 #602)
-#603 := [th-lemma arith assign-bounds 1 1]: #598
-#592 := [unit-resolution #603 #600 #609]: #669
-#663 := (not #669)
-#674 := (or #663 #671)
-#36 := (= #35 #32)
-#135 := (or #132 #36)
-#683 := (forall (vars (?v0 Int)) (:pat #682) #135)
-#138 := (forall (vars (?v0 Int)) #135)
-#686 := (iff #138 #683)
-#684 := (iff #135 #135)
-#685 := [refl]: #684
-#687 := [quant-intro #685]: #686
-#194 := (~ #138 #138)
-#182 := (~ #135 #135)
-#178 := [refl]: #182
-#171 := [nnf-pos #178]: #194
-#33 := (<= 0::Int #32)
-#37 := (implies #33 #36)
-#38 := (forall (vars (?v0 Int)) #37)
-#141 := (iff #38 #138)
-#122 := (not #33)
-#123 := (or #122 #36)
-#126 := (forall (vars (?v0 Int)) #123)
-#139 := (iff #126 #138)
-#136 := (iff #123 #135)
-#133 := (iff #122 #132)
-#129 := (iff #33 #130)
-#131 := [rewrite]: #129
-#134 := [monotonicity #131]: #133
-#137 := [monotonicity #134]: #136
-#140 := [quant-intro #137]: #139
-#127 := (iff #38 #126)
-#124 := (iff #37 #123)
-#125 := [rewrite]: #124
-#128 := [quant-intro #125]: #127
-#142 := [trans #128 #140]: #141
-#121 := [asserted]: #38
-#143 := [mp #121 #142]: #138
-#172 := [mp~ #143 #171]: #138
-#688 := [mp #172 #687]: #683
-#329 := (not #683)
-#665 := (or #329 #663 #671)
-#332 := (= #15 #13)
-#351 := (>= #13 0::Int)
-#352 := (not #351)
-#667 := (or #352 #332)
-#325 := (or #329 #667)
-#316 := (iff #325 #665)
-#309 := (or #329 #674)
-#314 := (iff #309 #665)
-#315 := [rewrite]: #314
-#650 := (iff #325 #309)
-#664 := (iff #667 #674)
-#670 := (iff #332 #671)
-#668 := [rewrite]: #670
-#337 := (iff #352 #663)
-#326 := (iff #351 #669)
-#456 := [rewrite]: #326
-#338 := [monotonicity #456]: #337
-#324 := [monotonicity #338 #668]: #664
-#313 := [monotonicity #324]: #650
-#652 := [trans #313 #315]: #316
-#666 := [quant-inst #13]: #325
-#653 := [mp #666 #652]: #665
-#593 := [unit-resolution #653 #688]: #674
-#594 := [unit-resolution #593 #592]: #671
-#595 := (not #671)
-#589 := (or #595 #654)
-#596 := [th-lemma arith triangle-eq]: #589
-#580 := [unit-resolution #596 #594]: #654
-[th-lemma arith farkas 1 -1 -1 1 #600 #119 #580 #609]: false
-unsat
-4f28f42d6f2b6fbb94a4ff1e55f0a807d8afe0f8 147 0
-#2 := false
-#10 := 0::Int
-decl f7 :: Int
-#9 := f7
-#54 := -1::Int
-#55 := (* -1::Int f7)
-#73 := (>= f7 0::Int)
-#80 := (if #73 f7 #55)
-#617 := (* -1::Int #80)
-#282 := (+ #55 #617)
-#625 := (<= #282 0::Int)
-#313 := (= #55 #80)
-#74 := (not #73)
-#280 := (+ f7 #617)
-#281 := (<= #280 0::Int)
-#228 := (= f7 #80)
-#283 := [hypothesis]: #73
-#229 := (or #74 #228)
-#314 := [def-axiom]: #229
-#619 := [unit-resolution #314 #283]: #228
-#620 := (not #228)
-#621 := (or #620 #281)
-#622 := [th-lemma arith triangle-eq]: #621
-#623 := [unit-resolution #622 #619]: #281
-#319 := (>= #80 0::Int)
-#316 := (not #319)
-decl f5 :: (-> S4 Int S3)
-#23 := (:var 0 Int)
-decl f6 :: S4
-#8 := f6
-#25 := (f5 f6 #23)
-#649 := (pattern #25)
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#7 := f4
-#26 := (f3 f4 #25)
-#27 := (= #26 #23)
-#110 := (>= #23 0::Int)
-#112 := (not #110)
-#115 := (or #112 #27)
-#650 := (forall (vars (?v0 Int)) (:pat #649) #115)
-#118 := (forall (vars (?v0 Int)) #115)
-#653 := (iff #118 #650)
-#651 := (iff #115 #115)
-#652 := [refl]: #651
-#654 := [quant-intro #652]: #653
-#155 := (~ #118 #118)
-#154 := (~ #115 #115)
-#151 := [refl]: #154
-#156 := [nnf-pos #151]: #155
-#24 := (<= 0::Int #23)
-#28 := (implies #24 #27)
-#29 := (forall (vars (?v0 Int)) #28)
-#121 := (iff #29 #118)
-#102 := (not #24)
-#103 := (or #102 #27)
-#106 := (forall (vars (?v0 Int)) #103)
-#119 := (iff #106 #118)
-#116 := (iff #103 #115)
-#113 := (iff #102 #112)
-#109 := (iff #24 #110)
-#111 := [rewrite]: #109
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#107 := (iff #29 #106)
-#104 := (iff #28 #103)
-#105 := [rewrite]: #104
-#108 := [quant-intro #105]: #107
-#122 := [trans #108 #120]: #121
-#101 := [asserted]: #29
-#123 := [mp #101 #122]: #118
-#152 := [mp~ #123 #156]: #118
-#655 := [mp #152 #654]: #650
-#85 := (f5 f6 #80)
-#88 := (f3 f4 #85)
-#91 := (= #88 #80)
-#94 := (not #91)
-#12 := (- f7)
-#11 := (< f7 0::Int)
-#13 := (if #11 #12 f7)
-#14 := (f5 f6 #13)
-#15 := (f3 f4 #14)
-#16 := (= #15 #13)
-#17 := (not #16)
-#97 := (iff #17 #94)
-#58 := (if #11 #55 f7)
-#61 := (f5 f6 #58)
-#64 := (f3 f4 #61)
-#67 := (= #64 #58)
-#70 := (not #67)
-#95 := (iff #70 #94)
-#92 := (iff #67 #91)
-#83 := (= #58 #80)
-#77 := (if #74 #55 f7)
-#81 := (= #77 #80)
-#82 := [rewrite]: #81
-#78 := (= #58 #77)
-#75 := (iff #11 #74)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#84 := [trans #79 #82]: #83
-#89 := (= #64 #88)
-#86 := (= #61 #85)
-#87 := [monotonicity #84]: #86
-#90 := [monotonicity #87]: #89
-#93 := [monotonicity #90 #84]: #92
-#96 := [monotonicity #93]: #95
-#71 := (iff #17 #70)
-#68 := (iff #16 #67)
-#59 := (= #13 #58)
-#56 := (= #12 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#65 := (= #15 #64)
-#62 := (= #14 #61)
-#63 := [monotonicity #60]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66 #60]: #68
-#72 := [monotonicity #69]: #71
-#98 := [trans #72 #96]: #97
-#53 := [asserted]: #17
-#99 := [mp #53 #98]: #94
-#630 := (not #650)
-#304 := (or #630 #316 #91)
-#636 := (or #316 #91)
-#305 := (or #630 #636)
-#638 := (iff #305 #304)
-#639 := [rewrite]: #638
-#637 := [quant-inst #80]: #305
-#640 := [mp #637 #639]: #304
-#618 := [unit-resolution #640 #99 #655]: #316
-#624 := [th-lemma arith farkas -1 1 1 #283 #618 #623]: false
-#262 := [lemma #624]: #74
-#315 := (or #73 #313)
-#306 := [def-axiom]: #315
-#267 := [unit-resolution #306 #262]: #313
-#268 := (not #313)
-#628 := (or #268 #625)
-#626 := [th-lemma arith triangle-eq]: #628
-#629 := [unit-resolution #626 #267]: #625
-#641 := (<= #80 0::Int)
-#615 := (or #641 #319)
-#616 := [th-lemma arith farkas 1 1]: #615
-#338 := [unit-resolution #616 #618]: #641
-[th-lemma arith farkas 1 1 1 #338 #262 #629]: false
-unsat
-7e6da58556dd56d85be0ea32c44b6f00c868dac5 431 0
-WARNING: For problems containing quantifiers, the model finding capabilities of Z3 work better when the formula does not contain nested quantifiers. You can use PULL_NESTED_QUANTIFIERS=true to eliminate nested quantifiers.
-#2 := false
-#446 := -1::Int
-decl f4 :: (-> S3 S2 Int)
-decl f7 :: (-> S4 Int S2)
-decl f9 :: S2
-#28 := f9
-decl f5 :: S3
-#11 := f5
-#29 := (f4 f5 f9)
-#27 := 4::Int
-#30 := (* 4::Int #29)
-#10 := 1::Int
-#112 := (+ 1::Int #30)
-decl f8 :: S4
-#17 := f8
-#115 := (f7 f8 #112)
-#362 := (f4 f5 #115)
-#662 := (* -1::Int #362)
-#673 := (+ #30 #662)
-#649 := (>= #673 -1::Int)
-#672 := (= #673 -1::Int)
-#41 := 0::Int
-#664 := (>= #29 0::Int)
-#644 := (= #362 0::Int)
-#593 := (not #644)
-#640 := (<= #362 0::Int)
-#628 := (not #640)
-#447 := (<= #362 1::Int)
-#752 := (not #447)
-decl f6 :: (-> S2 S2 S1)
-#7 := (:var 0 S2)
-#452 := (f6 #7 #115)
-#768 := (pattern #452)
-#451 := (= #7 #115)
-#18 := (f7 f8 1::Int)
-#19 := (= #7 #18)
-decl f1 :: S1
-#3 := f1
-#449 := (= #452 f1)
-#453 := (not #449)
-#432 := (or #453 #19 #451)
-#770 := (forall (vars (?v1 S2)) (:pat #768) #432)
-#426 := (not #770)
-#437 := (or #447 #426)
-#438 := (not #437)
-decl f3 :: (-> S2 S1)
-#118 := (f3 #115)
-#121 := (= #118 f1)
-#127 := (not #121)
-#771 := (or #127 #438)
-decl ?v1!0 :: (-> S2 S2)
-#772 := (?v1!0 #115)
-#767 := (= #772 #115)
-#425 := (= #772 #18)
-#773 := (f6 #772 #115)
-#774 := (= #773 f1)
-#769 := (not #774)
-#409 := (or #769 #425 #767)
-#766 := (not #409)
-#751 := (or #121 #447 #766)
-#413 := (not #751)
-#764 := (not #771)
-#414 := (or #764 #413)
-#415 := (not #414)
-#12 := (f4 f5 #7)
-#804 := (pattern #12)
-#8 := (f3 #7)
-#803 := (pattern #8)
-#219 := (?v1!0 #7)
-#222 := (= #219 #7)
-#221 := (= #219 #18)
-#202 := (f6 #219 #7)
-#203 := (= #202 f1)
-#220 := (not #203)
-#223 := (or #220 #221 #222)
-#224 := (not #223)
-#89 := (<= #12 1::Int)
-#9 := (= #8 f1)
-#266 := (or #9 #89 #224)
-#290 := (not #266)
-#14 := (:var 1 S2)
-#15 := (f6 #7 #14)
-#776 := (pattern #15)
-#20 := (= #7 #14)
-#16 := (= #15 f1)
-#73 := (not #16)
-#93 := (or #73 #19 #20)
-#777 := (forall (vars (?v1 S2)) (:pat #776) #93)
-#782 := (not #777)
-#785 := (or #89 #782)
-#788 := (not #785)
-#242 := (not #9)
-#791 := (or #242 #788)
-#794 := (not #791)
-#797 := (or #794 #290)
-#800 := (not #797)
-#805 := (forall (vars (?v0 S2)) (:pat #803 #804) #800)
-#96 := (forall (vars (?v1 S2)) #93)
-#225 := (not #96)
-#281 := (or #89 #225)
-#282 := (not #281)
-#283 := (or #242 #282)
-#289 := (not #283)
-#291 := (or #289 #290)
-#292 := (not #291)
-#297 := (forall (vars (?v0 S2)) #292)
-#806 := (iff #297 #805)
-#801 := (iff #292 #800)
-#798 := (iff #291 #797)
-#795 := (iff #289 #794)
-#792 := (iff #283 #791)
-#789 := (iff #282 #788)
-#786 := (iff #281 #785)
-#783 := (iff #225 #782)
-#780 := (iff #96 #777)
-#778 := (iff #93 #93)
-#779 := [refl]: #778
-#781 := [quant-intro #779]: #780
-#784 := [monotonicity #781]: #783
-#787 := [monotonicity #784]: #786
-#790 := [monotonicity #787]: #789
-#793 := [monotonicity #790]: #792
-#796 := [monotonicity #793]: #795
-#799 := [monotonicity #796]: #798
-#802 := [monotonicity #799]: #801
-#807 := [quant-intro #802]: #806
-#90 := (not #89)
-#99 := (and #90 #96)
-#248 := (or #242 #99)
-#271 := (and #248 #266)
-#274 := (forall (vars (?v0 S2)) #271)
-#298 := (iff #274 #297)
-#295 := (iff #271 #292)
-#286 := (and #283 #266)
-#293 := (iff #286 #292)
-#294 := [rewrite]: #293
-#287 := (iff #271 #286)
-#284 := (iff #248 #283)
-#214 := (iff #99 #282)
-#215 := [rewrite]: #214
-#285 := [monotonicity #215]: #284
-#288 := [monotonicity #285]: #287
-#296 := [trans #288 #294]: #295
-#299 := [quant-intro #296]: #298
-#216 := (not #90)
-#230 := (or #216 #224)
-#247 := (or #9 #230)
-#249 := (and #248 #247)
-#252 := (forall (vars (?v0 S2)) #249)
-#275 := (iff #252 #274)
-#272 := (iff #249 #271)
-#269 := (iff #247 #266)
-#260 := (or #89 #224)
-#263 := (or #9 #260)
-#267 := (iff #263 #266)
-#268 := [rewrite]: #267
-#264 := (iff #247 #263)
-#261 := (iff #230 #260)
-#258 := (iff #216 #89)
-#259 := [rewrite]: #258
-#262 := [monotonicity #259]: #261
-#265 := [monotonicity #262]: #264
-#270 := [trans #265 #268]: #269
-#273 := [monotonicity #270]: #272
-#276 := [quant-intro #273]: #275
-#102 := (iff #9 #99)
-#105 := (forall (vars (?v0 S2)) #102)
-#253 := (~ #105 #252)
-#250 := (~ #102 #249)
-#240 := (~ #99 #99)
-#238 := (~ #96 #96)
-#236 := (~ #93 #93)
-#237 := [refl]: #236
-#239 := [nnf-pos #237]: #238
-#234 := (~ #90 #90)
-#235 := [refl]: #234
-#241 := [monotonicity #235 #239]: #240
-#231 := (not #99)
-#232 := (~ #231 #230)
-#226 := (~ #225 #224)
-#227 := [sk]: #226
-#217 := (~ #216 #216)
-#218 := [refl]: #217
-#233 := [nnf-neg #218 #227]: #232
-#245 := (~ #9 #9)
-#246 := [refl]: #245
-#243 := (~ #242 #242)
-#244 := [refl]: #243
-#251 := [nnf-pos #244 #246 #233 #241]: #250
-#254 := [nnf-pos #251]: #253
-#21 := (or #19 #20)
-#22 := (implies #16 #21)
-#23 := (forall (vars (?v1 S2)) #22)
-#13 := (< 1::Int #12)
-#24 := (and #13 #23)
-#25 := (iff #9 #24)
-#26 := (forall (vars (?v0 S2)) #25)
-#108 := (iff #26 #105)
-#74 := (or #73 #21)
-#77 := (forall (vars (?v1 S2)) #74)
-#80 := (and #13 #77)
-#83 := (iff #9 #80)
-#86 := (forall (vars (?v0 S2)) #83)
-#106 := (iff #86 #105)
-#103 := (iff #83 #102)
-#100 := (iff #80 #99)
-#97 := (iff #77 #96)
-#94 := (iff #74 #93)
-#95 := [rewrite]: #94
-#98 := [quant-intro #95]: #97
-#91 := (iff #13 #90)
-#92 := [rewrite]: #91
-#101 := [monotonicity #92 #98]: #100
-#104 := [monotonicity #101]: #103
-#107 := [quant-intro #104]: #106
-#87 := (iff #26 #86)
-#84 := (iff #25 #83)
-#81 := (iff #24 #80)
-#78 := (iff #23 #77)
-#75 := (iff #22 #74)
-#76 := [rewrite]: #75
-#79 := [quant-intro #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#109 := [trans #88 #107]: #108
-#72 := [asserted]: #26
-#110 := [mp #72 #109]: #105
-#255 := [mp~ #110 #254]: #252
-#256 := [mp #255 #276]: #274
-#300 := [mp #256 #299]: #297
-#808 := [mp #300 #807]: #805
-#756 := (not #805)
-#753 := (or #756 #415)
-#757 := [quant-inst #115]: #753
-#566 := [unit-resolution #757 #808]: #415
-#730 := (or #414 #771)
-#736 := [def-axiom]: #730
-#621 := [unit-resolution #736 #566]: #771
-#602 := (or #764 #438)
-#138 := (>= #29 1::Int)
-#139 := (or #127 #138)
-#142 := (not #139)
-#35 := (<= 1::Int #29)
-#31 := (+ #30 1::Int)
-#32 := (f7 f8 #31)
-#33 := (f3 #32)
-#34 := (= #33 f1)
-#36 := (implies #34 #35)
-#37 := (not #36)
-#145 := (iff #37 #142)
-#128 := (or #127 #35)
-#133 := (not #128)
-#143 := (iff #133 #142)
-#140 := (iff #128 #139)
-#136 := (iff #35 #138)
-#137 := [rewrite]: #136
-#141 := [monotonicity #137]: #140
-#144 := [monotonicity #141]: #143
-#134 := (iff #37 #133)
-#131 := (iff #36 #128)
-#124 := (implies #121 #35)
-#129 := (iff #124 #128)
-#130 := [rewrite]: #129
-#125 := (iff #36 #124)
-#122 := (iff #34 #121)
-#119 := (= #33 #118)
-#116 := (= #32 #115)
-#113 := (= #31 #112)
-#114 := [rewrite]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [monotonicity #120]: #122
-#126 := [monotonicity #123]: #125
-#132 := [trans #126 #130]: #131
-#135 := [monotonicity #132]: #134
-#146 := [trans #135 #144]: #145
-#111 := [asserted]: #37
-#147 := [mp #111 #146]: #142
-#148 := [not-or-elim #147]: #121
-#744 := (or #764 #127 #438)
-#748 := [def-axiom]: #744
-#626 := [unit-resolution #748 #148]: #602
-#627 := [unit-resolution #626 #621]: #438
-#758 := (or #437 #752)
-#395 := [def-axiom]: #758
-#622 := [unit-resolution #395 #627]: #752
-#596 := (or #628 #447)
-#603 := [th-lemma arith farkas 1 1]: #596
-#562 := [unit-resolution #603 #622]: #628
-#595 := (or #593 #640)
-#597 := [th-lemma arith triangle-eq]: #595
-#604 := [unit-resolution #597 #562]: #593
-#623 := (or #664 #644)
-#42 := (:var 0 Int)
-#44 := (f7 f8 #42)
-#815 := (pattern #44)
-#45 := (f4 f5 #44)
-#50 := (= #45 0::Int)
-#162 := (>= #42 0::Int)
-#192 := (or #162 #50)
-#822 := (forall (vars (?v0 Int)) (:pat #815) #192)
-#195 := (forall (vars (?v0 Int)) #192)
-#825 := (iff #195 #822)
-#823 := (iff #192 #192)
-#824 := [refl]: #823
-#826 := [quant-intro #824]: #825
-#212 := (~ #195 #195)
-#278 := (~ #192 #192)
-#279 := [refl]: #278
-#213 := [nnf-pos #279]: #212
-#49 := (< #42 0::Int)
-#51 := (implies #49 #50)
-#52 := (forall (vars (?v0 Int)) #51)
-#198 := (iff #52 #195)
-#176 := (not #49)
-#177 := (or #176 #50)
-#180 := (forall (vars (?v0 Int)) #177)
-#196 := (iff #180 #195)
-#193 := (iff #177 #192)
-#190 := (iff #176 #162)
-#163 := (not #162)
-#185 := (not #163)
-#188 := (iff #185 #162)
-#189 := [rewrite]: #188
-#186 := (iff #176 #185)
-#183 := (iff #49 #163)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#191 := [trans #187 #189]: #190
-#194 := [monotonicity #191]: #193
-#197 := [quant-intro #194]: #196
-#181 := (iff #52 #180)
-#178 := (iff #51 #177)
-#179 := [rewrite]: #178
-#182 := [quant-intro #179]: #181
-#199 := [trans #182 #197]: #198
-#175 := [asserted]: #52
-#200 := [mp #175 #199]: #195
-#280 := [mp~ #200 #213]: #195
-#827 := [mp #280 #826]: #822
-#518 := (not #822)
-#629 := (or #518 #664 #644)
-#678 := (>= #112 0::Int)
-#650 := (or #678 #644)
-#630 := (or #518 #650)
-#638 := (iff #630 #629)
-#636 := (or #518 #623)
-#634 := (iff #636 #629)
-#637 := [rewrite]: #634
-#632 := (iff #630 #636)
-#624 := (iff #650 #623)
-#665 := (iff #678 #664)
-#666 := [rewrite]: #665
-#625 := [monotonicity #666]: #624
-#633 := [monotonicity #625]: #632
-#639 := [trans #633 #637]: #638
-#631 := [quant-inst #112]: #630
-#635 := [mp #631 #639]: #629
-#606 := [unit-resolution #635 #827]: #623
-#607 := [unit-resolution #606 #604]: #664
-#667 := (not #664)
-#651 := (or #667 #672)
-#46 := (= #45 #42)
-#166 := (or #163 #46)
-#816 := (forall (vars (?v0 Int)) (:pat #815) #166)
-#169 := (forall (vars (?v0 Int)) #166)
-#819 := (iff #169 #816)
-#817 := (iff #166 #166)
-#818 := [refl]: #817
-#820 := [quant-intro #818]: #819
-#210 := (~ #169 #169)
-#209 := (~ #166 #166)
-#206 := [refl]: #209
-#211 := [nnf-pos #206]: #210
-#43 := (<= 0::Int #42)
-#47 := (implies #43 #46)
-#48 := (forall (vars (?v0 Int)) #47)
-#172 := (iff #48 #169)
-#153 := (not #43)
-#154 := (or #153 #46)
-#157 := (forall (vars (?v0 Int)) #154)
-#170 := (iff #157 #169)
-#167 := (iff #154 #166)
-#164 := (iff #153 #163)
-#160 := (iff #43 #162)
-#161 := [rewrite]: #160
-#165 := [monotonicity #161]: #164
-#168 := [monotonicity #165]: #167
-#171 := [quant-intro #168]: #170
-#158 := (iff #48 #157)
-#155 := (iff #47 #154)
-#156 := [rewrite]: #155
-#159 := [quant-intro #156]: #158
-#173 := [trans #159 #171]: #172
-#152 := [asserted]: #48
-#174 := [mp #152 #173]: #169
-#207 := [mp~ #174 #211]: #169
-#821 := [mp #207 #820]: #816
-#655 := (not #816)
-#656 := (or #655 #667 #672)
-#661 := (= #362 #112)
-#679 := (not #678)
-#663 := (or #679 #661)
-#657 := (or #655 #663)
-#643 := (iff #657 #656)
-#653 := (or #655 #651)
-#641 := (iff #653 #656)
-#642 := [rewrite]: #641
-#659 := (iff #657 #653)
-#652 := (iff #663 #651)
-#670 := (iff #661 #672)
-#671 := [rewrite]: #670
-#668 := (iff #679 #667)
-#669 := [monotonicity #666]: #668
-#654 := [monotonicity #669 #671]: #652
-#645 := [monotonicity #654]: #659
-#646 := [trans #645 #642]: #643
-#658 := [quant-inst #112]: #657
-#647 := [mp #658 #646]: #656
-#608 := [unit-resolution #647 #821]: #651
-#618 := [unit-resolution #608 #607]: #672
-#598 := (not #672)
-#619 := (or #598 #649)
-#574 := [th-lemma arith triangle-eq]: #619
-#575 := [unit-resolution #574 #618]: #649
-#149 := (not #138)
-#150 := [not-or-elim #147]: #149
-[th-lemma arith farkas -4 1 1 #150 #622 #575]: false
-unsat
-f0add7d14def5da0b06e595882e28df041b2cf29 58 0
-#2 := false
-decl f8 :: S2
-#18 := f8
-decl f6 :: S2
-#14 := f6
-#20 := (= f6 f8)
-decl f3 :: (-> S4 S5 S2)
-decl f5 :: (-> S2 S3 S5)
-decl f7 :: S3
-#15 := f7
-#16 := (f5 f6 f7)
-decl f4 :: S4
-#7 := f4
-#17 := (f3 f4 #16)
-#19 := (= #17 f8)
-#45 := (not #19)
-#46 := (or #45 #20)
-#49 := (not #46)
-#21 := (implies #19 #20)
-#22 := (not #21)
-#50 := (iff #22 #49)
-#47 := (iff #21 #46)
-#48 := [rewrite]: #47
-#51 := [monotonicity #48]: #50
-#44 := [asserted]: #22
-#54 := [mp #44 #51]: #49
-#52 := [not-or-elim #54]: #19
-#125 := (= f6 #17)
-#124 := (= #17 f6)
-#9 := (:var 0 S3)
-#8 := (:var 1 S2)
-#10 := (f5 #8 #9)
-#540 := (pattern #10)
-#11 := (f3 f4 #10)
-#12 := (= #11 #8)
-#541 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #540) #12)
-#13 := (forall (vars (?v0 S2) (?v1 S3)) #12)
-#544 := (iff #13 #541)
-#542 := (iff #12 #12)
-#543 := [refl]: #542
-#545 := [quant-intro #543]: #544
-#67 := (~ #13 #13)
-#65 := (~ #12 #12)
-#66 := [refl]: #65
-#68 := [nnf-pos #66]: #67
-#43 := [asserted]: #13
-#57 := [mp~ #43 #68]: #13
-#546 := [mp #57 #545]: #541
-#211 := (not #541)
-#126 := (or #211 #124)
-#212 := [quant-inst #14 #15]: #126
-#210 := [unit-resolution #212 #546]: #124
-#203 := [symm #210]: #125
-#214 := [trans #203 #52]: #20
-#53 := (not #20)
-#55 := [not-or-elim #54]: #53
-[unit-resolution #55 #214]: false
-unsat
-86345bce2206ce27e174d4b1d6d3e0182564f8a1 106 0
-#2 := false
-decl f11 :: (-> S9 S5 S3)
-decl f16 :: S5
-#34 := f16
-decl f12 :: S9
-#25 := f12
-#39 := (f11 f12 f16)
-decl f6 :: (-> S6 S7 S3)
-decl f13 :: S7
-#29 := f13
-decl f7 :: S6
-#14 := f7
-#38 := (f6 f7 f13)
-#40 := (= #38 #39)
-decl f5 :: (-> S2 S3 S5)
-decl f14 :: S3
-#30 := f14
-decl f15 :: S2
-#31 := f15
-#35 := (f5 f15 f14)
-#165 := (f11 f12 #35)
-#233 := (= #165 #39)
-#573 := (= #39 #165)
-#36 := (= f16 #35)
-decl f8 :: (-> S3 S2 S7)
-#32 := (f8 f14 f15)
-#33 := (= f13 #32)
-#37 := (and #33 #36)
-#68 := (not #37)
-#69 := (or #68 #40)
-#72 := (not #69)
-#41 := (implies #37 #40)
-#42 := (not #41)
-#73 := (iff #42 #72)
-#70 := (iff #41 #69)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#67 := [asserted]: #42
-#77 := [mp #67 #74]: #72
-#75 := [not-or-elim #77]: #37
-#78 := [and-elim #75]: #36
-#579 := [monotonicity #78]: #573
-#570 := [symm #579]: #233
-#213 := (= #38 #165)
-#569 := (= f14 #165)
-#251 := (= #165 f14)
-#9 := (:var 0 S3)
-#8 := (:var 1 S2)
-#10 := (f5 #8 #9)
-#580 := (pattern #10)
-#26 := (f11 f12 #10)
-#27 := (= #26 #9)
-#600 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #580) #27)
-#28 := (forall (vars (?v0 S2) (?v1 S3)) #27)
-#603 := (iff #28 #600)
-#601 := (iff #27 #27)
-#602 := [refl]: #601
-#604 := [quant-intro #602]: #603
-#88 := (~ #28 #28)
-#107 := (~ #27 #27)
-#108 := [refl]: #107
-#89 := [nnf-pos #108]: #88
-#66 := [asserted]: #28
-#109 := [mp~ #66 #89]: #28
-#605 := [mp #109 #604]: #600
-#256 := (not #600)
-#253 := (or #256 #251)
-#257 := [quant-inst #31 #30]: #253
-#568 := [unit-resolution #257 #605]: #251
-#228 := [symm #568]: #569
-#229 := (= #38 f14)
-#254 := (f6 f7 #32)
-#255 := (= #254 f14)
-#16 := (:var 0 S2)
-#15 := (:var 1 S3)
-#17 := (f8 #15 #16)
-#587 := (pattern #17)
-#18 := (f6 f7 #17)
-#19 := (= #18 #15)
-#588 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #587) #19)
-#20 := (forall (vars (?v0 S3) (?v1 S2)) #19)
-#591 := (iff #20 #588)
-#589 := (iff #19 #19)
-#590 := [refl]: #589
-#592 := [quant-intro #590]: #591
-#84 := (~ #20 #20)
-#83 := (~ #19 #19)
-#102 := [refl]: #83
-#85 := [nnf-pos #102]: #84
-#64 := [asserted]: #20
-#103 := [mp~ #64 #85]: #20
-#593 := [mp #103 #592]: #588
-#574 := (not #588)
-#230 := (or #574 #255)
-#361 := [quant-inst #30 #31]: #230
-#241 := [unit-resolution #361 #593]: #255
-#577 := (= #38 #254)
-#76 := [and-elim #75]: #33
-#578 := [monotonicity #76]: #577
-#571 := [trans #578 #241]: #229
-#555 := [trans #571 #228]: #213
-#217 := [trans #555 #570]: #40
-#79 := (not #40)
-#80 := [not-or-elim #77]: #79
-[unit-resolution #80 #217]: false
-unsat
-7180d528e452ef46d73483bf56a7d7018ee1b306 113 0
-#2 := false
-decl f3 :: (-> S2 S3 S4)
-decl f8 :: S3
-#30 := f8
-decl f11 :: S2
-#38 := f11
-#48 := (f3 f11 f8)
-decl f4 :: (-> S5 S4 S2)
-decl f13 :: S4
-#45 := f13
-decl f5 :: (-> S6 S3 S5)
-decl f10 :: S3
-#34 := f10
-decl f6 :: (-> S7 S2 S6)
-decl f12 :: S4
-#41 := f12
-decl f9 :: S3
-#31 := f9
-decl f7 :: S7
-#7 := f7
-#39 := (f6 f7 f11)
-#40 := (f5 #39 f9)
-#42 := (f4 #40 f12)
-#43 := (f6 f7 #42)
-#44 := (f5 #43 f10)
-#46 := (f4 #44 f13)
-#47 := (f3 #46 f8)
-#49 := (= #47 #48)
-#261 := (f3 #42 f8)
-#271 := (= #261 #48)
-#270 := (= #261 f12)
-#32 := (= f8 f9)
-#549 := (if #32 #270 #271)
-#23 := (:var 0 S3)
-#21 := (:var 1 S4)
-#19 := (:var 2 S3)
-#17 := (:var 3 S2)
-#18 := (f6 f7 #17)
-#20 := (f5 #18 #19)
-#22 := (f4 #20 #21)
-#24 := (f3 #22 #23)
-#593 := (pattern #24)
-#26 := (f3 #17 #23)
-#108 := (= #24 #26)
-#107 := (= #24 #21)
-#25 := (= #23 #19)
-#93 := (if #25 #107 #108)
-#594 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #593) #93)
-#100 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #93)
-#597 := (iff #100 #594)
-#595 := (iff #93 #93)
-#596 := [refl]: #595
-#598 := [quant-intro #596]: #597
-#27 := (if #25 #21 #26)
-#28 := (= #24 #27)
-#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #28)
-#97 := (iff #29 #100)
-#94 := (iff #28 #93)
-#99 := [rewrite]: #94
-#98 := [quant-intro #99]: #97
-#91 := (~ #29 #29)
-#90 := (~ #28 #28)
-#105 := [refl]: #90
-#92 := [nnf-pos #105]: #91
-#73 := [asserted]: #29
-#106 := [mp~ #73 #92]: #29
-#95 := [mp #106 #98]: #100
-#599 := [mp #95 #598]: #594
-#236 := (not #594)
-#547 := (or #236 #549)
-#551 := [quant-inst #38 #31 #41 #30]: #547
-#550 := [unit-resolution #551 #599]: #549
-#548 := (not #549)
-#264 := (or #548 #271)
-#33 := (not #32)
-#35 := (= f8 f10)
-#36 := (not #35)
-#37 := (and #33 #36)
-#75 := (not #37)
-#76 := (or #75 #49)
-#79 := (not #76)
-#50 := (implies #37 #49)
-#51 := (not #50)
-#80 := (iff #51 #79)
-#77 := (iff #50 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#74 := [asserted]: #51
-#84 := [mp #74 #81]: #79
-#82 := [not-or-elim #84]: #37
-#83 := [and-elim #82]: #33
-#542 := (or #548 #32 #271)
-#543 := [def-axiom]: #542
-#387 := [unit-resolution #543 #83]: #264
-#388 := [unit-resolution #387 #550]: #271
-#263 := (= #47 #261)
-#260 := (= #47 f13)
-#242 := (if #35 #260 #263)
-#367 := (or #236 #242)
-#574 := [quant-inst #42 #34 #45 #30]: #367
-#389 := [unit-resolution #574 #599]: #242
-#247 := (not #242)
-#531 := (or #247 #263)
-#85 := [and-elim #82]: #36
-#582 := (or #247 #35 #263)
-#583 := [def-axiom]: #582
-#532 := [unit-resolution #583 #85]: #531
-#533 := [unit-resolution #532 #389]: #263
-#529 := [trans #533 #388]: #49
-#86 := (not #49)
-#87 := [not-or-elim #84]: #86
-[unit-resolution #87 #529]: false
-unsat
-1c419ffe565f74df1755b00362bfce413a0bbb21 74 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f6 :: (-> S2 S3 S1)
-decl f5 :: S3
-#8 := f5
-decl f4 :: S2
-#7 := f4
-#11 := (f6 f4 f5)
-#12 := (= #11 f1)
-decl f3 :: (-> S2 S3 S1)
-#9 := (f3 f4 f5)
-#10 := (= #9 f1)
-#70 := (not #10)
-#77 := (iff #70 #12)
-#81 := (iff #77 false)
-#83 := (iff #10 false)
-#43 := (iff #10 #12)
-#59 := (or #43 #10 #12)
-#62 := (not #59)
-#1 := true
-#16 := (iff #12 true)
-#15 := (iff #10 true)
-#17 := (or #15 #16)
-#13 := (and #12 true)
-#14 := (iff #10 #13)
-#18 := (or #14 #17)
-#19 := (not #18)
-#65 := (iff #19 #62)
-#50 := (or #10 #12)
-#53 := (or #43 #50)
-#56 := (not #53)
-#63 := (iff #56 #62)
-#60 := (iff #53 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#57 := (iff #19 #56)
-#54 := (iff #18 #53)
-#51 := (iff #17 #50)
-#48 := (iff #16 #12)
-#49 := [rewrite]: #48
-#46 := (iff #15 #10)
-#47 := [rewrite]: #46
-#52 := [monotonicity #47 #49]: #51
-#44 := (iff #14 #43)
-#41 := (iff #13 #12)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#55 := [monotonicity #45 #52]: #54
-#58 := [monotonicity #55]: #57
-#66 := [trans #58 #64]: #65
-#40 := [asserted]: #19
-#67 := [mp #40 #66]: #62
-#71 := [not-or-elim #67]: #70
-#84 := [iff-false #71]: #83
-#92 := (iff #77 #10)
-#87 := (iff #70 false)
-#90 := (iff #87 #10)
-#91 := [rewrite]: #90
-#88 := (iff #77 #87)
-#85 := (iff #12 false)
-#72 := (not #12)
-#73 := [not-or-elim #67]: #72
-#86 := [iff-false #73]: #85
-#89 := [monotonicity #86]: #88
-#93 := [trans #89 #91]: #92
-#82 := [trans #93 #84]: #81
-#68 := (not #43)
-#78 := (iff #68 #77)
-#79 := [rewrite]: #78
-#69 := [not-or-elim #67]: #68
-#80 := [mp #69 #79]: #77
-[mp #80 #82]: false
-unsat
76d09b53549e91e8b6b69b6b905b5e8307464c6f 106 0
#2 := false
decl f7 :: S2
@@ -10684,1133 +1668,6 @@
#215 := [quant-inst #19]: #210
[unit-resolution #215 #568 #555]: false
unsat
-1396ebdf2db554fa58d5de90d7aa27d442610f3c 29 0
-#2 := false
-#1 := true
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S1 S1)
-decl f2 :: S1
-#4 := f2
-decl f4 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f4 #7)
-#9 := (= #8 f1)
-#10 := (exists (vars (?v0 S2)) #9)
-#11 := (if #10 f1 f2)
-#12 := (f3 #11)
-#13 := (= #12 f1)
-#14 := (implies #13 true)
-#15 := (not #14)
-#44 := (iff #15 false)
-#39 := (not true)
-#42 := (iff #39 false)
-#43 := [rewrite]: #42
-#40 := (iff #15 #39)
-#37 := (iff #14 true)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#36 := [asserted]: #15
-[mp #36 #45]: false
-unsat
-352ef3cbf5b05cf656dc82749237c3b497c01e97 113 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 Int S1)
-#21 := 42::Int
-decl f4 :: (-> S3 Int S2)
-#19 := 3::Int
-decl f6 :: S3
-#17 := f6
-#20 := (f4 f6 3::Int)
-#22 := (f3 #20 42::Int)
-#23 := (= #22 f1)
-decl f5 :: S3
-#7 := f5
-#139 := (f4 f5 3::Int)
-#223 := (f3 #139 42::Int)
-#224 := (= #223 f1)
-#10 := (:var 0 Int)
-#8 := (:var 1 Int)
-#9 := (f4 f5 #8)
-#11 := (f3 #9 #10)
-#12 := (pattern #11)
-#27 := 0::Int
-#49 := -1::Int
-#50 := (* -1::Int #10)
-#51 := (+ #8 #50)
-#52 := (<= #51 0::Int)
-#13 := (= #11 f1)
-#55 := (iff #13 #52)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #12) #55)
-#83 := (~ #58 #58)
-#81 := (~ #55 #55)
-#82 := [refl]: #81
-#84 := [nnf-pos #82]: #83
-#14 := (<= #8 #10)
-#15 := (iff #13 #14)
-#16 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #12) #15)
-#59 := (iff #16 #58)
-#56 := (iff #15 #55)
-#53 := (iff #14 #52)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#60 := [quant-intro #57]: #59
-#46 := [asserted]: #16
-#61 := [mp #46 #60]: #58
-#73 := [mp~ #61 #84]: #58
-#190 := (not #58)
-#191 := (or #190 #224)
-#225 := (* -1::Int 42::Int)
-#216 := (+ 3::Int #225)
-#227 := (<= #216 0::Int)
-#228 := (iff #224 #227)
-#192 := (or #190 #228)
-#529 := (iff #192 #191)
-#531 := (iff #191 #191)
-#532 := [rewrite]: #531
-#186 := (iff #228 #224)
-#1 := true
-#201 := (iff #224 true)
-#202 := (iff #201 #224)
-#543 := [rewrite]: #202
-#206 := (iff #228 #201)
-#551 := (iff #227 true)
-#203 := -39::Int
-#547 := (<= -39::Int 0::Int)
-#550 := (iff #547 true)
-#545 := [rewrite]: #550
-#548 := (iff #227 #547)
-#214 := (= #216 -39::Int)
-#229 := -42::Int
-#209 := (+ 3::Int -42::Int)
-#333 := (= #209 -39::Int)
-#540 := [rewrite]: #333
-#544 := (= #216 #209)
-#226 := (= #225 -42::Int)
-#230 := [rewrite]: #226
-#546 := [monotonicity #230]: #544
-#215 := [trans #546 #540]: #214
-#549 := [monotonicity #215]: #548
-#541 := [trans #549 #545]: #551
-#542 := [monotonicity #541]: #206
-#527 := [trans #542 #543]: #186
-#530 := [monotonicity #527]: #529
-#533 := [trans #530 #532]: #529
-#193 := [quant-inst #19 #21]: #192
-#528 := [mp #193 #533]: #191
-#534 := [unit-resolution #528 #73]: #224
-#536 := (= #22 #223)
-#178 := (= #20 #139)
-#537 := (= #139 #20)
-#172 := (= f5 f6)
-#18 := (= f6 f5)
-#48 := (not #18)
-#62 := (or #48 #23)
-#65 := (not #62)
-#24 := (implies #18 #23)
-#25 := (not #24)
-#66 := (iff #25 #65)
-#63 := (iff #24 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#47 := [asserted]: #25
-#70 := [mp #47 #67]: #65
-#68 := [not-or-elim #70]: #18
-#535 := [symm #68]: #172
-#177 := [monotonicity #535]: #537
-#538 := [symm #177]: #178
-#539 := [monotonicity #538]: #536
-#525 := [trans #539 #534]: #23
-#69 := (not #23)
-#71 := [not-or-elim #70]: #69
-[unit-resolution #71 #525]: false
-unsat
-8fa5494ea43f950aa9add5e070d1d34c34426a1b 29 0
-#2 := false
-#1 := true
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S1 S1)
-decl f2 :: S1
-#4 := f2
-decl f4 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f4 #7)
-#9 := (= #8 f1)
-#10 := (forall (vars (?v0 S2)) #9)
-#11 := (if #10 f1 f2)
-#12 := (f3 #11)
-#13 := (= #12 f1)
-#14 := (implies #13 true)
-#15 := (not #14)
-#44 := (iff #15 false)
-#39 := (not true)
-#42 := (iff #39 false)
-#43 := [rewrite]: #42
-#40 := (iff #15 #39)
-#37 := (iff #14 true)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#36 := [asserted]: #15
-[mp #36 #45]: false
-unsat
-2fd48adc6f5c51aec7f5f7945dc6937d8ac8fd61 424 0
-#2 := false
-decl f9 :: (-> S6 S7 S7)
-decl f12 :: S7
-#22 := f12
-decl f13 :: (-> S9 S2 S6)
-decl f5 :: (-> S4 Int S2)
-#49 := 2::Int
-decl f6 :: S4
-#11 := f6
-#50 := (f5 f6 2::Int)
-decl f14 :: S9
-#28 := f14
-#51 := (f13 f14 #50)
-#52 := (f9 #51 f12)
-#14 := 1::Int
-#44 := (f5 f6 1::Int)
-#45 := (f13 f14 #44)
-#53 := (f9 #45 #52)
-#46 := (f9 #45 f12)
-#41 := 0::Int
-#42 := (f5 f6 0::Int)
-#43 := (f13 f14 #42)
-#47 := (f9 #43 #46)
-decl f10 :: (-> S8 S3 S6)
-decl f4 :: S3
-#7 := f4
-decl f11 :: S8
-#19 := f11
-#40 := (f10 f11 f4)
-#48 := (f9 #40 #47)
-#54 := (= #48 #53)
-#654 := (f9 #40 #46)
-decl f3 :: (-> S3 S2 S2)
-#337 := (f3 f4 #42)
-#338 := (f13 f14 #337)
-#656 := (f9 #338 #654)
-#321 := (= #656 #53)
-#353 := (= #53 #656)
-#391 := (= #52 #654)
-#248 := (f9 #40 f12)
-#596 := (f3 f4 #44)
-#593 := (f13 f14 #596)
-#597 := (f9 #593 #248)
-#389 := (= #597 #654)
-#584 := (= #654 #597)
-#31 := (:var 0 S7)
-#26 := (:var 2 S3)
-#27 := (f10 f11 #26)
-#36 := (f9 #27 #31)
-#29 := (:var 1 S2)
-#34 := (f3 #26 #29)
-#35 := (f13 f14 #34)
-#37 := (f9 #35 #36)
-#670 := (pattern #37)
-#30 := (f13 f14 #29)
-#32 := (f9 #30 #31)
-#33 := (f9 #27 #32)
-#669 := (pattern #33)
-#38 := (= #33 #37)
-#671 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S7)) (:pat #669 #670) #38)
-#39 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S7)) #38)
-#674 := (iff #39 #671)
-#672 := (iff #38 #38)
-#673 := [refl]: #672
-#675 := [quant-intro #673]: #674
-#161 := (~ #39 #39)
-#179 := (~ #38 #38)
-#180 := [refl]: #179
-#162 := [nnf-pos #180]: #161
-#103 := [asserted]: #39
-#181 := [mp~ #103 #162]: #39
-#676 := [mp #181 #675]: #671
-#323 := (not #671)
-#575 := (or #323 #584)
-#577 := [quant-inst #7 #44 #22]: #575
-#430 := [unit-resolution #577 #676]: #584
-#390 := [symm #430]: #389
-#387 := (= #52 #597)
-#435 := (= f12 #248)
-#332 := (= #248 f12)
-#20 := (:var 0 S3)
-#21 := (f10 f11 #20)
-#662 := (pattern #21)
-#23 := (f9 #21 f12)
-#24 := (= #23 f12)
-#663 := (forall (vars (?v0 S3)) (:pat #662) #24)
-#25 := (forall (vars (?v0 S3)) #24)
-#666 := (iff #25 #663)
-#664 := (iff #24 #24)
-#665 := [refl]: #664
-#667 := [quant-intro #665]: #666
-#159 := (~ #25 #25)
-#158 := (~ #24 #24)
-#177 := [refl]: #158
-#160 := [nnf-pos #177]: #159
-#102 := [asserted]: #25
-#178 := [mp~ #102 #160]: #25
-#668 := [mp #178 #667]: #663
-#335 := (not #663)
-#339 := (or #335 #332)
-#318 := [quant-inst #7]: #339
-#431 := [unit-resolution #318 #668]: #332
-#436 := [symm #431]: #435
-#384 := (= #51 #593)
-#399 := (= #50 #596)
-decl f7 :: (-> S5 S2 Int)
-decl f8 :: S5
-#12 := f8
-#254 := (f7 f8 #44)
-#580 := (+ 1::Int #254)
-#581 := (f5 f6 #580)
-#412 := (= #581 #596)
-#582 := (= #596 #581)
-#8 := (:var 0 S2)
-#9 := (f3 f4 #8)
-#10 := (pattern #9)
-#13 := (f7 f8 #8)
-#90 := (+ 1::Int #13)
-#93 := (f5 f6 #90)
-#96 := (= #9 #93)
-#99 := (forall (vars (?v0 S2)) (:pat #10) #96)
-#175 := (~ #99 #99)
-#173 := (~ #96 #96)
-#174 := [refl]: #173
-#176 := [nnf-pos #174]: #175
-#15 := (+ #13 1::Int)
-#16 := (f5 f6 #15)
-#17 := (= #9 #16)
-#18 := (forall (vars (?v0 S2)) (:pat #10) #17)
-#100 := (iff #18 #99)
-#97 := (iff #17 #96)
-#94 := (= #16 #93)
-#91 := (= #15 #90)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#98 := [monotonicity #95]: #97
-#101 := [quant-intro #98]: #100
-#89 := [asserted]: #18
-#104 := [mp #89 #101]: #99
-#157 := [mp~ #104 #176]: #99
-#585 := (not #99)
-#567 := (or #585 #582)
-#568 := [quant-inst #44]: #567
-#278 := [unit-resolution #568 #157]: #582
-#398 := [symm #278]: #412
-#400 := (= #50 #581)
-#522 := (f7 f8 #581)
-#450 := (f5 f6 #522)
-#451 := (= #450 #581)
-#677 := (pattern #13)
-#56 := (f5 f6 #13)
-#57 := (= #56 #8)
-#678 := (forall (vars (?v0 S2)) (:pat #677) #57)
-#58 := (forall (vars (?v0 S2)) #57)
-#681 := (iff #58 #678)
-#679 := (iff #57 #57)
-#680 := [refl]: #679
-#682 := [quant-intro #680]: #681
-#163 := (~ #58 #58)
-#182 := (~ #57 #57)
-#183 := [refl]: #182
-#164 := [nnf-pos #183]: #163
-#106 := [asserted]: #58
-#165 := [mp~ #106 #164]: #58
-#683 := [mp #165 #682]: #678
-#453 := (not #678)
-#458 := (or #453 #451)
-#441 := [quant-inst #581]: #458
-#437 := [unit-resolution #441 #683]: #451
-#408 := (= #50 #450)
-#407 := (= 2::Int #522)
-#410 := (= #522 2::Int)
-#247 := -1::Int
-#507 := (* -1::Int #522)
-#488 := (+ #254 #507)
-#484 := (<= #488 -1::Int)
-#452 := (= #488 -1::Int)
-#520 := (>= #254 -1::Int)
-#515 := (>= #254 1::Int)
-#631 := (= #254 1::Int)
-#59 := (:var 0 Int)
-#61 := (f5 f6 #59)
-#684 := (pattern #61)
-#62 := (f7 f8 #61)
-#63 := (= #62 #59)
-#117 := (>= #59 0::Int)
-#118 := (not #117)
-#121 := (or #118 #63)
-#685 := (forall (vars (?v0 Int)) (:pat #684) #121)
-#124 := (forall (vars (?v0 Int)) #121)
-#688 := (iff #124 #685)
-#686 := (iff #121 #121)
-#687 := [refl]: #686
-#689 := [quant-intro #687]: #688
-#167 := (~ #124 #124)
-#166 := (~ #121 #121)
-#184 := [refl]: #166
-#168 := [nnf-pos #184]: #167
-#60 := (<= 0::Int #59)
-#64 := (implies #60 #63)
-#65 := (forall (vars (?v0 Int)) #64)
-#127 := (iff #65 #124)
-#108 := (not #60)
-#109 := (or #108 #63)
-#112 := (forall (vars (?v0 Int)) #109)
-#125 := (iff #112 #124)
-#122 := (iff #109 #121)
-#119 := (iff #108 #118)
-#115 := (iff #60 #117)
-#116 := [rewrite]: #115
-#120 := [monotonicity #116]: #119
-#123 := [monotonicity #120]: #122
-#126 := [quant-intro #123]: #125
-#113 := (iff #65 #112)
-#110 := (iff #64 #109)
-#111 := [rewrite]: #110
-#114 := [quant-intro #111]: #113
-#128 := [trans #114 #126]: #127
-#107 := [asserted]: #65
-#129 := [mp #107 #128]: #124
-#185 := [mp~ #129 #168]: #124
-#690 := [mp #185 #689]: #685
-#641 := (not #685)
-#623 := (or #641 #631)
-#360 := (>= 1::Int 0::Int)
-#361 := (not #360)
-#632 := (or #361 #631)
-#627 := (or #641 #632)
-#628 := (iff #627 #623)
-#618 := (iff #623 #623)
-#619 := [rewrite]: #618
-#626 := (iff #632 #631)
-#344 := (or false #631)
-#347 := (iff #344 #631)
-#625 := [rewrite]: #347
-#345 := (iff #632 #344)
-#630 := (iff #361 false)
-#1 := true
-#651 := (not true)
-#652 := (iff #651 false)
-#311 := [rewrite]: #652
-#629 := (iff #361 #651)
-#354 := (iff #360 true)
-#355 := [rewrite]: #354
-#633 := [monotonicity #355]: #629
-#634 := [trans #633 #311]: #630
-#346 := [monotonicity #634]: #345
-#340 := [trans #346 #625]: #626
-#617 := [monotonicity #340]: #628
-#614 := [trans #617 #619]: #628
-#624 := [quant-inst #14]: #627
-#615 := [mp #624 #614]: #623
-#433 := [unit-resolution #615 #690]: #631
-#438 := (not #631)
-#417 := (or #438 #515)
-#420 := [th-lemma arith triangle-eq]: #417
-#424 := [unit-resolution #420 #433]: #515
-#426 := (not #515)
-#427 := (or #426 #520)
-#425 := [th-lemma arith farkas 1 1]: #427
-#428 := [unit-resolution #425 #424]: #520
-#525 := (not #520)
-#482 := (or #641 #525 #452)
-#518 := (= #522 #580)
-#516 := (>= #580 0::Int)
-#517 := (not #516)
-#519 := (or #517 #518)
-#489 := (or #641 #519)
-#493 := (iff #489 #482)
-#513 := (or #525 #452)
-#479 := (or #641 #513)
-#490 := (iff #479 #482)
-#492 := [rewrite]: #490
-#481 := (iff #489 #479)
-#508 := (iff #519 #513)
-#506 := (iff #518 #452)
-#512 := [rewrite]: #506
-#521 := (iff #517 #525)
-#523 := (iff #516 #520)
-#524 := [rewrite]: #523
-#526 := [monotonicity #524]: #521
-#514 := [monotonicity #526 #512]: #508
-#483 := [monotonicity #514]: #481
-#494 := [trans #483 #492]: #493
-#448 := [quant-inst #580]: #489
-#504 := [mp #448 #494]: #482
-#416 := [unit-resolution #504 #690 #428]: #452
-#419 := (not #452)
-#421 := (or #419 #484)
-#422 := [th-lemma arith triangle-eq]: #421
-#418 := [unit-resolution #422 #416]: #484
-#505 := (>= #488 -1::Int)
-#423 := (or #419 #505)
-#413 := [th-lemma arith triangle-eq]: #423
-#403 := [unit-resolution #413 #416]: #505
-#404 := (<= #254 1::Int)
-#405 := (or #438 #404)
-#406 := [th-lemma arith triangle-eq]: #405
-#409 := [unit-resolution #406 #433]: #404
-#414 := [th-lemma arith eq-propagate -1 -1 1 1 #424 #409 #403 #418]: #410
-#415 := [symm #414]: #407
-#411 := [monotonicity #415]: #408
-#401 := [trans #411 #437]: #400
-#402 := [trans #401 #398]: #399
-#386 := [monotonicity #402]: #384
-#388 := [monotonicity #386 #436]: #387
-#392 := [trans #388 #390]: #391
-#351 := (= #45 #338)
-#350 := (= #44 #337)
-#658 := (f7 f8 #42)
-#586 := (+ 1::Int #658)
-#578 := (f5 f6 #586)
-#357 := (= #578 #337)
-#587 := (= #337 #578)
-#590 := (or #585 #587)
-#579 := [quant-inst #42]: #590
-#393 := [unit-resolution #579 #157]: #587
-#367 := [symm #393]: #357
-#348 := (= #44 #578)
-#570 := (f7 f8 #578)
-#447 := (f5 f6 #570)
-#449 := (= #447 #578)
-#454 := (or #453 #449)
-#455 := [quant-inst #578]: #454
-#394 := [unit-resolution #455 #683]: #449
-#365 := (= #44 #447)
-#364 := (= 1::Int #570)
-#362 := (= #570 1::Int)
-#564 := (* -1::Int #658)
-#565 := (+ #570 #564)
-#538 := (<= #565 1::Int)
-#562 := (= #565 1::Int)
-#573 := (>= #658 -1::Int)
-#589 := (>= #658 0::Int)
-#659 := (= #658 0::Int)
-#642 := (or #641 #659)
-#443 := (>= 0::Int 0::Int)
-#650 := (not #443)
-#660 := (or #650 #659)
-#643 := (or #641 #660)
-#644 := (iff #643 #642)
-#645 := (iff #642 #642)
-#647 := [rewrite]: #645
-#639 := (iff #660 #659)
-#637 := (or false #659)
-#301 := (iff #637 #659)
-#302 := [rewrite]: #301
-#299 := (iff #660 #637)
-#653 := (iff #650 false)
-#310 := (iff #650 #651)
-#655 := (iff #443 true)
-#661 := [rewrite]: #655
-#315 := [monotonicity #661]: #310
-#295 := [trans #315 #311]: #653
-#300 := [monotonicity #295]: #299
-#640 := [trans #300 #302]: #639
-#281 := [monotonicity #640]: #644
-#286 := [trans #281 #647]: #644
-#638 := [quant-inst #41]: #643
-#287 := [mp #638 #286]: #642
-#395 := [unit-resolution #287 #690]: #659
-#396 := (not #659)
-#385 := (or #396 #589)
-#397 := [th-lemma arith triangle-eq]: #385
-#374 := [unit-resolution #397 #395]: #589
-#376 := (not #589)
-#377 := (or #376 #573)
-#378 := [th-lemma arith farkas 1 1]: #377
-#379 := [unit-resolution #378 #374]: #573
-#560 := (not #573)
-#551 := (or #641 #560 #562)
-#571 := (= #570 #586)
-#576 := (>= #586 0::Int)
-#583 := (not #576)
-#572 := (or #583 #571)
-#552 := (or #641 #572)
-#548 := (iff #552 #551)
-#547 := (or #560 #562)
-#554 := (or #641 #547)
-#557 := (iff #554 #551)
-#558 := [rewrite]: #557
-#555 := (iff #552 #554)
-#549 := (iff #572 #547)
-#566 := (iff #571 #562)
-#546 := [rewrite]: #566
-#561 := (iff #583 #560)
-#569 := (iff #576 #573)
-#574 := [rewrite]: #569
-#563 := [monotonicity #574]: #561
-#550 := [monotonicity #563 #546]: #549
-#556 := [monotonicity #550]: #555
-#559 := [trans #556 #558]: #548
-#553 := [quant-inst #586]: #552
-#537 := [mp #553 #559]: #551
-#380 := [unit-resolution #537 #690 #379]: #562
-#381 := (not #562)
-#382 := (or #381 #538)
-#375 := [th-lemma arith triangle-eq]: #382
-#383 := [unit-resolution #375 #380]: #538
-#540 := (>= #565 1::Int)
-#368 := (or #381 #540)
-#369 := [th-lemma arith triangle-eq]: #368
-#370 := [unit-resolution #369 #380]: #540
-#588 := (<= #658 0::Int)
-#372 := (or #396 #588)
-#371 := [th-lemma arith triangle-eq]: #372
-#373 := [unit-resolution #371 #395]: #588
-#363 := [th-lemma arith eq-propagate -1 -1 -1 -1 #374 #373 #370 #383]: #362
-#356 := [symm #363]: #364
-#366 := [monotonicity #356]: #365
-#349 := [trans #366 #394]: #348
-#341 := [trans #349 #367]: #350
-#352 := [monotonicity #341]: #351
-#319 := [monotonicity #352 #392]: #353
-#322 := [symm #319]: #321
-#312 := (= #48 #656)
-#324 := (or #323 #312)
-#657 := [quant-inst #7 #42 #46]: #324
-#342 := [unit-resolution #657 #676]: #312
-#313 := [trans #342 #322]: #54
-#55 := (not #54)
-#105 := [asserted]: #55
-[unit-resolution #105 #313]: false
-unsat
-7a4c9001ff099c38b0602b196e3bc37f301b1551 24 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1)
-#7 := (:var 0 S2)
-#8 := (f3 #7)
-#9 := (= #8 f1)
-#10 := (forall (vars (?v0 S2)) #9)
-#11 := (not #10)
-#12 := (or #10 #11)
-#13 := (not #12)
-#42 := (iff #13 false)
-#1 := true
-#37 := (not true)
-#40 := (iff #37 false)
-#41 := [rewrite]: #40
-#38 := (iff #13 #37)
-#35 := (iff #12 true)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#43 := [trans #39 #41]: #42
-#34 := [asserted]: #13
-[mp #34 #43]: false
-unsat
-5e86b4c9726ef5b2868f22c9ea608e9e3558803e 344 0
-#2 := false
-decl f7 :: (-> S5 Int S2)
-#28 := 6::Int
-decl f8 :: S5
-#14 := f8
-#29 := (f7 f8 6::Int)
-decl f3 :: (-> S3 S2 S2)
-decl f5 :: (-> S4 S2 Int)
-#21 := 4::Int
-#22 := (f7 f8 4::Int)
-decl f4 :: S3
-#7 := f4
-#23 := (f3 f4 #22)
-decl f6 :: S4
-#10 := f6
-#24 := (f5 f6 #23)
-#25 := (* 4::Int #24)
-#26 := (f7 f8 #25)
-#27 := (f3 f4 #26)
-#30 := (= #27 #29)
-#526 := (f3 f4 #29)
-#490 := (= #526 #29)
-#552 := (f5 f6 #29)
-#67 := -10::Int
-#528 := (+ -10::Int #552)
-#508 := (f7 f8 #528)
-#454 := (f3 f4 #508)
-#509 := (= #526 #454)
-#12 := 10::Int
-#525 := (>= #552 10::Int)
-#514 := (if #525 #509 #490)
-#8 := (:var 0 S2)
-#9 := (f3 f4 #8)
-#665 := (pattern #9)
-#11 := (f5 f6 #8)
-#664 := (pattern #11)
-#182 := (= #9 #8)
-#68 := (+ -10::Int #11)
-#71 := (f7 f8 #68)
-#74 := (f3 f4 #71)
-#181 := (= #9 #74)
-#88 := (>= #11 10::Int)
-#169 := (if #88 #181 #182)
-#666 := (forall (vars (?v0 S2)) (:pat #664 #665) #169)
-#184 := (forall (vars (?v0 S2)) #169)
-#669 := (iff #184 #666)
-#667 := (iff #169 #169)
-#668 := [refl]: #667
-#670 := [quant-intro #668]: #669
-#93 := (if #88 #74 #8)
-#98 := (= #9 #93)
-#101 := (forall (vars (?v0 S2)) #98)
-#185 := (iff #101 #184)
-#170 := (iff #98 #169)
-#183 := [rewrite]: #170
-#186 := [quant-intro #183]: #185
-#173 := (~ #101 #101)
-#171 := (~ #98 #98)
-#172 := [refl]: #171
-#174 := [nnf-pos #172]: #173
-#15 := (- #11 10::Int)
-#16 := (f7 f8 #15)
-#17 := (f3 f4 #16)
-#13 := (< #11 10::Int)
-#18 := (if #13 #8 #17)
-#19 := (= #9 #18)
-#20 := (forall (vars (?v0 S2)) #19)
-#104 := (iff #20 #101)
-#77 := (if #13 #8 #74)
-#80 := (= #9 #77)
-#83 := (forall (vars (?v0 S2)) #80)
-#102 := (iff #83 #101)
-#99 := (iff #80 #98)
-#96 := (= #77 #93)
-#86 := (not #88)
-#90 := (if #86 #8 #74)
-#94 := (= #90 #93)
-#95 := [rewrite]: #94
-#91 := (= #77 #90)
-#87 := (iff #13 #86)
-#89 := [rewrite]: #87
-#92 := [monotonicity #89]: #91
-#97 := [trans #92 #95]: #96
-#100 := [monotonicity #97]: #99
-#103 := [quant-intro #100]: #102
-#84 := (iff #20 #83)
-#81 := (iff #19 #80)
-#78 := (= #18 #77)
-#75 := (= #17 #74)
-#72 := (= #16 #71)
-#69 := (= #15 #68)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [quant-intro #82]: #84
-#105 := [trans #85 #103]: #104
-#66 := [asserted]: #20
-#106 := [mp #66 #105]: #101
-#159 := [mp~ #106 #174]: #101
-#187 := [mp #159 #186]: #184
-#671 := [mp #187 #670]: #666
-#320 := (not #666)
-#516 := (or #320 #514)
-#484 := [quant-inst #29]: #516
-#469 := [unit-resolution #484 #671]: #514
-#450 := (not #525)
-#515 := (<= #552 6::Int)
-#553 := (= #552 6::Int)
-#36 := (:var 0 Int)
-#38 := (f7 f8 #36)
-#678 := (pattern #38)
-#39 := (f5 f6 #38)
-#40 := (= #39 #36)
-#35 := 0::Int
-#119 := (>= #36 0::Int)
-#120 := (not #119)
-#123 := (or #120 #40)
-#679 := (forall (vars (?v0 Int)) (:pat #678) #123)
-#126 := (forall (vars (?v0 Int)) #123)
-#682 := (iff #126 #679)
-#680 := (iff #123 #123)
-#681 := [refl]: #680
-#683 := [quant-intro #681]: #682
-#165 := (~ #126 #126)
-#164 := (~ #123 #123)
-#176 := [refl]: #164
-#166 := [nnf-pos #176]: #165
-#37 := (<= 0::Int #36)
-#41 := (implies #37 #40)
-#42 := (forall (vars (?v0 Int)) #41)
-#129 := (iff #42 #126)
-#110 := (not #37)
-#111 := (or #110 #40)
-#114 := (forall (vars (?v0 Int)) #111)
-#127 := (iff #114 #126)
-#124 := (iff #111 #123)
-#121 := (iff #110 #120)
-#117 := (iff #37 #119)
-#118 := [rewrite]: #117
-#122 := [monotonicity #118]: #121
-#125 := [monotonicity #122]: #124
-#128 := [quant-intro #125]: #127
-#115 := (iff #42 #114)
-#112 := (iff #41 #111)
-#113 := [rewrite]: #112
-#116 := [quant-intro #113]: #115
-#130 := [trans #116 #128]: #129
-#109 := [asserted]: #42
-#131 := [mp #109 #130]: #126
-#177 := [mp~ #131 #166]: #126
-#684 := [mp #177 #683]: #679
-#611 := (not #679)
-#545 := (or #611 #553)
-#549 := (>= 6::Int 0::Int)
-#551 := (not #549)
-#554 := (or #551 #553)
-#546 := (or #611 #554)
-#547 := (iff #546 #545)
-#529 := (iff #545 #545)
-#530 := [rewrite]: #529
-#543 := (iff #554 #553)
-#550 := (or false #553)
-#540 := (iff #550 #553)
-#542 := [rewrite]: #540
-#561 := (iff #554 #550)
-#559 := (iff #551 false)
-#1 := true
-#619 := (not true)
-#616 := (iff #619 false)
-#617 := [rewrite]: #616
-#557 := (iff #551 #619)
-#555 := (iff #549 true)
-#556 := [rewrite]: #555
-#558 := [monotonicity #556]: #557
-#560 := [trans #558 #617]: #559
-#539 := [monotonicity #560]: #561
-#544 := [trans #539 #542]: #543
-#533 := [monotonicity #544]: #547
-#531 := [trans #533 #530]: #547
-#541 := [quant-inst #28]: #546
-#534 := [mp #541 #531]: #545
-#470 := [unit-resolution #534 #684]: #553
-#477 := (not #553)
-#478 := (or #477 #515)
-#479 := [th-lemma arith triangle-eq]: #478
-#464 := [unit-resolution #479 #470]: #515
-#480 := (not #515)
-#441 := (or #480 #450)
-#442 := [th-lemma arith farkas 1 1]: #441
-#449 := [unit-resolution #442 #464]: #450
-#491 := (not #514)
-#485 := (or #491 #525 #490)
-#492 := [def-axiom]: #485
-#451 := [unit-resolution #492 #449 #469]: #490
-#404 := (= #27 #526)
-#641 := (f5 f6 #26)
-#638 := (+ -10::Int #641)
-#345 := (f7 f8 #638)
-#360 := (f3 f4 #345)
-#403 := (= #360 #526)
-#416 := (= #345 #29)
-#411 := (= #638 6::Int)
-#312 := (f5 f6 #22)
-#249 := -1::Int
-#518 := (* -1::Int #312)
-#519 := (+ #24 #518)
-#524 := (<= #519 0::Int)
-#517 := (= #24 #312)
-#303 := (= #23 #22)
-#297 := (+ -10::Int #312)
-#639 := (f7 f8 #297)
-#301 := (f3 f4 #639)
-#302 := (= #23 #301)
-#317 := (>= #312 10::Int)
-#304 := (if #317 #302 #303)
-#643 := (or #320 #304)
-#644 := [quant-inst #22]: #643
-#452 := [unit-resolution #644 #671]: #304
-#640 := (not #317)
-#447 := (<= #312 4::Int)
-#625 := (= #312 4::Int)
-#612 := (or #611 #625)
-#256 := (>= 4::Int 0::Int)
-#633 := (not #256)
-#629 := (or #633 #625)
-#606 := (or #611 #629)
-#613 := (iff #606 #612)
-#608 := (iff #612 #612)
-#615 := [rewrite]: #608
-#609 := (iff #629 #625)
-#618 := (or false #625)
-#466 := (iff #618 #625)
-#467 := [rewrite]: #466
-#624 := (iff #629 #618)
-#622 := (iff #633 false)
-#620 := (iff #633 #619)
-#626 := (iff #256 true)
-#630 := [rewrite]: #626
-#621 := [monotonicity #630]: #620
-#623 := [trans #621 #617]: #622
-#465 := [monotonicity #623]: #624
-#610 := [trans #465 #467]: #609
-#614 := [monotonicity #610]: #613
-#444 := [trans #614 #615]: #613
-#607 := [quant-inst #21]: #606
-#446 := [mp #607 #444]: #612
-#453 := [unit-resolution #446 #684]: #625
-#455 := (not #625)
-#456 := (or #455 #447)
-#457 := [th-lemma arith triangle-eq]: #456
-#458 := [unit-resolution #457 #453]: #447
-#459 := (not #447)
-#460 := (or #459 #640)
-#443 := [th-lemma arith farkas 1 1]: #460
-#461 := [unit-resolution #443 #458]: #640
-#645 := (not #304)
-#647 := (or #645 #317 #303)
-#649 := [def-axiom]: #647
-#431 := [unit-resolution #649 #461 #452]: #303
-#434 := [monotonicity #431]: #517
-#436 := (not #517)
-#437 := (or #436 #524)
-#438 := [th-lemma arith triangle-eq]: #437
-#280 := [unit-resolution #438 #434]: #524
-#520 := (>= #519 0::Int)
-#439 := (or #436 #520)
-#435 := [th-lemma arith triangle-eq]: #439
-#440 := [unit-resolution #435 #434]: #520
-#600 := (>= #312 4::Int)
-#419 := (or #455 #600)
-#422 := [th-lemma arith triangle-eq]: #419
-#426 := [unit-resolution #422 #453]: #600
-#504 := (* -1::Int #641)
-#505 := (+ #25 #504)
-#582 := (<= #505 0::Int)
-#503 := (= #505 0::Int)
-#597 := (>= #24 0::Int)
-#429 := (not #520)
-#428 := (not #600)
-#427 := (or #597 #428 #429)
-#430 := [th-lemma arith assign-bounds 1 1]: #427
-#418 := [unit-resolution #430 #426 #440]: #597
-#499 := (not #597)
-#598 := (or #499 #503)
-#586 := (or #611 #499 #503)
-#593 := (= #641 #25)
-#596 := (>= #25 0::Int)
-#498 := (not #596)
-#594 := (or #498 #593)
-#588 := (or #611 #594)
-#587 := (iff #588 #586)
-#577 := (or #611 #598)
-#590 := (iff #577 #586)
-#591 := [rewrite]: #590
-#579 := (iff #588 #577)
-#595 := (iff #594 #598)
-#501 := (iff #593 #503)
-#502 := [rewrite]: #501
-#500 := (iff #498 #499)
-#482 := (iff #596 #597)
-#497 := [rewrite]: #482
-#493 := [monotonicity #497]: #500
-#599 := [monotonicity #493 #502]: #595
-#589 := [monotonicity #599]: #579
-#592 := [trans #589 #591]: #587
-#580 := [quant-inst #25]: #588
-#581 := [mp #580 #592]: #586
-#421 := [unit-resolution #581 #684]: #598
-#423 := [unit-resolution #421 #418]: #503
-#424 := (not #503)
-#420 := (or #424 #582)
-#425 := [th-lemma arith triangle-eq]: #420
-#415 := [unit-resolution #425 #423]: #582
-#583 := (>= #505 0::Int)
-#405 := (or #424 #583)
-#407 := [th-lemma arith triangle-eq]: #405
-#408 := [unit-resolution #407 #423]: #583
-#412 := [th-lemma arith eq-propagate 1 1 -4 -4 -4 -4 #408 #415 #426 #458 #440 #280]: #411
-#409 := [monotonicity #412]: #416
-#401 := [monotonicity #409]: #403
-#361 := (= #27 #360)
-#362 := (= #27 #26)
-#642 := (>= #641 10::Int)
-#363 := (if #642 #361 #362)
-#634 := (or #320 #363)
-#356 := [quant-inst #26]: #634
-#417 := [unit-resolution #356 #671]: #363
-#410 := (not #582)
-#413 := (or #642 #410 #428 #429)
-#414 := [th-lemma arith assign-bounds 1 4 4]: #413
-#400 := [unit-resolution #414 #426 #415 #440]: #642
-#631 := (not #642)
-#357 := (not #363)
-#635 := (or #357 #631 #361)
-#632 := [def-axiom]: #635
-#402 := [unit-resolution #632 #400 #417]: #361
-#386 := [trans #402 #401]: #404
-#388 := [trans #386 #451]: #30
-#31 := (not #30)
-#107 := [asserted]: #31
-[unit-resolution #107 #388]: false
-unsat
-013f2c4f5eccbaac1754336d2ce477a569c8d0cd 1 0
-unsat
-8954c874576a1a34e48535e83e9151ff299d36aa 95 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S3 S2 S1)
-decl f10 :: (-> S5 S6 S2)
-decl f12 :: (-> S3 S6)
-decl f6 :: S3
-#19 := f6
-#43 := (f12 f6)
-decl f11 :: S5
-#42 := f11
-#44 := (f10 f11 #43)
-decl f8 :: (-> S4 S2 S3)
-decl f9 :: S4
-#29 := f9
-#45 := (f8 f9 #44)
-#53 := (f3 #45 #44)
-#54 := (= #53 f1)
-#55 := (not #54)
-#140 := [asserted]: #55
-decl f4 :: S3
-#7 := f4
-#46 := (f12 f4)
-#47 := (f10 f11 #46)
-#50 := (f8 f9 #47)
-#51 := (f3 #50 #44)
-#52 := (= #51 f1)
-#139 := [asserted]: #52
-#48 := (f3 #45 #47)
-#49 := (= #48 f1)
-#138 := [asserted]: #49
-#8 := (:var 0 S2)
-#12 := (:var 1 S2)
-#34 := (f8 f9 #12)
-#35 := (f3 #34 #8)
-#30 := (:var 2 S2)
-#31 := (f8 f9 #30)
-#32 := (f3 #31 #12)
-#635 := (pattern #32 #35)
-#37 := (f3 #31 #8)
-#38 := (= #37 f1)
-#36 := (= #35 f1)
-#112 := (not #36)
-#33 := (= #32 f1)
-#120 := (not #33)
-#129 := (or #120 #112 #38)
-#636 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S2)) (:pat #635) #129)
-#132 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S2)) #129)
-#639 := (iff #132 #636)
-#637 := (iff #129 #129)
-#638 := [refl]: #637
-#640 := [quant-intro #638]: #639
-#146 := (~ #132 #132)
-#162 := (~ #129 #129)
-#163 := [refl]: #162
-#147 := [nnf-pos #163]: #146
-#39 := (implies #36 #38)
-#40 := (implies #33 #39)
-#41 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S2)) #40)
-#135 := (iff #41 #132)
-#114 := (or #112 #38)
-#121 := (or #120 #114)
-#126 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S2)) #121)
-#133 := (iff #126 #132)
-#130 := (iff #121 #129)
-#131 := [rewrite]: #130
-#134 := [quant-intro #131]: #133
-#127 := (iff #41 #126)
-#124 := (iff #40 #121)
-#117 := (implies #33 #114)
-#122 := (iff #117 #121)
-#123 := [rewrite]: #122
-#118 := (iff #40 #117)
-#115 := (iff #39 #114)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116]: #118
-#125 := [trans #119 #123]: #124
-#128 := [quant-intro #125]: #127
-#136 := [trans #128 #134]: #135
-#111 := [asserted]: #41
-#137 := [mp #111 #136]: #132
-#164 := [mp~ #137 #147]: #132
-#641 := [mp #164 #640]: #636
-#305 := (not #52)
-#219 := (not #49)
-#307 := (not #636)
-#298 := (or #307 #219 #305 #54)
-#220 := (or #219 #305 #54)
-#309 := (or #307 #220)
-#311 := (iff #309 #298)
-#308 := [rewrite]: #311
-#310 := [quant-inst #44 #47 #44]: #309
-#312 := [mp #310 #308]: #298
-[unit-resolution #312 #641 #138 #139 #140]: false
-unsat
-b66bf263776a429b47555990b2282b5f0c94c465 59 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f22 :: (-> Int S1)
-#70 := 1::Int
-#71 := (f22 1::Int)
-#72 := (= #71 f1)
-#73 := (not #72)
-#163 := [asserted]: #73
-#57 := (:var 0 Int)
-#58 := (f22 #57)
-#695 := (pattern #58)
-#59 := (= #58 f1)
-#696 := (forall (vars (?v0 Int)) (:pat #695) #59)
-#160 := (forall (vars (?v0 Int)) #59)
-#699 := (iff #160 #696)
-#697 := (iff #59 #59)
-#698 := [refl]: #697
-#700 := [quant-intro #698]: #699
-#174 := (~ #160 #160)
-#192 := (~ #59 #59)
-#193 := [refl]: #192
-#175 := [nnf-pos #193]: #174
-decl f17 :: (-> S10 S1)
-decl f23 :: (-> S13 S10 S10)
-decl f26 :: S10
-#62 := f26
-decl f24 :: (-> S14 Int S13)
-decl f25 :: S14
-#60 := f25
-#61 := (f24 f25 #57)
-#63 := (f23 #61 f26)
-#64 := (f17 #63)
-#65 := (= #64 f1)
-#66 := (not #65)
-#67 := (or #65 #66)
-#68 := (and #59 #67)
-#69 := (forall (vars (?v0 Int)) #68)
-#161 := (iff #69 #160)
-#158 := (iff #68 #59)
-#1 := true
-#153 := (and #59 true)
-#156 := (iff #153 #59)
-#157 := [rewrite]: #156
-#154 := (iff #68 #153)
-#150 := (iff #67 true)
-#152 := [rewrite]: #150
-#155 := [monotonicity #152]: #154
-#159 := [trans #155 #157]: #158
-#162 := [quant-intro #159]: #161
-#149 := [asserted]: #69
-#165 := [mp #149 #162]: #160
-#194 := [mp~ #165 #175]: #160
-#701 := [mp #194 #700]: #696
-#253 := (not #696)
-#338 := (or #253 #72)
-#339 := [quant-inst #70]: #338
-[unit-resolution #339 #701 #163]: false
-unsat
d9c8c0d6c38991be073d0ed9988535642e4f47a6 396 0
#2 := false
decl f12 :: (-> S9 S10 S4)
@@ -12208,3 +2065,404 @@
#247 := [asserted]: #123
[unit-resolution #247 #607]: false
unsat
+c4f4c8220660d1979009b33a643f0927bee816b1 1 0
+unsat
+db6426d59fdd57da8ca5d11de399761d1f1443de 1 0
+unsat
+e7ef76d73ccb9bc09d2b5368495a7a59d1bae3dc 1 0
+unsat
+8578dab7bf88c7d119f9af2e5f7eaf948f1bdb87 84 0
+WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
+#2 := false
+#8 := 0::Int
+#7 := (:var 0 Int)
+#49 := (<= #7 0::Int)
+#50 := (not #49)
+#47 := (>= #7 0::Int)
+#45 := (not #47)
+#53 := (or #45 #50)
+#56 := (forall (vars (?v0 Int)) #53)
+#525 := (not #56)
+#218 := (<= 0::Int 0::Int)
+#539 := (not #218)
+#207 := (>= 0::Int 0::Int)
+#201 := (not #207)
+#537 := (or #201 #539)
+#526 := (or #525 #537)
+#170 := (iff #526 #525)
+#527 := (or #525 false)
+#530 := (iff #527 #525)
+#169 := [rewrite]: #530
+#164 := (iff #526 #527)
+#523 := (iff #537 false)
+#182 := (or false false)
+#185 := (iff #182 false)
+#522 := [rewrite]: #185
+#183 := (iff #537 #182)
+#178 := (iff #539 false)
+#1 := true
+#543 := (not true)
+#222 := (iff #543 false)
+#544 := [rewrite]: #222
+#194 := (iff #539 #543)
+#198 := (iff #218 true)
+#535 := [rewrite]: #198
+#536 := [monotonicity #535]: #194
+#520 := [trans #536 #544]: #178
+#534 := (iff #201 false)
+#538 := (iff #201 #543)
+#541 := (iff #207 true)
+#542 := [rewrite]: #541
+#326 := [monotonicity #542]: #538
+#193 := [trans #326 #544]: #534
+#184 := [monotonicity #193 #520]: #183
+#524 := [trans #184 #522]: #523
+#528 := [monotonicity #524]: #164
+#531 := [trans #528 #169]: #170
+#521 := [quant-inst #8]: #526
+#529 := [mp #521 #531]: #525
+#69 := (~ #56 #56)
+#67 := (~ #53 #53)
+#68 := [refl]: #67
+#70 := [nnf-pos #68]: #69
+#10 := (< 0::Int #7)
+#9 := (< #7 0::Int)
+#11 := (or #9 #10)
+#12 := (forall (vars (?v0 Int)) #11)
+#13 := (if #12 false true)
+#14 := (not #13)
+#59 := (iff #14 #56)
+#57 := (iff #12 #56)
+#54 := (iff #11 #53)
+#51 := (iff #10 #50)
+#52 := [rewrite]: #51
+#46 := (iff #9 #45)
+#48 := [rewrite]: #46
+#55 := [monotonicity #48 #52]: #54
+#58 := [quant-intro #55]: #57
+#43 := (iff #14 #12)
+#35 := (not #12)
+#38 := (not #35)
+#41 := (iff #38 #12)
+#42 := [rewrite]: #41
+#39 := (iff #14 #38)
+#36 := (iff #13 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#60 := [trans #44 #58]: #59
+#34 := [asserted]: #14
+#61 := [mp #34 #60]: #56
+#63 := [mp~ #61 #70]: #56
+[unit-resolution #63 #529]: false
+unsat
+252d255c564463d916bc68156eea8dbe7fb0be0a 165 0
+WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
+#2 := false
+#7 := 0::Int
+#8 := (:var 0 Int)
+#55 := (<= #8 0::Int)
+#56 := (not #55)
+#52 := (>= #8 0::Int)
+#51 := (not #52)
+#59 := (or #51 #56)
+#62 := (forall (vars (?v0 Int)) #59)
+#95 := (not #62)
+#587 := (<= 0::Int 0::Int)
+#586 := (not #587)
+#585 := (>= 0::Int 0::Int)
+#248 := (not #585)
+#593 := (or #248 #586)
+#290 := (or #95 #593)
+#569 := (iff #290 #95)
+#292 := (or #95 false)
+#572 := (iff #292 #95)
+#287 := [rewrite]: #572
+#293 := (iff #290 #292)
+#576 := (iff #593 false)
+#578 := (or false false)
+#575 := (iff #578 false)
+#579 := [rewrite]: #575
+#300 := (iff #593 #578)
+#201 := (iff #586 false)
+#1 := true
+#594 := (not true)
+#592 := (iff #594 false)
+#595 := [rewrite]: #592
+#306 := (iff #586 #594)
+#304 := (iff #587 true)
+#305 := [rewrite]: #304
+#307 := [monotonicity #305]: #306
+#577 := [trans #307 #595]: #201
+#581 := (iff #248 false)
+#589 := (iff #248 #594)
+#233 := (iff #585 true)
+#234 := [rewrite]: #233
+#249 := [monotonicity #234]: #589
+#582 := [trans #249 #595]: #581
+#301 := [monotonicity #582 #577]: #300
+#580 := [trans #301 #579]: #576
+#571 := [monotonicity #580]: #293
+#573 := [trans #571 #287]: #569
+#291 := [quant-inst #7]: #290
+#570 := [mp #291 #573]: #95
+decl z3name!0 :: bool
+#92 := z3name!0
+#15 := 3::Int
+#39 := -1::Int
+#99 := (if z3name!0 -1::Int 3::Int)
+#284 := (= #99 3::Int)
+#604 := (not #284)
+#602 := (>= #99 3::Int)
+#259 := (not #602)
+#102 := (<= #99 0::Int)
+#65 := (if #62 -1::Int 3::Int)
+#71 := (<= #65 0::Int)
+#103 := (~ #71 #102)
+#100 := (= #65 #99)
+#97 := (~ #62 z3name!0)
+#88 := (or z3name!0 #95)
+#93 := (not z3name!0)
+#94 := (or #93 #62)
+#89 := (and #94 #88)
+#96 := [intro-def]: #89
+#98 := [apply-def #96]: #97
+#101 := [monotonicity #98]: #100
+#104 := [monotonicity #101]: #103
+#13 := 1::Int
+#14 := (- 1::Int)
+#10 := (< 0::Int #8)
+#9 := (< #8 0::Int)
+#11 := (or #9 #10)
+#12 := (forall (vars (?v0 Int)) #11)
+#16 := (if #12 #14 3::Int)
+#17 := (< 0::Int #16)
+#18 := (not #17)
+#84 := (iff #18 #71)
+#42 := (if #12 -1::Int 3::Int)
+#45 := (< 0::Int #42)
+#48 := (not #45)
+#82 := (iff #48 #71)
+#72 := (not #71)
+#77 := (not #72)
+#80 := (iff #77 #71)
+#81 := [rewrite]: #80
+#78 := (iff #48 #77)
+#75 := (iff #45 #72)
+#68 := (< 0::Int #65)
+#73 := (iff #68 #72)
+#74 := [rewrite]: #73
+#69 := (iff #45 #68)
+#66 := (= #42 #65)
+#63 := (iff #12 #62)
+#60 := (iff #11 #59)
+#57 := (iff #10 #56)
+#58 := [rewrite]: #57
+#53 := (iff #9 #51)
+#54 := [rewrite]: #53
+#61 := [monotonicity #54 #58]: #60
+#64 := [quant-intro #61]: #63
+#67 := [monotonicity #64]: #66
+#70 := [monotonicity #67]: #69
+#76 := [trans #70 #74]: #75
+#79 := [monotonicity #76]: #78
+#83 := [trans #79 #81]: #82
+#49 := (iff #18 #48)
+#46 := (iff #17 #45)
+#43 := (= #16 #42)
+#40 := (= #14 -1::Int)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#50 := [monotonicity #47]: #49
+#85 := [trans #50 #83]: #84
+#38 := [asserted]: #18
+#86 := [mp #38 #85]: #71
+#133 := [mp~ #86 #104]: #102
+#389 := (not #102)
+#596 := (or #259 #389)
+#270 := [th-lemma arith farkas 1 1]: #596
+#271 := [unit-resolution #270 #133]: #259
+#603 := [hypothesis]: #284
+#605 := (or #604 #602)
+#606 := [th-lemma arith triangle-eq]: #605
+#601 := [unit-resolution #606 #603 #271]: false
+#607 := [lemma #601]: #604
+#286 := (or z3name!0 #284)
+#265 := [def-axiom]: #286
+#574 := [unit-resolution #265 #607]: z3name!0
+decl ?v0!1 :: Int
+#115 := ?v0!1
+#118 := (<= ?v0!1 0::Int)
+#119 := (not #118)
+#116 := (>= ?v0!1 0::Int)
+#117 := (not #116)
+#120 := (or #117 #119)
+#121 := (not #120)
+#126 := (or z3name!0 #121)
+#129 := (and #94 #126)
+#130 := (~ #89 #129)
+#127 := (~ #88 #126)
+#122 := (~ #95 #121)
+#123 := [sk]: #122
+#113 := (~ z3name!0 z3name!0)
+#114 := [refl]: #113
+#128 := [monotonicity #114 #123]: #127
+#111 := (~ #94 #94)
+#109 := (~ #62 #62)
+#107 := (~ #59 #59)
+#108 := [refl]: #107
+#110 := [nnf-pos #108]: #109
+#105 := (~ #93 #93)
+#106 := [refl]: #105
+#112 := [monotonicity #106 #110]: #111
+#131 := [monotonicity #112 #128]: #130
+#132 := [mp~ #96 #131]: #129
+#136 := [and-elim #132]: #94
+#563 := [unit-resolution #136 #574]: #62
+[unit-resolution #563 #570]: false
+unsat
+8a78832884e41117489fba88c88de0b5cacb832a 143 0
+#2 := false
+#10 := 0::Int
+#8 := (:var 0 Int)
+#68 := (<= #8 0::Int)
+#69 := (not #68)
+#146 := (not false)
+#149 := (or #146 #69)
+#152 := (not #149)
+#155 := (forall (vars (?v0 Int)) #152)
+#182 := (iff #155 false)
+#177 := (forall (vars (?v0 Int)) false)
+#180 := (iff #177 false)
+#181 := [elim-unused]: #180
+#178 := (iff #155 #177)
+#175 := (iff #152 false)
+#1 := true
+#170 := (not true)
+#173 := (iff #170 false)
+#174 := [rewrite]: #173
+#171 := (iff #152 #170)
+#168 := (iff #149 true)
+#163 := (or true #69)
+#166 := (iff #163 true)
+#167 := [rewrite]: #166
+#164 := (iff #149 #163)
+#161 := (iff #146 true)
+#162 := [rewrite]: #161
+#165 := [monotonicity #162]: #164
+#169 := [trans #165 #167]: #168
+#172 := [monotonicity #169]: #171
+#176 := [trans #172 #174]: #175
+#179 := [quant-intro #176]: #178
+#183 := [trans #179 #181]: #182
+#59 := -1::Int
+#60 := (* -1::Int #8)
+#7 := (:var 1 Int)
+#61 := (+ #7 #60)
+#62 := (<= #61 0::Int)
+#65 := (not #62)
+#72 := (or #65 #69)
+#75 := (forall (vars (?v1 Int)) #72)
+#78 := (not #75)
+#81 := (or #78 #69)
+#107 := (not #81)
+#125 := (forall (vars (?v0 Int)) #107)
+#158 := (iff #125 #155)
+#129 := (forall (vars (?v1 Int)) #69)
+#132 := (not #129)
+#135 := (or #132 #69)
+#138 := (not #135)
+#141 := (forall (vars (?v0 Int)) #138)
+#156 := (iff #141 #155)
+#157 := [rewrite]: #156
+#142 := (iff #125 #141)
+#143 := [rewrite]: #142
+#159 := [trans #143 #157]: #158
+#118 := (and #75 #68)
+#121 := (forall (vars (?v0 Int)) #118)
+#126 := (iff #121 #125)
+#115 := (iff #118 #107)
+#124 := [rewrite]: #115
+#127 := [quant-intro #124]: #126
+#103 := (not #69)
+#106 := (and #75 #103)
+#110 := (forall (vars (?v0 Int)) #106)
+#122 := (iff #110 #121)
+#119 := (iff #106 #118)
+#116 := (iff #103 #68)
+#117 := [rewrite]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#84 := (exists (vars (?v0 Int)) #81)
+#87 := (not #84)
+#111 := (~ #87 #110)
+#108 := (~ #107 #106)
+#104 := (~ #103 #103)
+#105 := [refl]: #104
+#94 := (not #78)
+#95 := (~ #94 #75)
+#100 := (~ #75 #75)
+#98 := (~ #72 #72)
+#99 := [refl]: #98
+#101 := [nnf-pos #99]: #100
+#102 := [nnf-neg #101]: #95
+#109 := [nnf-neg #102 #105]: #108
+#112 := [nnf-neg #109]: #111
+#11 := (< 0::Int #8)
+#9 := (<= #7 #8)
+#12 := (implies #9 #11)
+#13 := (forall (vars (?v1 Int)) #12)
+#14 := (implies #13 #11)
+#15 := (exists (vars (?v0 Int)) #14)
+#16 := (not #15)
+#90 := (iff #16 #87)
+#37 := (not #9)
+#38 := (or #37 #11)
+#41 := (forall (vars (?v1 Int)) #38)
+#47 := (not #41)
+#48 := (or #47 #11)
+#53 := (exists (vars (?v0 Int)) #48)
+#56 := (not #53)
+#88 := (iff #56 #87)
+#85 := (iff #53 #84)
+#82 := (iff #48 #81)
+#70 := (iff #11 #69)
+#71 := [rewrite]: #70
+#79 := (iff #47 #78)
+#76 := (iff #41 #75)
+#73 := (iff #38 #72)
+#66 := (iff #37 #65)
+#63 := (iff #9 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#74 := [monotonicity #67 #71]: #73
+#77 := [quant-intro #74]: #76
+#80 := [monotonicity #77]: #79
+#83 := [monotonicity #80 #71]: #82
+#86 := [quant-intro #83]: #85
+#89 := [monotonicity #86]: #88
+#57 := (iff #16 #56)
+#54 := (iff #15 #53)
+#51 := (iff #14 #48)
+#44 := (implies #41 #11)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #14 #44)
+#42 := (iff #13 #41)
+#39 := (iff #12 #38)
+#40 := [rewrite]: #39
+#43 := [quant-intro #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#55 := [quant-intro #52]: #54
+#58 := [monotonicity #55]: #57
+#91 := [trans #58 #89]: #90
+#36 := [asserted]: #16
+#92 := [mp #36 #91]: #87
+#113 := [mp~ #92 #112]: #110
+#114 := [mp #113 #123]: #121
+#128 := [mp #114 #127]: #125
+#160 := [mp #128 #159]: #155
+[mp #160 #183]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs2 Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,4557 @@
+7a16ef230bca5702aa346494226903ec25809d32 6 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((@x28 (rewrite (= (not true) false))))
+(mp (asserted (not true)) @x28 false))))
+
+27731fc512042f0ea1785a47796a8bfd64c4a8cf 7 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((@x34 (monotonicity (rewrite (= (or |p$| (not |p$|)) true)) (= (not (or |p$| (not |p$|))) (not true)))))
+(let ((@x38 (trans @x34 (rewrite (= (not true) false)) (= (not (or |p$| (not |p$|))) false))))
+(mp (asserted (not (or |p$| (not |p$|)))) @x38 false)))))
+
+5330fb77bfecb903300c8a50f577df102088abaa 9 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((@x34 (monotonicity (rewrite (= (and |p$| true) |p$|)) (= (= (and |p$| true) |p$|) (= |p$| |p$|)))))
+(let ((@x38 (trans @x34 (rewrite (= (= |p$| |p$|) true)) (= (= (and |p$| true) |p$|) true))))
+(let ((@x41 (monotonicity @x38 (= (not (= (and |p$| true) |p$|)) (not true)))))
+(let ((@x45 (trans @x41 (rewrite (= (not true) false)) (= (not (= (and |p$| true) |p$|)) false))))
+(mp (asserted (not (= (and |p$| true) |p$|))) @x45 false)))))))
+
+c2e74b12f4c731d0ea3ac811d94ac5a723029e93 13 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x8 (not |p$|)))
+(let (($x7 (or |p$| |q$|)))
+(let (($x9 (and $x7 $x8)))
+(let ((@x39 (monotonicity (rewrite (= (=> $x9 |q$|) (or (not $x9) |q$|))) (= (not (=> $x9 |q$|)) (not (or (not $x9) |q$|))))))
+(let ((@x40 (|not-or-elim| (mp (asserted (not (=> $x9 |q$|))) @x39 (not (or (not $x9) |q$|))) $x9)))
+(let ((@x43 (|and-elim| @x40 $x8)))
+(let ((@x45 (|not-or-elim| (mp (asserted (not (=> $x9 |q$|))) @x39 (not (or (not $x9) |q$|))) (not |q$|))))
+(let ((@x41 (|and-elim| @x40 $x7)))
+(|unit-resolution| @x41 @x45 @x43 false)))))))))))
+
+800409db22b453674c1b66520bda2d5bafbf81b4 11 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x10 (and |c$| |d$|)))
+(let (($x7 (and |a$| |b$|)))
+(let (($x11 (or $x7 $x10)))
+(let (($x12 (=> $x11 $x11)))
+(let (($x13 (not $x12)))
+(let ((@x43 (trans (monotonicity (rewrite (= $x12 true)) (= $x13 (not true))) (rewrite (= (not true) false)) (= $x13 false))))
+(mp (asserted $x13) @x43 false)))))))))
+
+8ba22a36afac456bfdc7db71e8b371143686dc86 23 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x11 (and |p1$| |p3$|)))
+(let (($x10 (and |p3$| |p2$|)))
+(let (($x12 (or $x10 $x11)))
+(let (($x13 (=> |p1$| $x12)))
+(let (($x14 (or $x13 |p1$|)))
+(let (($x7 (and |p1$| |p2$|)))
+(let (($x9 (or $x7 |p3$|)))
+(let (($x15 (=> $x9 $x14)))
+(let (($x16 (not $x15)))
+(let (($x38 (not |p1$|)))
+(let (($x39 (or $x38 $x12)))
+(let (($x42 (or $x39 |p1$|)))
+(let (($x48 (not $x9)))
+(let (($x49 (or $x48 $x42)))
+(let (($x54 (not $x49)))
+(let ((@x65 (trans (monotonicity (rewrite (= $x49 true)) (= $x54 (not true))) (rewrite (= (not true) false)) (= $x54 false))))
+(let ((@x47 (monotonicity (monotonicity (rewrite (= $x13 $x39)) (= $x14 $x42)) (= $x15 (=> $x9 $x42)))))
+(let ((@x56 (monotonicity (trans @x47 (rewrite (= (=> $x9 $x42) $x49)) (= $x15 $x49)) (= $x16 $x54))))
+(mp (asserted $x16) (trans @x56 @x65 (= $x16 false)) false)))))))))))))))))))))
+
+9d0d2643780c0052a3bf06c1fd96112084da5890 24 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x6 (= |p$| |p$|)))
+(let (($x7 (= $x6 |p$|)))
+(let (($x8 (= $x7 |p$|)))
+(let (($x9 (= $x8 |p$|)))
+(let (($x10 (= $x9 |p$|)))
+(let (($x11 (= $x10 |p$|)))
+(let (($x12 (= $x11 |p$|)))
+(let (($x13 (= $x12 |p$|)))
+(let (($x14 (= $x13 |p$|)))
+(let (($x15 (not $x14)))
+(let ((@x38 (rewrite (= $x6 true))))
+(let ((@x43 (rewrite (= (= true |p$|) |p$|))))
+(let ((@x45 (trans (monotonicity @x38 (= $x7 (= true |p$|))) @x43 (= $x7 |p$|))))
+(let ((@x51 (monotonicity (trans (monotonicity @x45 (= $x8 $x6)) @x38 (= $x8 true)) (= $x9 (= true |p$|)))))
+(let ((@x57 (trans (monotonicity (trans @x51 @x43 (= $x9 |p$|)) (= $x10 $x6)) @x38 (= $x10 true))))
+(let ((@x61 (trans (monotonicity @x57 (= $x11 (= true |p$|))) @x43 (= $x11 |p$|))))
+(let ((@x67 (monotonicity (trans (monotonicity @x61 (= $x12 $x6)) @x38 (= $x12 true)) (= $x13 (= true |p$|)))))
+(let ((@x73 (trans (monotonicity (trans @x67 @x43 (= $x13 |p$|)) (= $x14 $x6)) @x38 (= $x14 true))))
+(let ((@x80 (trans (monotonicity @x73 (= $x15 (not true))) (rewrite (= (not true) false)) (= $x15 false))))
+(mp (asserted $x15) @x80 false))))))))))))))))))))))
+
+63439e1fd6656fc5a2376d7e5f00d0dd92c536a2 34 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x98 (not |b$|)))
+(let (($x17 (not |c$|)))
+(let (($x36 (or |p$| (and |q$| (not |q$|)))))
+(let (($x37 (and (not |p$|) $x36)))
+(let (($x38 (or |c$| $x37)))
+(let (($x39 (not $x38)))
+(let ((@x120 (monotonicity (rewrite (= (and |q$| (not |q$|)) false)) (= $x36 (or |p$| false)))))
+(let ((@x127 (monotonicity (trans @x120 (rewrite (= (or |p$| false) |p$|)) (= $x36 |p$|)) (= $x37 (and (not |p$|) |p$|)))))
+(let ((@x131 (trans @x127 (rewrite (= (and (not |p$|) |p$|) false)) (= $x37 false))))
+(let ((@x138 (trans (monotonicity @x131 (= $x38 (or |c$| false))) (rewrite (= (or |c$| false) |c$|)) (= $x38 |c$|))))
+(let ((@x143 (mp (asserted $x39) (monotonicity @x138 (= $x39 $x17)) $x17)))
+(let (($x101 (or $x98 |c$|)))
+(let ((@x93 (monotonicity (rewrite (= (or |x$| (not |x$|)) true)) (= (and |b$| (or |x$| (not |x$|))) (and |b$| true)))))
+(let ((@x97 (trans @x93 (rewrite (= (and |b$| true) |b$|)) (= (and |b$| (or |x$| (not |x$|))) |b$|))))
+(let ((@x103 (monotonicity (monotonicity @x97 (= (not (and |b$| (or |x$| (not |x$|)))) $x98)) (= (or (not (and |b$| (or |x$| (not |x$|)))) |c$|) $x101))))
+(let ((@x106 (mp (asserted (or (not (and |b$| (or |x$| (not |x$|)))) |c$|)) @x103 $x101)))
+(let (($x108 (not |d$|)))
+(let (($x111 (or $x108 |c$|)))
+(let ((@x110 (monotonicity (rewrite (= (or |d$| false) |d$|)) (= (not (or |d$| false)) $x108))))
+(let ((@x116 (mp (asserted (or (not (or |d$| false)) |c$|)) (monotonicity @x110 (= (or (not (or |d$| false)) |c$|) $x111)) $x111)))
+(let (($x64 (or |a$| |b$| |c$| |d$|)))
+(let ((@x67 (mp (asserted (or |a$| (or |b$| (or |c$| |d$|)))) (rewrite (= (or |a$| (or |b$| (or |c$| |d$|))) $x64)) $x64)))
+(let ((@x160 (|unit-resolution| @x67 (|unit-resolution| @x106 @x143 $x98) @x143 (|unit-resolution| @x116 @x143 $x108) |a$|)))
+(let (($x81 (not |a$|)))
+(let (($x84 (or $x81 |b$|)))
+(let ((@x76 (monotonicity (rewrite (= (and |c$| $x17) false)) (= (or |a$| (and |c$| $x17)) (or |a$| false)))))
+(let ((@x80 (trans @x76 (rewrite (= (or |a$| false) |a$|)) (= (or |a$| (and |c$| $x17)) |a$|))))
+(let ((@x86 (monotonicity (monotonicity @x80 (= (not (or |a$| (and |c$| $x17))) $x81)) (= (or (not (or |a$| (and |c$| $x17))) |b$|) $x84))))
+(let ((@x89 (mp (asserted (or (not (or |a$| (and |c$| $x17))) |b$|)) @x86 $x84)))
+(|unit-resolution| @x89 @x160 (|unit-resolution| @x106 @x143 $x98) false))))))))))))))))))))))))))))))))
+
+c1a1d5a3f58100ecdaa72705a063eeccc5044c46 27 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x15 (|symm_f$| |b$| |a$|)))
+(let ((?x14 (|symm_f$| |a$| |b$|)))
+(let (($x16 (= ?x14 ?x15)))
+(let (($x50 (not $x16)))
+(let ((@x45 (monotonicity (rewrite (= (= |a$| |a$|) true)) (= (and (= |a$| |a$|) $x16) (and true $x16)))))
+(let ((@x49 (trans @x45 (rewrite (= (and true $x16) $x16)) (= (and (= |a$| |a$|) $x16) $x16))))
+(let ((@x55 (mp (asserted (not (and (= |a$| |a$|) $x16))) (monotonicity @x49 (= (not (and (= |a$| |a$|) $x16)) $x50)) $x50)))
+(let (($x59 (forall ((?v0 |A$|) (?v1 |A$|) )(!(let ((?x8 (|symm_f$| ?v1 ?v0)))
+(let ((?x7 (|symm_f$| ?v0 ?v1)))
+(= ?x7 ?x8))) :pattern ( (|symm_f$| ?v0 ?v1) ) :pattern ( (|symm_f$| ?v1 ?v0) )))
+))
+(let (($x10 (forall ((?v0 |A$|) (?v1 |A$|) )(let ((?x8 (|symm_f$| ?v1 ?v0)))
+(let ((?x7 (|symm_f$| ?v0 ?v1)))
+(= ?x7 ?x8))))
+))
+(let ((?x8 (|symm_f$| ?0 ?1)))
+(let ((?x7 (|symm_f$| ?1 ?0)))
+(let (($x9 (= ?x7 ?x8)))
+(let ((@x58 (|mp~| (asserted $x10) (|nnf-pos| (refl (|~| $x9 $x9)) (|~| $x10 $x10)) $x10)))
+(let ((@x66 (mp @x58 (|quant-intro| (refl (= $x9 $x9)) (= $x10 $x59)) $x59)))
+(let (($x70 (or (not $x59) $x16)))
+(let ((@x71 ((_ |quant-inst| |a$| |b$|) $x70)))
+(|unit-resolution| @x71 @x66 @x55 false)))))))))))))))))))
+
+d1ba851b4b433507a4e12ae0555630bd23204076 38 0
+unsat
+((set-logic AUFLIA)
+(declare-fun ?v0!0 () Int)
+(declare-fun ?v1!1 () Int)
+(proof
+(let (($x46 (|p$| ?v0!0)))
+(let (($x48 (not $x46)))
+(let (($x61 (not (or $x46 (|p$| ?v1!1)))))
+(let ((@x77 (monotonicity (rewrite (= (not $x48) $x46)) (= (and (not $x48) $x61) (and $x46 $x61)))))
+(let (($x55 (not $x48)))
+(let (($x65 (and $x55 $x61)))
+(let (($x39 (forall ((?v0 Int) )(let (($x10 (forall ((?v1 Int) )(let (($x6 (|p$| ?v1)))
+(or (|p$| ?v0) $x6)))
+))
+(or (not (|p$| ?v0)) $x10)))
+))
+(let (($x42 (not $x39)))
+(let (($x50 (forall ((?v1 Int) )(let (($x6 (|p$| ?v1)))
+(let (($x46 (|p$| ?v0!0)))
+(or $x46 $x6))))
+))
+(let ((@x67 (|nnf-neg| (refl (|~| $x55 $x55)) (sk (|~| (not $x50) $x61)) (|~| (not (or $x48 $x50)) $x65))))
+(let (($x12 (forall ((?v0 Int) )(let (($x10 (forall ((?v1 Int) )(let (($x6 (|p$| ?v1)))
+(or (|p$| ?v0) $x6)))
+))
+(let (($x6 (|p$| ?v0)))
+(=> $x6 $x10))))
+))
+(let (($x13 (not $x12)))
+(let (($x10 (forall ((?v1 Int) )(let (($x6 (|p$| ?v1)))
+(or (|p$| ?0) $x6)))
+))
+(let ((@x41 (|quant-intro| (rewrite (= (=> (|p$| ?0) $x10) (or (not (|p$| ?0)) $x10))) (= $x12 $x39))))
+(let ((@x70 (|mp~| (mp (asserted $x13) (monotonicity @x41 (= $x13 $x42)) $x42) (trans (sk (|~| $x42 (not (or $x48 $x50)))) @x67 (|~| $x42 $x65)) $x65)))
+(let ((@x79 (|not-or-elim| (|and-elim| (mp @x70 @x77 (and $x46 $x61)) $x61) $x48)))
+(let ((@x72 (|and-elim| (mp @x70 @x77 (and $x46 $x61)) $x46)))
+(|unit-resolution| @x72 @x79 false))))))))))))))))))))
+
+19f6b54cdb476573f91d167cec6fca10e0e66fc7 27 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x72 (forall ((?v0 |A$|) )(!(let (($x8 (|p$| ?v0)))
+(not $x8)) :pattern ( (|p$| ?v0) )))
+))
+(let (($x6 (|p$| |x$|)))
+(let ((@x46 (monotonicity (rewrite (= (=> $x6 (|p$| |y$|)) (or (not $x6) (|p$| |y$|)))) (= (not (=> $x6 (|p$| |y$|))) (not (or (not $x6) (|p$| |y$|)))))))
+(let ((@x49 (mp (asserted (not (=> $x6 (|p$| |y$|)))) @x46 (not (or (not $x6) (|p$| |y$|))))))
+(let ((@x47 (|not-or-elim| @x49 $x6)))
+(let (($x40 (not $x6)))
+(let (($x75 (or $x40 $x72)))
+(let (($x12 (forall ((?v0 |A$|) )(let (($x8 (|p$| ?v0)))
+(not $x8)))
+))
+(let (($x62 (or $x40 $x12)))
+(let ((@x74 (|quant-intro| (refl (= (not (|p$| ?0)) (not (|p$| ?0)))) (= $x12 $x72))))
+(let (($x9 (exists ((?v0 |A$|) )(|p$| ?v0))
+))
+(let (($x13 (ite $x6 (not $x9) $x12)))
+(let ((@x58 (|nnf-neg| (refl (|~| (not (|p$| ?0)) (not (|p$| ?0)))) (|~| (not $x9) $x12))))
+(let ((@x65 (|nnf-pos| (refl (|~| $x6 $x6)) (refl (|~| $x40 $x40)) @x58 (|nnf-pos| (refl (|~| (not (|p$| ?0)) (not (|p$| ?0)))) (|~| $x12 $x12)) (|~| $x13 (and $x62 (or $x6 $x12))))))
+(let ((@x78 (mp (|and-elim| (|mp~| (asserted $x13) @x65 (and $x62 (or $x6 $x12))) $x62) (monotonicity @x74 (= $x62 $x75)) $x75)))
+(let (($x86 (or (not $x72) $x40)))
+(let ((@x87 ((_ |quant-inst| |x$|) $x86)))
+(|unit-resolution| @x87 @x47 (|unit-resolution| @x78 @x47 $x72) false))))))))))))))))))))
+
+e86ca8427589ec8e24e5a85d218331bfb59ff385 7 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((@x33 (monotonicity (rewrite (= (= 3 3) true)) (= (not (= 3 3)) (not true)))))
+(let ((@x37 (trans @x33 (rewrite (= (not true) false)) (= (not (= 3 3)) false))))
+(mp (asserted (not (= 3 3))) @x37 false)))))
+
+77108fa1aa6a8a356ebdd1a376316f26d90399cb 7 0
+unsat
+((set-logic AUFLIRA)
+(proof
+(let ((@x33 (monotonicity (rewrite (= (= 3.0 3.0) true)) (= (not (= 3.0 3.0)) (not true)))))
+(let ((@x37 (trans @x33 (rewrite (= (not true) false)) (= (not (= 3.0 3.0)) false))))
+(mp (asserted (not (= 3.0 3.0))) @x37 false)))))
+
+98abe835b7d13273c58720c5dadf713cd8637495 9 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((@x35 (monotonicity (rewrite (= (+ 3 1) 4)) (= (= (+ 3 1) 4) (= 4 4)))))
+(let ((@x39 (trans @x35 (rewrite (= (= 4 4) true)) (= (= (+ 3 1) 4) true))))
+(let ((@x42 (monotonicity @x39 (= (not (= (+ 3 1) 4)) (not true)))))
+(let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= (not (= (+ 3 1) 4)) false))))
+(mp (asserted (not (= (+ 3 1) 4))) @x46 false)))))))
+
+0382c7d04a37d9ca60cac3282bc80f6b329ab12f 16 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x10 (+ |z$| |x$|)))
+(let ((?x11 (+ |y$| ?x10)))
+(let ((?x8 (+ |y$| |z$|)))
+(let ((?x9 (+ |x$| ?x8)))
+(let (($x12 (= ?x9 ?x11)))
+(let (($x13 (not $x12)))
+(let ((@x43 (monotonicity (rewrite (= ?x10 (+ |x$| |z$|))) (= ?x11 (+ |y$| (+ |x$| |z$|))))))
+(let ((@x47 (trans @x43 (rewrite (= (+ |y$| (+ |x$| |z$|)) (+ |x$| |y$| |z$|))) (= ?x11 (+ |x$| |y$| |z$|)))))
+(let ((@x50 (monotonicity (rewrite (= ?x9 (+ |x$| |y$| |z$|))) @x47 (= $x12 (= (+ |x$| |y$| |z$|) (+ |x$| |y$| |z$|))))))
+(let ((@x54 (trans @x50 (rewrite (= (= (+ |x$| |y$| |z$|) (+ |x$| |y$| |z$|)) true)) (= $x12 true))))
+(let ((@x61 (trans (monotonicity @x54 (= $x13 (not true))) (rewrite (= (not true) false)) (= $x13 false))))
+(mp (asserted $x13) @x61 false))))))))))))))
+
+c608fc7154ce1246a30c68f4d20c1d35cedba663 11 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((@x39 (monotonicity (rewrite (= (<= 3 8) true)) (= (ite (<= 3 8) 8 3) (ite true 8 3)))))
+(let ((@x43 (trans @x39 (rewrite (= (ite true 8 3) 8)) (= (ite (<= 3 8) 8 3) 8))))
+(let ((@x46 (monotonicity @x43 (= (< 5 (ite (<= 3 8) 8 3)) (< 5 8)))))
+(let ((@x50 (trans @x46 (rewrite (= (< 5 8) true)) (= (< 5 (ite (<= 3 8) 8 3)) true))))
+(let ((@x53 (monotonicity @x50 (= (not (< 5 (ite (<= 3 8) 8 3))) (not true)))))
+(let ((@x57 (trans @x53 (rewrite (= (not true) false)) (= (not (< 5 (ite (<= 3 8) 8 3))) false))))
+(mp (asserted (not (< 5 (ite (<= 3 8) 8 3)))) @x57 false)))))))))
+
+4bdd1f2f245666e5db75e9d320ea9e892060d851 88 0
+unsat
+((set-logic AUFLIRA)
+(proof
+(let ((?x42 (* (~ 1.0) |x$|)))
+(let (($x81 (>= |x$| 0.0)))
+(let ((?x88 (ite $x81 |x$| ?x42)))
+(let ((?x111 (* (~ 1.0) ?x88)))
+(let ((?x146 (+ |x$| ?x111)))
+(let (($x147 (<= ?x146 0.0)))
+(let (($x131 (= |x$| ?x88)))
+(let ((?x43 (* (~ 1.0) |y$|)))
+(let ((?x44 (+ ?x42 ?x43)))
+(let ((?x7 (+ |x$| |y$|)))
+(let (($x69 (>= ?x7 0.0)))
+(let ((?x76 (ite $x69 ?x7 ?x44)))
+(let ((?x149 (* (~ 1.0) ?x76)))
+(let ((?x177 (+ ?x44 ?x149)))
+(let (($x179 (>= ?x177 0.0)))
+(let (($x128 (= ?x44 ?x76)))
+(let (($x70 (not $x69)))
+(let (($x93 (>= |y$| 0.0)))
+(let (($x94 (not $x93)))
+(let (($x152 (>= (+ ?x7 ?x149) 0.0)))
+(let (($x127 (= ?x7 ?x76)))
+(let (($x188 (not $x179)))
+(let ((@x159 (hypothesis $x93)))
+(let ((?x100 (ite $x93 |y$| ?x43)))
+(let ((?x112 (* (~ 1.0) ?x100)))
+(let ((?x113 (+ ?x76 ?x111 ?x112)))
+(let (($x114 (<= ?x113 0.0)))
+(let (($x119 (not $x114)))
+(let ((?x18 (+ (ite (< |x$| 0.0) (- |x$|) |x$|) (ite (< |y$| 0.0) (- |y$|) |y$|))))
+(let (($x20 (not (<= (ite (< ?x7 0.0) (- ?x7) ?x7) ?x18))))
+(let (($x15 (< |y$| 0.0)))
+(let ((?x57 (ite $x15 ?x43 |y$|)))
+(let (($x12 (< |x$| 0.0)))
+(let ((?x52 (ite $x12 ?x42 |x$|)))
+(let ((?x60 (+ ?x52 ?x57)))
+(let (($x9 (< ?x7 0.0)))
+(let ((?x47 (ite $x9 ?x44 ?x7)))
+(let (($x63 (<= ?x47 ?x60)))
+(let ((@x104 (trans (monotonicity (rewrite (= $x15 $x94)) (= ?x57 (ite $x94 ?x43 |y$|))) (rewrite (= (ite $x94 ?x43 |y$|) ?x100)) (= ?x57 ?x100))))
+(let ((@x87 (monotonicity (rewrite (= $x12 (not $x81))) (= ?x52 (ite (not $x81) ?x42 |x$|)))))
+(let ((@x92 (trans @x87 (rewrite (= (ite (not $x81) ?x42 |x$|) ?x88)) (= ?x52 ?x88))))
+(let ((@x80 (trans (monotonicity (rewrite (= $x9 $x70)) (= ?x47 (ite $x70 ?x44 ?x7))) (rewrite (= (ite $x70 ?x44 ?x7) ?x76)) (= ?x47 ?x76))))
+(let ((@x110 (monotonicity @x80 (monotonicity @x92 @x104 (= ?x60 (+ ?x88 ?x100))) (= $x63 (<= ?x76 (+ ?x88 ?x100))))))
+(let ((@x118 (trans @x110 (rewrite (= (<= ?x76 (+ ?x88 ?x100)) $x114)) (= $x63 $x114))))
+(let ((@x59 (monotonicity (rewrite (= (- |y$|) ?x43)) (= (ite $x15 (- |y$|) |y$|) ?x57))))
+(let ((@x54 (monotonicity (rewrite (= (- |x$|) ?x42)) (= (ite $x12 (- |x$|) |x$|) ?x52))))
+(let ((@x49 (monotonicity (rewrite (= (- ?x7) ?x44)) (= (ite $x9 (- ?x7) ?x7) ?x47))))
+(let ((@x65 (monotonicity @x49 (monotonicity @x54 @x59 (= ?x18 ?x60)) (= (<= (ite $x9 (- ?x7) ?x7) ?x18) $x63))))
+(let ((@x123 (trans (monotonicity @x65 (= $x20 (not $x63))) (monotonicity @x118 (= (not $x63) $x119)) (= $x20 $x119))))
+(let ((@x124 (mp (asserted $x20) @x123 $x119)))
+(let (($x137 (= |y$| ?x100)))
+(let ((@x172 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x137) (<= (+ |y$| ?x112) 0.0))) (|unit-resolution| (|def-axiom| (or $x94 $x137)) @x159 $x137) (<= (+ |y$| ?x112) 0.0))))
+(let ((?x148 (+ ?x42 ?x111)))
+(let (($x151 (<= ?x148 0.0)))
+(let (($x132 (= ?x42 ?x88)))
+(let (($x82 (not $x81)))
+(let ((@x157 ((_ |th-lemma| arith triangle-eq) (or (not $x131) $x147))))
+(let ((@x158 (|unit-resolution| @x157 (|unit-resolution| (|def-axiom| (or $x82 $x131)) (hypothesis $x81) $x131) $x147)))
+(let ((@x162 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1) (or $x69 $x82 $x94)) (hypothesis $x81) @x159 $x69)))
+(let ((@x126 (|def-axiom| (or $x70 $x127))))
+(let ((@x166 ((_ |th-lemma| arith triangle-eq) (or (not $x127) $x152))))
+(let ((@x173 ((_ |th-lemma| arith farkas 1 -1 -1 1) @x172 (|unit-resolution| @x166 (|unit-resolution| @x126 @x162 $x127) $x152) @x124 @x158 false)))
+(let ((@x136 (|def-axiom| (or $x81 $x132))))
+(let ((@x182 (|unit-resolution| @x136 (|unit-resolution| (lemma @x173 (or $x82 $x94)) @x159 $x82) $x132)))
+(let ((@x187 ((_ |th-lemma| arith farkas 2 -1 -1 1 1) @x159 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x132) $x151)) @x182 $x151) @x172 @x124 (hypothesis $x179) false)))
+(let ((@x196 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x128) $x179)) (hypothesis $x128) (hypothesis $x188) false)))
+(let ((@x197 (lemma @x196 (or (not $x128) $x179))))
+(let ((@x199 (|unit-resolution| @x197 (|unit-resolution| (lemma @x187 (or $x188 $x94)) @x159 $x188) (not $x128))))
+(let ((@x130 (|def-axiom| (or $x69 $x128))))
+(let ((@x202 (|unit-resolution| @x166 (|unit-resolution| @x126 (|unit-resolution| @x130 @x199 $x69) $x127) $x152)))
+(let ((@x203 ((_ |th-lemma| arith farkas 2 1 1 1 1) (|unit-resolution| (lemma @x173 (or $x82 $x94)) @x159 $x82) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x132) $x151)) @x182 $x151) @x172 @x124 @x202 false)))
+(let ((@x204 (lemma @x203 $x94)))
+(let ((@x210 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x81 $x93 $x70)) (hypothesis $x69) @x204 $x81)))
+(let ((@x134 (|def-axiom| (or $x82 $x131))))
+(let ((@x214 (|unit-resolution| @x166 (|unit-resolution| @x126 (hypothesis $x69) $x127) $x152)))
+(let ((?x145 (+ ?x43 ?x112)))
+(let (($x176 (<= ?x145 0.0)))
+(let (($x138 (= ?x43 ?x100)))
+(let ((@x219 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x138) $x176)) (|unit-resolution| (|def-axiom| (or $x93 $x138)) @x204 $x138) $x176)))
+(let ((@x220 ((_ |th-lemma| arith farkas 2 1 1 1 1) @x204 @x219 @x124 @x214 (|unit-resolution| @x157 (|unit-resolution| @x134 @x210 $x131) $x147) false)))
+(let ((@x224 (|unit-resolution| @x197 (|unit-resolution| @x130 (lemma @x220 $x70) $x128) $x179)))
+(let ((@x229 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x132) $x151)) (hypothesis $x132) (lemma ((_ |th-lemma| arith farkas 1 -1 -1 1) @x219 @x124 @x224 (hypothesis $x151) false) (not $x151)) false)))
+(let ((@x232 (|unit-resolution| @x134 (|unit-resolution| @x136 (lemma @x229 (not $x132)) $x81) $x131)))
+((_ |th-lemma| arith farkas -2 1 -1 -1 1) (|unit-resolution| @x136 (lemma @x229 (not $x132)) $x81) @x219 @x124 @x224 (|unit-resolution| @x157 @x232 $x147) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+f8d266138153a7b5a745c746bbb489254a734ae0 16 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x10 (|p$| true)))
+(let (($x7 (< 2 3)))
+(let (($x8 (ite $x7 true false)))
+(let ((?x9 (|p$| $x8)))
+(let (($x11 (= ?x9 ?x10)))
+(let (($x12 (not $x11)))
+(let ((@x50 (monotonicity (monotonicity (rewrite (= $x7 true)) (= (|p$| $x7) ?x10)) (= (= (|p$| $x7) ?x10) (= ?x10 ?x10)))))
+(let ((@x54 (trans @x50 (rewrite (= (= ?x10 ?x10) true)) (= (= (|p$| $x7) ?x10) true))))
+(let ((@x61 (trans (monotonicity @x54 (= (not (= (|p$| $x7) ?x10)) (not true))) (rewrite (= (not true) false)) (= (not (= (|p$| $x7) ?x10)) false))))
+(let ((@x41 (monotonicity (monotonicity (rewrite (= $x8 $x7)) (= ?x9 (|p$| $x7))) (= $x11 (= (|p$| $x7) ?x10)))))
+(let ((@x44 (monotonicity @x41 (= $x12 (not (= (|p$| $x7) ?x10))))))
+(mp (asserted $x12) (trans @x44 @x61 (= $x12 false)) false))))))))))))))
+
+81a816463ea508b010daafde9e601b0b985afe71 16 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x11 (< |x$| 1)))
+(let ((?x35 (+ 3 |x$|)))
+(let (($x38 (<= 4 ?x35)))
+(let (($x41 (or $x38 $x11)))
+(let (($x44 (not $x41)))
+(let ((@x55 (monotonicity (rewrite (= $x38 (>= |x$| 1))) (rewrite (= $x11 (not (>= |x$| 1)))) (= $x41 (or (>= |x$| 1) (not (>= |x$| 1)))))))
+(let ((@x59 (trans @x55 (rewrite (= (or (>= |x$| 1) (not (>= |x$| 1))) true)) (= $x41 true))))
+(let ((@x66 (trans (monotonicity @x59 (= $x44 (not true))) (rewrite (= (not true) false)) (= $x44 false))))
+(let ((@x40 (monotonicity (rewrite (= (+ |x$| 3) ?x35)) (= (<= 4 (+ |x$| 3)) $x38))))
+(let ((@x46 (monotonicity (monotonicity @x40 (= (or (<= 4 (+ |x$| 3)) $x11) $x41)) (= (not (or (<= 4 (+ |x$| 3)) $x11)) $x44))))
+(let ((@x68 (trans @x46 @x66 (= (not (or (<= 4 (+ |x$| 3)) $x11)) false))))
+(mp (asserted (not (or (<= 4 (+ |x$| 3)) $x11))) @x68 false))))))))))))))
+
+3da41aa632fdaf484d160ab8b5a2c83b931d3de7 18 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x52 (= (+ |x$| (* (~ 1) |y$|)) (~ 4))))
+(let ((@x46 (monotonicity (rewrite (= (+ |x$| 4) (+ 4 |x$|))) (= (= |y$| (+ |x$| 4)) (= |y$| (+ 4 |x$|))))))
+(let ((@x55 (trans @x46 (rewrite (= (= |y$| (+ 4 |x$|)) $x52)) (= (= |y$| (+ |x$| 4)) $x52))))
+(let ((@x84 (monotonicity (mp (asserted (= |y$| (+ |x$| 4))) @x55 $x52) (= (>= (+ |x$| (* (~ 1) |y$|)) 0) (>= (~ 4) 0)))))
+(let ((@x88 (trans @x84 (rewrite (= (>= (~ 4) 0) false)) (= (>= (+ |x$| (* (~ 1) |y$|)) 0) false))))
+(let (($x68 (>= (+ |x$| (* (~ 1) |y$|)) 0)))
+(let ((@x74 (monotonicity (rewrite (= (< 0 (+ (* (~ 1) |x$|) |y$|)) (not $x68))) (= (not (< 0 (+ (* (~ 1) |x$|) |y$|))) (not (not $x68))))))
+(let ((@x78 (trans @x74 (rewrite (= (not (not $x68)) $x68)) (= (not (< 0 (+ (* (~ 1) |x$|) |y$|))) $x68))))
+(let (($x62 (< 0 (+ (* (~ 1) |x$|) |y$|))))
+(let (($x65 (not $x62)))
+(let (($x15 (not (< 0 (- |y$| |x$|)))))
+(let ((@x64 (monotonicity (rewrite (= (- |y$| |x$|) (+ (* (~ 1) |x$|) |y$|))) (= (< 0 (- |y$| |x$|)) $x62))))
+(let ((@x81 (mp (asserted $x15) (trans (monotonicity @x64 (= $x15 $x65)) @x78 (= $x15 $x68)) $x68)))
+(mp @x81 @x88 false))))))))))))))))
+
+e43b05132d28d45640c9d0131930806093dbb0e2 11 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((@x37 (monotonicity (rewrite (= (+ 2 2) 4)) (= (= (+ 2 2) 5) (= 4 5)))))
+(let ((@x41 (trans @x37 (rewrite (= (= 4 5) false)) (= (= (+ 2 2) 5) false))))
+(let ((@x44 (monotonicity @x41 (= (not (= (+ 2 2) 5)) (not false)))))
+(let ((@x48 (trans @x44 (rewrite (= (not false) true)) (= (not (= (+ 2 2) 5)) true))))
+(let ((@x51 (monotonicity @x48 (= (not (not (= (+ 2 2) 5))) (not true)))))
+(let ((@x55 (trans @x51 (rewrite (= (not true) false)) (= (not (not (= (+ 2 2) 5))) false))))
+(mp (asserted (not (not (= (+ 2 2) 5)))) @x55 false)))))))))
+
+135df42816691c806246099ddf6fc7f6b81a2f42 19 0
+unsat
+((set-logic AUFLIRA)
+(proof
+(let ((?x10 (* 7.0 |a$|)))
+(let ((?x7 (* 3.0 |x$|)))
+(let ((?x11 (+ ?x7 ?x10)))
+(let (($x46 (>= ?x11 4.0)))
+(let (($x44 (not $x46)))
+(let ((@x43 (mp (asserted (< ?x11 4.0)) (rewrite (= (< ?x11 4.0) $x44)) $x44)))
+(let ((?x15 (* 2.0 |x$|)))
+(let (($x48 (<= ?x15 3.0)))
+(let (($x49 (not $x48)))
+(let ((@x52 (mp (asserted (< 3.0 ?x15)) (rewrite (= (< 3.0 ?x15) $x49)) $x49)))
+(let (($x56 (>= |a$| 0.0)))
+(let ((@x60 (monotonicity (rewrite (= (< |a$| 0.0) (not $x56))) (= (not (< |a$| 0.0)) (not (not $x56))))))
+(let ((@x64 (trans @x60 (rewrite (= (not (not $x56)) $x56)) (= (not (< |a$| 0.0)) $x56))))
+(let ((@x65 (mp (asserted (not (< |a$| 0.0))) @x64 $x56)))
+((_ |th-lemma| arith farkas 7 3/2 1) @x65 @x52 @x43 false)))))))))))))))))
+
+de926642fcc1657dfaa079f1656df9cc74f3caaf 22 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x17 (not false)))
+(let (($x13 (<= 0 |x$|)))
+(let (($x14 (not $x13)))
+(let (($x15 (or $x14 $x13)))
+(let ((?x8 (- 1)))
+(let ((?x10 (* ?x8 |x$|)))
+(let ((?x11 (+ |y$| ?x10)))
+(let (($x12 (<= 0 ?x11)))
+(let (($x16 (or $x12 $x15)))
+(let (($x18 (= $x16 $x17)))
+(let (($x19 (not $x18)))
+(let ((@x58 (rewrite (= (or (<= 0 (+ |y$| (* (~ 1) |x$|))) true) true))))
+(let ((@x48 (monotonicity (monotonicity (rewrite (= ?x8 (~ 1))) (= ?x10 (* (~ 1) |x$|))) (= ?x11 (+ |y$| (* (~ 1) |x$|))))))
+(let ((@x56 (monotonicity (monotonicity @x48 (= $x12 (<= 0 (+ |y$| (* (~ 1) |x$|))))) (rewrite (= $x15 true)) (= $x16 (or (<= 0 (+ |y$| (* (~ 1) |x$|))) true)))))
+(let ((@x65 (monotonicity (trans @x56 @x58 (= $x16 true)) (rewrite (= $x17 true)) (= $x18 (= true true)))))
+(let ((@x69 (trans @x65 (rewrite (= (= true true) true)) (= $x18 true))))
+(let ((@x76 (trans (monotonicity @x69 (= $x19 (not true))) (rewrite (= (not true) false)) (= $x19 false))))
+(mp (asserted $x19) @x76 false))))))))))))))))))))
+
+c19a59241b121ac2665c4fbd7ba1fa2d48fef984 159 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x22 (= |m$| |n$|)))
+(let ((@x478 (symm (commutativity (= $x22 (= |n$| |m$|))) (= (= |n$| |m$|) $x22))))
+(let (($x18 (= |n$| |m$|)))
+(let ((?x100 (* (~ 1) |m$|)))
+(let ((?x101 (+ |n$| ?x100)))
+(let (($x116 (>= ?x101 0)))
+(let ((?x76 (* (~ 1) |n$a|)))
+(let ((?x94 (+ |m$| ?x76)))
+(let (($x125 (<= ?x94 0)))
+(let ((?x77 (+ |n$| ?x76)))
+(let (($x86 (>= ?x77 0)))
+(let (($x259 (or $x86 $x125)))
+(let ((@x265 (monotonicity (rewrite (= (and (not $x86) (not $x125)) (not $x259))) (= (not (and (not $x86) (not $x125))) (not (not $x259))))))
+(let ((@x269 (trans @x265 (rewrite (= (not (not $x259)) $x259)) (= (not (and (not $x86) (not $x125))) $x259))))
+(let (($x126 (not $x125)))
+(let (($x85 (not $x86)))
+(let (($x141 (and $x85 $x126)))
+(let (($x208 (not $x141)))
+(let (($x28 (= |n$a| |m$|)))
+(let (($x35 (and $x28 $x22)))
+(let (($x78 (<= ?x77 0)))
+(let (($x79 (not $x78)))
+(let (($x11 (= |m$| |n$a|)))
+(let (($x82 (and $x11 $x79)))
+(let (($x89 (and $x22 $x85)))
+(let (($x93 (>= ?x94 0)))
+(let (($x92 (not $x93)))
+(let (($x97 (and $x92 $x79)))
+(let (($x26 (= |n$a| |n$|)))
+(let (($x102 (<= ?x101 0)))
+(let (($x103 (not $x102)))
+(let (($x106 (and $x103 $x26)))
+(let (($x109 (and $x103 $x85)))
+(let (($x112 (and $x28 $x103)))
+(let (($x115 (not $x116)))
+(let (($x119 (and $x26 $x115)))
+(let (($x122 (and $x79 $x115)))
+(let (($x129 (and $x126 $x22)))
+(let (($x132 (and $x126 $x103)))
+(let (($x135 (and $x18 $x92)))
+(let (($x16 (= |n$| |n$a|)))
+(let (($x138 (and $x16 $x126)))
+(let (($x144 (and $x115 $x11)))
+(let (($x147 (and $x115 $x92)))
+(let (($x195 (or $x147 $x144 $x141 $x138 $x135 $x132 $x129 $x122 $x119 $x112 $x109 $x106 $x97 $x89 $x82 $x35)))
+(let (($x38 (or (and (< |m$| |n$a|) (< |n$a| |n$|)) (or (and $x22 (< |n$| |n$a|)) (or (and $x11 (< |n$a| |n$|)) $x35)))))
+(let (($x40 (or (and (< |m$| |n$|) (< |n$| |n$a|)) (or (and (< |m$| |n$|) $x26) $x38))))
+(let (($x43 (or (and (< |n$a| |n$|) (< |n$| |m$|)) (or (and $x26 (< |n$| |m$|)) (or (and $x28 (< |m$| |n$|)) $x40)))))
+(let (($x45 (or (and (< |n$a| |m$|) (< |m$| |n$|)) (or (and (< |n$a| |m$|) $x22) $x43))))
+(let (($x48 (or (and (< |n$| |n$a|) (< |n$a| |m$|)) (or (and $x16 (< |n$a| |m$|)) (or (and $x18 (< |m$| |n$a|)) $x45)))))
+(let (($x50 (or (and (< |n$| |m$|) (< |m$| |n$a|)) (or (and (< |n$| |m$|) $x11) $x48))))
+(let (($x51 (not $x50)))
+(let (($x168 (or $x119 (or $x112 (or $x109 (or $x106 (or $x97 (or $x89 (or $x82 $x35)))))))))
+(let (($x189 (or $x144 (or $x141 (or $x138 (or $x135 (or $x132 (or $x129 (or $x122 $x168)))))))))
+(let (($x187 (= $x48 (or $x141 (or $x138 (or $x135 (or $x132 (or $x129 (or $x122 $x168)))))))))
+(let (($x184 (= (or (and $x16 (< |n$a| |m$|)) (or (and $x18 (< |m$| |n$a|)) $x45)) (or $x138 (or $x135 (or $x132 (or $x129 (or $x122 $x168))))))))
+(let (($x181 (= (or (and $x18 (< |m$| |n$a|)) $x45) (or $x135 (or $x132 (or $x129 (or $x122 $x168)))))))
+(let (($x169 (= (or (and $x26 (< |n$| |m$|)) (or (and $x28 (< |m$| |n$|)) $x40)) $x168)))
+(let (($x166 (= (or (and $x28 (< |m$| |n$|)) $x40) (or $x112 (or $x109 (or $x106 (or $x97 (or $x89 (or $x82 $x35)))))))))
+(let (($x160 (= (or (and (< |m$| |n$|) $x26) $x38) (or $x106 (or $x97 (or $x89 (or $x82 $x35)))))))
+(let (($x154 (= (or (and $x22 (< |n$| |n$a|)) (or (and $x11 (< |n$a| |n$|)) $x35)) (or $x89 (or $x82 $x35)))))
+(let ((@x81 (rewrite (= (< |n$a| |n$|) $x79))))
+(let ((@x152 (monotonicity (monotonicity @x81 (= (and $x11 (< |n$a| |n$|)) $x82)) (= (or (and $x11 (< |n$a| |n$|)) $x35) (or $x82 $x35)))))
+(let ((@x88 (rewrite (= (< |n$| |n$a|) $x85))))
+(let ((@x155 (monotonicity (monotonicity @x88 (= (and $x22 (< |n$| |n$a|)) $x89)) @x152 $x154)))
+(let ((@x96 (rewrite (= (< |m$| |n$a|) $x92))))
+(let ((@x99 (monotonicity @x96 @x81 (= (and (< |m$| |n$a|) (< |n$a| |n$|)) $x97))))
+(let ((@x158 (monotonicity @x99 @x155 (= $x38 (or $x97 (or $x89 (or $x82 $x35)))))))
+(let ((@x105 (rewrite (= (< |m$| |n$|) $x103))))
+(let ((@x161 (monotonicity (monotonicity @x105 (= (and (< |m$| |n$|) $x26) $x106)) @x158 $x160)))
+(let ((@x111 (monotonicity @x105 @x88 (= (and (< |m$| |n$|) (< |n$| |n$a|)) $x109))))
+(let ((@x164 (monotonicity @x111 @x161 (= $x40 (or $x109 (or $x106 (or $x97 (or $x89 (or $x82 $x35)))))))))
+(let ((@x167 (monotonicity (monotonicity @x105 (= (and $x28 (< |m$| |n$|)) $x112)) @x164 $x166)))
+(let ((@x118 (rewrite (= (< |n$| |m$|) $x115))))
+(let ((@x170 (monotonicity (monotonicity @x118 (= (and $x26 (< |n$| |m$|)) $x119)) @x167 $x169)))
+(let ((@x124 (monotonicity @x81 @x118 (= (and (< |n$a| |n$|) (< |n$| |m$|)) $x122))))
+(let ((@x128 (rewrite (= (< |n$a| |m$|) $x126))))
+(let ((@x176 (monotonicity (monotonicity @x128 (= (and (< |n$a| |m$|) $x22) $x129)) (monotonicity @x124 @x170 (= $x43 (or $x122 $x168))) (= (or (and (< |n$a| |m$|) $x22) $x43) (or $x129 (or $x122 $x168))))))
+(let ((@x134 (monotonicity @x128 @x105 (= (and (< |n$a| |m$|) (< |m$| |n$|)) $x132))))
+(let ((@x179 (monotonicity @x134 @x176 (= $x45 (or $x132 (or $x129 (or $x122 $x168)))))))
+(let ((@x182 (monotonicity (monotonicity @x96 (= (and $x18 (< |m$| |n$a|)) $x135)) @x179 $x181)))
+(let ((@x185 (monotonicity (monotonicity @x128 (= (and $x16 (< |n$a| |m$|)) $x138)) @x182 $x184)))
+(let ((@x143 (monotonicity @x88 @x128 (= (and (< |n$| |n$a|) (< |n$a| |m$|)) $x141))))
+(let ((@x191 (monotonicity (monotonicity @x118 (= (and (< |n$| |m$|) $x11) $x144)) (monotonicity @x143 @x185 $x187) (= (or (and (< |n$| |m$|) $x11) $x48) $x189))))
+(let ((@x149 (monotonicity @x118 @x96 (= (and (< |n$| |m$|) (< |m$| |n$a|)) $x147))))
+(let ((@x199 (trans (monotonicity @x149 @x191 (= $x50 (or $x147 $x189))) (rewrite (= (or $x147 $x189) $x195)) (= $x50 $x195))))
+(let ((@x203 (mp (asserted $x51) (monotonicity @x199 (= $x51 (not $x195))) (not $x195))))
+(let ((@x270 (mp (|not-or-elim| @x203 $x208) @x269 $x259)))
+(let (($x271 (not $x16)))
+(let (($x272 (or $x271 $x125)))
+(let ((@x278 (monotonicity (rewrite (= $x138 (not $x272))) (= (not $x138) (not (not $x272))))))
+(let ((@x282 (trans @x278 (rewrite (= (not (not $x272)) $x272)) (= (not $x138) $x272))))
+(let ((@x283 (mp (|not-or-elim| @x203 (not $x138)) @x282 $x272)))
+(let (($x284 (not $x18)))
+(let (($x309 (not $x22)))
+(let ((@x432 (hypothesis $x79)))
+(let (($x384 (or $x93 $x78)))
+(let ((@x390 (monotonicity (rewrite (= $x97 (not $x384))) (= (not $x97) (not (not $x384))))))
+(let ((@x394 (trans @x390 (rewrite (= (not (not $x384)) $x384)) (= (not $x97) $x384))))
+(let ((@x395 (mp (|not-or-elim| @x203 (not $x97)) @x394 $x384)))
+(let (($x246 (not $x11)))
+(let (($x408 (or $x246 $x78)))
+(let ((@x414 (monotonicity (rewrite (= $x82 (not $x408))) (= (not $x82) (not (not $x408))))))
+(let ((@x418 (trans @x414 (rewrite (= (not (not $x408)) $x408)) (= (not $x82) $x408))))
+(let ((@x419 (mp (|not-or-elim| @x203 (not $x82)) @x418 $x408)))
+(let ((@x437 ((_ |th-lemma| arith triangle-eq) (or $x11 $x126 $x92))))
+(let ((@x438 (|unit-resolution| @x437 (|unit-resolution| @x419 @x432 $x246) (|unit-resolution| @x395 @x432 $x93) $x126)))
+(let (($x310 (or $x125 $x309)))
+(let ((@x316 (monotonicity (rewrite (= $x129 (not $x310))) (= (not $x129) (not (not $x310))))))
+(let ((@x320 (trans @x316 (rewrite (= (not (not $x310)) $x310)) (= (not $x129) $x310))))
+(let ((@x321 (mp (|not-or-elim| @x203 (not $x129)) @x320 $x310)))
+(let ((@x448 (mp (|unit-resolution| @x321 @x438 $x309) (monotonicity (commutativity (= $x22 $x18)) (= $x309 $x284)) $x284)))
+(let (($x322 (or $x78 $x116)))
+(let ((@x328 (monotonicity (rewrite (= $x122 (not $x322))) (= (not $x122) (not (not $x322))))))
+(let ((@x332 (trans @x328 (rewrite (= (not (not $x322)) $x322)) (= (not $x122) $x322))))
+(let ((@x333 (mp (|not-or-elim| @x203 (not $x122)) @x332 $x322)))
+(let (($x297 (or $x125 $x102)))
+(let ((@x303 (monotonicity (rewrite (= $x132 (not $x297))) (= (not $x132) (not (not $x297))))))
+(let ((@x307 (trans @x303 (rewrite (= (not (not $x297)) $x297)) (= (not $x132) $x297))))
+(let ((@x308 (mp (|not-or-elim| @x203 (not $x132)) @x307 $x297)))
+(let ((@x442 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x18 $x103 $x115)) (|unit-resolution| @x308 @x438 $x102) (|unit-resolution| @x333 @x432 $x116) $x18)))
+(let ((@x457 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x16 $x79 $x85)) (lemma (|unit-resolution| @x442 @x448 false) $x78) (or $x16 $x85))))
+(let ((@x458 (|unit-resolution| @x457 (|unit-resolution| @x283 (hypothesis $x126) $x271) (|unit-resolution| @x270 (hypothesis $x126) $x86) false)))
+(let ((@x459 (lemma @x458 $x125)))
+(let (($x73 (or $x116 $x93)))
+(let ((@x240 (monotonicity (rewrite (= $x147 (not $x73))) (= (not $x147) (not (not $x73))))))
+(let ((@x244 (trans @x240 (rewrite (= (not (not $x73)) $x73)) (= (not $x147) $x73))))
+(let ((@x245 (mp (|not-or-elim| @x203 (not $x147)) @x244 $x73)))
+(let (($x247 (or $x116 $x246)))
+(let ((@x253 (monotonicity (rewrite (= $x144 (not $x247))) (= (not $x144) (not (not $x247))))))
+(let ((@x257 (trans @x253 (rewrite (= (not (not $x247)) $x247)) (= (not $x144) $x247))))
+(let ((@x258 (mp (|not-or-elim| @x203 (not $x144)) @x257 $x247)))
+(let ((@x463 (|unit-resolution| @x437 (|unit-resolution| @x258 (hypothesis $x115) $x246) (|unit-resolution| @x245 (hypothesis $x115) $x93) @x459 false)))
+(let (($x334 (not $x26)))
+(let (($x372 (or $x102 $x334)))
+(let ((@x378 (monotonicity (rewrite (= $x106 (not $x372))) (= (not $x106) (not (not $x372))))))
+(let ((@x382 (trans @x378 (rewrite (= (not (not $x372)) $x372)) (= (not $x106) $x372))))
+(let ((@x383 (mp (|not-or-elim| @x203 (not $x106)) @x382 $x372)))
+(let ((@x473 (mp (|unit-resolution| @x383 (hypothesis $x103) $x334) (monotonicity (commutativity (= $x26 $x16)) (= $x334 $x271)) $x271)))
+(let (($x360 (or $x102 $x86)))
+(let ((@x366 (monotonicity (rewrite (= $x109 (not $x360))) (= (not $x109) (not (not $x360))))))
+(let ((@x370 (trans @x366 (rewrite (= (not (not $x360)) $x360)) (= (not $x109) $x360))))
+(let ((@x371 (mp (|not-or-elim| @x203 (not $x109)) @x370 $x360)))
+(let ((@x467 (|unit-resolution| @x457 (|unit-resolution| @x371 (hypothesis $x103) $x86) $x16)))
+(let ((@x476 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x18 $x103 $x115)) (lemma (|unit-resolution| @x467 @x473 false) $x102) (lemma @x463 $x116) $x18)))
+(let (($x285 (or $x284 $x93)))
+(let ((@x291 (monotonicity (rewrite (= $x135 (not $x285))) (= (not $x135) (not (not $x285))))))
+(let ((@x295 (trans @x291 (rewrite (= (not (not $x285)) $x285)) (= (not $x135) $x285))))
+(let ((@x296 (mp (|not-or-elim| @x203 (not $x135)) @x295 $x285)))
+(let ((@x486 (mp (|unit-resolution| @x437 (|unit-resolution| @x296 @x476 $x93) @x459 $x11) (symm (commutativity (= $x28 $x11)) (= $x11 $x28)) $x28)))
+(let (($x420 (or (not $x28) $x309)))
+(let ((@x426 (monotonicity (rewrite (= $x35 (not $x420))) (= (not $x35) (not (not $x420))))))
+(let ((@x430 (trans @x426 (rewrite (= (not (not $x420)) $x420)) (= (not $x35) $x420))))
+(let ((@x431 (mp (|not-or-elim| @x203 (not $x35)) @x430 $x420)))
+(|unit-resolution| @x431 @x486 (mp @x476 @x478 $x22) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+ad69b5703e25623b7fccdbcfa3db5949b2899f42 927 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x131 (* (~ 1) |x4$|)))
+(let (($x436 (>= |x4$| 0)))
+(let ((?x443 (ite $x436 |x4$| ?x131)))
+(let ((?x454 (* (~ 1) ?x443)))
+(let ((?x675 (+ |x4$| ?x454)))
+(let (($x676 (<= ?x675 0)))
+(let (($x782 (not $x676)))
+(let ((?x672 (+ ?x131 ?x454)))
+(let (($x673 (<= ?x672 0)))
+(let (($x743 (not $x673)))
+(let ((?x653 (* (~ 1) |x11$|)))
+(let ((?x654 (+ |x2$| ?x653)))
+(let (($x656 (>= ?x654 0)))
+(let (($x708 (not $x656)))
+(let (($x71 (= |x2$| |x11$|)))
+(let ((@x1263 (hypothesis $x656)))
+(let (($x655 (<= ?x654 0)))
+(let ((?x165 (* (~ 1) |x6$|)))
+(let (($x386 (>= |x6$| 0)))
+(let ((?x393 (ite $x386 |x6$| ?x165)))
+(let ((?x404 (* (~ 1) ?x393)))
+(let ((?x669 (+ |x6$| ?x404)))
+(let (($x934 (<= ?x669 0)))
+(let (($x610 (= |x6$| ?x393)))
+(let (($x411 (>= |x5$| 0)))
+(let (($x286 (>= |x9$| 0)))
+(let (($x671 (>= ?x669 0)))
+(let (($x287 (not $x286)))
+(let ((@x1426 (hypothesis $x287)))
+(let ((?x233 (* (~ 1) |x10$|)))
+(let (($x311 (>= |x10$| 0)))
+(let ((?x318 (ite $x311 |x10$| ?x233)))
+(let ((?x329 (* (~ 1) ?x318)))
+(let ((?x660 (+ |x10$| ?x329)))
+(let (($x1369 (<= ?x660 0)))
+(let (($x642 (= |x10$| ?x318)))
+(let (($x643 (= ?x233 ?x318)))
+(let (($x1119 (not $x643)))
+(let ((?x1101 (+ ?x233 ?x329)))
+(let (($x1247 (<= ?x1101 0)))
+(let (($x1259 (not $x1247)))
+(let ((?x216 (* (~ 1) |x9$|)))
+(let ((?x293 (ite $x286 |x9$| ?x216)))
+(let ((?x304 (* (~ 1) ?x293)))
+(let ((?x1498 (+ ?x216 ?x304)))
+(let (($x1543 (>= ?x1498 0)))
+(let (($x635 (= ?x216 ?x293)))
+(let ((@x639 (|def-axiom| (or $x286 $x635))))
+(let ((@x1553 (|unit-resolution| @x639 @x1426 $x635)))
+(let ((@x1572 ((_ |th-lemma| arith triangle-eq) (or (not $x635) $x1543))))
+(let ((@x1573 (|unit-resolution| @x1572 @x1553 $x1543)))
+(let ((?x182 (* (~ 1) |x7$|)))
+(let (($x361 (>= |x7$| 0)))
+(let ((?x368 (ite $x361 |x7$| ?x182)))
+(let ((?x379 (* (~ 1) ?x368)))
+(let ((?x666 (+ |x7$| ?x379)))
+(let (($x838 (<= ?x666 0)))
+(let (($x618 (= |x7$| ?x368)))
+(let (($x412 (not $x411)))
+(let ((@x842 (hypothesis $x412)))
+(let ((?x775 (+ ?x165 ?x404)))
+(let (($x778 (<= ?x775 0)))
+(let (($x611 (= ?x165 ?x393)))
+(let (($x387 (not $x386)))
+(let (($x362 (not $x361)))
+(let ((@x1025 (hypothesis $x362)))
+(let ((@x1024 (hypothesis $x386)))
+(let ((?x405 (+ |x5$| |x7$| ?x404)))
+(let (($x617 (>= ?x405 0)))
+(let (($x406 (= ?x405 0)))
+(let ((?x330 (+ |x9$| |x11$| ?x329)))
+(let (($x331 (= ?x330 0)))
+(let ((?x305 (+ |x8$| |x10$| ?x304)))
+(let (($x306 (= ?x305 0)))
+(let ((?x199 (* (~ 1) |x8$|)))
+(let (($x336 (>= |x8$| 0)))
+(let ((?x343 (ite $x336 |x8$| ?x199)))
+(let ((?x354 (* (~ 1) ?x343)))
+(let ((?x355 (+ |x7$| |x9$| ?x354)))
+(let (($x356 (= ?x355 0)))
+(let ((?x380 (+ |x6$| |x8$| ?x379)))
+(let (($x381 (= ?x380 0)))
+(let ((?x148 (* (~ 1) |x5$|)))
+(let ((?x418 (ite $x411 |x5$| ?x148)))
+(let ((?x429 (* (~ 1) ?x418)))
+(let ((?x430 (+ |x4$| |x6$| ?x429)))
+(let (($x431 (= ?x430 0)))
+(let ((?x455 (+ |x3$| |x5$| ?x454)))
+(let (($x456 (= ?x455 0)))
+(let ((?x114 (* (~ 1) |x3$|)))
+(let (($x461 (>= |x3$| 0)))
+(let ((?x468 (ite $x461 |x3$| ?x114)))
+(let ((?x479 (* (~ 1) ?x468)))
+(let ((?x480 (+ |x2$| |x4$| ?x479)))
+(let (($x481 (= ?x480 0)))
+(let ((?x96 (* (~ 1) |x2$|)))
+(let (($x486 (>= |x2$| 0)))
+(let ((?x493 (ite $x486 |x2$| ?x96)))
+(let ((?x504 (* (~ 1) ?x493)))
+(let ((?x505 (+ |x3$| |x1$| ?x504)))
+(let (($x506 (= ?x505 0)))
+(let (($x535 (and $x506 $x481 $x456 $x431 $x406 $x381 $x356 $x306 $x331)))
+(let (($x546 (not (or (not $x535) (and (= |x1$| |x10$|) $x71)))))
+(let (($x70 (= |x1$| |x10$|)))
+(let (($x72 (and $x70 $x71)))
+(let (($x62 (and (= |x10$| (- (ite (< |x9$| 0) (- |x9$|) |x9$|) |x8$|)) (= |x11$| (- (ite (< |x10$| 0) (- |x10$|) |x10$|) |x9$|)))))
+(let (($x64 (and (= |x8$| (- (ite (< |x7$| 0) (- |x7$|) |x7$|) |x6$|)) (and (= |x9$| (- (ite (< |x8$| 0) (- |x8$|) |x8$|) |x7$|)) $x62))))
+(let (($x66 (and (= |x6$| (- (ite (< |x5$| 0) (- |x5$|) |x5$|) |x4$|)) (and (= |x7$| (- (ite (< |x6$| 0) (- |x6$|) |x6$|) |x5$|)) $x64))))
+(let (($x68 (and (= |x4$| (- (ite (< |x3$| 0) (- |x3$|) |x3$|) |x2$|)) (and (= |x5$| (- (ite (< |x4$| 0) (- |x4$|) |x4$|) |x3$|)) $x66))))
+(let (($x73 (=> (and (= |x3$| (- (ite (< |x2$| 0) (- |x2$|) |x2$|) |x1$|)) $x68) $x72)))
+(let (($x74 (not $x73)))
+(let (($x57 (< |x10$| 0)))
+(let ((?x236 (ite $x57 ?x233 |x10$|)))
+(let ((?x242 (+ ?x216 ?x236)))
+(let (($x247 (= |x11$| ?x242)))
+(let (($x51 (< |x9$| 0)))
+(let ((?x219 (ite $x51 ?x216 |x9$|)))
+(let ((?x225 (+ ?x199 ?x219)))
+(let (($x230 (= |x10$| ?x225)))
+(let (($x250 (and $x230 $x247)))
+(let (($x45 (< |x8$| 0)))
+(let ((?x202 (ite $x45 ?x199 |x8$|)))
+(let ((?x208 (+ ?x182 ?x202)))
+(let (($x213 (= |x9$| ?x208)))
+(let (($x253 (and $x213 $x250)))
+(let (($x39 (< |x7$| 0)))
+(let ((?x185 (ite $x39 ?x182 |x7$|)))
+(let ((?x191 (+ ?x165 ?x185)))
+(let (($x196 (= |x8$| ?x191)))
+(let (($x256 (and $x196 $x253)))
+(let (($x33 (< |x6$| 0)))
+(let ((?x168 (ite $x33 ?x165 |x6$|)))
+(let ((?x174 (+ ?x148 ?x168)))
+(let (($x179 (= |x7$| ?x174)))
+(let (($x259 (and $x179 $x256)))
+(let (($x27 (< |x5$| 0)))
+(let ((?x151 (ite $x27 ?x148 |x5$|)))
+(let ((?x157 (+ ?x131 ?x151)))
+(let (($x162 (= |x6$| ?x157)))
+(let (($x262 (and $x162 $x259)))
+(let (($x21 (< |x4$| 0)))
+(let ((?x134 (ite $x21 ?x131 |x4$|)))
+(let ((?x140 (+ ?x114 ?x134)))
+(let (($x145 (= |x5$| ?x140)))
+(let (($x265 (and $x145 $x262)))
+(let (($x15 (< |x3$| 0)))
+(let ((?x117 (ite $x15 ?x114 |x3$|)))
+(let ((?x123 (+ ?x96 ?x117)))
+(let (($x128 (= |x4$| ?x123)))
+(let (($x268 (and $x128 $x265)))
+(let (($x8 (< |x2$| 0)))
+(let ((?x99 (ite $x8 ?x96 |x2$|)))
+(let ((?x106 (+ (* (~ 1) |x1$|) ?x99)))
+(let (($x111 (= |x3$| ?x106)))
+(let (($x271 (and $x111 $x268)))
+(let (($x278 (or (not $x271) $x72)))
+(let (($x526 (and $x456 (and $x431 (and $x406 (and $x381 (and $x356 (and $x306 $x331))))))))
+(let (($x524 (= $x262 (and $x431 (and $x406 (and $x381 (and $x356 (and $x306 $x331))))))))
+(let ((@x317 (monotonicity (rewrite (= $x57 (not $x311))) (= ?x236 (ite (not $x311) ?x233 |x10$|)))))
+(let ((@x322 (trans @x317 (rewrite (= (ite (not $x311) ?x233 |x10$|) ?x318)) (= ?x236 ?x318))))
+(let ((@x328 (monotonicity (monotonicity @x322 (= ?x242 (+ ?x216 ?x318))) (= $x247 (= |x11$| (+ ?x216 ?x318))))))
+(let ((@x335 (trans @x328 (rewrite (= (= |x11$| (+ ?x216 ?x318)) $x331)) (= $x247 $x331))))
+(let ((@x292 (monotonicity (rewrite (= $x51 $x287)) (= ?x219 (ite $x287 ?x216 |x9$|)))))
+(let ((@x300 (monotonicity (trans @x292 (rewrite (= (ite $x287 ?x216 |x9$|) ?x293)) (= ?x219 ?x293)) (= ?x225 (+ ?x199 ?x293)))))
+(let ((@x310 (trans (monotonicity @x300 (= $x230 (= |x10$| (+ ?x199 ?x293)))) (rewrite (= (= |x10$| (+ ?x199 ?x293)) $x306)) (= $x230 $x306))))
+(let ((@x342 (monotonicity (rewrite (= $x45 (not $x336))) (= ?x202 (ite (not $x336) ?x199 |x8$|)))))
+(let ((@x347 (trans @x342 (rewrite (= (ite (not $x336) ?x199 |x8$|) ?x343)) (= ?x202 ?x343))))
+(let ((@x353 (monotonicity (monotonicity @x347 (= ?x208 (+ ?x182 ?x343))) (= $x213 (= |x9$| (+ ?x182 ?x343))))))
+(let ((@x360 (trans @x353 (rewrite (= (= |x9$| (+ ?x182 ?x343)) $x356)) (= $x213 $x356))))
+(let ((@x516 (monotonicity @x360 (monotonicity @x310 @x335 (= $x250 (and $x306 $x331))) (= $x253 (and $x356 (and $x306 $x331))))))
+(let ((@x367 (monotonicity (rewrite (= $x39 $x362)) (= ?x185 (ite $x362 ?x182 |x7$|)))))
+(let ((@x375 (monotonicity (trans @x367 (rewrite (= (ite $x362 ?x182 |x7$|) ?x368)) (= ?x185 ?x368)) (= ?x191 (+ ?x165 ?x368)))))
+(let ((@x385 (trans (monotonicity @x375 (= $x196 (= |x8$| (+ ?x165 ?x368)))) (rewrite (= (= |x8$| (+ ?x165 ?x368)) $x381)) (= $x196 $x381))))
+(let ((@x519 (monotonicity @x385 @x516 (= $x256 (and $x381 (and $x356 (and $x306 $x331)))))))
+(let ((@x392 (monotonicity (rewrite (= $x33 $x387)) (= ?x168 (ite $x387 ?x165 |x6$|)))))
+(let ((@x400 (monotonicity (trans @x392 (rewrite (= (ite $x387 ?x165 |x6$|) ?x393)) (= ?x168 ?x393)) (= ?x174 (+ ?x148 ?x393)))))
+(let ((@x410 (trans (monotonicity @x400 (= $x179 (= |x7$| (+ ?x148 ?x393)))) (rewrite (= (= |x7$| (+ ?x148 ?x393)) $x406)) (= $x179 $x406))))
+(let ((@x522 (monotonicity @x410 @x519 (= $x259 (and $x406 (and $x381 (and $x356 (and $x306 $x331))))))))
+(let ((@x417 (monotonicity (rewrite (= $x27 $x412)) (= ?x151 (ite $x412 ?x148 |x5$|)))))
+(let ((@x425 (monotonicity (trans @x417 (rewrite (= (ite $x412 ?x148 |x5$|) ?x418)) (= ?x151 ?x418)) (= ?x157 (+ ?x131 ?x418)))))
+(let ((@x435 (trans (monotonicity @x425 (= $x162 (= |x6$| (+ ?x131 ?x418)))) (rewrite (= (= |x6$| (+ ?x131 ?x418)) $x431)) (= $x162 $x431))))
+(let ((@x442 (monotonicity (rewrite (= $x21 (not $x436))) (= ?x134 (ite (not $x436) ?x131 |x4$|)))))
+(let ((@x447 (trans @x442 (rewrite (= (ite (not $x436) ?x131 |x4$|) ?x443)) (= ?x134 ?x443))))
+(let ((@x453 (monotonicity (monotonicity @x447 (= ?x140 (+ ?x114 ?x443))) (= $x145 (= |x5$| (+ ?x114 ?x443))))))
+(let ((@x460 (trans @x453 (rewrite (= (= |x5$| (+ ?x114 ?x443)) $x456)) (= $x145 $x456))))
+(let ((@x467 (monotonicity (rewrite (= $x15 (not $x461))) (= ?x117 (ite (not $x461) ?x114 |x3$|)))))
+(let ((@x472 (trans @x467 (rewrite (= (ite (not $x461) ?x114 |x3$|) ?x468)) (= ?x117 ?x468))))
+(let ((@x478 (monotonicity (monotonicity @x472 (= ?x123 (+ ?x96 ?x468))) (= $x128 (= |x4$| (+ ?x96 ?x468))))))
+(let ((@x485 (trans @x478 (rewrite (= (= |x4$| (+ ?x96 ?x468)) $x481)) (= $x128 $x481))))
+(let ((@x531 (monotonicity @x485 (monotonicity @x460 (monotonicity @x435 @x522 $x524) (= $x265 $x526)) (= $x268 (and $x481 $x526)))))
+(let ((@x492 (monotonicity (rewrite (= $x8 (not $x486))) (= ?x99 (ite (not $x486) ?x96 |x2$|)))))
+(let ((@x497 (trans @x492 (rewrite (= (ite (not $x486) ?x96 |x2$|) ?x493)) (= ?x99 ?x493))))
+(let ((@x503 (monotonicity (monotonicity @x497 (= ?x106 (+ (* (~ 1) |x1$|) ?x493))) (= $x111 (= |x3$| (+ (* (~ 1) |x1$|) ?x493))))))
+(let ((@x510 (trans @x503 (rewrite (= (= |x3$| (+ (* (~ 1) |x1$|) ?x493)) $x506)) (= $x111 $x506))))
+(let ((@x539 (trans (monotonicity @x510 @x531 (= $x271 (and $x506 (and $x481 $x526)))) (rewrite (= (and $x506 (and $x481 $x526)) $x535)) (= $x271 $x535))))
+(let ((@x545 (monotonicity (monotonicity @x539 (= (not $x271) (not $x535))) (= $x278 (or (not $x535) $x72)))))
+(let ((@x238 (monotonicity (rewrite (= (- |x10$|) ?x233)) (= (ite $x57 (- |x10$|) |x10$|) ?x236))))
+(let ((@x241 (monotonicity @x238 (= (- (ite $x57 (- |x10$|) |x10$|) |x9$|) (- ?x236 |x9$|)))))
+(let ((@x246 (trans @x241 (rewrite (= (- ?x236 |x9$|) ?x242)) (= (- (ite $x57 (- |x10$|) |x10$|) |x9$|) ?x242))))
+(let ((@x249 (monotonicity @x246 (= (= |x11$| (- (ite $x57 (- |x10$|) |x10$|) |x9$|)) $x247))))
+(let ((@x221 (monotonicity (rewrite (= (- |x9$|) ?x216)) (= (ite $x51 (- |x9$|) |x9$|) ?x219))))
+(let ((@x224 (monotonicity @x221 (= (- (ite $x51 (- |x9$|) |x9$|) |x8$|) (- ?x219 |x8$|)))))
+(let ((@x229 (trans @x224 (rewrite (= (- ?x219 |x8$|) ?x225)) (= (- (ite $x51 (- |x9$|) |x9$|) |x8$|) ?x225))))
+(let ((@x232 (monotonicity @x229 (= (= |x10$| (- (ite $x51 (- |x9$|) |x9$|) |x8$|)) $x230))))
+(let ((@x204 (monotonicity (rewrite (= (- |x8$|) ?x199)) (= (ite $x45 (- |x8$|) |x8$|) ?x202))))
+(let ((@x207 (monotonicity @x204 (= (- (ite $x45 (- |x8$|) |x8$|) |x7$|) (- ?x202 |x7$|)))))
+(let ((@x212 (trans @x207 (rewrite (= (- ?x202 |x7$|) ?x208)) (= (- (ite $x45 (- |x8$|) |x8$|) |x7$|) ?x208))))
+(let ((@x215 (monotonicity @x212 (= (= |x9$| (- (ite $x45 (- |x8$|) |x8$|) |x7$|)) $x213))))
+(let ((@x255 (monotonicity @x215 (monotonicity @x232 @x249 (= $x62 $x250)) (= (and (= |x9$| (- (ite $x45 (- |x8$|) |x8$|) |x7$|)) $x62) $x253))))
+(let ((@x187 (monotonicity (rewrite (= (- |x7$|) ?x182)) (= (ite $x39 (- |x7$|) |x7$|) ?x185))))
+(let ((@x190 (monotonicity @x187 (= (- (ite $x39 (- |x7$|) |x7$|) |x6$|) (- ?x185 |x6$|)))))
+(let ((@x195 (trans @x190 (rewrite (= (- ?x185 |x6$|) ?x191)) (= (- (ite $x39 (- |x7$|) |x7$|) |x6$|) ?x191))))
+(let ((@x198 (monotonicity @x195 (= (= |x8$| (- (ite $x39 (- |x7$|) |x7$|) |x6$|)) $x196))))
+(let ((@x170 (monotonicity (rewrite (= (- |x6$|) ?x165)) (= (ite $x33 (- |x6$|) |x6$|) ?x168))))
+(let ((@x173 (monotonicity @x170 (= (- (ite $x33 (- |x6$|) |x6$|) |x5$|) (- ?x168 |x5$|)))))
+(let ((@x178 (trans @x173 (rewrite (= (- ?x168 |x5$|) ?x174)) (= (- (ite $x33 (- |x6$|) |x6$|) |x5$|) ?x174))))
+(let ((@x181 (monotonicity @x178 (= (= |x7$| (- (ite $x33 (- |x6$|) |x6$|) |x5$|)) $x179))))
+(let ((@x261 (monotonicity @x181 (monotonicity @x198 @x255 (= $x64 $x256)) (= (and (= |x7$| (- (ite $x33 (- |x6$|) |x6$|) |x5$|)) $x64) $x259))))
+(let ((@x153 (monotonicity (rewrite (= (- |x5$|) ?x148)) (= (ite $x27 (- |x5$|) |x5$|) ?x151))))
+(let ((@x156 (monotonicity @x153 (= (- (ite $x27 (- |x5$|) |x5$|) |x4$|) (- ?x151 |x4$|)))))
+(let ((@x161 (trans @x156 (rewrite (= (- ?x151 |x4$|) ?x157)) (= (- (ite $x27 (- |x5$|) |x5$|) |x4$|) ?x157))))
+(let ((@x164 (monotonicity @x161 (= (= |x6$| (- (ite $x27 (- |x5$|) |x5$|) |x4$|)) $x162))))
+(let ((@x136 (monotonicity (rewrite (= (- |x4$|) ?x131)) (= (ite $x21 (- |x4$|) |x4$|) ?x134))))
+(let ((@x139 (monotonicity @x136 (= (- (ite $x21 (- |x4$|) |x4$|) |x3$|) (- ?x134 |x3$|)))))
+(let ((@x144 (trans @x139 (rewrite (= (- ?x134 |x3$|) ?x140)) (= (- (ite $x21 (- |x4$|) |x4$|) |x3$|) ?x140))))
+(let ((@x147 (monotonicity @x144 (= (= |x5$| (- (ite $x21 (- |x4$|) |x4$|) |x3$|)) $x145))))
+(let ((@x267 (monotonicity @x147 (monotonicity @x164 @x261 (= $x66 $x262)) (= (and (= |x5$| (- (ite $x21 (- |x4$|) |x4$|) |x3$|)) $x66) $x265))))
+(let ((@x119 (monotonicity (rewrite (= (- |x3$|) ?x114)) (= (ite $x15 (- |x3$|) |x3$|) ?x117))))
+(let ((@x122 (monotonicity @x119 (= (- (ite $x15 (- |x3$|) |x3$|) |x2$|) (- ?x117 |x2$|)))))
+(let ((@x127 (trans @x122 (rewrite (= (- ?x117 |x2$|) ?x123)) (= (- (ite $x15 (- |x3$|) |x3$|) |x2$|) ?x123))))
+(let ((@x130 (monotonicity @x127 (= (= |x4$| (- (ite $x15 (- |x3$|) |x3$|) |x2$|)) $x128))))
+(let ((@x101 (monotonicity (rewrite (= (- |x2$|) ?x96)) (= (ite $x8 (- |x2$|) |x2$|) ?x99))))
+(let ((@x104 (monotonicity @x101 (= (- (ite $x8 (- |x2$|) |x2$|) |x1$|) (- ?x99 |x1$|)))))
+(let ((@x110 (trans @x104 (rewrite (= (- ?x99 |x1$|) ?x106)) (= (- (ite $x8 (- |x2$|) |x2$|) |x1$|) ?x106))))
+(let ((@x113 (monotonicity @x110 (= (= |x3$| (- (ite $x8 (- |x2$|) |x2$|) |x1$|)) $x111))))
+(let ((@x273 (monotonicity @x113 (monotonicity @x130 @x267 (= $x68 $x268)) (= (and (= |x3$| (- (ite $x8 (- |x2$|) |x2$|) |x1$|)) $x68) $x271))))
+(let ((@x282 (trans (monotonicity @x273 (= $x73 (=> $x271 $x72))) (rewrite (= (=> $x271 $x72) $x278)) (= $x73 $x278))))
+(let ((@x550 (trans (monotonicity @x282 (= $x74 (not $x278))) (monotonicity @x545 (= (not $x278) $x546)) (= $x74 $x546))))
+(let ((@x552 (|not-or-elim| (mp (asserted $x74) @x550 $x546) $x535)))
+(let ((@x557 (|and-elim| @x552 $x406)))
+(let ((@x851 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x406) $x617)) @x557 $x617)))
+(let ((@x948 ((_ |th-lemma| arith triangle-eq) (or (not $x610) $x934))))
+(let ((@x1027 (|unit-resolution| @x948 (|unit-resolution| (|def-axiom| (or $x387 $x610)) @x1024 $x610) $x934)))
+(let ((@x1030 (lemma ((_ |th-lemma| arith farkas 1 1 1 1 1) @x1027 @x851 @x1025 @x842 @x1024 false) (or $x361 $x411 $x387))))
+(let ((@x615 (|def-axiom| (or $x386 $x611))))
+(let ((@x1061 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x611) $x778)) (|unit-resolution| @x615 (|unit-resolution| @x1030 @x1025 @x842 $x387) $x611) $x778)))
+(let ((@x1062 ((_ |th-lemma| arith farkas 1 1 1 1 1) (|unit-resolution| @x1030 @x1025 @x842 $x387) @x1025 @x851 @x842 @x1061 false)))
+(let ((@x1064 (lemma @x1062 (or $x361 $x411))))
+(let ((@x621 (|def-axiom| (or $x362 $x618))))
+(let ((@x863 ((_ |th-lemma| arith triangle-eq) (or (not $x618) $x838))))
+(let ((@x1087 (|unit-resolution| @x863 (|unit-resolution| @x621 (|unit-resolution| @x1064 @x842 $x361) $x618) $x838)))
+(let ((?x663 (+ |x8$| ?x354)))
+(let (($x661 (<= ?x663 0)))
+(let (($x626 (= |x8$| ?x343)))
+(let (($x665 (>= ?x663 0)))
+(let ((@x1538 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x661 $x665)) (hypothesis (not $x661)) $x665)))
+(let (($x627 (= ?x199 ?x343)))
+(let (($x337 (not $x336)))
+(let ((@x1527 (hypothesis $x337)))
+(let ((@x631 (|def-axiom| (or $x336 $x627))))
+(let ((@x1528 (|unit-resolution| @x631 @x1527 $x627)))
+(let ((?x664 (+ ?x199 ?x354)))
+(let (($x873 (<= ?x664 0)))
+(let (($x1510 (not $x873)))
+(let ((@x856 (hypothesis $x665)))
+(let ((@x1516 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x627) $x873)) (hypothesis $x627) (hypothesis $x1510) false)))
+(let ((@x1517 (lemma @x1516 (or (not $x627) $x873))))
+(let ((@x1532 (|unit-resolution| @x1517 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1) (or (not $x665) $x336 $x1510)) @x1527 @x856 $x1510) @x1528 false)))
+(let ((@x629 (|def-axiom| (or $x337 $x626))))
+(let ((@x1540 (|unit-resolution| @x629 (|unit-resolution| (lemma @x1532 (or $x336 (not $x665))) @x1538 $x336) $x626)))
+(let ((@x1127 ((_ |th-lemma| arith triangle-eq) (or (not $x626) $x661))))
+(let ((@x1542 (lemma (|unit-resolution| @x1127 @x1540 (hypothesis (not $x661)) false) $x661)))
+(let ((@x1206 (hypothesis $x838)))
+(let ((@x1211 (hypothesis $x661)))
+(let ((@x843 (hypothesis $x387)))
+(let (($x625 (>= ?x380 0)))
+(let ((@x558 (|and-elim| @x552 $x381)))
+(let ((@x833 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x381) $x625)) @x558 $x625)))
+(let (($x633 (>= ?x355 0)))
+(let ((@x559 (|and-elim| @x552 $x356)))
+(let ((@x1125 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x356) $x633)) @x559 $x633)))
+(let ((@x1429 (lemma ((_ |th-lemma| arith farkas 1 1 1 1 1 1) @x1125 @x1426 @x833 @x843 @x1211 @x1206 false) (or $x286 $x386 (not $x661) (not $x838)))))
+(let ((@x1915 (|unit-resolution| (|unit-resolution| @x1429 @x1542 (or $x286 $x386 (not $x838))) @x1087 @x1426 $x386)))
+(let ((@x613 (|def-axiom| (or $x387 $x610))))
+(let ((@x1917 (|unit-resolution| @x948 (|unit-resolution| @x613 @x1915 $x610) $x934)))
+(let ((?x678 (+ |x3$| ?x479)))
+(let (($x670 (>= ?x678 0)))
+(let (($x586 (= |x3$| ?x468)))
+(let ((?x929 (+ ?x148 ?x429)))
+(let (($x1022 (>= ?x929 0)))
+(let (($x603 (= ?x148 ?x418)))
+(let ((@x607 (|def-axiom| (or $x411 $x603))))
+(let ((@x994 (|unit-resolution| @x607 @x842 $x603)))
+(let ((@x1037 ((_ |th-lemma| arith triangle-eq) (or (not $x603) $x1022))))
+(let ((@x1038 (|unit-resolution| @x1037 @x994 $x1022)))
+(let (($x462 (not $x461)))
+(let ((@x686 (hypothesis $x462)))
+(let (($x601 (>= ?x455 0)))
+(let ((@x555 (|and-elim| @x552 $x456)))
+(let ((@x685 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x456) $x601)) @x555 $x601)))
+(let (($x608 (<= ?x430 0)))
+(let ((@x556 (|and-elim| @x552 $x431)))
+(let ((@x810 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x431) $x608)) @x556 $x608)))
+(let ((?x755 (+ |x5$| ?x429)))
+(let (($x773 (<= ?x755 0)))
+(let (($x931 (<= ?x929 0)))
+(let ((@x997 ((_ |th-lemma| arith triangle-eq) (or (not $x603) $x931))))
+(let ((@x998 (|unit-resolution| @x997 @x994 $x931)))
+(let ((@x1067 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x773 (not $x931) $x411)) @x998 @x842 $x773)))
+(let (($x609 (>= ?x430 0)))
+(let ((@x797 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x431) $x609)) @x556 $x609)))
+(let ((@x801 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x386 (not $x773) (not $x601) $x461 $x782 (not $x609)))))
+(let (($x594 (= |x4$| ?x443)))
+(let ((@x1070 ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x436 (not $x931) $x411 (not $x609) $x386))))
+(let ((@x597 (|def-axiom| (or (not $x436) $x594))))
+(let ((@x1072 (|unit-resolution| @x597 (|unit-resolution| @x1070 @x843 @x797 @x842 @x998 $x436) $x594)))
+(let ((@x691 ((_ |th-lemma| arith triangle-eq) (or (not $x594) $x676))))
+(let ((@x1073 (|unit-resolution| @x691 @x1072 (|unit-resolution| @x801 @x843 @x797 @x1067 @x686 @x685 $x782) false)))
+(let ((@x1081 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 1 -1 1 -1) (or $x743 (not $x601) $x461 (not $x1022) (not $x608) $x387)) (|unit-resolution| (lemma @x1073 (or $x386 $x461 $x411)) @x686 @x842 $x386) @x810 @x685 @x686 @x1038 $x743)))
+(let (($x595 (= ?x131 ?x443)))
+(let (($x437 (not $x436)))
+(let ((@x1082 (|unit-resolution| @x613 (|unit-resolution| (lemma @x1073 (or $x386 $x461 $x411)) @x686 @x842 $x386) $x610)))
+(let ((@x806 ((_ |th-lemma| arith triangle-eq) (or (not $x610) $x671))))
+(let (($x668 (>= ?x666 0)))
+(let ((@x924 ((_ |th-lemma| arith triangle-eq) (or (not $x618) $x668))))
+(let ((@x1086 (|unit-resolution| @x924 (|unit-resolution| @x621 (|unit-resolution| @x1064 @x842 $x361) $x618) $x668)))
+(let ((@x1092 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x336 (not $x625) (not $x838) (not $x934) (not $x617) $x411))))
+(let ((@x1093 (|unit-resolution| @x1092 (|unit-resolution| @x948 @x1082 $x934) @x833 @x842 @x851 @x1087 $x336)))
+(let ((@x681 (hypothesis $x668)))
+(let ((@x692 (|unit-resolution| @x691 (|unit-resolution| @x597 (hypothesis $x436) $x594) $x676)))
+(let ((@x687 (hypothesis $x436)))
+(let (($x616 (<= ?x405 0)))
+(let ((@x696 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x406) $x616)) @x557 $x616)))
+(let ((@x697 (hypothesis $x671)))
+(let (($x624 (<= ?x380 0)))
+(let ((@x701 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x381) $x624)) @x558 $x624)))
+(let ((@x702 (hypothesis $x336)))
+(let ((@x707 (lemma ((_ |th-lemma| arith farkas 1 -1 1 -1 1 -1 -1 1 1) @x702 @x701 @x697 @x696 @x687 @x692 @x686 @x685 @x681 false) (or $x461 $x337 (not $x671) $x437 (not $x668)))))
+(let ((@x1094 (|unit-resolution| @x707 @x1093 @x1086 @x686 (|unit-resolution| @x806 @x1082 $x671) $x437)))
+(let ((@x599 (|def-axiom| (or $x436 $x595))))
+(let ((@x738 ((_ |th-lemma| arith triangle-eq) (or (not $x595) $x673))))
+(let ((@x1098 (lemma (|unit-resolution| @x738 (|unit-resolution| @x599 @x1094 $x595) @x1081 false) (or $x461 $x411))))
+(let ((@x589 (|def-axiom| (or $x462 $x586))))
+(let ((@x1268 ((_ |th-lemma| arith triangle-eq) (or (not $x586) $x670))))
+(let ((@x1269 (|unit-resolution| @x1268 (|unit-resolution| @x589 (|unit-resolution| @x1098 @x842 $x461) $x586) $x670)))
+(let (($x667 (>= ?x675 0)))
+(let (($x1499 (<= ?x1498 0)))
+(let ((@x1556 ((_ |th-lemma| arith triangle-eq) (or (not $x635) $x1499))))
+(let ((@x1557 (|unit-resolution| @x1556 @x1553 $x1499)))
+(let (($x930 (>= ?x672 0)))
+(let ((@x964 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x595) $x930)) (|unit-resolution| @x599 (hypothesis $x437) $x595) $x930)))
+(let ((@x939 (|unit-resolution| @x738 (|unit-resolution| @x599 (hypothesis $x437) $x595) $x673)))
+(let ((@x1185 (hypothesis $x411)))
+(let (($x1090 (not $x838)))
+(let (($x837 (>= ?x775 0)))
+(let ((@x890 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x611) $x837)) (hypothesis $x611) (hypothesis (not $x837)) false)))
+(let ((@x891 (lemma @x890 (or (not $x611) $x837))))
+(let ((@x1133 (|unit-resolution| @x891 (|unit-resolution| @x615 @x843 $x611) $x837)))
+(let ((?x776 (+ ?x182 ?x379)))
+(let (($x777 (<= ?x776 0)))
+(let (($x900 (not $x777)))
+(let ((@x904 (hypothesis $x900)))
+(let (($x619 (= ?x182 ?x368)))
+(let (($x821 (not $x619)))
+(let ((@x823 ((_ |th-lemma| arith triangle-eq) (or $x821 $x777))))
+(let ((@x907 (lemma (|unit-resolution| @x823 (hypothesis $x619) @x904 false) (or $x821 $x777))))
+(let ((@x623 (|def-axiom| (or $x361 $x619))))
+(let ((@x1363 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x777 $x362 $x1090)) (|unit-resolution| @x623 (|unit-resolution| @x907 @x904 $x821) $x361) @x904 $x1090)))
+(let ((@x1364 (|unit-resolution| @x621 (|unit-resolution| @x623 (|unit-resolution| @x907 @x904 $x821) $x361) $x618)))
+(let ((@x1366 (lemma (|unit-resolution| @x863 @x1364 @x1363 false) $x777)))
+(let ((@x1447 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 1 -1 1 -1) (or $x900 (not $x625) $x336 (not $x837) (not $x616) $x412)) @x833 @x1366 @x696 (or $x336 (not $x837) $x412))))
+(let ((@x1476 (|unit-resolution| @x1127 (|unit-resolution| @x629 (|unit-resolution| @x1447 @x1133 @x1185 $x336) $x626) $x661)))
+(let ((?x1358 (+ ?x96 ?x504)))
+(let (($x1367 (<= ?x1358 0)))
+(let (($x579 (= ?x96 ?x493)))
+(let (($x487 (not $x486)))
+(let (($x602 (= |x5$| ?x418)))
+(let ((@x605 (|def-axiom| (or $x412 $x602))))
+(let ((@x792 ((_ |th-lemma| arith triangle-eq) (or (not $x602) $x773))))
+(let ((@x1187 (|unit-resolution| @x792 (|unit-resolution| @x605 @x1185 $x602) $x773)))
+(let ((@x761 (hypothesis $x437)))
+(let ((@x1357 (lemma ((_ |th-lemma| arith farkas 1 1 1 1 1) @x1185 @x797 @x761 @x843 @x1187 false) (or $x436 $x412 $x386))))
+(let ((@x826 ((_ |th-lemma| arith triangle-eq) (or (not $x594) $x667))))
+(let ((@x1468 (|unit-resolution| @x826 (|unit-resolution| @x597 (|unit-resolution| @x1357 @x843 @x1185 $x436) $x594) $x667)))
+(let ((@x1115 ((_ |th-lemma| arith triangle-eq) (or (not $x626) $x665))))
+(let ((@x1471 (|unit-resolution| @x1115 (|unit-resolution| @x629 (|unit-resolution| @x1447 @x1133 @x1185 $x336) $x626) $x665)))
+(let ((@x1472 (|unit-resolution| @x691 (|unit-resolution| @x597 (|unit-resolution| @x1357 @x843 @x1185 $x436) $x594) $x676)))
+(let ((@x1473 (|unit-resolution| (|unit-resolution| @x801 @x797 @x685 (or $x386 (not $x773) $x461 $x782)) @x1472 @x1187 @x843 $x461)))
+(let ((@x1475 (|unit-resolution| @x1268 (|unit-resolution| @x589 @x1473 $x586) $x670)))
+(let ((@x848 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x611) $x778)) (|unit-resolution| @x615 @x843 $x611) $x778)))
+(let ((?x657 (+ |x9$| ?x304)))
+(let (($x659 (>= ?x657 0)))
+(let (($x634 (= |x9$| ?x293)))
+(let (($x774 (>= ?x755 0)))
+(let ((@x789 ((_ |th-lemma| arith triangle-eq) (or (not $x602) $x774))))
+(let ((@x1477 (|unit-resolution| @x789 (|unit-resolution| @x605 @x1185 $x602) $x774)))
+(let (($x858 (not $x665)))
+(let (($x901 (not $x667)))
+(let (($x815 (not $x774)))
+(let (($x1196 (not $x661)))
+(let (($x798 (not $x773)))
+(let (($x564 (not $x70)))
+(let (($x658 (<= ?x657 0)))
+(let ((@x1379 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1 1 1 1 1) (or $x286 $x361 (not $x633) $x900 (not $x625) $x386 $x1196)) @x1025 @x833 @x1125 @x843 @x1366 @x1211 $x286)))
+(let ((@x637 (|def-axiom| (or $x287 $x634))))
+(let ((@x1149 ((_ |th-lemma| arith triangle-eq) (or (not $x634) $x658))))
+(let (($x1354 (>= ?x776 0)))
+(let ((@x1385 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x821 $x1354)) (|unit-resolution| @x623 @x1025 $x619) $x1354)))
+(let ((@x1207 (hypothesis $x773)))
+(let ((@x866 (hypothesis $x676)))
+(let ((@x1388 (|unit-resolution| (|unit-resolution| @x801 @x797 @x685 (or $x386 $x798 $x461 $x782)) @x866 @x1207 @x843 $x461)))
+(let ((@x1390 (|unit-resolution| @x1268 (|unit-resolution| @x589 @x1388 $x586) $x670)))
+(let ((@x898 (hypothesis $x667)))
+(let (($x641 (>= ?x305 0)))
+(let ((@x560 (|and-elim| @x552 $x306)))
+(let ((@x1136 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x306) $x641)) @x560 $x641)))
+(let ((@x1199 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x361 $x311 $x1196 (not $x633) (not $x658) (not $x641)))))
+(let ((@x1393 (|unit-resolution| (|unit-resolution| @x1199 @x1136 @x1125 (or $x361 $x311 $x1196 (not $x658))) (|unit-resolution| @x1149 (|unit-resolution| @x637 @x1379 $x634) $x658) @x1211 @x1025 $x311)))
+(let ((@x645 (|def-axiom| (or (not $x311) $x642))))
+(let ((@x1396 ((_ |th-lemma| arith triangle-eq) (or (not $x642) $x1369))))
+(let (($x1139 (not $x658)))
+(let (($x1374 (not $x1354)))
+(let (($x1260 (not $x670)))
+(let (($x1104 (not $x778)))
+(let (($x1373 (not $x1369)))
+(let ((@x1137 (hypothesis $x658)))
+(let ((@x1370 (hypothesis $x1354)))
+(let (($x592 (<= ?x480 0)))
+(let ((@x554 (|and-elim| @x552 $x481)))
+(let ((@x1252 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x481) $x592)) @x554 $x592)))
+(let (($x600 (<= ?x455 0)))
+(let ((@x830 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x456) $x600)) @x555 $x600)))
+(let ((@x1249 (hypothesis $x670)))
+(let ((@x1248 (hypothesis $x778)))
+(let (($x764 (not $x655)))
+(let ((@x1253 (hypothesis $x764)))
+(let (($x649 (>= ?x330 0)))
+(let ((@x561 (|and-elim| @x552 $x331)))
+(let ((@x1256 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x331) $x649)) @x561 $x649)))
+(let ((@x1371 (hypothesis $x1369)))
+(let ((@x1372 ((_ |th-lemma| arith farkas -1 1 -1 -1 1 -1 -1 -1 1 1 -1 1 1) @x1136 @x1371 @x1256 @x1253 @x1248 @x851 @x898 @x1249 @x830 @x1252 @x1370 @x701 @x1137 false)))
+(let ((@x1376 (lemma @x1372 (or $x655 $x1373 $x1104 $x901 $x1260 $x1374 $x1139))))
+(let ((@x1398 (|unit-resolution| @x1376 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x1393 $x642) $x1369) @x848 @x898 @x1390 @x1385 (|unit-resolution| @x1149 (|unit-resolution| @x637 @x1379 $x634) $x658) $x655)))
+(let ((@x1277 ((_ |th-lemma| arith triangle-eq) (or $x71 $x764 $x708))))
+(let (($x565 (not $x71)))
+(let (($x566 (or $x564 $x565)))
+(let ((@x572 (monotonicity (rewrite (= $x72 (not $x566))) (= (not $x72) (not (not $x566))))))
+(let ((@x576 (trans @x572 (rewrite (= (not (not $x566)) $x566)) (= (not $x72) $x566))))
+(let ((@x577 (mp (|not-or-elim| (mp (asserted $x74) @x550 $x546) (not $x72)) @x576 $x566)))
+(let ((?x650 (+ |x1$| ?x233)))
+(let (($x652 (>= ?x650 0)))
+(let (($x632 (<= ?x355 0)))
+(let ((@x855 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x356) $x632)) @x559 $x632)))
+(let ((@x897 (hypothesis $x774)))
+(let (($x585 (>= ?x505 0)))
+(let ((@x553 (|and-elim| @x552 $x506)))
+(let ((@x1284 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x506) $x585)) @x553 $x585)))
+(let ((@x1404 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 1 1) (or $x487 $x1260 (not $x592) (not $x600) $x901 $x361 (not $x617) $x386 $x1104))))
+(let ((@x1406 (|unit-resolution| @x1404 @x830 @x851 @x1252 (or $x487 $x1260 $x901 $x361 $x386 $x1104))))
+(let ((@x583 (|def-axiom| (or $x486 $x579))))
+(let ((@x1408 (|unit-resolution| @x583 (|unit-resolution| @x1406 @x1025 @x843 @x848 @x898 @x1390 $x487) $x579)))
+(let ((@x1411 ((_ |th-lemma| arith triangle-eq) (or (not $x579) $x1367))))
+(let ((@x1413 ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -3 3 2 -2 -2 2 1 -1 -1 1 -1 1 -1) (|unit-resolution| @x1411 @x1408 $x1367) @x1284 @x897 @x810 @x898 @x830 @x848 @x851 @x1390 @x1252 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x1393 $x642) $x1369) @x1256 @x1263 @x855 @x1385 @x701 @x856 $x652)))
+(let (($x651 (<= ?x650 0)))
+(let (($x648 (<= ?x330 0)))
+(let ((@x713 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x331) $x648)) @x561 $x648)))
+(let (($x662 (>= ?x660 0)))
+(let ((@x1165 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x642) $x662)) (hypothesis $x642) (hypothesis (not $x662)) false)))
+(let ((@x1166 (lemma @x1165 (or (not $x642) $x662))))
+(let (($x593 (>= ?x480 0)))
+(let ((@x718 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x481) $x593)) @x554 $x593)))
+(let (($x679 (<= ?x678 0)))
+(let ((@x723 ((_ |th-lemma| arith triangle-eq) (or (not $x586) $x679))))
+(let (($x584 (<= ?x505 0)))
+(let ((@x1296 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x506) $x584)) @x553 $x584)))
+(let (($x1368 (>= ?x1358 0)))
+(let ((@x1419 ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -3 3 2 -2 -2 2 1 -1 -1 1 -1 1 -1) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x579) $x1368)) @x1408 $x1368) @x1296 @x1207 @x797 @x866 @x685 @x1133 @x696 (|unit-resolution| @x723 (|unit-resolution| @x589 @x1388 $x586) $x679) @x718 (|unit-resolution| @x1166 (|unit-resolution| @x645 @x1393 $x642) $x662) @x713 @x1398 @x1125 @x1366 @x833 @x1211 $x651)))
+(let ((@x1304 ((_ |th-lemma| arith triangle-eq) (or $x70 (not $x651) (not $x652)))))
+(let ((@x1420 (|unit-resolution| @x1304 @x1419 @x1413 (|unit-resolution| @x577 (|unit-resolution| @x1277 @x1398 @x1263 $x71) $x564) false)))
+(let ((@x1478 (|unit-resolution| (lemma @x1420 (or $x361 $x798 $x782 $x1196 $x815 $x901 $x708 $x858 $x386)) @x1263 @x1472 @x1476 @x1477 @x1468 @x1187 @x1471 @x843 $x361)))
+(let ((@x1481 (|unit-resolution| @x1429 (|unit-resolution| @x863 (|unit-resolution| @x621 @x1478 $x618) $x838) @x1476 @x843 $x286)))
+(let ((@x1144 ((_ |th-lemma| arith triangle-eq) (or (not $x634) $x659))))
+(let ((@x1483 (|unit-resolution| @x1144 (|unit-resolution| @x637 @x1481 $x634) $x659)))
+(let (($x1302 (not $x652)))
+(let ((@x729 (hypothesis $x659)))
+(let (($x640 (<= ?x305 0)))
+(let ((@x728 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x306) $x640)) @x560 $x640)))
+(let ((@x1258 ((_ |th-lemma| arith farkas 1/2 -1 -1/2 -1/2 1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 1) @x681 @x855 @x701 (hypothesis $x1247) @x1256 @x1253 @x1252 @x1249 @x830 @x729 @x728 @x898 @x1248 @x851 @x856 false)))
+(let ((@x1262 (lemma @x1258 (or $x655 (not $x668) $x1259 $x1260 (not $x659) $x901 $x1104 $x858))))
+(let ((@x1309 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1119 $x1247)) (hypothesis $x643) (hypothesis $x1259) false)))
+(let ((@x1310 (lemma @x1309 (or $x1119 $x1247))))
+(let ((@x1424 (|unit-resolution| @x1310 (|unit-resolution| @x1262 @x1253 @x856 @x1249 @x681 @x898 @x1248 @x729 $x1259) $x1119)))
+(let ((@x647 (|def-axiom| (or $x311 $x643))))
+(let ((@x1431 (|unit-resolution| @x1396 (|unit-resolution| @x645 (|unit-resolution| @x647 @x1424 $x311) $x642) $x1369)))
+(let ((@x1432 ((_ |th-lemma| arith farkas -2 -1 2 1 -1 2 -1 1 1 -1 1 1 1 -1 -1 1) @x855 @x701 @x856 @x729 @x728 (|unit-resolution| @x647 @x1424 $x311) @x1431 @x1256 @x1253 @x1248 @x851 @x898 @x1249 @x830 @x1252 @x681 false)))
+(let ((@x1485 (|unit-resolution| (lemma @x1432 (or $x655 $x858 (not $x659) $x1104 $x901 $x1260 (not $x668))) @x1483 @x1471 @x848 @x1468 @x1475 (|unit-resolution| @x924 (|unit-resolution| @x621 @x1478 $x618) $x668) $x655)))
+(let ((@x1449 (|unit-resolution| @x629 (|unit-resolution| @x1447 (hypothesis $x837) @x1185 $x336) $x626)))
+(let ((@x865 (hypothesis $x837)))
+(let (($x1301 (not $x651)))
+(let ((@x1318 (hypothesis $x1301)))
+(let ((?x1142 (+ |x2$| ?x504)))
+(let (($x1237 (>= ?x1142 0)))
+(let (($x578 (= |x2$| ?x493)))
+(let (($x1409 (not $x579)))
+(let (($x1437 (not $x1368)))
+(let ((@x867 (hypothesis $x679)))
+(let ((@x1436 ((_ |th-lemma| arith farkas -1 1 1 -1 -2 -1 2 1 1 -1 -1 1 -1 1 1) @x1137 @x1136 @x865 @x696 @x866 @x867 @x685 @x718 @x1125 @x1211 @x1296 @x1318 @x1207 @x797 (hypothesis $x1368) false)))
+(let ((@x1439 (lemma @x1436 (or $x1437 $x1139 (not $x837) $x782 (not $x679) $x1196 $x651 $x798))))
+(let ((@x1451 (|unit-resolution| @x1439 @x1318 @x865 @x866 @x867 (|unit-resolution| @x1127 @x1449 $x661) @x1137 @x1187 $x1437)))
+(let ((@x1441 (hypothesis $x579)))
+(let ((@x1442 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1409 $x1368)) @x1441 (hypothesis $x1437) false)))
+(let ((@x1443 (lemma @x1442 (or $x1409 $x1368))))
+(let ((@x581 (|def-axiom| (or $x487 $x578))))
+(let ((@x1454 (|unit-resolution| @x581 (|unit-resolution| @x583 (|unit-resolution| @x1443 @x1451 $x1409) $x486) $x578)))
+(let ((@x1298 ((_ |th-lemma| arith triangle-eq) (or (not $x578) $x1237))))
+(let ((@x1456 ((_ |th-lemma| arith farkas 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 1/2 -1/2 1) @x1249 @x1252 (|unit-resolution| @x1298 @x1454 $x1237) @x1296 @x1318 @x1187 @x797 @x1137 @x1136 @x865 @x696 @x1125 (|unit-resolution| @x1127 @x1449 $x661) @x1185 false)))
+(let ((@x1490 (|unit-resolution| (lemma @x1456 (or $x651 $x1260 $x1139 (not $x837) $x412 $x782 (not $x679))) (|unit-resolution| @x1149 (|unit-resolution| @x637 @x1481 $x634) $x658) @x1475 @x1133 @x1185 @x1472 (|unit-resolution| @x723 (|unit-resolution| @x589 @x1473 $x586) $x679) $x651)))
+(let ((@x1491 (|unit-resolution| @x1304 @x1490 (|unit-resolution| @x577 (|unit-resolution| @x1277 @x1485 @x1263 $x71) $x564) $x1302)))
+(let (($x1236 (<= ?x1142 0)))
+(let ((@x1291 ((_ |th-lemma| arith triangle-eq) (or (not $x578) $x1236))))
+(let ((@x1461 (|unit-resolution| @x1291 (|unit-resolution| @x581 (hypothesis $x486) $x578) $x1236)))
+(let ((@x1463 ((_ |th-lemma| arith farkas -1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -2 -2 2 1) @x1284 (hypothesis $x1302) @x897 @x810 @x729 @x728 @x1248 @x851 @x1249 @x1252 @x855 @x856 (hypothesis $x486) @x898 @x830 @x1461 false)))
+(let ((@x1465 (lemma @x1463 (or $x487 $x652 $x815 (not $x659) $x1104 $x1260 $x858 $x901))))
+(let ((@x1493 (|unit-resolution| @x583 (|unit-resolution| @x1465 @x1491 @x1477 @x1483 @x848 @x1475 @x1471 @x1468 $x487) $x579)))
+(let ((@x1495 ((_ |th-lemma| arith farkas -1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -2 2 1) @x1284 @x1491 @x1477 @x810 @x1483 @x728 @x848 @x851 @x1475 @x1252 @x855 @x1471 @x1468 @x830 (|unit-resolution| @x1411 @x1493 $x1367) false)))
+(let (($x704 (not $x671)))
+(let ((@x1150 (|unit-resolution| @x1149 (|unit-resolution| @x637 (hypothesis $x286) $x634) $x658)))
+(let ((@x1076 (hypothesis $x286)))
+(let (($x312 (not $x311)))
+(let (($x1162 (not $x642)))
+(let (($x732 (not $x662)))
+(let ((@x1145 (|unit-resolution| @x1144 (|unit-resolution| @x637 @x1076 $x634) $x659)))
+(let ((@x709 (hypothesis $x708)))
+(let ((@x714 (hypothesis $x662)))
+(let (($x845 (not $x611)))
+(let (($x870 (not $x837)))
+(let ((?x674 (+ ?x114 ?x479)))
+(let (($x677 (<= ?x674 0)))
+(let (($x587 (= ?x114 ?x468)))
+(let ((@x591 (|def-axiom| (or $x461 $x587))))
+(let ((@x760 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x587) $x677)) (|unit-resolution| @x591 @x686 $x587) $x677)))
+(let ((@x942 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1) (or $x676 $x436 $x743)) @x939 @x761 $x676)))
+(let ((@x864 (|unit-resolution| @x863 (|unit-resolution| @x621 (hypothesis $x361) $x618) $x838)))
+(let ((@x839 (hypothesis $x361)))
+(let ((@x868 ((_ |th-lemma| arith farkas -1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -2 1) @x833 @x867 @x729 @x728 @x718 @x714 @x713 @x709 @x685 @x866 @x696 @x865 @x839 @x864 false)))
+(let ((@x877 (|unit-resolution| (lemma @x868 (or $x362 (not $x679) (not $x659) $x732 $x656 $x782 $x870)) @x865 @x729 @x714 @x709 @x866 @x867 $x362)))
+(let ((@x880 ((_ |th-lemma| arith farkas -1 1 -1 1 -1 -1 1 1 -1 1 1 -1 1) @x833 @x867 @x729 @x728 @x718 @x714 @x713 @x709 @x685 @x866 @x696 @x865 (|unit-resolution| @x823 (|unit-resolution| @x623 @x877 $x619) $x777) false)))
+(let ((@x882 (lemma @x880 (or $x870 (not $x679) (not $x659) $x732 $x656 $x782))))
+(let ((@x943 (|unit-resolution| @x882 @x942 @x729 @x714 @x709 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x679 (not $x677) $x461)) @x760 @x686 $x679) $x870)))
+(let ((@x946 (|unit-resolution| @x613 (|unit-resolution| @x615 (|unit-resolution| @x891 @x943 $x845) $x386) $x610)))
+(let ((@x952 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x411 $x743 (not $x601) $x461 $x436)) @x761 @x685 @x686 @x939 $x411)))
+(let ((@x958 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x361 (not $x934) (not $x617) $x436 $x798 (not $x609)))))
+(let ((@x959 (|unit-resolution| @x958 @x761 @x851 @x797 (|unit-resolution| @x792 (|unit-resolution| @x605 @x952 $x602) $x773) (|unit-resolution| @x948 @x946 $x934) $x361)))
+(let ((@x965 ((_ |th-lemma| arith farkas -1 -1 1 1 -1 -1 1 1 1 -1 -1 1 1) @x833 @x729 @x728 @x760 @x718 @x714 @x713 @x709 (|unit-resolution| @x948 @x946 $x934) @x851 @x964 @x830 (|unit-resolution| @x863 (|unit-resolution| @x621 @x959 $x618) $x838) false)))
+(let ((@x972 (|unit-resolution| (lemma @x965 (or $x436 (not $x659) $x732 $x656 $x461)) @x686 @x714 @x709 @x729 $x436)))
+(let ((@x976 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x411 (not $x601) $x461 $x437 $x782)) (|unit-resolution| @x691 (|unit-resolution| @x597 @x972 $x594) $x676) @x685 @x686 @x972 $x411)))
+(let ((@x979 (|unit-resolution| @x882 (|unit-resolution| @x691 (|unit-resolution| @x597 @x972 $x594) $x676) @x729 @x714 @x709 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x679 (not $x677) $x461)) @x760 @x686 $x679) $x870)))
+(let ((@x982 (|unit-resolution| @x613 (|unit-resolution| @x615 (|unit-resolution| @x891 @x979 $x845) $x386) $x610)))
+(let ((@x933 ((_ |th-lemma| arith farkas -1 -1 1 1 -1 -1 1 1 -1 1 -2 2 -1 1 1) @x833 @x729 @x728 (hypothesis $x677) @x718 @x714 @x713 @x709 @x697 @x696 @x897 @x810 @x898 @x830 (hypothesis $x777) false)))
+(let ((@x969 (lemma @x933 (or $x900 (not $x659) (not $x677) $x732 $x656 $x704 $x815 $x901))))
+(let ((@x984 (|unit-resolution| @x969 @x760 @x729 @x714 @x709 (|unit-resolution| @x806 @x982 $x671) (|unit-resolution| @x789 (|unit-resolution| @x605 @x976 $x602) $x774) (|unit-resolution| @x826 (|unit-resolution| @x597 @x972 $x594) $x667) $x900)))
+(let ((@x987 (|unit-resolution| @x621 (|unit-resolution| @x623 (|unit-resolution| @x907 @x984 $x821) $x361) $x618)))
+(let ((@x989 ((_ |th-lemma| arith farkas -1 -1 1 1 -1 -1 1 1 -1 1 -2 2 -2 -1 1 1) @x833 @x729 @x728 @x760 @x718 @x714 @x713 @x709 (|unit-resolution| @x806 @x982 $x671) @x696 (|unit-resolution| @x789 (|unit-resolution| @x605 @x976 $x602) $x774) @x810 (|unit-resolution| @x623 (|unit-resolution| @x907 @x984 $x821) $x361) (|unit-resolution| @x826 (|unit-resolution| @x597 @x972 $x594) $x667) @x830 (|unit-resolution| @x863 @x987 $x838) false)))
+(let ((@x970 (|unit-resolution| (lemma @x989 (or $x461 (not $x659) $x732 $x656)) @x714 @x729 @x709 $x461)))
+(let ((@x992 (|unit-resolution| @x723 (|unit-resolution| @x589 @x970 $x586) $x679)))
+(let ((@x1009 (|unit-resolution| @x891 (|unit-resolution| @x882 @x942 @x729 @x714 @x709 @x992 $x870) $x845)))
+(let ((@x1012 (|unit-resolution| @x948 (|unit-resolution| @x613 (|unit-resolution| @x615 @x1009 $x386) $x610) $x934)))
+(let ((@x751 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x656 $x655)) @x709 $x655)))
+(let ((@x999 (hypothesis $x934)))
+(let ((@x1002 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 2) (or $x361 (not $x934) (not $x617) $x436 (not $x609) (not $x931) $x411))))
+(let ((@x1004 (|unit-resolution| @x621 (|unit-resolution| @x1002 @x842 @x797 @x851 @x761 @x999 @x998 $x361) $x618)))
+(let ((@x762 (hypothesis $x655)))
+(let ((@x1006 ((_ |th-lemma| arith farkas 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1) @x833 @x999 @x851 @x842 @x729 @x728 @x718 @x714 @x713 @x762 @x685 @x939 @x867 @x761 (|unit-resolution| @x863 @x1004 $x838) false)))
+(let ((@x1008 (lemma @x1006 (or $x411 (not $x934) (not $x659) $x732 $x764 (not $x679) $x436))))
+(let ((@x1014 (|unit-resolution| @x605 (|unit-resolution| @x1008 @x1012 @x729 @x714 @x751 @x992 @x761 $x411) $x602)))
+(let ((@x1016 (|unit-resolution| @x958 (|unit-resolution| @x792 @x1014 $x773) @x851 @x761 @x1012 @x797 $x361)))
+(let ((@x1019 ((_ |th-lemma| arith farkas -1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1) @x830 @x964 (|unit-resolution| @x863 (|unit-resolution| @x621 @x1016 $x618) $x838) @x833 @x1012 @x851 @x729 @x728 @x718 @x714 @x713 @x709 @x992 @x970 false)))
+(let ((@x1023 (|unit-resolution| (lemma @x1019 (or $x436 (not $x659) $x732 $x656)) @x714 @x729 @x709 $x436)))
+(let ((@x1033 (|unit-resolution| @x882 (|unit-resolution| @x691 (|unit-resolution| @x597 @x1023 $x594) $x676) @x729 @x714 @x709 @x992 $x870)))
+(let ((@x1035 (|unit-resolution| @x615 (|unit-resolution| @x891 @x1033 $x845) $x386)))
+(let ((@x1041 (|unit-resolution| @x863 (|unit-resolution| @x621 (|unit-resolution| @x1030 @x842 @x1035 $x361) $x618) $x838)))
+(let ((@x1044 ((_ |th-lemma| arith farkas -1 1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1 1) (|unit-resolution| @x948 (|unit-resolution| @x613 @x1035 $x610) $x934) @x851 @x1041 @x833 @x729 @x728 @x718 @x714 @x713 @x709 @x992 @x1038 @x810 @x970 @x1035 false)))
+(let ((@x1049 (|unit-resolution| (lemma @x1044 (or $x411 (not $x659) $x732 $x656)) @x714 @x729 @x709 $x411)))
+(let ((@x895 (|unit-resolution| @x723 (|unit-resolution| @x589 (hypothesis $x461) $x586) $x679)))
+(let ((@x899 ((_ |th-lemma| arith farkas -1/2 1/2 1 -1 -1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1/2 1) @x830 @x898 @x897 @x810 (hypothesis $x777) @x833 @x895 @x729 @x728 @x718 @x714 @x713 @x709 @x696 @x697 (hypothesis $x461) false)))
+(let ((@x903 (lemma @x899 (or $x900 $x901 $x815 (not $x659) $x732 $x656 $x704 $x462))))
+(let ((@x1052 (|unit-resolution| @x903 (|unit-resolution| @x789 (|unit-resolution| @x605 @x1049 $x602) $x774) @x970 @x729 @x714 @x709 (|unit-resolution| @x826 (|unit-resolution| @x597 @x1023 $x594) $x667) (|unit-resolution| @x806 (|unit-resolution| @x613 @x1035 $x610) $x671) $x900)))
+(let ((@x1055 (|unit-resolution| @x621 (|unit-resolution| @x623 (|unit-resolution| @x907 @x1052 $x821) $x361) $x618)))
+(let ((@x1057 ((_ |th-lemma| arith farkas 1 -1 1/2 -1/2 1 1/2 -1/2 -1/2 1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1) (|unit-resolution| @x789 (|unit-resolution| @x605 @x1049 $x602) $x774) @x810 (|unit-resolution| @x826 (|unit-resolution| @x597 @x1023 $x594) $x667) @x830 (|unit-resolution| @x623 (|unit-resolution| @x907 @x1052 $x821) $x361) (|unit-resolution| @x806 (|unit-resolution| @x613 @x1035 $x610) $x671) @x696 (|unit-resolution| @x863 @x1055 $x838) @x833 @x729 @x728 @x718 @x714 @x713 @x709 @x992 @x970 false)))
+(let ((@x1167 (|unit-resolution| (lemma @x1057 (or $x732 (not $x659) $x656)) @x709 @x1145 $x732)))
+(let ((@x1169 (|unit-resolution| @x645 (|unit-resolution| @x1166 @x1167 $x1162) $x312)))
+(let ((@x1191 ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x336 $x311 $x1139 (not $x641) $x287))))
+(let ((@x1216 (|unit-resolution| @x629 (|unit-resolution| @x1191 @x1169 @x1136 @x1076 @x1150 $x336) $x626)))
+(let ((@x1217 (|unit-resolution| @x1127 @x1216 $x661)))
+(let ((@x1131 (|unit-resolution| @x723 (|unit-resolution| @x589 (|unit-resolution| @x1098 @x842 $x461) $x586) $x679)))
+(let (($x1103 (>= ?x1101 0)))
+(let ((@x1158 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1119 $x1103)) (hypothesis $x643) (hypothesis (not $x1103)) false)))
+(let ((@x1159 (lemma @x1158 (or $x1119 $x1103))))
+(let ((@x1110 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x934 $x671)) (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x704 $x1104 $x386)) @x848 @x843 $x704) $x934)))
+(let ((@x1112 (|unit-resolution| @x629 (|unit-resolution| @x1092 @x1110 @x833 @x851 @x842 @x1087 $x336) $x626)))
+(let ((@x841 (hypothesis $x311)))
+(let ((@x860 (lemma ((_ |th-lemma| arith farkas 1 1 1 1 1 1 1 1 1) @x856 @x855 @x851 @x843 @x729 @x728 @x848 @x842 @x841 false) (or $x411 $x858 $x386 (not $x659) $x312))))
+(let ((@x1117 (|unit-resolution| @x860 (|unit-resolution| @x1115 @x1112 $x665) @x842 @x729 @x843 $x312)))
+(let ((@x1122 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1119 $x1103)) (|unit-resolution| @x647 @x1117 $x643) $x1103)))
+(let ((@x1138 ((_ |th-lemma| arith farkas 1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 -2 2 1) @x833 @x1137 @x1136 @x1087 @x696 @x1133 @x713 @x709 @x718 (|unit-resolution| @x691 @x1072 $x676) @x685 @x1131 (|unit-resolution| @x1127 @x1112 $x661) @x1125 @x1122 false)))
+(let ((@x1172 (|unit-resolution| (lemma @x1138 (or $x386 $x1139 $x656 $x411 (not $x659))) @x842 @x709 @x1150 @x1145 $x386)))
+(let ((@x1152 ((_ |th-lemma| arith farkas -1/2 1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1) @x701 @x681 @x697 @x696 (hypothesis $x1103) @x1150 @x1136 @x713 @x709 @x718 @x866 @x685 @x867 @x1076 false)))
+(let ((@x1155 (lemma @x1152 (or (not $x1103) (not $x668) $x704 $x656 $x782 (not $x679) $x287))))
+(let ((@x1175 (|unit-resolution| @x1155 (|unit-resolution| @x806 (|unit-resolution| @x613 @x1172 $x610) $x671) (|unit-resolution| @x1159 (|unit-resolution| @x647 @x1169 $x643) $x1103) @x709 @x1131 @x1086 @x1076 $x782)))
+(let ((@x1177 (|unit-resolution| @x1092 @x1087 @x833 @x842 (|unit-resolution| @x948 (|unit-resolution| @x613 @x1172 $x610) $x934) @x851 $x336)))
+(let ((@x1102 (lemma ((_ |th-lemma| arith farkas 1 1 1 1 1 1 1 1 1) @x856 @x701 @x1086 @x855 @x761 @x998 @x842 @x797 @x1076 false) (or $x436 $x858 $x411 $x287))))
+(let ((@x1180 (|unit-resolution| @x1102 (|unit-resolution| @x1115 (|unit-resolution| @x629 @x1177 $x626) $x665) @x842 @x1076 $x436)))
+(let ((@x1184 (lemma (|unit-resolution| @x691 (|unit-resolution| @x597 @x1180 $x594) @x1175 false) (or $x411 $x287 $x656))))
+(let ((@x1220 (|unit-resolution| @x789 (|unit-resolution| @x605 (|unit-resolution| @x1184 @x709 @x1076 $x411) $x602) $x774)))
+(let ((@x1193 (|unit-resolution| @x629 (|unit-resolution| @x1191 (hypothesis $x312) @x1136 @x1076 @x1150 $x336) $x626)))
+(let ((@x1188 (hypothesis $x312)))
+(let ((@x1200 (|unit-resolution| @x1199 (|unit-resolution| @x1127 @x1193 $x661) @x1136 @x1188 @x1150 @x1125 $x361)))
+(let ((@x1203 ((_ |th-lemma| arith farkas -1 1 -1 -1 -1 1 1 -1 1) @x1185 @x701 (|unit-resolution| @x924 (|unit-resolution| @x621 @x1200 $x618) $x668) @x1076 (|unit-resolution| @x1115 @x1193 $x665) @x855 @x761 @x797 @x1187 false)))
+(let ((@x1205 (lemma @x1203 (or $x436 $x412 $x287 $x311))))
+(let ((@x1221 (|unit-resolution| @x1205 (|unit-resolution| @x1184 @x709 @x1076 $x411) @x1076 @x1169 $x436)))
+(let (($x816 (not $x608)))
+(let (($x1197 (not $x633)))
+(let (($x1189 (not $x641)))
+(let (($x741 (not $x616)))
+(let ((@x1224 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 -1 1 1 -1 1 1 -1) (or $x704 $x741 $x311 $x1139 $x1189 $x815 $x1196 $x1197 $x437 $x816)) @x1169 @x696 @x1125 @x1136 @x810 @x1150 @x1221 @x1220 @x1217 $x704)))
+(let ((@x1225 (|unit-resolution| @x792 (|unit-resolution| @x605 (|unit-resolution| @x1184 @x709 @x1076 $x411) $x602) $x773)))
+(let ((@x1229 (|unit-resolution| @x621 (|unit-resolution| @x1199 @x1217 @x1136 @x1169 @x1150 @x1125 $x361) $x618)))
+(let ((@x1209 (|unit-resolution| @x589 (|unit-resolution| @x801 @x843 @x797 @x1207 @x866 @x685 $x461) $x586)))
+(let ((@x1212 ((_ |th-lemma| arith farkas -1 -2 2 -1 1 1 -1 -1 1 -1 1 -1 -1 1 1) @x696 @x1211 @x1125 @x1137 @x1136 (hypothesis $x1103) @x713 @x709 @x718 (|unit-resolution| @x723 @x1209 $x679) @x833 @x1206 @x866 @x685 @x1133 false)))
+(let ((@x1231 (|unit-resolution| (lemma @x1212 (or $x386 $x1196 $x1139 (not $x1103) $x656 $x1090 $x782 $x798)) @x1217 @x1150 (|unit-resolution| @x1159 (|unit-resolution| @x647 @x1169 $x643) $x1103) @x709 (|unit-resolution| @x863 @x1229 $x838) (|unit-resolution| @x691 (|unit-resolution| @x597 @x1221 $x594) $x676) @x1225 $x386)))
+(let ((@x1235 (lemma (|unit-resolution| @x806 (|unit-resolution| @x613 @x1231 $x610) @x1224 false) (or $x656 $x287))))
+(let ((@x1502 (|unit-resolution| @x1235 (|unit-resolution| (lemma @x1495 (or $x708 $x412 $x386)) @x843 @x1185 $x708) $x287)))
+(let ((@x1504 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1 1 1 1 1) (or $x286 $x361 $x1197 $x900 (not $x625) $x386 $x1196)) @x1502 @x833 @x1125 @x843 @x1366 @x1476 $x361)))
+(let ((@x1506 (|unit-resolution| @x863 (|unit-resolution| @x621 @x1504 $x618) (|unit-resolution| @x1429 @x1502 @x1476 @x843 $x1090) false)))
+(let ((@x1508 (lemma @x1506 (or $x386 $x412))))
+(let ((@x1815 (|unit-resolution| @x1508 @x1185 $x386)))
+(let (($x1513 (not $x627)))
+(let ((@x1519 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 -1 1 1) (or $x1510 $x1197 $x387 $x1374 (not $x624) $x286)) @x1385 @x1125 @x1426 @x1024 @x701 $x1510)))
+(let ((@x1522 (|unit-resolution| @x629 (|unit-resolution| @x631 (|unit-resolution| @x1517 @x1519 $x1513) $x336) $x626)))
+(let ((@x1524 ((_ |th-lemma| arith farkas 1 1 1 1 1) @x1426 @x1125 (|unit-resolution| @x1127 @x1522 $x661) @x1025 (|unit-resolution| @x631 (|unit-resolution| @x1517 @x1519 $x1513) $x336) false)))
+(let ((@x1526 (lemma @x1524 (or $x361 $x286 $x387))))
+(let ((@x1826 (|unit-resolution| @x924 (|unit-resolution| @x621 (|unit-resolution| @x1526 @x1815 @x1426 $x361) $x618) $x668)))
+(let (($x705 (not $x668)))
+(let ((@x1734 (|unit-resolution| @x806 (|unit-resolution| @x613 @x1024 $x610) $x671)))
+(let ((@x1670 (|unit-resolution| @x924 (|unit-resolution| @x621 @x839 $x618) $x668)))
+(let (($x1500 (>= ?x664 0)))
+(let ((@x1546 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1513 $x1500)) @x1528 $x1500)))
+(let ((@x1547 (|unit-resolution| @x1517 @x1528 $x873)))
+(let ((@x1550 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 1 1) (or $x437 $x815 $x816 $x704 $x741 $x1510 $x1197 $x286 $x336)) @x1426 @x696 @x1527 @x1125 @x810 @x697 @x1477 @x1547 $x437)))
+(let ((@x1552 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x595) $x930)) (|unit-resolution| @x599 @x1550 $x595) $x930)))
+(let ((@x1558 (|unit-resolution| @x738 (|unit-resolution| @x599 @x1550 $x595) $x673)))
+(let (($x740 (not $x624)))
+(let (($x742 (not $x601)))
+(let ((@x1560 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 1 1 1 2 2) (or $x461 $x815 $x816 $x742 $x705 $x740 $x1510 $x1197 $x286 $x743 $x704 $x741))))
+(let ((@x1561 (|unit-resolution| @x1560 @x1426 @x810 @x696 @x701 @x1125 @x685 @x697 @x681 @x1558 @x1477 @x1547 $x461)))
+(let ((@x1566 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 1 1) (or $x311 (not $x1499) $x1189 $x286 $x705 $x412 $x704 $x741 $x740))))
+(let ((@x1568 (|unit-resolution| @x645 (|unit-resolution| @x1566 @x1557 @x701 @x1185 @x1136 @x1426 @x697 @x681 @x696 $x311) $x642)))
+(let ((@x1570 ((_ |th-lemma| arith assign-bounds -1 1 1 -1 -1 -1 -3 3 1 -1 1 1 -2 2 2 -2) (|unit-resolution| @x1396 @x1568 $x1369) @x1256 (|unit-resolution| @x1268 (|unit-resolution| @x589 @x1561 $x586) $x670) @x1252 @x830 @x1206 @x999 @x851 @x833 @x1557 @x1136 @x1552 @x1187 @x797 @x1546 @x855 $x655)))
+(let ((@x1574 (|unit-resolution| @x723 (|unit-resolution| @x589 @x1561 $x586) $x679)))
+(let ((@x1576 ((_ |th-lemma| arith assign-bounds -1 1 1 -1 -1 -1 -3 3 1 -1 1 1 -2 2 2 -2) (|unit-resolution| @x1166 @x1568 $x662) @x713 @x1574 @x718 @x685 @x681 @x697 @x696 @x701 @x1573 @x728 @x1558 @x1477 @x810 @x1547 @x1125 $x656)))
+(let (($x813 (not $x593)))
+(let (($x869 (not $x679)))
+(let (($x1579 (or $x486 $x286 $x336 $x869 $x813 $x742 $x705 $x704 $x741 $x740 $x743 $x815 $x816 $x1510 $x1197)))
+(let ((@x1581 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1 1 1 1 1 3 3 1 1 2 2 2 2) $x1579) @x1426 @x685 @x810 @x696 @x701 @x1527 @x1125 @x718 @x697 @x681 @x1558 @x1477 @x1574 @x1547 $x486)))
+(let (($x812 (not $x640)))
+(let (($x1586 (not $x1543)))
+(let (($x1585 (not $x585)))
+(let (($x1584 (not $x1236)))
+(let (($x1587 (or $x652 $x1584 $x1585 $x815 $x816 $x1510 $x1197 $x704 $x741 $x869 $x813 $x1586 $x812)))
+(let ((@x1589 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1) $x1587) @x1574 @x810 @x696 @x1125 @x728 @x1284 @x697 @x1477 @x718 @x1547 @x1573 (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1581 $x578) $x1236) $x652)))
+(let (($x1564 (not $x1499)))
+(let (($x1401 (not $x592)))
+(let (($x956 (not $x617)))
+(let (($x955 (not $x934)))
+(let (($x1593 (not $x632)))
+(let (($x1592 (not $x1500)))
+(let (($x799 (not $x609)))
+(let (($x1591 (not $x584)))
+(let (($x1321 (not $x1237)))
+(let (($x1594 (or $x651 $x1321 $x1591 $x798 $x799 $x1592 $x1593 $x955 $x956 $x1260 $x1401 $x1564 $x1189)))
+(let ((@x1596 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1) $x1594) (|unit-resolution| @x1268 (|unit-resolution| @x589 @x1561 $x586) $x670) @x797 @x851 @x855 @x1136 @x1296 @x1187 @x1252 @x999 (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1581 $x578) $x1237) @x1557 @x1546 $x651)))
+(let ((@x1597 (|unit-resolution| @x1304 @x1596 @x1589 (|unit-resolution| @x577 (|unit-resolution| @x1277 @x1576 @x1570 $x71) $x564) false)))
+(let ((@x1671 (|unit-resolution| (lemma @x1597 (or $x286 $x955 $x704 $x336 $x705 $x1090 $x412)) @x1670 @x697 @x1527 @x999 @x864 @x1185 $x286)))
+(let ((@x1673 (|unit-resolution| @x1149 (|unit-resolution| @x637 @x1671 $x634) $x658)))
+(let ((@x1676 (|unit-resolution| (|unit-resolution| @x1191 @x1136 (or $x336 $x311 $x1139 $x287)) @x1673 @x1671 @x1527 $x311)))
+(let ((@x1677 (|unit-resolution| @x1235 @x1671 $x656)))
+(let (($x1654 (or $x655 $x705 $x704 $x1139 $x1104 $x815 $x1564 $x798 $x955 $x1592 $x1090 $x708 $x312)))
+(let ((@x1602 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x841 $x642) $x1369)))
+(let ((@x1600 (hypothesis $x1500)))
+(let ((@x1623 (hypothesis $x1499)))
+(let ((@x1604 ((_ |th-lemma| arith farkas 2 2 2 2 1 1 1 1 1 1 1 1 1 1) (hypothesis $x487) @x1602 @x1256 @x1263 @x1136 @x761 @x1207 @x797 @x999 @x851 @x1600 @x855 @x841 @x1137 false)))
+(let ((@x1620 (|unit-resolution| (lemma @x1604 (or $x486 $x708 $x436 $x798 $x955 $x1592 $x312 $x1139)) @x761 @x1263 @x1207 @x999 @x1600 @x841 @x1137 $x486)))
+(let (($x1626 (not $x930)))
+(let (($x1089 (not $x625)))
+(let (($x1402 (not $x600)))
+(let (($x1625 (not $x649)))
+(let (($x1627 (or $x1301 $x1584 $x1585 $x798 $x799 $x1592 $x1593 $x955 $x956 $x1373 $x1625 $x655 $x1402 $x1090 $x1089 $x1626)))
+(let ((@x1629 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 1 -1 -1 1 2 -2 1 -1 -1 1 1 -1 -1) $x1627) @x964 @x797 @x851 @x833 @x855 @x1256 @x1284 @x1253 @x1207 @x999 @x830 @x1206 @x1602 @x1600 (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1620 $x578) $x1236) $x1301)))
+(let ((@x1630 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1) $x1594) @x1629 @x797 @x851 @x855 @x1136 @x1623 @x1207 (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1620 $x578) $x1237) @x999 @x1252 @x1296 @x1600 $x1260)))
+(let (($x757 (not $x587)))
+(let (($x1607 (>= ?x674 0)))
+(let (($x1611 (not $x1607)))
+(let ((@x1609 (hypothesis $x673)))
+(let ((@x1610 ((_ |th-lemma| arith farkas 1 1 -1 1 -1 -1 -1 -1 1 1 -1 1 1) @x685 @x697 @x696 @x681 @x701 @x1609 @x1252 @x1371 @x1256 @x1253 @x1137 @x1136 (hypothesis $x1607) false)))
+(let ((@x1613 (lemma @x1610 (or $x1611 $x704 $x705 $x743 $x1373 $x655 $x1139))))
+(let ((@x1618 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x757 $x1607)) (hypothesis $x587) (hypothesis $x1611) false)))
+(let ((@x1619 (lemma @x1618 (or $x757 $x1607))))
+(let ((@x1632 (|unit-resolution| @x1619 (|unit-resolution| @x1613 @x939 @x681 @x697 @x1602 @x1253 @x1137 $x1611) $x757)))
+(let ((@x1635 (|unit-resolution| @x1268 (|unit-resolution| @x589 (|unit-resolution| @x591 @x1632 $x461) $x586) @x1630 false)))
+(let ((@x1637 (lemma @x1635 (or $x436 $x705 $x704 $x655 $x1139 $x1564 $x798 $x955 $x1592 $x1090 $x708 $x312))))
+(let ((@x1638 (|unit-resolution| @x1637 @x1253 @x697 @x681 @x1137 @x1623 @x1207 @x999 @x1600 @x1206 @x1263 @x841 $x436)))
+(let ((@x1641 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -2 -2 2 -2 2) (or $x1354 $x705 $x437 $x815 $x816 $x704 $x741)) @x1638 @x696 @x697 @x681 @x897 @x810 $x1354)))
+(let ((@x1644 (|unit-resolution| @x1376 (|unit-resolution| @x826 (|unit-resolution| @x597 @x1638 $x594) $x667) @x1248 @x1137 @x1253 @x1641 @x1602 $x1260)))
+(let ((@x1648 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x673 $x437 $x782)) (|unit-resolution| @x691 (|unit-resolution| @x597 @x1638 $x594) $x676) @x1638 $x673)))
+(let ((@x1650 (|unit-resolution| @x1619 (|unit-resolution| @x1613 @x1648 @x681 @x697 @x1602 @x1253 @x1137 $x1611) $x757)))
+(let ((@x1653 (|unit-resolution| @x1268 (|unit-resolution| @x589 (|unit-resolution| @x591 @x1650 $x461) $x586) @x1644 false)))
+(let ((@x1681 (|unit-resolution| (lemma @x1653 $x1654) @x1670 @x697 @x1673 @x1248 @x1477 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2) (or $x1499 $x1139 $x287)) @x1673 @x1671 $x1499) @x1187 @x999 @x1546 @x864 @x1677 @x1676 $x655)))
+(let (($x1665 (or $x436 $x815 $x1510 $x704 $x764 $x705 $x708 $x798 $x955 $x1090 $x1592 $x312 $x1139)))
+(let (($x1658 (or $x652 $x1584 $x1585 $x798 $x799 $x1592 $x1593 $x955 $x956 $x1373 $x1625 $x708 $x1402 $x1090 $x1089 $x1626)))
+(let ((@x1660 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 2 2 1 1 1 1 1 -1 -1) $x1658) (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1620 $x578) $x1236) @x797 @x851 @x833 @x855 @x1256 @x964 @x1263 @x1207 @x999 @x830 @x1206 @x1602 @x1600 @x1284 $x652)))
+(let ((@x1661 (|unit-resolution| @x1304 @x1660 (|unit-resolution| @x577 (|unit-resolution| @x1277 @x762 @x1263 $x71) $x564) $x1301)))
+(let ((@x1664 ((_ |th-lemma| arith farkas 1 -1 1 -1 -1 1 2 -2 1 -1 -1 1 1 -1 -1 1) (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1620 $x578) $x1237) @x1296 @x897 @x810 (hypothesis $x873) @x1125 @x697 @x696 (|unit-resolution| @x1166 (|unit-resolution| @x645 @x841 $x642) $x662) @x713 @x762 @x685 @x681 @x701 @x939 @x1661 false)))
+(let ((@x1682 (|unit-resolution| (lemma @x1664 $x1665) @x1681 @x1547 @x697 @x1477 @x1670 @x1677 @x1187 @x999 @x864 @x1546 @x1676 @x1673 $x436)))
+(let ((@x1694 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -2 2 -2 -2 2 -1) (or $x930 $x815 $x816 $x704 $x362 $x741 $x901)) @x696 @x810 (or $x930 $x815 $x704 $x362 $x901))))
+(let ((@x1695 (|unit-resolution| @x1694 (|unit-resolution| @x826 (|unit-resolution| @x597 @x1682 $x594) $x667) @x697 @x839 @x1477 $x930)))
+(let ((@x1667 ((_ |th-lemma| arith farkas 1 -1 1 -1 -1 -1 1 1 -1 1 1) @x681 @x701 @x697 @x696 (hypothesis $x487) @x1371 @x1256 @x1263 @x1137 @x1136 @x1185 false)))
+(let ((@x1669 (lemma @x1667 (or $x486 $x705 $x704 $x1373 $x708 $x1139 $x412))))
+(let ((@x1696 (|unit-resolution| @x1669 @x1670 @x697 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x1676 $x642) $x1369) @x1677 @x1673 @x1185 $x486)))
+(let ((@x1699 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 2 2 1 1 1 1 1 -1 -1) $x1658) (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1696 $x578) $x1236) @x797 @x851 @x833 @x855 @x1256 @x1695 @x1677 @x1187 @x999 @x830 @x864 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x1676 $x642) $x1369) @x1546 @x1284 $x652)))
+(let ((@x1700 (|unit-resolution| @x1304 @x1699 (|unit-resolution| @x577 (|unit-resolution| @x1277 @x1681 @x1677 $x71) $x564) $x1301)))
+(let ((@x1702 ((_ |th-lemma| arith farkas -2 -1 1 -1 -1 1 1 -1 -2 2 -1 1 1 -1 -1 1 1) @x1682 (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1696 $x578) $x1237) @x1296 @x1700 @x1477 @x810 @x1547 @x1125 @x697 @x696 (|unit-resolution| @x1166 (|unit-resolution| @x645 @x1676 $x642) $x662) @x713 @x1681 @x685 @x1670 @x701 (|unit-resolution| @x691 (|unit-resolution| @x597 @x1682 $x594) $x676) false)))
+(let ((@x1736 (|unit-resolution| (lemma @x1702 (or $x362 $x704 $x955 $x412 $x1104 $x336)) @x1527 @x1027 @x1185 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x778 $x387 $x955)) @x1027 @x1024 $x778) @x1734 $x362)))
+(let ((@x1737 (|unit-resolution| (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1) (or $x705 $x361 $x900)) @x1366 (or $x705 $x361)) @x1736 $x705)))
+(let ((@x1741 (|unit-resolution| @x1149 (|unit-resolution| @x637 (|unit-resolution| @x1526 @x1736 @x1024 $x286) $x634) $x658)))
+(let ((@x1743 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x821 $x1354)) (|unit-resolution| @x623 @x1736 $x619) $x1354)))
+(let ((@x1744 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 2 1 2 2 2) (or $x1374 $x1139 $x1189 $x1090 $x1197 $x1196 $x311)) @x1743 @x1542 @x1741 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x838 $x668)) @x1737 $x838) @x1136 @x1125 $x311)))
+(let ((@x1747 (|unit-resolution| @x1235 (|unit-resolution| @x1526 @x1736 @x1024 $x286) $x656)))
+(let ((@x1750 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1) (or $x486 $x336 $x1373 $x1625 $x708 $x1139 $x1189)) @x1527 @x1136 @x1256 @x1747 @x1741 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x1744 $x642) $x1369) $x486)))
+(let ((@x1719 (|unit-resolution| @x958 @x851 @x797 (or $x361 $x955 $x436 $x798))))
+(let ((@x1755 (|unit-resolution| @x826 (|unit-resolution| @x597 (|unit-resolution| @x1719 @x1736 @x1027 @x1187 $x436) $x594) $x667)))
+(let (($x1756 (or $x652 $x901 $x1584 $x1585 $x815 $x816 $x1592 $x1593 $x1373 $x1625 $x708 $x1402 $x1089 $x900)))
+(let ((@x1758 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1) $x1756) @x1747 @x810 @x833 @x855 @x1256 @x1284 @x830 @x1477 @x1755 @x1366 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x1744 $x642) $x1369) @x1546 (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1750 $x578) $x1236) $x652)))
+(let ((@x1709 (|unit-resolution| (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1) (or $x705 $x361 $x900)) @x1366 (or $x705 $x361)) @x1025 $x705)))
+(let ((@x1715 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 2 1 2 2 2) (or $x1374 $x1139 $x1189 $x1090 $x1197 $x1196 $x311)) @x1385 @x1542 @x1137 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x838 $x668)) @x1709 $x838) @x1136 @x1125 $x311)))
+(let ((@x1722 (|unit-resolution| @x691 (|unit-resolution| @x597 (|unit-resolution| @x1719 @x1025 @x999 @x1207 $x436) $x594) $x676)))
+(let (($x1723 (or $x1611 $x955 $x956 $x1401 $x1373 $x1625 $x655 $x1139 $x1189 $x798 $x799 $x782 $x742 $x740 $x1374)))
+(let ((@x1725 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 1 -1 -1 1 1 -1 1 -2 2 -1 1 -1 1) $x1723) @x1253 @x797 @x851 @x701 @x1136 @x1256 @x685 @x1137 @x1722 @x1207 @x999 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x1715 $x642) $x1369) @x1385 @x1252 $x1611)))
+(let ((@x1726 (|unit-resolution| @x826 (|unit-resolution| @x597 (|unit-resolution| @x1719 @x1025 @x999 @x1207 $x436) $x594) $x667)))
+(let ((@x1729 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 1 1) (or $x462 $x361 $x901 $x815 $x816 $x1402 $x1089 $x900 $x336)) @x1025 @x810 @x830 @x833 @x1527 @x897 @x1726 @x1366 $x462)))
+(let ((@x1733 (lemma (|unit-resolution| @x1619 (|unit-resolution| @x591 @x1729 $x587) @x1725 false) (or $x655 $x1139 $x798 $x955 $x361 $x336 $x815))))
+(let ((@x1760 (|unit-resolution| @x1277 (|unit-resolution| @x1733 @x1741 @x1187 @x1027 @x1736 @x1527 @x1477 $x655) @x1747 $x71)))
+(let ((@x1765 (|unit-resolution| @x691 (|unit-resolution| @x597 (|unit-resolution| @x1719 @x1736 @x1027 @x1187 $x436) $x594) $x676)))
+(let ((@x1766 ((_ |th-lemma| arith farkas -1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1 1) @x1765 (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1750 $x578) $x1237) @x1296 @x1187 @x797 @x1547 @x1125 (|unit-resolution| @x1166 (|unit-resolution| @x645 @x1744 $x642) $x662) @x713 (|unit-resolution| @x1733 @x1741 @x1187 @x1027 @x1736 @x1527 @x1477 $x655) @x685 @x701 @x1743 (|unit-resolution| @x1304 (|unit-resolution| @x577 @x1760 $x564) @x1758 $x1301) false)))
+(let ((@x1768 (lemma @x1766 (or $x336 $x387 $x412))))
+(let ((@x1829 (|unit-resolution| (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2) (or $x873 $x1196 $x337)) @x1542 (or $x873 $x337)) (|unit-resolution| @x1768 @x1185 @x1815 $x336) $x873)))
+(let ((@x1820 (|unit-resolution| @x806 (|unit-resolution| @x613 @x1815 $x610) $x671)))
+(let ((@x1805 (hypothesis $x1139)))
+(let ((@x1807 (|unit-resolution| @x1556 @x1553 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1) (or $x658 $x286 $x1564)) @x1426 @x1805 $x1564) false)))
+(let ((@x1811 (|unit-resolution| @x637 (|unit-resolution| (lemma @x1807 (or $x286 $x658)) @x1805 $x286) $x634)))
+(let ((@x1813 (lemma (|unit-resolution| @x1149 @x1811 @x1805 false) $x658)))
+(let (($x1791 (or $x1586 $x815 $x816 $x704 $x741 $x1510 $x1197 $x1139 $x461 $x742 $x705 $x740 $x743)))
+(let ((@x1831 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 2 4 4 2 2 1 2 2 2 2 2) $x1791) @x810 @x696 @x701 @x1125 @x1813 @x685 (or $x1586 $x815 $x704 $x1510 $x461 $x705 $x743))))
+(let ((@x1833 (|unit-resolution| @x589 (|unit-resolution| @x1831 @x1820 @x1573 @x1826 @x1609 @x1477 @x1829 $x461) $x586)))
+(let ((@x1836 (|unit-resolution| @x1566 @x701 @x1136 @x696 (or $x311 $x1564 $x286 $x705 $x412 $x704))))
+(let ((@x1838 (|unit-resolution| @x645 (|unit-resolution| @x1836 @x1820 @x1557 @x1426 @x1185 @x1826 $x311) $x642)))
+(let ((@x1842 (|unit-resolution| (|unit-resolution| @x1669 @x1813 (or $x486 $x705 $x704 $x1373 $x708 $x412)) (|unit-resolution| @x1396 @x1838 $x1369) @x1263 @x1826 @x1820 @x1185 $x486)))
+(let ((@x1846 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1) $x1587) @x810 @x696 @x1125 @x728 @x718 @x1284 (or $x652 $x1584 $x815 $x1510 $x704 $x869 $x1586))))
+(let ((@x1847 (|unit-resolution| @x1846 (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1842 $x578) $x1236) @x1573 @x1820 @x1477 (|unit-resolution| @x723 @x1833 $x679) @x1829 $x652)))
+(let ((@x1818 (|unit-resolution| @x1115 (|unit-resolution| @x629 (|unit-resolution| @x1768 @x1185 @x1815 $x336) $x626) $x665)))
+(let ((@x1821 ((_ |th-lemma| arith farkas -1 1/3 -1/3 4/3 1/3 -1/3 -1/3 1/3 1/3 -1/3 1/3 -2/3 2/3 2/3 -2/3 1/3 -1/3 1) @x701 @x1820 @x696 @x1185 @x1249 @x1252 @x1371 @x1256 @x1253 @x1623 @x1136 @x1187 @x797 @x1818 @x855 (hypothesis $x930) @x830 @x681 false)))
+(let ((@x1849 (|unit-resolution| (lemma @x1821 (or $x655 $x412 $x1260 $x1373 $x1564 $x1626 $x705)) @x1185 (|unit-resolution| @x1268 @x1833 $x670) (|unit-resolution| @x1396 @x1838 $x1369) @x1557 (hypothesis $x930) @x1826 $x655)))
+(let ((@x1852 (|unit-resolution| @x1304 (|unit-resolution| @x577 (|unit-resolution| @x1277 @x1849 @x1263 $x71) $x564) @x1847 $x1301)))
+(let ((@x1855 ((_ |th-lemma| arith farkas 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1) @x701 @x1820 @x696 (|unit-resolution| @x1268 @x1833 $x670) @x1252 (|unit-resolution| @x1166 @x1838 $x662) @x713 @x1849 @x1557 @x1136 @x1609 @x685 (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1842 $x578) $x1237) @x1296 @x1852 @x1826 false)))
+(let ((@x1858 (|unit-resolution| (lemma @x1855 (or $x412 $x743 $x708 $x1626 $x286)) @x939 @x1263 @x964 @x1426 $x412)))
+(let ((@x1860 (|unit-resolution| @x997 (|unit-resolution| @x607 @x1858 $x603) $x931)))
+(let ((@x1861 (|unit-resolution| @x1037 (|unit-resolution| @x607 @x1858 $x603) $x1022)))
+(let ((@x1865 (|unit-resolution| @x863 (|unit-resolution| @x621 (|unit-resolution| @x1064 @x1858 $x361) $x618) $x838)))
+(let ((@x1868 (|unit-resolution| (|unit-resolution| @x1070 @x797 (or $x436 (not $x931) $x411 $x386)) @x1860 @x761 @x1858 $x386)))
+(let ((@x1874 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2 2 2 2 2) (or (not $x1022) $x798 $x336 $x1090 $x955 $x956 $x1089)) @x833 @x851 (or (not $x1022) $x798 $x336 $x1090 $x955))))
+(let ((@x1875 (|unit-resolution| @x1874 (|unit-resolution| @x948 (|unit-resolution| @x613 @x1868 $x610) $x934) @x1865 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x773 (not $x931) $x411)) @x1860 @x1858 $x773) @x1861 $x336)))
+(let ((@x1877 (|unit-resolution| @x1115 (|unit-resolution| @x629 @x1875 $x626) $x665)))
+(let ((@x1878 (|unit-resolution| @x924 (|unit-resolution| @x621 (|unit-resolution| @x1064 @x1858 $x361) $x618) $x668)))
+(let ((@x1879 (|unit-resolution| @x806 (|unit-resolution| @x613 @x1868 $x610) $x671)))
+(let (($x1000 (not $x931)))
+(let ((@x1881 ((_ |th-lemma| arith assign-bounds 2 2 1 1 1 1 1 1 1 1 1) (or $x311 $x705 $x740 $x704 $x741 $x1564 $x1189 $x436 $x799 $x858 $x1593 $x1000))))
+(let ((@x1882 (|unit-resolution| @x1881 @x761 @x696 @x701 @x855 @x1136 @x797 @x1879 @x1878 @x1877 @x1860 @x1557 $x311)))
+(let ((@x1887 (|unit-resolution| @x1268 (|unit-resolution| @x589 (|unit-resolution| @x1098 @x1858 $x461) $x586) $x670)))
+(let ((@x1888 (|unit-resolution| @x723 (|unit-resolution| @x589 (|unit-resolution| @x1098 @x1858 $x461) $x586) $x679)))
+(let ((@x1892 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2 2 2 2 2) (or (not $x1022) $x798 $x486 $x782 $x869 $x742 $x813)) @x685 @x718 (or (not $x1022) $x798 $x486 $x782 $x869))))
+(let ((@x1893 (|unit-resolution| @x1892 @x1861 @x942 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x773 $x1000 $x411)) @x1860 @x1858 $x773) @x1888 $x486)))
+(let (($x1078 (not $x1022)))
+(let (($x1896 (or $x652 $x1090 $x1089 $x955 $x956 $x869 $x813 $x1586 $x812 $x1584 $x1585 $x816 $x1196 $x1197 $x1078)))
+(let ((@x1898 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -2 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1) $x1896) @x1888 @x810 @x851 @x833 @x1125 @x728 @x1284 @x718 (|unit-resolution| @x948 (|unit-resolution| @x613 @x1868 $x610) $x934) @x1865 @x1861 @x1542 @x1573 (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1893 $x578) $x1236) $x652)))
+(let (($x1900 (or $x651 $x705 $x740 $x704 $x741 $x1260 $x1401 $x1564 $x1189 $x1321 $x1591 $x799 $x858 $x1593 $x1000)))
+(let ((@x1902 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -2 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1) $x1900) @x1879 @x797 @x696 @x701 @x855 @x1136 @x1296 @x1252 @x1878 @x1877 @x1887 @x1860 (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1893 $x578) $x1237) @x1557 $x651)))
+(let ((@x1905 (|unit-resolution| @x1277 (|unit-resolution| @x577 (|unit-resolution| @x1304 @x1902 @x1898 $x70) $x565) @x1263 $x764)))
+(let ((@x1906 ((_ |th-lemma| arith farkas -1 -1 -1 1 -3 3 -1 1 -1 1 1 -1 -2 -2 2 2 1) @x1256 @x1905 @x964 @x830 @x1878 @x701 @x1879 @x696 @x1887 @x1252 @x1557 @x1136 @x797 @x1877 @x855 @x1860 (|unit-resolution| @x1396 (|unit-resolution| @x645 @x1882 $x642) $x1369) false)))
+(let ((@x1919 (|unit-resolution| @x597 (|unit-resolution| (lemma @x1906 (or $x436 $x708 $x286)) @x1426 @x1263 $x436) $x594)))
+(let ((@x1922 (|unit-resolution| @x1892 @x1038 (|unit-resolution| @x691 @x1919 $x676) @x1067 @x1131 $x486)))
+(let ((@x1925 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -2 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1) $x1896) @x1917 @x810 @x851 @x833 @x1125 @x728 @x1284 @x718 @x1131 @x1087 @x1038 @x1542 @x1573 (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1922 $x578) $x1236) $x652)))
+(let ((@x1929 (|unit-resolution| @x629 (|unit-resolution| @x1874 @x1917 @x1087 @x1067 @x1038 $x336) $x626)))
+(let ((@x1931 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -2 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1) $x1900) (|unit-resolution| @x1115 @x1929 $x665) @x797 @x696 @x701 @x855 @x1136 @x1296 @x1252 @x1086 (|unit-resolution| @x806 (|unit-resolution| @x613 @x1915 $x610) $x671) @x1269 @x998 (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1922 $x578) $x1237) @x1557 $x651)))
+(let ((@x1934 (|unit-resolution| @x1277 (|unit-resolution| @x577 (|unit-resolution| @x1304 @x1931 @x1925 $x70) $x565) @x1263 $x764)))
+(let ((@x1910 ((_ |th-lemma| arith farkas -1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1) @x1256 @x1253 @x898 @x830 @x1249 @x1252 @x1206 @x833 @x999 @x851 (hypothesis $x1543) @x728 (hypothesis $x1247) false)))
+(let ((@x1935 (|unit-resolution| (lemma @x1910 (or $x1259 $x655 $x901 $x1260 $x1090 $x955 $x1586)) @x1934 (|unit-resolution| @x826 @x1919 $x667) @x1269 @x1087 @x1917 @x1573 $x1259)))
+(let ((@x1938 (|unit-resolution| @x645 (|unit-resolution| @x647 (|unit-resolution| @x1310 @x1935 $x1119) $x311) $x642)))
+(let ((@x1940 ((_ |th-lemma| arith farkas -1 -1 -2 -1 1 -1 1 1 -1 1 -1 -1 1 1) @x1256 @x1934 (|unit-resolution| @x647 (|unit-resolution| @x1310 @x1935 $x1119) $x311) (|unit-resolution| @x826 @x1919 $x667) @x830 @x1269 @x1252 @x1087 @x833 @x1917 @x851 @x1573 @x728 (|unit-resolution| @x1396 @x1938 $x1369) false)))
+(let ((@x1943 (|unit-resolution| (lemma @x1940 (or $x411 $x708 $x286)) @x1426 @x1263 $x411)))
+(let ((@x1944 (|unit-resolution| @x1508 @x1943 $x386)))
+(let ((@x1948 (|unit-resolution| (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2) (or $x873 $x1196 $x337)) @x1542 (or $x873 $x337)) (|unit-resolution| @x1768 @x1943 @x1944 $x336) $x873)))
+(let ((@x1950 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 -1 1 1) (or $x1510 $x1197 $x387 $x1374 $x740 $x286)) @x1125 @x701 (or $x1510 $x387 $x1374 $x286))))
+(let ((@x1956 (|unit-resolution| @x924 (|unit-resolution| @x621 (|unit-resolution| @x1526 @x1944 @x1426 $x361) $x618) $x668)))
+(let ((@x1958 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -2 -2 2 -2 2) (or $x1354 $x705 $x437 $x815 $x816 $x704 $x741)) @x696 @x810 (or $x1354 $x705 $x437 $x815 $x704))))
+(let ((@x1959 (|unit-resolution| @x1958 @x1956 (|unit-resolution| @x789 (|unit-resolution| @x605 @x1943 $x602) $x774) (|unit-resolution| (lemma @x1906 (or $x436 $x708 $x286)) @x1426 @x1263 $x436) (|unit-resolution| @x1950 @x1948 @x1426 @x1944 $x1374) (|unit-resolution| @x806 (|unit-resolution| @x613 @x1944 $x610) $x671) false)))
+(let ((@x1992 (|unit-resolution| (lemma @x1959 (or $x286 $x708)) @x1263 $x286)))
+(let ((@x1240 (|unit-resolution| @x613 (|unit-resolution| @x1070 @x761 @x797 @x998 @x842 $x386) $x610)))
+(let ((@x1242 (|unit-resolution| @x1092 (|unit-resolution| @x948 @x1240 $x934) @x833 @x842 @x1087 @x851 $x336)))
+(let ((@x1244 (|unit-resolution| @x1115 (|unit-resolution| @x629 @x1242 $x626) (|unit-resolution| @x1102 @x761 @x842 @x1076 $x858) false)))
+(let ((@x1325 (|unit-resolution| @x597 (|unit-resolution| (lemma @x1244 (or $x436 $x411 $x287)) @x842 @x1076 $x436) $x594)))
+(let ((@x1265 (|unit-resolution| @x629 (|unit-resolution| @x1092 @x1110 @x833 @x842 @x1087 @x851 $x336) $x626)))
+(let ((@x1270 (|unit-resolution| @x860 (|unit-resolution| @x1115 @x1265 $x665) @x842 @x729 @x843 $x312)))
+(let ((@x1274 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1119 $x1247)) (|unit-resolution| @x647 @x1270 $x643) $x1247)))
+(let ((@x1275 (|unit-resolution| @x1262 @x1274 @x1086 @x1269 @x729 @x898 @x848 (|unit-resolution| @x1115 @x1265 $x665) $x655)))
+(let ((@x1287 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x486 $x813 $x411 $x782 $x742 $x869)) @x866 @x685 @x842 @x1131 @x718 $x486)))
+(let ((@x1293 ((_ |th-lemma| arith assign-bounds 1 -3/2 3/2 -1 1/2 -1/2 1/2 -1/2 -1 1 1/2 -1/2 -1/2 1/2 1/2 -1/2 1/2) (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1287 $x578) $x1236) @x718 @x1131 @x1284 @x1087 @x729 @x728 @x833 @x1038 @x810 @x848 @x851 (|unit-resolution| @x1159 (|unit-resolution| @x647 @x1270 $x643) $x1103) @x713 @x1275 @x685 @x866 $x652)))
+(let ((@x1300 ((_ |th-lemma| arith assign-bounds 1 -3/2 3/2 -1 1/2 -1/2 1/2 -1/2 -1 1 1/2 -1/2 -1/2 1/2 1/2 -1/2 1/2) (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1287 $x578) $x1237) @x1252 @x1269 @x1296 @x1086 @x1137 @x1136 @x701 @x998 @x797 @x1133 @x696 @x1274 @x1256 @x1263 @x830 @x898 $x651)))
+(let ((@x1305 (|unit-resolution| @x1304 @x1300 @x1293 (|unit-resolution| @x577 (|unit-resolution| @x1277 @x1275 @x1263 $x71) $x564) false)))
+(let ((@x1329 (|unit-resolution| (lemma @x1305 (or $x386 $x1139 $x708 $x901 (not $x659) $x782 $x411)) (|unit-resolution| @x826 @x1325 $x667) (|unit-resolution| @x1235 @x1076 $x656) @x1150 @x1145 (|unit-resolution| @x691 @x1325 $x676) @x842 $x386)))
+(let ((@x1331 (|unit-resolution| @x948 (|unit-resolution| @x613 @x1329 $x610) $x934)))
+(let ((@x1333 ((_ |th-lemma| arith assign-bounds 2 -1) (or $x778 $x387 $x955))))
+(let ((@x1336 (|unit-resolution| @x629 (|unit-resolution| @x1092 @x1331 @x833 @x842 @x1087 @x851 $x336) $x626)))
+(let ((@x1337 (|unit-resolution| @x1115 @x1336 $x665)))
+(let ((@x1313 (|unit-resolution| @x629 (|unit-resolution| @x1092 @x1027 @x833 @x842 @x1087 @x851 $x336) $x626)))
+(let ((@x1315 ((_ |th-lemma| arith farkas -1 -1 -1 1 -1 1 -1 1 1) @x1024 @x841 @x729 @x728 @x851 @x842 (|unit-resolution| @x1115 @x1313 $x665) @x855 @x1027 false)))
+(let ((@x1338 (|unit-resolution| (lemma @x1315 (or $x312 $x387 (not $x659) $x411)) @x1329 @x1145 @x842 $x312)))
+(let ((@x1341 (|unit-resolution| @x1262 (|unit-resolution| @x1310 (|unit-resolution| @x647 @x1338 $x643) $x1247) @x1337 @x1269 @x1145 (|unit-resolution| @x826 @x1325 $x667) (|unit-resolution| @x1333 @x1331 @x1329 $x778) @x1086 $x655)))
+(let ((@x1343 (|unit-resolution| @x577 (|unit-resolution| @x1277 @x1341 (|unit-resolution| @x1235 @x1076 $x656) $x71) $x564)))
+(let ((@x1344 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x486 $x813 $x411 $x782 $x742 $x869)) (|unit-resolution| @x691 @x1325 $x676) @x685 @x842 @x1131 @x718 $x486)))
+(let ((@x1320 ((_ |th-lemma| arith farkas 1 -1 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 1) @x681 @x701 @x856 @x855 @x697 @x1150 @x1136 @x696 (hypothesis $x1237) @x1252 @x1249 @x1296 @x1318 (hypothesis $x931) @x797 @x1076 false)))
+(let ((@x1323 (lemma @x1320 (or $x651 $x705 $x858 $x704 $x1321 $x1260 $x1000 $x287))))
+(let ((@x1348 (|unit-resolution| @x1323 @x1086 @x1337 (|unit-resolution| @x806 (|unit-resolution| @x613 @x1329 $x610) $x671) (|unit-resolution| @x1298 (|unit-resolution| @x581 @x1344 $x578) $x1237) @x1269 @x998 @x1076 $x651)))
+(let ((@x1351 ((_ |th-lemma| arith farkas -1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1) @x1331 @x1145 @x728 @x851 @x1337 @x855 (|unit-resolution| @x1291 (|unit-resolution| @x581 @x1344 $x578) $x1236) @x718 @x1131 @x1284 (|unit-resolution| @x1304 @x1348 @x1343 $x1302) @x1038 @x810 @x1329 false)))
+(let ((@x1353 (lemma @x1351 (or $x411 $x287))))
+(let ((@x1993 (|unit-resolution| @x1353 @x1992 $x411)))
+(let ((@x1994 (|unit-resolution| @x1508 @x1993 $x386)))
+(let ((@x1996 (|unit-resolution| @x948 (|unit-resolution| @x613 @x1994 $x610) $x934)))
+(let ((@x1998 (|unit-resolution| @x792 (|unit-resolution| @x605 @x1993 $x602) $x773)))
+(let ((@x1964 (|unit-resolution| @x613 (|unit-resolution| @x1508 (|unit-resolution| @x1353 @x1076 $x411) $x386) $x610)))
+(let ((@x1967 (|unit-resolution| @x789 (|unit-resolution| @x605 (|unit-resolution| @x1353 @x1076 $x411) $x602) $x774)))
+(let ((@x1970 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 -1 1 1 -1 1 1 -1) (or $x704 $x741 $x311 $x1139 $x1189 $x815 $x1196 $x1197 $x437 $x816)) @x696 @x1125 @x1136 @x810 (or $x704 $x311 $x1139 $x815 $x1196 $x437))))
+(let ((@x1973 (|unit-resolution| (|unit-resolution| @x1970 @x1542 @x1813 (or $x704 $x311 $x815 $x437)) (|unit-resolution| @x1205 @x1188 @x1076 (|unit-resolution| @x1353 @x1076 $x411) $x436) @x1188 @x1967 (|unit-resolution| @x806 @x1964 $x671) false)))
+(let ((@x2008 (|unit-resolution| @x1115 (|unit-resolution| @x629 (|unit-resolution| @x1768 @x1993 @x1994 $x336) $x626) $x665)))
+(let ((@x2012 (|unit-resolution| @x1144 (|unit-resolution| @x637 @x1992 $x634) $x659)))
+(let ((@x2049 (lemma ((_ |th-lemma| arith farkas 1 -1 1 -1 -1 -1 1 -1 1 1) @x729 @x728 @x856 @x855 @x1207 @x761 @x797 @x999 @x851 @x841 false) (or $x436 (not $x659) $x858 $x798 $x955 $x312))))
+(let ((@x2050 (|unit-resolution| @x2049 @x2012 @x2008 @x1998 @x1996 (|unit-resolution| (lemma @x1973 (or $x311 $x287)) @x1992 $x311) $x436)))
+(let ((@x2000 (|unit-resolution| @x645 (|unit-resolution| (lemma @x1973 (or $x311 $x287)) @x1992 $x311) $x642)))
+(let ((@x2001 (|unit-resolution| @x1396 @x2000 $x1369)))
+(let ((@x2002 (|unit-resolution| @x1333 @x1996 @x1994 $x778)))
+(let ((@x2053 (|unit-resolution| @x806 (|unit-resolution| @x613 @x1994 $x610) $x671)))
+(let ((@x2006 (|unit-resolution| @x1768 @x1993 @x1994 $x336)))
+(let ((@x2027 (|unit-resolution| @x691 (|unit-resolution| @x597 (|unit-resolution| @x1719 @x1025 @x1996 @x1998 $x436) $x594) $x676)))
+(let ((@x2028 (|unit-resolution| @x826 (|unit-resolution| @x597 (|unit-resolution| @x1719 @x1025 @x1996 @x1998 $x436) $x594) $x667)))
+(let ((@x1982 (|unit-resolution| (|unit-resolution| @x1376 @x1813 (or $x655 $x1373 $x1104 $x901 $x1260 $x1374)) @x1253 @x1370 @x898 @x1248 @x1371 $x1260)))
+(let ((@x1984 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 1 -1 -1 1 1 -1 1 -2 2 -1 1 -1 1) $x1723) @x797 @x851 @x701 @x1136 @x1256 @x1813 @x685 @x1252 (or $x1611 $x955 $x1373 $x655 $x798 $x782 $x1374))))
+(let ((@x1986 (|unit-resolution| @x1619 (|unit-resolution| @x1984 @x1253 @x1370 @x866 @x1207 @x999 @x1371 $x1611) $x757)))
+(let ((@x1989 (|unit-resolution| @x1268 (|unit-resolution| @x589 (|unit-resolution| @x591 @x1986 $x461) $x586) @x1982 false)))
+(let ((@x1991 (lemma @x1989 (or $x655 $x1374 $x901 $x1104 $x1373 $x782 $x798 $x955))))
+(let ((@x2029 (|unit-resolution| @x1991 @x1385 @x2028 @x2002 @x2001 @x2027 @x1998 @x1996 $x655)))
+(let ((@x2009 (|unit-resolution| @x789 (|unit-resolution| @x605 @x1993 $x602) $x774)))
+(let ((@x2004 (|unit-resolution| @x1277 (|unit-resolution| @x1991 @x1370 @x898 @x2002 @x2001 @x866 @x1998 @x1996 $x655) @x1263 $x71)))
+(let ((@x2010 (|unit-resolution| @x1166 @x2000 $x662)))
+(let (($x731 (not $x659)))
+(let (($x814 (not $x648)))
+(let (($x2015 (or $x652 $x1585 $x732 $x814 $x764 $x901 $x1402 $x858 $x1593 $x815 $x816 $x900 $x1089 $x731 $x812 (not $x1367))))
+(let ((@x2017 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 1 1 -1 1 -1 1 -1 1 1 -1 -2 2 1) $x2015) (|unit-resolution| @x1411 @x1441 $x1367) @x810 @x833 @x855 @x728 @x713 @x1284 (|unit-resolution| @x1991 @x1370 @x898 @x2002 @x2001 @x866 @x1998 @x1996 $x655) @x2012 @x2010 @x2009 @x2008 @x898 @x1366 @x830 $x652)))
+(let (($x2019 (or $x651 $x1591 $x1373 $x1625 $x708 $x782 $x742 $x1196 $x1197 $x798 $x799 $x1374 $x740 $x1139 $x1189 $x1437)))
+(let ((@x2021 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 1 1 -1 1 -1 1 -1 1 1 -1 -2 2 1) $x2019) (|unit-resolution| @x1443 @x1441 $x1368) @x797 @x701 @x1125 @x1136 @x1256 @x1296 @x1263 @x1813 @x866 @x1998 @x1542 @x2001 @x1370 @x685 $x651)))
+(let ((@x2022 (|unit-resolution| @x1304 @x2021 @x2017 (|unit-resolution| @x577 @x2004 $x564) false)))
+(let ((@x2032 (|unit-resolution| (lemma @x2022 (or $x1409 $x708 $x782 $x1374 $x901)) @x2027 @x1263 @x1385 @x2028 $x1409)))
+(let ((@x2035 (|unit-resolution| @x1291 (|unit-resolution| @x581 (|unit-resolution| @x583 @x2032 $x486) $x578) $x1236)))
+(let ((@x2038 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -2 -2 2 2 -2 2) (or $x1500 $x858 $x487 $x732 $x814 $x764 $x731 $x812)) @x2029 @x713 @x728 @x2012 @x2010 @x2008 (|unit-resolution| @x583 @x2032 $x486) $x1500)))
+(let ((@x2040 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1) $x1756) @x810 @x833 @x855 @x1256 @x1366 @x830 @x1284 (or $x652 $x901 $x1584 $x815 $x1592 $x1373 $x708))))
+(let ((@x2042 (|unit-resolution| @x1304 (|unit-resolution| @x2040 @x2038 @x2035 @x1263 @x2009 @x2028 @x2001 $x652) (|unit-resolution| @x577 (|unit-resolution| @x1277 @x2029 @x1263 $x71) $x564) $x1301)))
+(let ((@x2043 (|unit-resolution| @x1298 (|unit-resolution| @x581 (|unit-resolution| @x583 @x2032 $x486) $x578) $x1237)))
+(let ((@x2044 ((_ |th-lemma| arith farkas 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 1) @x2010 @x713 @x2029 @x2043 @x1296 @x2042 @x2027 @x685 @x1542 @x1125 @x1998 @x797 @x1385 @x701 @x2006 false)))
+(let ((@x2055 (|unit-resolution| @x621 (|unit-resolution| (lemma @x2044 (or $x361 $x708)) @x1263 $x361) $x618)))
+(let ((@x1979 (lemma (|unit-resolution| @x924 (hypothesis $x618) (hypothesis $x705) false) (or (not $x618) $x668))))
+(let ((@x2056 (|unit-resolution| @x1979 @x2055 $x668)))
+(let ((@x2059 (|unit-resolution| @x1991 (|unit-resolution| @x826 (|unit-resolution| @x597 @x2050 $x594) $x667) (|unit-resolution| @x1958 @x2050 @x2009 @x2056 @x2053 $x1354) @x2002 @x2001 (|unit-resolution| @x691 (|unit-resolution| @x597 @x2050 $x594) $x676) @x1998 @x1996 $x655)))
+(let ((@x2061 (|unit-resolution| (|unit-resolution| @x1669 @x1813 (or $x486 $x705 $x704 $x1373 $x708 $x412)) @x2056 @x1263 @x2001 @x2053 @x1993 $x486)))
+(let ((@x2063 (|unit-resolution| @x589 (|unit-resolution| @x707 @x2050 @x2053 @x2006 @x2056 $x461) $x586)))
+(let ((@x2065 (|unit-resolution| @x1465 (|unit-resolution| @x1268 @x2063 $x670) @x2009 @x2012 @x2002 @x2061 @x2008 (|unit-resolution| @x826 (|unit-resolution| @x597 @x2050 $x594) $x667) $x652)))
+(let ((@x2071 (|unit-resolution| @x1323 (|unit-resolution| @x1268 @x2063 $x670) @x1992 @x2008 @x2053 (|unit-resolution| @x1298 (|unit-resolution| @x581 @x2061 $x578) $x1237) (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x931 $x412 $x798)) @x1998 @x1993 $x931) @x2056 $x651)))
+(let ((@x2073 (|unit-resolution| @x577 (|unit-resolution| @x1304 @x2071 @x2065 $x70) (|unit-resolution| @x1277 @x2059 @x1263 $x71) false)))
+(let ((@x2074 (lemma @x2073 $x708)))
+(let ((@x1771 (|unit-resolution| @x621 (|unit-resolution| @x1526 (|unit-resolution| @x1235 @x709 $x287) @x1024 $x361) $x618)))
+(let ((@x1772 (|unit-resolution| @x924 @x1771 $x668)))
+(let ((@x1773 (|unit-resolution| @x1768 @x1185 @x1024 $x336)))
+(let ((@x1769 (|unit-resolution| @x1235 @x709 $x287)))
+(let ((@x1776 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 1 -1 -1 1 -1 1) (or $x437 $x815 $x816 $x704 $x741 $x1196 $x337 $x286 $x1197)) @x1769 @x696 @x1773 @x1125 @x810 @x1734 @x1477 @x1542 $x437)))
+(let ((@x1782 (|unit-resolution| @x1566 (|unit-resolution| @x1556 (|unit-resolution| @x639 @x1769 $x635) $x1499) @x701 @x1185 @x1136 @x1769 @x1734 @x1772 @x696 $x311)))
+(let ((@x1790 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1) (or $x658 $x286 $x1564)) (|unit-resolution| @x1556 (|unit-resolution| @x639 @x1769 $x635) $x1499) @x1769 $x658)))
+(let ((@x1793 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 2 4 4 2 2 1 2 2 2 2 2) $x1791) (|unit-resolution| @x738 (|unit-resolution| @x599 @x1776 $x595) $x673) @x810 @x696 @x701 @x1125 @x1790 @x1734 @x1772 (|unit-resolution| @x1572 (|unit-resolution| @x639 @x1769 $x635) $x1543) @x1477 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2) (or $x873 $x1196 $x337)) @x1773 @x1542 $x873) @x685 $x461)))
+(let ((@x1796 ((_ |th-lemma| arith farkas 4 -1 3 -3 -1 1 1 -1 -1 1 -1 2 -2 -2 2 -1 1 1) @x1773 @x701 @x1734 @x696 (|unit-resolution| @x723 (|unit-resolution| @x589 @x1793 $x586) $x679) @x718 (|unit-resolution| @x1166 (|unit-resolution| @x645 @x1782 $x642) $x662) @x713 @x709 (|unit-resolution| @x1572 (|unit-resolution| @x639 @x1769 $x635) $x1543) @x728 @x1477 @x810 @x1542 @x1125 (|unit-resolution| @x738 (|unit-resolution| @x599 @x1776 $x595) $x673) @x685 @x1772 false)))
+(let ((@x2081 (|unit-resolution| (lemma @x1796 (or $x656 $x412 $x387)) @x1815 @x1185 @x2074 false)))
+(let ((@x2082 (lemma @x2081 $x412)))
+(let ((@x2100 (|unit-resolution| @x863 (|unit-resolution| @x621 (|unit-resolution| @x1064 @x2082 $x361) $x618) $x838)))
+(let ((@x2117 (|unit-resolution| @x1572 (|unit-resolution| @x639 (|unit-resolution| @x1235 @x2074 $x287) $x635) $x1543)))
+(let ((@x2101 (|unit-resolution| (|unit-resolution| @x1429 @x1542 (or $x286 $x386 $x1090)) @x2100 (|unit-resolution| @x1235 @x2074 $x287) $x386)))
+(let ((@x2090 (|unit-resolution| @x1556 (|unit-resolution| @x639 (|unit-resolution| @x1235 @x2074 $x287) $x635) $x1499)))
+(let ((@x2078 (|unit-resolution| @x997 @x994 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x815 $x1000 $x411)) @x842 @x897 $x1000) false)))
+(let ((@x2097 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x774 $x773)) (|unit-resolution| (lemma @x2078 (or $x411 $x815)) @x2082 $x815) $x773)))
+(let ((@x2104 (|unit-resolution| @x1874 (|unit-resolution| @x948 (|unit-resolution| @x613 @x2101 $x610) $x934) @x2100 @x2097 (|unit-resolution| @x1037 (|unit-resolution| @x607 @x2082 $x603) $x1022) $x336)))
+(let ((@x2107 (|unit-resolution| @x1979 (|unit-resolution| @x621 (|unit-resolution| @x1064 @x2082 $x361) $x618) $x668)))
+(let ((@x2109 (|unit-resolution| @x1881 @x1188 @x696 @x701 @x855 @x1136 @x797 (|unit-resolution| @x806 (|unit-resolution| @x613 @x2101 $x610) $x671) @x2107 (|unit-resolution| @x1115 (|unit-resolution| @x629 @x2104 $x626) $x665) (|unit-resolution| @x997 (|unit-resolution| @x607 @x2082 $x603) $x931) @x2090 $x436)))
+(let ((@x2114 (|unit-resolution| @x723 (|unit-resolution| @x589 (|unit-resolution| @x1098 @x2082 $x461) $x586) $x679)))
+(let ((@x2115 ((_ |th-lemma| arith farkas 1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1) @x1136 (|unit-resolution| @x806 (|unit-resolution| @x613 @x2101 $x610) $x671) @x696 @x2090 @x2107 @x701 @x2114 @x718 @x713 @x2074 @x685 (|unit-resolution| @x691 (|unit-resolution| @x597 @x2109 $x594) $x676) (|unit-resolution| @x1159 (|unit-resolution| @x647 @x1188 $x643) $x1103) false)))
+(let ((@x2119 (|unit-resolution| @x1166 (|unit-resolution| @x645 (lemma @x2115 $x311) $x642) $x662)))
+(let ((@x2120 ((_ |th-lemma| arith farkas 1 -1 1 -1 1 1 -1 -1 3 -3 2 -2 2 -2 1 -1 1) @x2114 @x718 @x728 @x2119 @x713 (|unit-resolution| @x948 (|unit-resolution| @x613 @x2101 $x610) $x934) @x851 @x2117 @x2100 @x833 @x1542 @x1125 @x810 (|unit-resolution| @x1037 (|unit-resolution| @x607 @x2082 $x603) $x1022) @x1609 @x685 @x2074 false)))
+(let ((@x2121 (lemma @x2120 $x743)))
+(let (($x736 (not $x595)))
+(let ((@x2125 (|unit-resolution| @x599 (lemma (|unit-resolution| @x738 (hypothesis $x595) @x2121 false) $x736) $x436)))
+(|unit-resolution| @x691 (|unit-resolution| @x597 @x2125 $x594) (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x673 $x437 $x782)) @x2125 @x2121 $x782) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+8778062e40723924421e3a1f0c912b62e43b9b81 20 0
+unsat
+((set-logic AUFLIRA)
+(proof
+(let ((?x8 (* 2.0 |x$|)))
+(let ((?x10 (+ ?x8 1.0)))
+(let ((?x6 (+ |x$| |x$|)))
+(let (($x11 (< ?x6 ?x10)))
+(let (($x12 (or false $x11)))
+(let (($x13 (or $x11 $x12)))
+(let (($x14 (not $x13)))
+(let ((@x65 (monotonicity (rewrite (= (< ?x8 (+ 1.0 ?x8)) true)) (= (not (< ?x8 (+ 1.0 ?x8))) (not true)))))
+(let ((@x69 (trans @x65 (rewrite (= (not true) false)) (= (not (< ?x8 (+ 1.0 ?x8))) false))))
+(let ((?x38 (+ 1.0 ?x8)))
+(let (($x41 (< ?x8 ?x38)))
+(let ((@x43 (monotonicity (rewrite (= ?x6 ?x8)) (rewrite (= ?x10 ?x38)) (= $x11 $x41))))
+(let ((@x50 (trans (monotonicity @x43 (= $x12 (or false $x41))) (rewrite (= (or false $x41) $x41)) (= $x12 $x41))))
+(let ((@x57 (trans (monotonicity @x43 @x50 (= $x13 (or $x41 $x41))) (rewrite (= (or $x41 $x41) $x41)) (= $x13 $x41))))
+(let ((@x60 (monotonicity @x57 (= $x14 (not $x41)))))
+(mp (asserted $x14) (trans @x60 @x69 (= $x14 false)) false))))))))))))))))))
+
+bbf5431bd7e9448dc98de52e9b465f05ca123636 113 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x215 (mod |x$| 2)))
+(let ((?x249 (* (~ 1) ?x215)))
+(let ((?x9 (|mod$| |x$| 2)))
+(let ((?x250 (+ ?x9 ?x249)))
+(let (($x267 (>= ?x250 0)))
+(let (($x251 (= ?x250 0)))
+(let (($x203 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x30 (mod ?v0 ?v1)))
+(let ((?x99 (* (~ 1) ?v1)))
+(let ((?x96 (* (~ 1) ?v0)))
+(let ((?x142 (mod ?x96 ?x99)))
+(let ((?x148 (* (~ 1) ?x142)))
+(let (($x117 (<= ?v1 0)))
+(let ((?x168 (ite $x117 ?x148 ?x30)))
+(let (($x19 (= ?v1 0)))
+(let ((?x173 (ite $x19 ?v0 ?x168)))
+(let ((?x29 (|mod$| ?v0 ?v1)))
+(= ?x29 ?x173))))))))))) :pattern ( (|mod$| ?v0 ?v1) )))
+))
+(let (($x179 (forall ((?v0 Int) (?v1 Int) )(let ((?x30 (mod ?v0 ?v1)))
+(let ((?x99 (* (~ 1) ?v1)))
+(let ((?x96 (* (~ 1) ?v0)))
+(let ((?x142 (mod ?x96 ?x99)))
+(let ((?x148 (* (~ 1) ?x142)))
+(let (($x117 (<= ?v1 0)))
+(let ((?x168 (ite $x117 ?x148 ?x30)))
+(let (($x19 (= ?v1 0)))
+(let ((?x173 (ite $x19 ?v0 ?x168)))
+(let ((?x29 (|mod$| ?v0 ?v1)))
+(= ?x29 ?x173))))))))))))
+))
+(let ((?x30 (mod ?1 ?0)))
+(let ((?x99 (* (~ 1) ?0)))
+(let ((?x96 (* (~ 1) ?1)))
+(let ((?x142 (mod ?x96 ?x99)))
+(let ((?x148 (* (~ 1) ?x142)))
+(let (($x117 (<= ?0 0)))
+(let ((?x168 (ite $x117 ?x148 ?x30)))
+(let (($x19 (= ?0 0)))
+(let ((?x173 (ite $x19 ?1 ?x168)))
+(let ((?x29 (|mod$| ?1 ?0)))
+(let (($x176 (= ?x29 ?x173)))
+(let (($x36 (forall ((?v0 Int) (?v1 Int) )(let (($x19 (= ?v1 0)))
+(let ((?x34 (ite $x19 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
+(let ((?x29 (|mod$| ?v0 ?v1)))
+(= ?x29 ?x34)))))
+))
+(let (($x162 (forall ((?v0 Int) (?v1 Int) )(let ((?x99 (* (~ 1) ?v1)))
+(let ((?x96 (* (~ 1) ?v0)))
+(let ((?x142 (mod ?x96 ?x99)))
+(let ((?x148 (* (~ 1) ?x142)))
+(let ((?x30 (mod ?v0 ?v1)))
+(let (($x20 (< 0 ?v1)))
+(let ((?x153 (ite $x20 ?x30 ?x148)))
+(let (($x19 (= ?v1 0)))
+(let ((?x156 (ite $x19 ?v0 ?x153)))
+(let ((?x29 (|mod$| ?v0 ?v1)))
+(= ?x29 ?x156))))))))))))
+))
+(let ((@x167 (monotonicity (rewrite (= (< 0 ?0) (not $x117))) (= (ite (< 0 ?0) ?x30 ?x148) (ite (not $x117) ?x30 ?x148)))))
+(let ((@x172 (trans @x167 (rewrite (= (ite (not $x117) ?x30 ?x148) ?x168)) (= (ite (< 0 ?0) ?x30 ?x148) ?x168))))
+(let ((@x175 (monotonicity @x172 (= (ite $x19 ?1 (ite (< 0 ?0) ?x30 ?x148)) ?x173))))
+(let ((@x178 (monotonicity @x175 (= (= ?x29 (ite $x19 ?1 (ite (< 0 ?0) ?x30 ?x148))) $x176))))
+(let (($x20 (< 0 ?0)))
+(let ((?x153 (ite $x20 ?x30 ?x148)))
+(let ((?x156 (ite $x19 ?1 ?x153)))
+(let (($x159 (= ?x29 ?x156)))
+(let (($x160 (= (= ?x29 (ite $x19 ?1 (ite $x20 ?x30 (- (mod (- ?1) (- ?0)))))) $x159)))
+(let ((@x144 (monotonicity (rewrite (= (- ?1) ?x96)) (rewrite (= (- ?0) ?x99)) (= (mod (- ?1) (- ?0)) ?x142))))
+(let ((@x152 (trans (monotonicity @x144 (= (- (mod (- ?1) (- ?0))) (- ?x142))) (rewrite (= (- ?x142) ?x148)) (= (- (mod (- ?1) (- ?0))) ?x148))))
+(let ((@x155 (monotonicity @x152 (= (ite $x20 ?x30 (- (mod (- ?1) (- ?0)))) ?x153))))
+(let ((@x158 (monotonicity @x155 (= (ite $x19 ?1 (ite $x20 ?x30 (- (mod (- ?1) (- ?0))))) ?x156))))
+(let ((@x183 (trans (|quant-intro| (monotonicity @x158 $x160) (= $x36 $x162)) (|quant-intro| @x178 (= $x162 $x179)) (= $x36 $x179))))
+(let ((@x194 (|mp~| (mp (asserted $x36) @x183 $x179) (|nnf-pos| (refl (|~| $x176 $x176)) (|~| $x179 $x179)) $x179)))
+(let ((@x208 (mp @x194 (|quant-intro| (refl (= $x176 $x176)) (= $x179 $x203)) $x203)))
+(let (($x257 (or (not $x203) $x251)))
+(let ((?x212 (* (~ 1) 2)))
+(let ((?x211 (* (~ 1) |x$|)))
+(let ((?x213 (mod ?x211 ?x212)))
+(let ((?x214 (* (~ 1) ?x213)))
+(let (($x210 (<= 2 0)))
+(let ((?x216 (ite $x210 ?x214 ?x215)))
+(let (($x209 (= 2 0)))
+(let ((?x217 (ite $x209 |x$| ?x216)))
+(let (($x218 (= ?x9 ?x217)))
+(let ((@x231 (monotonicity (monotonicity (rewrite (= ?x212 (~ 2))) (= ?x213 (mod ?x211 (~ 2)))) (= ?x214 (* (~ 1) (mod ?x211 (~ 2)))))))
+(let ((@x234 (monotonicity (rewrite (= $x210 false)) @x231 (= ?x216 (ite false (* (~ 1) (mod ?x211 (~ 2))) ?x215)))))
+(let ((@x238 (trans @x234 (rewrite (= (ite false (* (~ 1) (mod ?x211 (~ 2))) ?x215) ?x215)) (= ?x216 ?x215))))
+(let ((@x241 (monotonicity (rewrite (= $x209 false)) @x238 (= ?x217 (ite false |x$| ?x215)))))
+(let ((@x248 (monotonicity (trans @x241 (rewrite (= (ite false |x$| ?x215) ?x215)) (= ?x217 ?x215)) (= $x218 (= ?x9 ?x215)))))
+(let ((@x261 (monotonicity (trans @x248 (rewrite (= (= ?x9 ?x215) $x251)) (= $x218 $x251)) (= (or (not $x203) $x218) $x257))))
+(let ((@x264 (trans @x261 (rewrite (= $x257 $x257)) (= (or (not $x203) $x218) $x257))))
+(let ((@x265 (mp ((_ |quant-inst| |x$| 2) (or (not $x203) $x218)) @x264 $x257)))
+(let ((@x324 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x251) $x267)) (|unit-resolution| @x265 @x208 $x251) $x267)))
+(let (($x292 (>= ?x215 0)))
+(let (($x83 (>= ?x9 0)))
+(let (($x86 (not $x83)))
+(let (($x14 (not (<= (+ |x$| 1) (+ |x$| (+ (* 2 ?x9) 1))))))
+(let ((@x88 (monotonicity (rewrite (= (>= (* 2 ?x9) 0) $x83)) (= (not (>= (* 2 ?x9) 0)) $x86))))
+(let ((?x10 (* 2 ?x9)))
+(let ((?x66 (+ 1 |x$| ?x10)))
+(let (($x71 (<= (+ 1 |x$|) ?x66)))
+(let (($x74 (not $x71)))
+(let ((@x82 (monotonicity (rewrite (= $x71 (>= ?x10 0))) (= $x74 (not (>= ?x10 0))))))
+(let ((@x65 (monotonicity (rewrite (= (+ ?x10 1) (+ 1 ?x10))) (= (+ |x$| (+ ?x10 1)) (+ |x$| (+ 1 ?x10))))))
+(let ((@x70 (trans @x65 (rewrite (= (+ |x$| (+ 1 ?x10)) ?x66)) (= (+ |x$| (+ ?x10 1)) ?x66))))
+(let ((@x73 (monotonicity (rewrite (= (+ |x$| 1) (+ 1 |x$|))) @x70 (= (<= (+ |x$| 1) (+ |x$| (+ ?x10 1))) $x71))))
+(let ((@x92 (trans (monotonicity @x73 (= $x14 $x74)) (trans @x82 @x88 (= $x74 $x86)) (= $x14 $x86))))
+(let ((@x93 (mp (asserted $x14) @x92 $x86)))
+((_ |th-lemma| arith farkas -1 1 1) @x93 (|unit-resolution| ((_ |th-lemma| arith) (or false $x292)) (|true-axiom| true) $x292) @x324 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+b5183bee77d63a5b887fd6f1c6035b47d90e65cb 112 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x211 (mod |x$| 2)))
+(let (($x305 (>= ?x211 2)))
+(let (($x306 (not $x305)))
+(let ((?x245 (* (~ 1) ?x211)))
+(let ((?x7 (|mod$| |x$| 2)))
+(let ((?x246 (+ ?x7 ?x245)))
+(let (($x262 (<= ?x246 0)))
+(let (($x247 (= ?x246 0)))
+(let (($x199 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x29 (mod ?v0 ?v1)))
+(let ((?x95 (* (~ 1) ?v1)))
+(let ((?x92 (* (~ 1) ?v0)))
+(let ((?x138 (mod ?x92 ?x95)))
+(let ((?x144 (* (~ 1) ?x138)))
+(let (($x113 (<= ?v1 0)))
+(let ((?x164 (ite $x113 ?x144 ?x29)))
+(let (($x18 (= ?v1 0)))
+(let ((?x169 (ite $x18 ?v0 ?x164)))
+(let ((?x28 (|mod$| ?v0 ?v1)))
+(= ?x28 ?x169))))))))))) :pattern ( (|mod$| ?v0 ?v1) )))
+))
+(let (($x175 (forall ((?v0 Int) (?v1 Int) )(let ((?x29 (mod ?v0 ?v1)))
+(let ((?x95 (* (~ 1) ?v1)))
+(let ((?x92 (* (~ 1) ?v0)))
+(let ((?x138 (mod ?x92 ?x95)))
+(let ((?x144 (* (~ 1) ?x138)))
+(let (($x113 (<= ?v1 0)))
+(let ((?x164 (ite $x113 ?x144 ?x29)))
+(let (($x18 (= ?v1 0)))
+(let ((?x169 (ite $x18 ?v0 ?x164)))
+(let ((?x28 (|mod$| ?v0 ?v1)))
+(= ?x28 ?x169))))))))))))
+))
+(let ((?x29 (mod ?1 ?0)))
+(let ((?x95 (* (~ 1) ?0)))
+(let ((?x92 (* (~ 1) ?1)))
+(let ((?x138 (mod ?x92 ?x95)))
+(let ((?x144 (* (~ 1) ?x138)))
+(let (($x113 (<= ?0 0)))
+(let ((?x164 (ite $x113 ?x144 ?x29)))
+(let (($x18 (= ?0 0)))
+(let ((?x169 (ite $x18 ?1 ?x164)))
+(let ((?x28 (|mod$| ?1 ?0)))
+(let (($x172 (= ?x28 ?x169)))
+(let (($x35 (forall ((?v0 Int) (?v1 Int) )(let (($x18 (= ?v1 0)))
+(let ((?x33 (ite $x18 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
+(let ((?x28 (|mod$| ?v0 ?v1)))
+(= ?x28 ?x33)))))
+))
+(let (($x158 (forall ((?v0 Int) (?v1 Int) )(let ((?x95 (* (~ 1) ?v1)))
+(let ((?x92 (* (~ 1) ?v0)))
+(let ((?x138 (mod ?x92 ?x95)))
+(let ((?x144 (* (~ 1) ?x138)))
+(let ((?x29 (mod ?v0 ?v1)))
+(let (($x19 (< 0 ?v1)))
+(let ((?x149 (ite $x19 ?x29 ?x144)))
+(let (($x18 (= ?v1 0)))
+(let ((?x152 (ite $x18 ?v0 ?x149)))
+(let ((?x28 (|mod$| ?v0 ?v1)))
+(= ?x28 ?x152))))))))))))
+))
+(let ((@x163 (monotonicity (rewrite (= (< 0 ?0) (not $x113))) (= (ite (< 0 ?0) ?x29 ?x144) (ite (not $x113) ?x29 ?x144)))))
+(let ((@x168 (trans @x163 (rewrite (= (ite (not $x113) ?x29 ?x144) ?x164)) (= (ite (< 0 ?0) ?x29 ?x144) ?x164))))
+(let ((@x171 (monotonicity @x168 (= (ite $x18 ?1 (ite (< 0 ?0) ?x29 ?x144)) ?x169))))
+(let ((@x174 (monotonicity @x171 (= (= ?x28 (ite $x18 ?1 (ite (< 0 ?0) ?x29 ?x144))) $x172))))
+(let (($x19 (< 0 ?0)))
+(let ((?x149 (ite $x19 ?x29 ?x144)))
+(let ((?x152 (ite $x18 ?1 ?x149)))
+(let (($x155 (= ?x28 ?x152)))
+(let (($x156 (= (= ?x28 (ite $x18 ?1 (ite $x19 ?x29 (- (mod (- ?1) (- ?0)))))) $x155)))
+(let ((@x140 (monotonicity (rewrite (= (- ?1) ?x92)) (rewrite (= (- ?0) ?x95)) (= (mod (- ?1) (- ?0)) ?x138))))
+(let ((@x148 (trans (monotonicity @x140 (= (- (mod (- ?1) (- ?0))) (- ?x138))) (rewrite (= (- ?x138) ?x144)) (= (- (mod (- ?1) (- ?0))) ?x144))))
+(let ((@x151 (monotonicity @x148 (= (ite $x19 ?x29 (- (mod (- ?1) (- ?0)))) ?x149))))
+(let ((@x154 (monotonicity @x151 (= (ite $x18 ?1 (ite $x19 ?x29 (- (mod (- ?1) (- ?0))))) ?x152))))
+(let ((@x179 (trans (|quant-intro| (monotonicity @x154 $x156) (= $x35 $x158)) (|quant-intro| @x174 (= $x158 $x175)) (= $x35 $x175))))
+(let ((@x190 (|mp~| (mp (asserted $x35) @x179 $x175) (|nnf-pos| (refl (|~| $x172 $x172)) (|~| $x175 $x175)) $x175)))
+(let ((@x204 (mp @x190 (|quant-intro| (refl (= $x172 $x172)) (= $x175 $x199)) $x199)))
+(let (($x253 (or (not $x199) $x247)))
+(let ((?x208 (* (~ 1) 2)))
+(let ((?x207 (* (~ 1) |x$|)))
+(let ((?x209 (mod ?x207 ?x208)))
+(let ((?x210 (* (~ 1) ?x209)))
+(let (($x206 (<= 2 0)))
+(let ((?x212 (ite $x206 ?x210 ?x211)))
+(let (($x205 (= 2 0)))
+(let ((?x213 (ite $x205 |x$| ?x212)))
+(let (($x214 (= ?x7 ?x213)))
+(let ((@x227 (monotonicity (monotonicity (rewrite (= ?x208 (~ 2))) (= ?x209 (mod ?x207 (~ 2)))) (= ?x210 (* (~ 1) (mod ?x207 (~ 2)))))))
+(let ((@x230 (monotonicity (rewrite (= $x206 false)) @x227 (= ?x212 (ite false (* (~ 1) (mod ?x207 (~ 2))) ?x211)))))
+(let ((@x234 (trans @x230 (rewrite (= (ite false (* (~ 1) (mod ?x207 (~ 2))) ?x211) ?x211)) (= ?x212 ?x211))))
+(let ((@x237 (monotonicity (rewrite (= $x205 false)) @x234 (= ?x213 (ite false |x$| ?x211)))))
+(let ((@x244 (monotonicity (trans @x237 (rewrite (= (ite false |x$| ?x211) ?x211)) (= ?x213 ?x211)) (= $x214 (= ?x7 ?x211)))))
+(let ((@x257 (monotonicity (trans @x244 (rewrite (= (= ?x7 ?x211) $x247)) (= $x214 $x247)) (= (or (not $x199) $x214) $x253))))
+(let ((@x260 (trans @x257 (rewrite (= $x253 $x253)) (= (or (not $x199) $x214) $x253))))
+(let ((@x261 (mp ((_ |quant-inst| |x$| 2) (or (not $x199) $x214)) @x260 $x253)))
+(let ((@x323 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x247) $x262)) (|unit-resolution| @x261 @x204 $x247) $x262)))
+(let (($x82 (>= ?x7 2)))
+(let ((?x56 (* 2 ?x7)))
+(let (($x75 (>= ?x56 3)))
+(let (($x65 (< (+ |x$| ?x56) (+ 3 |x$|))))
+(let (($x68 (not $x65)))
+(let ((@x77 (monotonicity (rewrite (= $x65 (not $x75))) (= $x68 (not (not $x75))))))
+(let ((@x86 (trans (trans @x77 (rewrite (= (not (not $x75)) $x75)) (= $x68 $x75)) (rewrite (= $x75 $x82)) (= $x68 $x82))))
+(let ((@x61 (monotonicity (rewrite (= (+ ?x7 ?x7) ?x56)) (= (+ |x$| (+ ?x7 ?x7)) (+ |x$| ?x56)))))
+(let ((@x67 (monotonicity @x61 (rewrite (= (+ |x$| 3) (+ 3 |x$|))) (= (< (+ |x$| (+ ?x7 ?x7)) (+ |x$| 3)) $x65))))
+(let ((@x70 (monotonicity @x67 (= (not (< (+ |x$| (+ ?x7 ?x7)) (+ |x$| 3))) $x68))))
+(let ((@x88 (trans @x70 @x86 (= (not (< (+ |x$| (+ ?x7 ?x7)) (+ |x$| 3))) $x82))))
+(let ((@x89 (mp (asserted (not (< (+ |x$| (+ ?x7 ?x7)) (+ |x$| 3)))) @x88 $x82)))
+((_ |th-lemma| arith farkas -1 1 1) @x89 @x323 (|unit-resolution| ((_ |th-lemma| arith) (or false $x306)) (|true-axiom| true) $x306) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+fb75370f1b646783db5a9a683587f9b2b11bd686 32 0
+unsat
+((set-logic <null>)
+(proof
+(let (($x7 (= |x$| 0.0)))
+(let (($x8 (not $x7)))
+(let ((@x43 (asserted $x8)))
+(let (($x99 (<= |x$| 0.0)))
+(let ((?x45 (* 2.0 |x$|)))
+(let (($x97 (<= ?x45 0.0)))
+(let (($x93 (= ?x45 0.0)))
+(let (($x14 (< 1.0 (ite (< |x$| 0.0) (- |x$|) |x$|))))
+(let (($x16 (or $x14 (not $x14))))
+(let ((?x19 (ite $x16 4.0 2.0)))
+(let (($x23 (not (not (= (+ |x$| |x$|) (* ?x19 |x$|))))))
+(let ((@x88 (rewrite (= (not (not (= ?x45 (* 4.0 |x$|)))) (= ?x45 (* 4.0 |x$|))))))
+(let (($x82 (= (not (= (+ |x$| |x$|) (* ?x19 |x$|))) (not (= ?x45 (* 4.0 |x$|))))))
+(let (($x55 (< 1.0 (ite (< |x$| 0.0) (* (~ 1.0) |x$|) |x$|))))
+(let (($x53 (= (ite (< |x$| 0.0) (- |x$|) |x$|) (ite (< |x$| 0.0) (* (~ 1.0) |x$|) |x$|))))
+(let ((@x57 (monotonicity (monotonicity (rewrite (= (- |x$|) (* (~ 1.0) |x$|))) $x53) (= $x14 $x55))))
+(let ((@x63 (monotonicity @x57 (monotonicity @x57 (= (not $x14) (not $x55))) (= $x16 (or $x55 (not $x55))))))
+(let ((@x67 (trans @x63 (rewrite (= (or $x55 (not $x55)) true)) (= $x16 true))))
+(let ((@x74 (trans (monotonicity @x67 (= ?x19 (ite true 4.0 2.0))) (rewrite (= (ite true 4.0 2.0) 4.0)) (= ?x19 4.0))))
+(let ((@x80 (monotonicity (rewrite (= (+ |x$| |x$|) ?x45)) (monotonicity @x74 (= (* ?x19 |x$|) (* 4.0 |x$|))) (= (= (+ |x$| |x$|) (* ?x19 |x$|)) (= ?x45 (* 4.0 |x$|))))))
+(let ((@x86 (monotonicity (monotonicity @x80 $x82) (= $x23 (not (not (= ?x45 (* 4.0 |x$|))))))))
+(let ((@x95 (trans (trans @x86 @x88 (= $x23 (= ?x45 (* 4.0 |x$|)))) (rewrite (= (= ?x45 (* 4.0 |x$|)) $x93)) (= $x23 $x93))))
+(let ((@x96 (mp (asserted $x23) @x95 $x93)))
+(let ((@x108 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1) (or $x99 (not $x97))) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x93) $x97)) @x96 $x97) $x99)))
+(let (($x100 (>= |x$| 0.0)))
+(let (($x98 (>= ?x45 0.0)))
+(let ((@x115 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1) (or $x100 (not $x98))) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x93) $x98)) @x96 $x98) $x100)))
+(|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x7 (not $x99) (not $x100))) @x115 @x108 @x43 false))))))))))))))))))))))))))))))
+
+bba1efa8562001b979c24cfd840c5185f0dad8b2 242 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x471 (div |m$| 2)))
+(let ((?x531 (* (~ 1) ?x471)))
+(let ((?x426 (mod |m$| 2)))
+(let ((?x453 (* (~ 1) ?x426)))
+(let ((?x368 (div |n$| 4)))
+(let ((?x541 (* (~ 2) ?x368)))
+(let ((?x316 (mod |n$| 4)))
+(let ((?x350 (* (~ 1) ?x316)))
+(let ((?x7 (+ |n$| |m$|)))
+(let ((?x259 (div ?x7 2)))
+(let ((?x540 (* (~ 1) ?x259)))
+(let ((?x201 (mod ?x7 2)))
+(let ((?x240 (* (~ 1) ?x201)))
+(let ((?x13 (|mod$| |n$| 4)))
+(let ((?x9 (|mod$| ?x7 2)))
+(let ((?x534 (+ |n$| |m$| ?x9 ?x13 ?x240 ?x540 ?x350 ?x541 ?x453 ?x531)))
+(let (($x535 (>= ?x534 2)))
+(let (($x492 (>= ?x426 0)))
+(let ((@x62 (|true-axiom| true)))
+(let ((?x484 (* (~ 2) ?x471)))
+(let ((?x485 (+ |m$| ?x453 ?x484)))
+(let (($x490 (<= ?x485 0)))
+(let (($x483 (= ?x485 0)))
+(let ((@x379 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x483) $x490)) (|unit-resolution| ((_ |th-lemma| arith) (or false $x483)) @x62 $x483) $x490)))
+(let ((?x351 (+ ?x13 ?x350)))
+(let (($x366 (<= ?x351 0)))
+(let (($x352 (= ?x351 0)))
+(let (($x189 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x37 (mod ?v0 ?v1)))
+(let ((?x71 (* (~ 1) ?v1)))
+(let ((?x68 (* (~ 1) ?v0)))
+(let ((?x114 (mod ?x68 ?x71)))
+(let ((?x120 (* (~ 1) ?x114)))
+(let (($x89 (<= ?v1 0)))
+(let ((?x140 (ite $x89 ?x120 ?x37)))
+(let (($x26 (= ?v1 0)))
+(let ((?x145 (ite $x26 ?v0 ?x140)))
+(let ((?x36 (|mod$| ?v0 ?v1)))
+(= ?x36 ?x145))))))))))) :pattern ( (|mod$| ?v0 ?v1) )))
+))
+(let (($x151 (forall ((?v0 Int) (?v1 Int) )(let ((?x37 (mod ?v0 ?v1)))
+(let ((?x71 (* (~ 1) ?v1)))
+(let ((?x68 (* (~ 1) ?v0)))
+(let ((?x114 (mod ?x68 ?x71)))
+(let ((?x120 (* (~ 1) ?x114)))
+(let (($x89 (<= ?v1 0)))
+(let ((?x140 (ite $x89 ?x120 ?x37)))
+(let (($x26 (= ?v1 0)))
+(let ((?x145 (ite $x26 ?v0 ?x140)))
+(let ((?x36 (|mod$| ?v0 ?v1)))
+(= ?x36 ?x145))))))))))))
+))
+(let ((?x37 (mod ?1 ?0)))
+(let ((?x71 (* (~ 1) ?0)))
+(let ((?x68 (* (~ 1) ?1)))
+(let ((?x114 (mod ?x68 ?x71)))
+(let ((?x120 (* (~ 1) ?x114)))
+(let (($x89 (<= ?0 0)))
+(let ((?x140 (ite $x89 ?x120 ?x37)))
+(let (($x26 (= ?0 0)))
+(let ((?x145 (ite $x26 ?1 ?x140)))
+(let ((?x36 (|mod$| ?1 ?0)))
+(let (($x148 (= ?x36 ?x145)))
+(let (($x43 (forall ((?v0 Int) (?v1 Int) )(let (($x26 (= ?v1 0)))
+(let ((?x41 (ite $x26 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
+(let ((?x36 (|mod$| ?v0 ?v1)))
+(= ?x36 ?x41)))))
+))
+(let (($x134 (forall ((?v0 Int) (?v1 Int) )(let ((?x71 (* (~ 1) ?v1)))
+(let ((?x68 (* (~ 1) ?v0)))
+(let ((?x114 (mod ?x68 ?x71)))
+(let ((?x120 (* (~ 1) ?x114)))
+(let ((?x37 (mod ?v0 ?v1)))
+(let (($x27 (< 0 ?v1)))
+(let ((?x125 (ite $x27 ?x37 ?x120)))
+(let (($x26 (= ?v1 0)))
+(let ((?x128 (ite $x26 ?v0 ?x125)))
+(let ((?x36 (|mod$| ?v0 ?v1)))
+(= ?x36 ?x128))))))))))))
+))
+(let ((@x139 (monotonicity (rewrite (= (< 0 ?0) (not $x89))) (= (ite (< 0 ?0) ?x37 ?x120) (ite (not $x89) ?x37 ?x120)))))
+(let ((@x144 (trans @x139 (rewrite (= (ite (not $x89) ?x37 ?x120) ?x140)) (= (ite (< 0 ?0) ?x37 ?x120) ?x140))))
+(let ((@x147 (monotonicity @x144 (= (ite $x26 ?1 (ite (< 0 ?0) ?x37 ?x120)) ?x145))))
+(let ((@x150 (monotonicity @x147 (= (= ?x36 (ite $x26 ?1 (ite (< 0 ?0) ?x37 ?x120))) $x148))))
+(let (($x27 (< 0 ?0)))
+(let ((?x125 (ite $x27 ?x37 ?x120)))
+(let ((?x128 (ite $x26 ?1 ?x125)))
+(let (($x131 (= ?x36 ?x128)))
+(let (($x132 (= (= ?x36 (ite $x26 ?1 (ite $x27 ?x37 (- (mod (- ?1) (- ?0)))))) $x131)))
+(let ((@x116 (monotonicity (rewrite (= (- ?1) ?x68)) (rewrite (= (- ?0) ?x71)) (= (mod (- ?1) (- ?0)) ?x114))))
+(let ((@x124 (trans (monotonicity @x116 (= (- (mod (- ?1) (- ?0))) (- ?x114))) (rewrite (= (- ?x114) ?x120)) (= (- (mod (- ?1) (- ?0))) ?x120))))
+(let ((@x127 (monotonicity @x124 (= (ite $x27 ?x37 (- (mod (- ?1) (- ?0)))) ?x125))))
+(let ((@x130 (monotonicity @x127 (= (ite $x26 ?1 (ite $x27 ?x37 (- (mod (- ?1) (- ?0))))) ?x128))))
+(let ((@x155 (trans (|quant-intro| (monotonicity @x130 $x132) (= $x43 $x134)) (|quant-intro| @x150 (= $x134 $x151)) (= $x43 $x151))))
+(let ((@x166 (|mp~| (mp (asserted $x43) @x155 $x151) (|nnf-pos| (refl (|~| $x148 $x148)) (|~| $x151 $x151)) $x151)))
+(let ((@x194 (mp @x166 (|quant-intro| (refl (= $x148 $x148)) (= $x151 $x189)) $x189)))
+(let (($x247 (not $x189)))
+(let (($x357 (or $x247 $x352)))
+(let ((?x317 (ite (<= 4 0) (* (~ 1) (mod (* (~ 1) |n$|) (* (~ 1) 4))) ?x316)))
+(let ((?x318 (ite (= 4 0) |n$| ?x317)))
+(let (($x319 (= ?x13 ?x318)))
+(let ((@x337 (rewrite (= (ite false (* (~ 1) (mod (* (~ 1) |n$|) (~ 4))) ?x316) ?x316))))
+(let (($x331 (= (* (~ 1) (mod (* (~ 1) |n$|) (* (~ 1) 4))) (* (~ 1) (mod (* (~ 1) |n$|) (~ 4))))))
+(let ((@x329 (monotonicity (rewrite (= (* (~ 1) 4) (~ 4))) (= (mod (* (~ 1) |n$|) (* (~ 1) 4)) (mod (* (~ 1) |n$|) (~ 4))))))
+(let ((@x335 (monotonicity (rewrite (= (<= 4 0) false)) (monotonicity @x329 $x331) (= ?x317 (ite false (* (~ 1) (mod (* (~ 1) |n$|) (~ 4))) ?x316)))))
+(let ((@x342 (monotonicity (rewrite (= (= 4 0) false)) (trans @x335 @x337 (= ?x317 ?x316)) (= ?x318 (ite false |n$| ?x316)))))
+(let ((@x349 (monotonicity (trans @x342 (rewrite (= (ite false |n$| ?x316) ?x316)) (= ?x318 ?x316)) (= $x319 (= ?x13 ?x316)))))
+(let ((@x361 (monotonicity (trans @x349 (rewrite (= (= ?x13 ?x316) $x352)) (= $x319 $x352)) (= (or $x247 $x319) $x357))))
+(let ((@x365 (mp ((_ |quant-inst| |n$| 4) (or $x247 $x319)) (trans @x361 (rewrite (= $x357 $x357)) (= (or $x247 $x319) $x357)) $x357)))
+(let ((@x570 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x352) $x366)) (|unit-resolution| @x365 @x194 $x352) $x366)))
+(let ((?x275 (* (~ 2) ?x259)))
+(let ((?x276 (+ |n$| |m$| ?x240 ?x275)))
+(let (($x281 (<= ?x276 0)))
+(let (($x274 (= ?x276 0)))
+(let ((@x560 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x274) $x281)) (|unit-resolution| ((_ |th-lemma| arith) (or false $x274)) @x62 $x274) $x281)))
+(let ((?x241 (+ ?x9 ?x240)))
+(let (($x257 (<= ?x241 0)))
+(let (($x242 (= ?x241 0)))
+(let (($x248 (or $x247 $x242)))
+(let (($x196 (<= 2 0)))
+(let ((?x202 (ite $x196 (* (~ 1) (mod (* (~ 1) ?x7) (* (~ 1) 2))) ?x201)))
+(let (($x195 (= 2 0)))
+(let ((?x203 (ite $x195 ?x7 ?x202)))
+(let (($x204 (= ?x9 ?x203)))
+(let ((?x223 (ite false (* (~ 1) (mod (+ (* (~ 1) |n$|) (* (~ 1) |m$|)) (~ 2))) ?x201)))
+(let (($x221 (= (* (~ 1) (mod (* (~ 1) ?x7) (* (~ 1) 2))) (* (~ 1) (mod (+ (* (~ 1) |n$|) (* (~ 1) |m$|)) (~ 2))))))
+(let (($x218 (= (mod (* (~ 1) ?x7) (* (~ 1) 2)) (mod (+ (* (~ 1) |n$|) (* (~ 1) |m$|)) (~ 2)))))
+(let ((@x216 (rewrite (= (* (~ 1) 2) (~ 2)))))
+(let ((@x219 (monotonicity (rewrite (= (* (~ 1) ?x7) (+ (* (~ 1) |n$|) (* (~ 1) |m$|)))) @x216 $x218)))
+(let ((@x208 (rewrite (= $x196 false))))
+(let ((@x229 (trans (monotonicity @x208 (monotonicity @x219 $x221) (= ?x202 ?x223)) (rewrite (= ?x223 ?x201)) (= ?x202 ?x201))))
+(let ((@x206 (rewrite (= $x195 false))))
+(let ((@x236 (trans (monotonicity @x206 @x229 (= ?x203 (ite false ?x7 ?x201))) (rewrite (= (ite false ?x7 ?x201) ?x201)) (= ?x203 ?x201))))
+(let ((@x246 (trans (monotonicity @x236 (= $x204 (= ?x9 ?x201))) (rewrite (= (= ?x9 ?x201) $x242)) (= $x204 $x242))))
+(let ((@x255 (trans (monotonicity @x246 (= (or $x247 $x204) $x248)) (rewrite (= $x248 $x248)) (= (or $x247 $x204) $x248))))
+(let ((@x256 (mp ((_ |quant-inst| (+ |n$| |m$|) 2) (or $x247 $x204)) @x255 $x248)))
+(let ((@x565 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x242) $x257)) (|unit-resolution| @x256 @x194 $x242) $x257)))
+(let ((?x384 (* (~ 4) ?x368)))
+(let ((?x385 (+ |n$| ?x350 ?x384)))
+(let (($x390 (<= ?x385 0)))
+(let (($x383 (= ?x385 0)))
+(let ((@x577 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x383) $x390)) (|unit-resolution| ((_ |th-lemma| arith) (or false $x383)) @x62 $x383) $x390)))
+(let (($x422 (<= ?x13 3)))
+(let (($x15 (= ?x13 3)))
+(let ((@x64 (asserted $x15)))
+(let ((@x581 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x15) $x422)) @x64 $x422)))
+(let (($x420 (<= ?x9 0)))
+(let (($x11 (= ?x9 0)))
+(let ((@x63 (asserted $x11)))
+(let ((@x553 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x11) $x420)) @x63 $x420)))
+(let ((@x494 ((_ |th-lemma| arith farkas -1 -1 2 -1 -1 -1 -1 -1 1) @x553 @x581 (hypothesis $x535) @x577 @x565 @x560 @x570 @x379 (|unit-resolution| ((_ |th-lemma| arith) (or false $x492)) @x62 $x492) false)))
+(let (($x304 (>= ?x485 0)))
+(let ((@x648 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x483) $x304)) (|unit-resolution| ((_ |th-lemma| arith) (or false $x483)) @x62 $x483) $x304)))
+(let (($x367 (>= ?x351 0)))
+(let ((@x473 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x352) $x367)) (|unit-resolution| @x365 @x194 $x352) $x367)))
+(let (($x421 (>= ?x9 0)))
+(let (($x282 (>= ?x276 0)))
+(let ((@x371 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x274) $x282)) (|unit-resolution| ((_ |th-lemma| arith) (or false $x274)) @x62 $x274) $x282)))
+(let (($x258 (>= ?x241 0)))
+(let ((@x377 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x242) $x258)) (|unit-resolution| @x256 @x194 $x242) $x258)))
+(let (($x391 (>= ?x385 0)))
+(let ((@x474 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x383) $x391)) (|unit-resolution| ((_ |th-lemma| arith) (or false $x383)) @x62 $x383) $x391)))
+(let (($x423 (>= ?x13 3)))
+(let ((@x261 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x15) $x423)) @x64 $x423)))
+(let ((?x19 (|mod$| |m$| 2)))
+(let ((?x454 (+ ?x19 ?x453)))
+(let (($x263 (>= ?x454 0)))
+(let (($x386 (= ?x454 0)))
+(let (($x486 (or $x247 $x386)))
+(let ((?x198 (* (~ 1) 2)))
+(let ((?x210 (* (~ 1) |m$|)))
+(let ((?x424 (mod ?x210 ?x198)))
+(let ((?x425 (* (~ 1) ?x424)))
+(let ((?x427 (ite $x196 ?x425 ?x426)))
+(let ((?x428 (ite $x195 |m$| ?x427)))
+(let (($x429 (= ?x19 ?x428)))
+(let ((@x594 (monotonicity (monotonicity @x216 (= ?x424 (mod ?x210 (~ 2)))) (= ?x425 (* (~ 1) (mod ?x210 (~ 2)))))))
+(let ((@x596 (monotonicity @x208 @x594 (= ?x427 (ite false (* (~ 1) (mod ?x210 (~ 2))) ?x426)))))
+(let ((@x603 (trans @x596 (rewrite (= (ite false (* (~ 1) (mod ?x210 (~ 2))) ?x426) ?x426)) (= ?x427 ?x426))))
+(let ((@x414 (trans (monotonicity @x206 @x603 (= ?x428 (ite false |m$| ?x426))) (rewrite (= (ite false |m$| ?x426) ?x426)) (= ?x428 ?x426))))
+(let ((@x482 (trans (monotonicity @x414 (= $x429 (= ?x19 ?x426))) (rewrite (= (= ?x19 ?x426) $x386)) (= $x429 $x386))))
+(let ((@x511 (trans (monotonicity @x482 (= (or $x247 $x429) $x486)) (rewrite (= $x486 $x486)) (= (or $x247 $x429) $x486))))
+(let ((@x512 (mp ((_ |quant-inst| |m$| 2) (or $x247 $x429)) @x511 $x486)))
+(let ((@x653 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x386) $x263)) (|unit-resolution| @x512 @x194 $x386) $x263)))
+(let (($x271 (>= ?x19 1)))
+(let (($x666 (not $x271)))
+(let (($x509 (<= ?x19 1)))
+(let (($x498 (>= ?x426 2)))
+(let (($x635 (not $x498)))
+(let (($x469 (<= ?x454 0)))
+(let ((@x659 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x386) $x469)) (|unit-resolution| @x512 @x194 $x386) $x469)))
+(let ((@x663 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x509 $x498 (not $x469))) @x659 (|unit-resolution| ((_ |th-lemma| arith) (or false $x635)) @x62 $x635) $x509)))
+(let (($x20 (= ?x19 1)))
+(let (($x168 (not $x20)))
+(let ((?x16 (|mod$| |n$| 2)))
+(let (($x18 (= ?x16 1)))
+(let (($x280 (>= ?x16 1)))
+(let (($x606 (not $x280)))
+(let (($x279 (<= ?x16 1)))
+(let ((?x430 (mod |n$| 2)))
+(let ((?x437 (* (~ 1) ?x430)))
+(let ((?x438 (+ ?x16 ?x437)))
+(let (($x455 (<= ?x438 0)))
+(let (($x439 (= ?x438 0)))
+(let (($x444 (or $x247 $x439)))
+(let ((?x209 (* (~ 1) |n$|)))
+(let ((?x461 (mod ?x209 ?x198)))
+(let ((?x462 (* (~ 1) ?x461)))
+(let ((?x431 (ite $x196 ?x462 ?x430)))
+(let ((?x432 (ite $x195 |n$| ?x431)))
+(let (($x433 (= ?x16 ?x432)))
+(let ((@x522 (monotonicity (monotonicity @x216 (= ?x461 (mod ?x209 (~ 2)))) (= ?x462 (* (~ 1) (mod ?x209 (~ 2)))))))
+(let ((@x521 (monotonicity @x208 @x522 (= ?x431 (ite false (* (~ 1) (mod ?x209 (~ 2))) ?x430)))))
+(let ((@x288 (trans @x521 (rewrite (= (ite false (* (~ 1) (mod ?x209 (~ 2))) ?x430) ?x430)) (= ?x431 ?x430))))
+(let ((@x538 (trans (monotonicity @x206 @x288 (= ?x432 (ite false |n$| ?x430))) (rewrite (= (ite false |n$| ?x430) ?x430)) (= ?x432 ?x430))))
+(let ((@x443 (trans (monotonicity @x538 (= $x433 (= ?x16 ?x430))) (rewrite (= (= ?x16 ?x430) $x439)) (= $x433 $x439))))
+(let ((@x451 (trans (monotonicity @x443 (= (or $x247 $x433) $x444)) (rewrite (= $x444 $x444)) (= (or $x247 $x433) $x444))))
+(let ((@x460 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x439) $x455)) (|unit-resolution| (mp ((_ |quant-inst| |n$| 2) (or $x247 $x433)) @x451 $x444) @x194 $x439) $x455)))
+(let ((@x463 (|unit-resolution| ((_ |th-lemma| arith) (or false (not (>= ?x430 2)))) @x62 (not (>= ?x430 2)))))
+(let ((@x295 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x279 (>= ?x430 2) (not $x455))) @x463 @x460 $x279)))
+(let ((@x292 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x18 (not $x279) $x606)) (hypothesis (not $x18)) (or (not $x279) $x606))))
+(let (($x623 (or (not (>= (+ |n$| ?x13 ?x350 ?x541 (* (~ 1) (div |n$| 2))) 2)) $x280)))
+(let ((?x491 (+ |n$| ?x437 (* (~ 2) (div |n$| 2)))))
+(let (($x397 (<= ?x491 0)))
+(let (($x508 (= ?x491 0)))
+(let ((@x614 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x508) $x397)) (|unit-resolution| ((_ |th-lemma| arith) (or false $x508)) @x62 $x508) $x397)))
+(let (($x601 (>= (+ |n$| ?x13 ?x350 ?x541 (* (~ 1) (div |n$| 2))) 2)))
+(let ((@x620 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x439) (>= ?x438 0))) (|unit-resolution| (mp ((_ |quant-inst| |n$| 2) (or $x247 $x433)) @x451 $x444) @x194 $x439) (>= ?x438 0))))
+(let ((@x621 ((_ |th-lemma| arith farkas -1 -2 1 1 1 1 1) @x620 (hypothesis $x601) @x614 @x570 @x577 @x581 (hypothesis $x606) false)))
+(let ((@x403 (|unit-resolution| (lemma @x621 $x623) (|unit-resolution| @x292 @x295 $x606) (not $x601))))
+(let ((@x406 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x508) (>= ?x491 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x508)) @x62 $x508) (>= ?x491 0))))
+(let ((@x411 (|unit-resolution| ((_ |th-lemma| arith) (or false (>= ?x430 0))) @x62 (>= ?x430 0))))
+(let (($x169 (or (not $x18) $x168)))
+(let ((@x175 (monotonicity (rewrite (= (and $x18 $x20) (not $x169))) (= (not (and $x18 $x20)) (not (not $x169))))))
+(let ((@x179 (trans @x175 (rewrite (= (not (not $x169)) $x169)) (= (not (and $x18 $x20)) $x169))))
+(let ((@x180 (mp (asserted (not (and $x18 $x20))) @x179 $x169)))
+(let ((@x664 (|unit-resolution| @x180 (lemma ((_ |th-lemma| arith farkas -1/2 -1/2 -1/2 -1/2 -1/2 1) @x411 @x406 @x473 @x474 @x261 @x403 false) $x18) $x168)))
+(let ((@x670 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x20 (not $x509) $x666)) @x664 (or (not $x509) $x666))))
+((_ |th-lemma| arith farkas 1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 1) (|unit-resolution| @x670 @x663 $x666) @x653 @x261 @x474 @x377 @x371 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x11) $x421)) @x63 $x421) @x473 @x648 (lemma @x494 (not $x535)) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+5e6ffeb79676694a9ab7732936a1e448ef9134cd 12 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x6 (exists ((?v0 Int) )false)
+))
+(let (($x5 (not $x6)))
+(let (($x7 (not $x5)))
+(let ((@x33 (monotonicity (|elim-unused| (= $x6 false)) (= $x5 (not false)))))
+(let ((@x40 (monotonicity (trans @x33 (rewrite (= (not false) true)) (= $x5 true)) (= $x7 (not true)))))
+(let ((@x44 (trans @x40 (rewrite (= (not true) false)) (= $x7 false))))
+(mp (asserted $x7) @x44 false)))))))))
+
+d02a9dcd83dfb0d3e50a887c4f5274a79c10c85e 12 0
+unsat
+((set-logic AUFLIRA)
+(proof
+(let (($x6 (exists ((?v0 Real) )false)
+))
+(let (($x5 (not $x6)))
+(let (($x7 (not $x5)))
+(let ((@x33 (monotonicity (|elim-unused| (= $x6 false)) (= $x5 (not false)))))
+(let ((@x40 (monotonicity (trans @x33 (rewrite (= (not false) true)) (= $x5 true)) (= $x7 (not true)))))
+(let ((@x44 (trans @x40 (rewrite (= (not true) false)) (= $x7 false))))
+(mp (asserted $x7) @x44 false)))))))))
+
+1a820d07cf476448545d144873b309b9cfc3a238 2 0
+unknown
+(error "line 6 column 10: proof is not available")
+23ed6364c527ef515dd659de8b496cfd59df4ec7 2 0
+unknown
+(error "line 6 column 10: proof is not available")
+9722ff2e938783a69202c957c858fb219ec0cdb0 2 0
+unknown
+(error "line 6 column 10: proof is not available")
+cb87115705dc568881932b35aa82751f3f97049c 22 0
+unsat
+((set-logic AUFLIA)
+(declare-fun ?v1!0 () Int)
+(declare-fun ?v0!1 () Int)
+(proof
+(let (($x51 (= ?v1!0 1)))
+(let (($x57 (not (or (not (and (= ?v0!1 0) $x51)) (not (= ?v0!1 ?v1!0))))))
+(let (($x41 (forall ((?v0 Int) (?v1 Int) )(or (not (and (= ?v0 0) (= ?v1 1))) (not (= ?v0 ?v1))))
+))
+(let (($x44 (not $x41)))
+(let (($x15 (forall ((?v0 Int) (?v1 Int) )(=> (and (= ?v0 0) (= ?v1 1)) (not (= ?v0 ?v1))))
+))
+(let (($x16 (not $x15)))
+(let (($x39 (= (=> (and (= ?1 0) (= ?0 1)) (not (= ?1 ?0))) (or (not (and (= ?1 0) (= ?0 1))) (not (= ?1 ?0))))))
+(let ((@x46 (monotonicity (|quant-intro| (rewrite $x39) (= $x15 $x41)) (= $x16 $x44))))
+(let ((@x63 (|not-or-elim| (|mp~| (mp (asserted $x16) @x46 $x44) (sk (|~| $x44 $x57)) $x57) (and (= ?v0!1 0) $x51))))
+(let ((@x65 (|and-elim| @x63 $x51)))
+(let (($x54 (= ?v0!1 ?v1!0)))
+(let ((@x66 (|not-or-elim| (|mp~| (mp (asserted $x16) @x46 $x44) (sk (|~| $x44 $x57)) $x57) $x54)))
+(let ((@x68 (trans (symm (|and-elim| @x63 (= ?v0!1 0)) (= 0 ?v0!1)) @x66 (= 0 ?v1!0))))
+(mp (trans @x68 @x65 (= 0 1)) (rewrite (= (= 0 1) false)) false))))))))))))))))
+
+d2d0a7794c4de3708d5541374fd9e0075ad5fa36 55 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x14 (exists ((?v0 Int) )(forall ((?v1 Int) )(let (($x10 (<= 0 ?v1)))
+(let (($x9 (< ?v1 0)))
+(let (($x11 (or $x9 $x10)))
+(let (($x7 (< ?v0 ?v1)))
+(=> $x7 $x11))))))
+)
+))
+(let (($x15 (not $x14)))
+(let (($x43 (exists ((?v0 Int) )(forall ((?v1 Int) )(let (($x10 (<= 0 ?v1)))
+(let (($x9 (< ?v1 0)))
+(let (($x11 (or $x9 $x10)))
+(let (($x7 (< ?v0 ?v1)))
+(let (($x36 (not $x7)))
+(or $x36 $x11)))))))
+)
+))
+(let (($x46 (not $x43)))
+(let (($x86 (exists ((?v0 Int) )true)
+))
+(let (($x40 (forall ((?v1 Int) )(let (($x10 (<= 0 ?v1)))
+(let (($x9 (< ?v1 0)))
+(let (($x11 (or $x9 $x10)))
+(let (($x7 (< ?0 ?v1)))
+(let (($x36 (not $x7)))
+(or $x36 $x11)))))))
+))
+(let (($x79 (forall ((?v1 Int) )true)
+))
+(let (($x10 (<= 0 ?0)))
+(let (($x9 (< ?0 0)))
+(let (($x11 (or $x9 $x10)))
+(let (($x7 (< ?1 ?0)))
+(let (($x36 (not $x7)))
+(let (($x37 (or $x36 $x11)))
+(let (($x58 (<= (+ ?0 (* (~ 1) ?1)) 0)))
+(let ((@x76 (rewrite (= (or $x58 (or (not (>= ?0 0)) (>= ?0 0))) true))))
+(let ((@x71 (monotonicity (rewrite (= $x9 (not (>= ?0 0)))) (rewrite (= $x10 (>= ?0 0))) (= $x11 (or (not (>= ?0 0)) (>= ?0 0))))))
+(let ((@x64 (monotonicity (rewrite (= $x7 (not $x58))) (= $x36 (not (not $x58))))))
+(let ((@x74 (monotonicity (trans @x64 (rewrite (= (not (not $x58)) $x58)) (= $x36 $x58)) @x71 (= $x37 (or $x58 (or (not (>= ?0 0)) (>= ?0 0)))))))
+(let ((@x85 (trans (|quant-intro| (trans @x74 @x76 (= $x37 true)) (= $x40 $x79)) (|elim-unused| (= $x79 true)) (= $x40 true))))
+(let ((@x92 (trans (|quant-intro| @x85 (= $x43 $x86)) (|elim-unused| (= $x86 true)) (= $x43 true))))
+(let ((@x99 (trans (monotonicity @x92 (= $x46 (not true))) (rewrite (= (not true) false)) (= $x46 false))))
+(let (($x13 (forall ((?v1 Int) )(let (($x10 (<= 0 ?v1)))
+(let (($x9 (< ?v1 0)))
+(let (($x11 (or $x9 $x10)))
+(let (($x7 (< ?0 ?v1)))
+(=> $x7 $x11))))))
+))
+(let ((@x45 (|quant-intro| (|quant-intro| (rewrite (= (=> $x7 $x11) $x37)) (= $x13 $x40)) (= $x14 $x43))))
+(let ((@x48 (monotonicity @x45 (= $x15 $x46))))
+(mp (asserted $x15) (trans @x48 @x99 (= $x15 false)) false)))))))))))))))))))))))))))
+
+75e4df9c205f7c15d7e530b5e1e97635aed16d82 42 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x15 (forall ((?v0 Int) (?v1 Int) )(let ((?x12 (* 2 ?v1)))
+(let ((?x9 (* 2 ?v0)))
+(let ((?x11 (+ ?x9 1)))
+(let (($x13 (< ?x11 ?x12)))
+(let (($x7 (< ?v0 ?v1)))
+(=> $x7 $x13)))))))
+))
+(let (($x16 (not $x15)))
+(let (($x53 (forall ((?v0 Int) (?v1 Int) )(let ((?x12 (* 2 ?v1)))
+(let ((?x9 (* 2 ?v0)))
+(let ((?x38 (+ 1 ?x9)))
+(let (($x41 (< ?x38 ?x12)))
+(let (($x7 (< ?v0 ?v1)))
+(let (($x47 (not $x7)))
+(or $x47 $x41))))))))
+))
+(let (($x56 (not $x53)))
+(let (($x82 (forall ((?v0 Int) (?v1 Int) )true)
+))
+(let ((?x12 (* 2 ?0)))
+(let ((?x9 (* 2 ?1)))
+(let ((?x38 (+ 1 ?x9)))
+(let (($x41 (< ?x38 ?x12)))
+(let (($x7 (< ?1 ?0)))
+(let (($x47 (not $x7)))
+(let (($x48 (or $x47 $x41)))
+(let (($x61 (>= (+ ?1 (* (~ 1) ?0)) 0)))
+(let (($x60 (not $x61)))
+(let ((@x72 (trans (monotonicity (rewrite (= $x7 $x60)) (= $x47 (not $x60))) (rewrite (= (not $x60) $x61)) (= $x47 $x61))))
+(let ((@x77 (monotonicity @x72 (rewrite (= $x41 $x60)) (= $x48 (or $x61 $x60)))))
+(let ((@x84 (|quant-intro| (trans @x77 (rewrite (= (or $x61 $x60) true)) (= $x48 true)) (= $x53 $x82))))
+(let ((@x91 (monotonicity (trans @x84 (|elim-unused| (= $x82 true)) (= $x53 true)) (= $x56 (not true)))))
+(let ((@x95 (trans @x91 (rewrite (= (not true) false)) (= $x56 false))))
+(let ((@x43 (monotonicity (rewrite (= (+ ?x9 1) ?x38)) (= (< (+ ?x9 1) ?x12) $x41))))
+(let ((@x46 (monotonicity @x43 (= (=> $x7 (< (+ ?x9 1) ?x12)) (=> $x7 $x41)))))
+(let ((@x52 (trans @x46 (rewrite (= (=> $x7 $x41) $x48)) (= (=> $x7 (< (+ ?x9 1) ?x12)) $x48))))
+(let ((@x58 (monotonicity (|quant-intro| @x52 (= $x15 $x53)) (= $x16 $x56))))
+(mp (asserted $x16) (trans @x58 @x95 (= $x16 false)) false))))))))))))))))))))))))))
+
+591a3beb5d84c4e2d6724bf947c2fd4fa44c6bbc 32 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x14 (forall ((?v0 Int) (?v1 Int) )(let ((?x11 (* 2 ?v1)))
+(let ((?x8 (* 2 ?v0)))
+(let ((?x10 (+ ?x8 1)))
+(let (($x12 (= ?x10 ?x11)))
+(not $x12))))))
+))
+(let (($x15 (not $x14)))
+(let (($x46 (forall ((?v0 Int) (?v1 Int) )(let ((?x11 (* 2 ?v1)))
+(let ((?x8 (* 2 ?v0)))
+(let ((?x37 (+ 1 ?x8)))
+(let (($x40 (= ?x37 ?x11)))
+(not $x40))))))
+))
+(let (($x49 (not $x46)))
+(let (($x61 (forall ((?v0 Int) (?v1 Int) )true)
+))
+(let ((?x11 (* 2 ?0)))
+(let ((?x8 (* 2 ?1)))
+(let ((?x37 (+ 1 ?x8)))
+(let (($x40 (= ?x37 ?x11)))
+(let (($x43 (not $x40)))
+(let ((@x60 (trans (monotonicity (rewrite (= $x40 false)) (= $x43 (not false))) (rewrite (= (not false) true)) (= $x43 true))))
+(let ((@x67 (trans (|quant-intro| @x60 (= $x46 $x61)) (|elim-unused| (= $x61 true)) (= $x46 true))))
+(let ((@x74 (trans (monotonicity @x67 (= $x49 (not true))) (rewrite (= (not true) false)) (= $x49 false))))
+(let ((@x42 (monotonicity (rewrite (= (+ ?x8 1) ?x37)) (= (= (+ ?x8 1) ?x11) $x40))))
+(let ((@x48 (|quant-intro| (monotonicity @x42 (= (not (= (+ ?x8 1) ?x11)) $x43)) (= $x14 $x46))))
+(let ((@x51 (monotonicity @x48 (= $x15 $x49))))
+(mp (asserted $x15) (trans @x51 @x74 (= $x15 false)) false)))))))))))))))))))
+
+ed6b5d78e5a12fb3a6471e02bc6e89ebc78c1a34 43 0
+unsat
+((set-logic AUFLIA)
+(declare-fun ?v0!1 () Int)
+(declare-fun ?v1!0 () Int)
+(proof
+(let ((?x78 (+ ?v1!0 ?v0!1)))
+(let (($x90 (>= ?x78 2)))
+(let (($x93 (not $x90)))
+(let (($x87 (= ?x78 2)))
+(let (($x81 (<= ?x78 2)))
+(let (($x84 (not $x81)))
+(let (($x71 (or (not (<= (+ ?v0!1 ?v1!0) 2)) (= (+ ?v0!1 ?v1!0) 2) (not (>= (+ ?v0!1 ?v1!0) 2)))))
+(let (($x72 (not $x71)))
+(let ((@x80 (rewrite (= (+ ?v0!1 ?v1!0) ?x78))))
+(let ((@x95 (monotonicity (monotonicity @x80 (= (>= (+ ?v0!1 ?v1!0) 2) $x90)) (= (not (>= (+ ?v0!1 ?v1!0) 2)) $x93))))
+(let ((@x86 (monotonicity (monotonicity @x80 (= (<= (+ ?v0!1 ?v1!0) 2) $x81)) (= (not (<= (+ ?v0!1 ?v1!0) 2)) $x84))))
+(let ((@x98 (monotonicity @x86 (monotonicity @x80 (= (= (+ ?v0!1 ?v1!0) 2) $x87)) @x95 (= $x71 (or $x84 $x87 $x93)))))
+(let (($x58 (forall ((?v0 Int) (?v1 Int) )(let (($x39 (not (>= (+ ?v0 ?v1) 2))))
+(let ((?x8 (+ ?v0 ?v1)))
+(let (($x10 (= ?x8 2)))
+(let (($x44 (not (<= ?x8 2))))
+(or $x44 $x10 $x39))))))
+))
+(let (($x61 (not $x58)))
+(let (($x14 (forall ((?v0 Int) (?v1 Int) )(or (< 2 (+ ?v0 ?v1)) (or (= (+ ?v0 ?v1) 2) (< (+ ?v0 ?v1) 2))))
+))
+(let (($x15 (not $x14)))
+(let (($x39 (not (>= (+ ?1 ?0) 2))))
+(let ((?x8 (+ ?1 ?0)))
+(let (($x10 (= ?x8 2)))
+(let (($x44 (not (<= ?x8 2))))
+(let (($x53 (or $x44 $x10 $x39)))
+(let (($x13 (or (< 2 ?x8) (or $x10 (< ?x8 2)))))
+(let ((@x49 (monotonicity (rewrite (= (< ?x8 2) $x39)) (= (or $x10 (< ?x8 2)) (or $x10 $x39)))))
+(let ((@x52 (monotonicity (rewrite (= (< 2 ?x8) $x44)) @x49 (= $x13 (or $x44 (or $x10 $x39))))))
+(let ((@x57 (trans @x52 (rewrite (= (or $x44 (or $x10 $x39)) $x53)) (= $x13 $x53))))
+(let ((@x64 (mp (asserted $x15) (monotonicity (|quant-intro| @x57 (= $x14 $x58)) (= $x15 $x61)) $x61)))
+(let ((@x76 (mp (|mp~| @x64 (sk (|~| $x61 $x72)) $x72) (monotonicity @x98 (= $x72 (not (or $x84 $x87 $x93)))) (not (or $x84 $x87 $x93)))))
+(let ((@x103 (|not-or-elim| @x76 (not $x87))))
+(let ((@x104 (|not-or-elim| @x76 $x90)))
+(let ((@x77 (|not-or-elim| @x76 $x81)))
+(|unit-resolution| (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x87 $x84 $x93)) @x77 (or $x87 $x93)) @x104 @x103 false)))))))))))))))))))))))))))))))))
+
+092a8c0984dc61be1fab786d699cb79093b7c5f2 46 0
+unsat
+((set-logic AUFLIA)
+(declare-fun ?v0!0 () Int)
+(proof
+(let (($x81 (<= ?v0!0 0)))
+(let (($x84 (<= ?v0!0 (~ 1))))
+(let (($x85 (not $x84)))
+(let ((@x103 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x85 $x81)) (hypothesis (not $x81)) $x85)))
+(let (($x82 (>= ?v0!0 1)))
+(let (($x83 (not $x82)))
+(let (($x86 (ite $x81 $x83 $x85)))
+(let (($x87 (not $x86)))
+(let (($x71 (forall ((?v0 Int) )(let (($x56 (not (<= ?v0 (~ 1)))))
+(let (($x59 (not (>= ?v0 1))))
+(ite (<= ?v0 0) $x59 $x56))))
+))
+(let (($x74 (not $x71)))
+(let (($x13 (forall ((?v0 Int) )(let (($x11 (< ?v0 1)))
+(let (($x7 (< 0 ?v0)))
+(ite $x7 (< 0 (+ ?v0 1)) $x11))))
+))
+(let (($x14 (not $x13)))
+(let (($x44 (forall ((?v0 Int) )(let (($x11 (< ?v0 1)))
+(let (($x38 (< 0 (+ 1 ?v0))))
+(let (($x7 (< 0 ?v0)))
+(ite $x7 $x38 $x11)))))
+))
+(let (($x56 (not (<= ?0 (~ 1)))))
+(let (($x59 (not (>= ?0 1))))
+(let (($x66 (ite (<= ?0 0) $x59 $x56)))
+(let (($x11 (< ?0 1)))
+(let (($x38 (< 0 (+ 1 ?0))))
+(let (($x7 (< 0 ?0)))
+(let (($x41 (ite $x7 $x38 $x11)))
+(let ((@x65 (monotonicity (rewrite (= $x7 (not (<= ?0 0)))) (rewrite (= $x38 $x56)) (rewrite (= $x11 $x59)) (= $x41 (ite (not (<= ?0 0)) $x56 $x59)))))
+(let ((@x70 (trans @x65 (rewrite (= (ite (not (<= ?0 0)) $x56 $x59) $x66)) (= $x41 $x66))))
+(let ((@x76 (monotonicity (|quant-intro| @x70 (= $x44 $x71)) (= (not $x44) $x74))))
+(let ((@x40 (monotonicity (rewrite (= (+ ?0 1) (+ 1 ?0))) (= (< 0 (+ ?0 1)) $x38))))
+(let ((@x43 (monotonicity @x40 (= (ite $x7 (< 0 (+ ?0 1)) $x11) $x41))))
+(let ((@x49 (monotonicity (|quant-intro| @x43 (= $x13 $x44)) (= $x14 (not $x44)))))
+(let ((@x90 (|mp~| (mp (asserted $x14) (trans @x49 @x76 (= $x14 $x74)) $x74) (sk (|~| $x74 $x87)) $x87)))
+(let ((@x106 (|unit-resolution| (|unit-resolution| (|def-axiom| (or $x86 $x81 $x84)) @x90 (or $x81 $x84)) @x103 (hypothesis (not $x81)) false)))
+(let ((@x107 (lemma @x106 $x81)))
+(let ((@x112 (|unit-resolution| (|def-axiom| (or $x86 (not $x81) $x82)) @x90 (or (not $x81) $x82))))
+(|unit-resolution| @x112 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x83 (not $x81))) @x107 $x83) @x107 false)))))))))))))))))))))))))))))))))
+
+a5ac1b17c244dd3aef6c7c1289500bca02b482d0 2 0
+unknown
+(error "line 6 column 10: proof is not available")
+f697308f77e23a8625c050b2aa7a7f131faf390d 2 0
+unknown
+(error "line 6 column 10: proof is not available")
+ad02a5379962c0c41aaf5c95191947c03228f5e6 39 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x16 (exists ((?v0 Int) (?v1 Int) (?v2 Int) )(let ((?x11 (- 6)))
+(let ((?x12 (* ?x11 ?v1)))
+(let ((?x9 (* 4 ?v0)))
+(let ((?x13 (+ ?x9 ?x12)))
+(= ?x13 1))))))
+))
+(let (($x7 (not $x16)))
+(let (($x17 (not $x7)))
+(let (($x59 (exists ((?v0 Int) (?v1 Int) )(let ((?x56 (* (~ 6) ?v1)))
+(let ((?x55 (* 4 ?v0)))
+(let ((?x57 (+ ?x55 ?x56)))
+(= ?x57 1)))))
+))
+(let (($x75 (exists ((?v0 Int) (?v1 Int) )false)
+))
+(let ((@x79 (|quant-intro| (rewrite (= (= (+ (* 4 ?1) (* (~ 6) ?0)) 1) false)) (= $x59 $x75))))
+(let ((@x83 (trans @x79 (|elim-unused| (= $x75 false)) (= $x59 false))))
+(let (($x51 (exists ((?v0 Int) (?v1 Int) (?v2 Int) )(let ((?x42 (* (~ 6) ?v1)))
+(let ((?x9 (* 4 ?v0)))
+(let ((?x45 (+ ?x9 ?x42)))
+(= ?x45 1)))))
+))
+(let ((?x42 (* (~ 6) ?1)))
+(let ((?x9 (* 4 ?2)))
+(let ((?x45 (+ ?x9 ?x42)))
+(let (($x48 (= ?x45 1)))
+(let ((?x11 (- 6)))
+(let ((?x12 (* ?x11 ?1)))
+(let ((?x13 (+ ?x9 ?x12)))
+(let (($x15 (= ?x13 1)))
+(let ((@x47 (monotonicity (monotonicity (rewrite (= ?x11 (~ 6))) (= ?x12 ?x42)) (= ?x13 ?x45))))
+(let ((@x63 (trans (|quant-intro| (monotonicity @x47 (= $x15 $x48)) (= $x16 $x51)) (|elim-unused| (= $x51 $x59)) (= $x16 $x59))))
+(let ((@x69 (monotonicity (monotonicity @x63 (= $x7 (not $x59))) (= $x17 (not (not $x59))))))
+(let ((@x73 (trans @x69 (rewrite (= (not (not $x59)) $x59)) (= $x17 $x59))))
+(mp (asserted $x17) (trans @x73 @x83 (= $x17 false)) false)))))))))))))))))))))))
+
+8a423de6b668d07fe5d90dcad74d7fbb1fcb9c11 52 0
+unsat
+((set-logic AUFLIA)
+(declare-fun ?v1!1 () Int)
+(declare-fun ?v2!0 () Int)
+(proof
+(let ((?x103 (+ ?v2!0 ?v1!1)))
+(let (($x104 (<= ?x103 0)))
+(let (($x106 (or (not (and (not (<= ?v1!1 0)) (not (<= ?v2!0 0)))) (not $x104))))
+(let (($x86 (forall ((?v1 Int) (?v2 Int) )(or (not (and (not (<= ?v1 0)) (not (<= ?v2 0)))) (not (<= (+ ?v2 ?v1) 0))))
+))
+(let (($x89 (not $x86)))
+(let (($x15 (exists ((?v0 Int) )(forall ((?v1 Int) (?v2 Int) )(let (($x10 (and (< 0 ?v1) (< 0 ?v2))))
+(=> $x10 (< 0 (+ ?v1 ?v2)))))
+)
+))
+(let (($x16 (not $x15)))
+(let (($x52 (forall ((?v1 Int) (?v2 Int) )(let ((?x37 (+ ?v2 ?v1)))
+(let (($x40 (< 0 ?x37)))
+(or (not (and (< 0 ?v1) (< 0 ?v2))) $x40))))
+))
+(let (($x83 (or (not (and (not (<= ?1 0)) (not (<= ?0 0)))) (not (<= (+ ?0 ?1) 0)))))
+(let ((?x37 (+ ?0 ?1)))
+(let (($x40 (< 0 ?x37)))
+(let (($x47 (or (not (and (< 0 ?1) (< 0 ?0))) $x40)))
+(let (($x77 (= (not (and (< 0 ?1) (< 0 ?0))) (not (and (not (<= ?1 0)) (not (<= ?0 0)))))))
+(let (($x10 (and (< 0 ?1) (< 0 ?0))))
+(let ((@x75 (monotonicity (rewrite (= (< 0 ?1) (not (<= ?1 0)))) (rewrite (= (< 0 ?0) (not (<= ?0 0)))) (= $x10 (and (not (<= ?1 0)) (not (<= ?0 0)))))))
+(let ((@x85 (monotonicity (monotonicity @x75 $x77) (rewrite (= $x40 (not (<= ?x37 0)))) (= $x47 $x83))))
+(let ((@x91 (monotonicity (|quant-intro| @x85 (= $x52 $x86)) (= (not $x52) $x89))))
+(let (($x55 (exists ((?v0 Int) )(forall ((?v1 Int) (?v2 Int) )(let ((?x37 (+ ?v2 ?v1)))
+(let (($x40 (< 0 ?x37)))
+(or (not (and (< 0 ?v1) (< 0 ?v2))) $x40))))
+)
+))
+(let (($x14 (forall ((?v1 Int) (?v2 Int) )(let (($x10 (and (< 0 ?v1) (< 0 ?v2))))
+(=> $x10 (< 0 (+ ?v1 ?v2)))))
+))
+(let ((@x42 (monotonicity (rewrite (= (+ ?1 ?0) ?x37)) (= (< 0 (+ ?1 ?0)) $x40))))
+(let ((@x45 (monotonicity @x42 (= (=> $x10 (< 0 (+ ?1 ?0))) (=> $x10 $x40)))))
+(let ((@x51 (trans @x45 (rewrite (= (=> $x10 $x40) $x47)) (= (=> $x10 (< 0 (+ ?1 ?0))) $x47))))
+(let ((@x61 (trans (|quant-intro| (|quant-intro| @x51 (= $x14 $x52)) (= $x15 $x55)) (|elim-unused| (= $x55 $x52)) (= $x15 $x52))))
+(let ((@x93 (trans (monotonicity @x61 (= $x16 (not $x52))) @x91 (= $x16 $x89))))
+(let ((@x110 (|mp~| (mp (asserted $x16) @x93 $x89) (sk (|~| $x89 (not $x106))) (not $x106))))
+(let ((@x116 (|not-or-elim| @x110 $x104)))
+(let (($x97 (<= ?v1!1 0)))
+(let (($x98 (not $x97)))
+(let ((@x114 (|and-elim| (|not-or-elim| @x110 (and $x98 (not (<= ?v2!0 0)))) $x98)))
+(let (($x99 (<= ?v2!0 0)))
+(let (($x100 (not $x99)))
+(let ((@x115 (|and-elim| (|not-or-elim| @x110 (and $x98 $x100)) $x100)))
+((_ |th-lemma| arith farkas 1 1 1) @x115 @x114 @x116 false)))))))))))))))))))))))))))))))))))
+
+7c93c190dc21779c8214786ce8c1fd4de433814f 46 0
+unsat
+((set-logic AUFLIRA)
+(declare-fun ?v1!1 () Int)
+(declare-fun ?v2!0 () Real)
+(proof
+(let (($x103 (<= ?v1!1 (~ 1))))
+(let (($x104 (not $x103)))
+(let (($x105 (or (not (and (not (<= ?v1!1 0)) (not (<= ?v2!0 0.0)))) $x104)))
+(let (($x86 (forall ((?v1 Int) (?v2 Real) )(or (not (and (not (<= ?v1 0)) (not (<= ?v2 0.0)))) (not (<= ?v1 (~ 1)))))
+))
+(let (($x89 (not $x86)))
+(let (($x18 (exists ((?v0 Int) )(forall ((?v1 Int) (?v2 Real) )(let (($x12 (and (< 0 ?v1) (< 0.0 ?v2))))
+(=> $x12 (< (- 1) ?v1))))
+)
+))
+(let (($x5 (not $x18)))
+(let (($x52 (forall ((?v1 Int) (?v2 Real) )(let (($x40 (< (~ 1) ?v1)))
+(or (not (and (< 0 ?v1) (< 0.0 ?v2))) $x40)))
+))
+(let (($x83 (or (not (and (not (<= ?1 0)) (not (<= ?0 0.0)))) (not (<= ?1 (~ 1))))))
+(let (($x40 (< (~ 1) ?1)))
+(let (($x47 (or (not (and (< 0 ?1) (< 0.0 ?0))) $x40)))
+(let (($x77 (= (not (and (< 0 ?1) (< 0.0 ?0))) (not (and (not (<= ?1 0)) (not (<= ?0 0.0)))))))
+(let (($x12 (and (< 0 ?1) (< 0.0 ?0))))
+(let ((@x75 (monotonicity (rewrite (= (< 0 ?1) (not (<= ?1 0)))) (rewrite (= (< 0.0 ?0) (not (<= ?0 0.0)))) (= $x12 (and (not (<= ?1 0)) (not (<= ?0 0.0)))))))
+(let ((@x85 (monotonicity (monotonicity @x75 $x77) (rewrite (= $x40 (not (<= ?1 (~ 1))))) (= $x47 $x83))))
+(let ((@x91 (monotonicity (|quant-intro| @x85 (= $x52 $x86)) (= (not $x52) $x89))))
+(let (($x55 (exists ((?v0 Int) )(forall ((?v1 Int) (?v2 Real) )(let (($x40 (< (~ 1) ?v1)))
+(or (not (and (< 0 ?v1) (< 0.0 ?v2))) $x40)))
+)
+))
+(let (($x17 (forall ((?v1 Int) (?v2 Real) )(let (($x12 (and (< 0 ?v1) (< 0.0 ?v2))))
+(=> $x12 (< (- 1) ?v1))))
+))
+(let ((@x42 (monotonicity (rewrite (= (- 1) (~ 1))) (= (< (- 1) ?1) $x40))))
+(let ((@x45 (monotonicity @x42 (= (=> $x12 (< (- 1) ?1)) (=> $x12 $x40)))))
+(let ((@x51 (trans @x45 (rewrite (= (=> $x12 $x40) $x47)) (= (=> $x12 (< (- 1) ?1)) $x47))))
+(let ((@x61 (trans (|quant-intro| (|quant-intro| @x51 (= $x17 $x52)) (= $x18 $x55)) (|elim-unused| (= $x55 $x52)) (= $x18 $x52))))
+(let ((@x93 (trans (monotonicity @x61 (= $x5 (not $x52))) @x91 (= $x5 $x89))))
+(let ((@x109 (|mp~| (mp (asserted $x5) @x93 $x89) (sk (|~| $x89 (not $x105))) (not $x105))))
+(let ((@x115 (|not-or-elim| @x109 $x103)))
+(let (($x97 (<= ?v1!1 0)))
+(let (($x98 (not $x97)))
+(let ((@x113 (|and-elim| (|not-or-elim| @x109 (and $x98 (not (<= ?v2!0 0.0)))) $x98)))
+(|unit-resolution| (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x104 $x97)) @x113 $x104) @x115 false)))))))))))))))))))))))))))))))
+
+39a3c02f6687608102bd092d376b8901575e5356 2 0
+unknown
+(error "line 6 column 10: proof is not available")
+3bdf1da3a49c7c0ce726c85bf6e844aabdd6afa0 36 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x13 (forall ((?v0 Int) )(let ((?x10 (* 2 |a$|)))
+(let ((?x9 (* 2 ?v0)))
+(let (($x11 (< ?x9 ?x10)))
+(let (($x7 (< ?v0 |a$|)))
+(=> $x7 $x11))))))
+))
+(let (($x14 (not $x13)))
+(let (($x40 (forall ((?v0 Int) )(let ((?x10 (* 2 |a$|)))
+(let ((?x9 (* 2 ?v0)))
+(let (($x11 (< ?x9 ?x10)))
+(let (($x7 (< ?v0 |a$|)))
+(let (($x36 (not $x7)))
+(or $x36 $x11)))))))
+))
+(let (($x43 (not $x40)))
+(let (($x69 (forall ((?v0 Int) )true)
+))
+(let ((?x10 (* 2 |a$|)))
+(let ((?x9 (* 2 ?0)))
+(let (($x11 (< ?x9 ?x10)))
+(let (($x7 (< ?0 |a$|)))
+(let (($x36 (not $x7)))
+(let (($x37 (or $x36 $x11)))
+(let (($x48 (>= (+ ?0 (* (~ 1) |a$|)) 0)))
+(let (($x47 (not $x48)))
+(let ((@x59 (trans (monotonicity (rewrite (= $x7 $x47)) (= $x36 (not $x47))) (rewrite (= (not $x47) $x48)) (= $x36 $x48))))
+(let ((@x64 (monotonicity @x59 (rewrite (= $x11 $x47)) (= $x37 (or $x48 $x47)))))
+(let ((@x71 (|quant-intro| (trans @x64 (rewrite (= (or $x48 $x47) true)) (= $x37 true)) (= $x40 $x69))))
+(let ((@x78 (monotonicity (trans @x71 (|elim-unused| (= $x69 true)) (= $x40 true)) (= $x43 (not true)))))
+(let ((@x82 (trans @x78 (rewrite (= (not true) false)) (= $x43 false))))
+(let ((@x45 (monotonicity (|quant-intro| (rewrite (= (=> $x7 $x11) $x37)) (= $x13 $x40)) (= $x14 $x43))))
+(mp (asserted $x14) (trans @x45 @x82 (= $x14 false)) false))))))))))))))))))))))
+
+0737ab0e9619ba68da155fd5dcce2691243e7d8d 24 0
+unsat
+((set-logic AUFLIA)
+(declare-fun ?v1!0 () Int)
+(proof
+(let (($x62 (>= ?v1!0 1)))
+(let (($x50 (forall ((?v1 Int) )(or (not (<= ?v1 0)) (not (>= ?v1 1))))
+))
+(let (($x53 (not $x50)))
+(let (($x12 (forall ((?v0 Int) (?v1 Int) )(or (< 0 ?v1) (< ?v1 1)))
+))
+(let (($x5 (not $x12)))
+(let (($x33 (forall ((?v1 Int) )(or (< 0 ?v1) (< ?v1 1)))
+))
+(let (($x11 (or (< 0 ?0) (< ?0 1))))
+(let ((@x49 (monotonicity (rewrite (= (< 0 ?0) (not (<= ?0 0)))) (rewrite (= (< ?0 1) (not (>= ?0 1)))) (= $x11 (or (not (<= ?0 0)) (not (>= ?0 1)))))))
+(let ((@x55 (monotonicity (|quant-intro| @x49 (= $x33 $x50)) (= (not $x33) $x53))))
+(let ((@x57 (trans (monotonicity (|elim-unused| (= $x12 $x33)) (= $x5 (not $x33))) @x55 (= $x5 $x53))))
+(let ((@x68 (|mp~| (mp (asserted $x5) @x57 $x53) (sk (|~| $x53 (not (or (not (<= ?v1!0 0)) (not $x62))))) (not (or (not (<= ?v1!0 0)) (not $x62))))))
+(let ((@x72 (|not-or-elim| @x68 $x62)))
+(let (($x63 (not $x62)))
+(let (($x60 (<= ?v1!0 0)))
+(let ((@x71 (|not-or-elim| @x68 $x60)))
+(|unit-resolution| (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x63 (not $x60))) @x71 $x63) @x72 false))))))))))))))))))
+
+40bda8c0d6f113a97f5dc1db7c4465fe4cb9ac06 26 0
+unsat
+((set-logic <null>)
+(proof
+(let (($x56 (<= |b$| 0)))
+(let (($x60 (or (not (and (not (<= |a$| 0)) (not (<= (* |a$| |b$|) 0)))) (not $x56))))
+(let (($x63 (not $x60)))
+(let (($x14 (not (=> (and (< 0 |a$|) (< 0 (* |a$| |b$|))) (< 0 |b$|)))))
+(let (($x12 (< 0 |b$|)))
+(let (($x36 (or (not (and (< 0 |a$|) (< 0 (* |a$| |b$|)))) $x12)))
+(let (($x54 (= (not (and (< 0 |a$|) (< 0 (* |a$| |b$|)))) (not (and (not (<= |a$| 0)) (not (<= (* |a$| |b$|) 0)))))))
+(let ((?x9 (* |a$| |b$|)))
+(let (($x46 (<= ?x9 0)))
+(let (($x47 (not $x46)))
+(let (($x42 (<= |a$| 0)))
+(let (($x43 (not $x42)))
+(let (($x50 (and $x43 $x47)))
+(let (($x11 (and (< 0 |a$|) (< 0 ?x9))))
+(let ((@x52 (monotonicity (rewrite (= (< 0 |a$|) $x43)) (rewrite (= (< 0 ?x9) $x47)) (= $x11 $x50))))
+(let ((@x62 (monotonicity (monotonicity @x52 $x54) (rewrite (= $x12 (not $x56))) (= $x36 $x60))))
+(let ((@x41 (monotonicity (rewrite (= (=> $x11 $x12) $x36)) (= $x14 (not $x36)))))
+(let ((@x67 (trans @x41 (monotonicity @x62 (= (not $x36) $x63)) (= $x14 $x63))))
+(let ((@x72 (|not-or-elim| (mp (asserted $x14) @x67 $x63) $x56)))
+(let ((@x70 (|and-elim| (|not-or-elim| (mp (asserted $x14) @x67 $x63) $x50) $x43)))
+(let ((@x71 (|and-elim| (|not-or-elim| (mp (asserted $x14) @x67 $x63) $x50) $x47)))
+((_ |th-lemma| arith farkas 1 1 1) @x71 @x70 @x72 false))))))))))))))))))))))))
+
+3f9914c501829bba4f4b416ce311c4f49855326d 26 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x13 (+ |y$| 1)))
+(let ((?x14 (* |a$| ?x13)))
+(let ((?x12 (* |a$| |x$|)))
+(let ((?x15 (+ ?x12 ?x14)))
+(let ((?x8 (+ |x$| 1)))
+(let ((?x10 (+ ?x8 |y$|)))
+(let ((?x11 (* |a$| ?x10)))
+(let (($x16 (= ?x11 ?x15)))
+(let (($x17 (not $x16)))
+(let (($x80 (= (= (+ |a$| ?x12 (* |a$| |y$|)) (+ |a$| ?x12 (* |a$| |y$|))) true)))
+(let (($x78 (= $x16 (= (+ |a$| ?x12 (* |a$| |y$|)) (+ |a$| ?x12 (* |a$| |y$|))))))
+(let ((@x74 (rewrite (= (+ ?x12 (+ |a$| (* |a$| |y$|))) (+ |a$| ?x12 (* |a$| |y$|))))))
+(let ((@x64 (monotonicity (rewrite (= ?x13 (+ 1 |y$|))) (= ?x14 (* |a$| (+ 1 |y$|))))))
+(let ((@x69 (trans @x64 (rewrite (= (* |a$| (+ 1 |y$|)) (+ |a$| (* |a$| |y$|)))) (= ?x14 (+ |a$| (* |a$| |y$|))))))
+(let ((@x76 (trans (monotonicity @x69 (= ?x15 (+ ?x12 (+ |a$| (* |a$| |y$|))))) @x74 (= ?x15 (+ |a$| ?x12 (* |a$| |y$|))))))
+(let ((@x56 (rewrite (= (* |a$| (+ 1 |x$| |y$|)) (+ |a$| ?x12 (* |a$| |y$|))))))
+(let ((@x44 (monotonicity (rewrite (= ?x8 (+ 1 |x$|))) (= ?x10 (+ (+ 1 |x$|) |y$|)))))
+(let ((@x49 (trans @x44 (rewrite (= (+ (+ 1 |x$|) |y$|) (+ 1 |x$| |y$|))) (= ?x10 (+ 1 |x$| |y$|)))))
+(let ((@x58 (trans (monotonicity @x49 (= ?x11 (* |a$| (+ 1 |x$| |y$|)))) @x56 (= ?x11 (+ |a$| ?x12 (* |a$| |y$|))))))
+(let ((@x86 (monotonicity (trans (monotonicity @x58 @x76 $x78) (rewrite $x80) (= $x16 true)) (= $x17 (not true)))))
+(let ((@x90 (trans @x86 (rewrite (= (not true) false)) (= $x17 false))))
+(mp (asserted $x17) @x90 false))))))))))))))))))))))))
+
+f65cca85cf5c1c666974448574788ae3b34595b7 23 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x14 (* 2.0 |x$|)))
+(let ((?x15 (* ?x14 |y$|)))
+(let ((?x10 (- 1.0 |y$|)))
+(let ((?x11 (* |x$| ?x10)))
+(let ((?x8 (+ 1.0 |y$|)))
+(let ((?x9 (* |x$| ?x8)))
+(let ((?x12 (- ?x9 ?x11)))
+(let (($x16 (= ?x12 ?x15)))
+(let (($x17 (not $x16)))
+(let ((@x71 (rewrite (= (= (* 2.0 (* |x$| |y$|)) (* 2.0 (* |x$| |y$|))) true))))
+(let ((?x39 (* |x$| |y$|)))
+(let ((?x61 (* 2.0 ?x39)))
+(let ((@x54 (rewrite (= (* |x$| (+ 1.0 (* (~ 1.0) |y$|))) (+ |x$| (* (~ 1.0) ?x39))))))
+(let ((@x50 (monotonicity (rewrite (= ?x10 (+ 1.0 (* (~ 1.0) |y$|)))) (= ?x11 (* |x$| (+ 1.0 (* (~ 1.0) |y$|)))))))
+(let ((@x59 (monotonicity (rewrite (= ?x9 (+ |x$| ?x39))) (trans @x50 @x54 (= ?x11 (+ |x$| (* (~ 1.0) ?x39)))) (= ?x12 (- (+ |x$| ?x39) (+ |x$| (* (~ 1.0) ?x39)))))))
+(let ((@x64 (trans @x59 (rewrite (= (- (+ |x$| ?x39) (+ |x$| (* (~ 1.0) ?x39))) ?x61)) (= ?x12 ?x61))))
+(let ((@x73 (trans (monotonicity @x64 (rewrite (= ?x15 ?x61)) (= $x16 (= ?x61 ?x61))) @x71 (= $x16 true))))
+(let ((@x80 (trans (monotonicity @x73 (= $x17 (not true))) (rewrite (= (not true) false)) (= $x17 false))))
+(mp (asserted $x17) @x80 false)))))))))))))))))))))
+
+2643ba95811453f95121cf28c15c748e73c8c127 51 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x25 (+ |b$| |d$|)))
+(let ((?x26 (+ ?x25 |e$|)))
+(let ((?x8 (+ 1 |p$|)))
+(let ((?x27 (* ?x8 ?x26)))
+(let ((?x22 (* |d$| |p$|)))
+(let ((?x20 (* ?x8 |d$|)))
+(let ((?x11 (+ |b$| |e$|)))
+(let ((?x18 (* 2 ?x8)))
+(let ((?x19 (* ?x18 ?x11)))
+(let ((?x21 (+ ?x19 ?x20)))
+(let ((?x23 (+ ?x21 ?x22)))
+(let ((?x24 (+ |u$| ?x23)))
+(let ((?x28 (- ?x24 ?x27)))
+(let ((?x15 (* |p$| |d$|)))
+(let ((?x12 (* ?x8 ?x11)))
+(let ((?x13 (+ |u$| ?x12)))
+(let ((?x16 (+ ?x13 ?x15)))
+(let (($x29 (= ?x16 ?x28)))
+(let (($x30 (not $x29)))
+(let ((?x53 (* |p$| |e$|)))
+(let ((?x52 (* |p$| |b$|)))
+(let ((?x68 (+ |u$| |b$| |e$| ?x15 ?x52 ?x53)))
+(let ((?x125 (+ |b$| |e$| |d$| ?x15 ?x52 ?x53)))
+(let ((?x83 (* 2 ?x53)))
+(let ((?x81 (* 2 ?x52)))
+(let ((?x82 (* 2 |e$|)))
+(let ((?x80 (* 2 |b$|)))
+(let ((?x114 (+ |u$| ?x80 ?x82 |d$| (* 2 ?x15) ?x81 ?x83)))
+(let ((@x124 (monotonicity (rewrite (= ?x26 (+ |b$| |e$| |d$|))) (= ?x27 (* ?x8 (+ |b$| |e$| |d$|))))))
+(let ((@x129 (trans @x124 (rewrite (= (* ?x8 (+ |b$| |e$| |d$|)) ?x125)) (= ?x27 ?x125))))
+(let ((@x116 (rewrite (= (+ |u$| (+ ?x80 ?x82 |d$| (* 2 ?x15) ?x81 ?x83)) ?x114))))
+(let ((?x106 (+ ?x80 ?x82 |d$| (* 2 ?x15) ?x81 ?x83)))
+(let ((?x95 (+ ?x80 ?x82 |d$| ?x15 ?x81 ?x83)))
+(let ((@x86 (rewrite (= (* (+ 2 (* 2 |p$|)) ?x11) (+ ?x80 ?x82 ?x81 ?x83)))))
+(let ((@x79 (monotonicity (rewrite (= ?x18 (+ 2 (* 2 |p$|)))) (= ?x19 (* (+ 2 (* 2 |p$|)) ?x11)))))
+(let ((@x94 (monotonicity (trans @x79 @x86 (= ?x19 (+ ?x80 ?x82 ?x81 ?x83))) (rewrite (= ?x20 (+ |d$| ?x15))) (= ?x21 (+ (+ ?x80 ?x82 ?x81 ?x83) (+ |d$| ?x15))))))
+(let ((@x99 (trans @x94 (rewrite (= (+ (+ ?x80 ?x82 ?x81 ?x83) (+ |d$| ?x15)) ?x95)) (= ?x21 ?x95))))
+(let ((@x110 (trans (monotonicity @x99 (rewrite (= ?x22 ?x15)) (= ?x23 (+ ?x95 ?x15))) (rewrite (= (+ ?x95 ?x15) ?x106)) (= ?x23 ?x106))))
+(let ((@x118 (trans (monotonicity @x110 (= ?x24 (+ |u$| ?x106))) @x116 (= ?x24 ?x114))))
+(let ((@x137 (trans (monotonicity @x118 @x129 (= ?x28 (- ?x114 ?x125))) (rewrite (= (- ?x114 ?x125) ?x68)) (= ?x28 ?x68))))
+(let ((@x62 (rewrite (= (+ |u$| (+ |b$| |e$| ?x52 ?x53)) (+ |u$| |b$| |e$| ?x52 ?x53)))))
+(let ((@x59 (monotonicity (rewrite (= ?x12 (+ |b$| |e$| ?x52 ?x53))) (= ?x13 (+ |u$| (+ |b$| |e$| ?x52 ?x53))))))
+(let ((@x67 (monotonicity (trans @x59 @x62 (= ?x13 (+ |u$| |b$| |e$| ?x52 ?x53))) (= ?x16 (+ (+ |u$| |b$| |e$| ?x52 ?x53) ?x15)))))
+(let ((@x72 (trans @x67 (rewrite (= (+ (+ |u$| |b$| |e$| ?x52 ?x53) ?x15) ?x68)) (= ?x16 ?x68))))
+(let ((@x143 (trans (monotonicity @x72 @x137 (= $x29 (= ?x68 ?x68))) (rewrite (= (= ?x68 ?x68) true)) (= $x29 true))))
+(let ((@x150 (trans (monotonicity @x143 (= $x30 (not true))) (rewrite (= (not true) false)) (= $x30 false))))
+(mp (asserted $x30) @x150 false)))))))))))))))))))))))))))))))))))))))))))))))))
+
+9377273e8e637d8916ed13b81bd56a602ea76d29 126 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x7 (|of_nat$| |x$|)))
+(let ((?x8 (* 2 ?x7)))
+(let ((?x9 (|nat$| ?x8)))
+(let ((?x147 (|of_nat$| ?x9)))
+(let ((?x160 (* (~ 1) ?x147)))
+(let ((?x161 (+ ?x8 ?x160)))
+(let (($x177 (<= ?x161 0)))
+(let (($x158 (= ?x161 0)))
+(let (($x150 (>= ?x7 0)))
+(let (($x239 (>= ?x147 1)))
+(let (($x237 (= ?x147 1)))
+(let ((?x11 (|nat$| 1)))
+(let ((?x200 (|of_nat$| ?x11)))
+(let (($x201 (= ?x200 1)))
+(let (($x128 (forall ((?v0 Int) )(!(let ((?x23 (|nat$| ?v0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x25 (= ?x24 ?v0)))
+(let (($x66 (>= ?v0 0)))
+(let (($x67 (not $x66)))
+(or $x67 $x25)))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x73 (forall ((?v0 Int) )(let ((?x23 (|nat$| ?v0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x25 (= ?x24 ?v0)))
+(let (($x66 (>= ?v0 0)))
+(let (($x67 (not $x66)))
+(or $x67 $x25)))))))
+))
+(let ((?x23 (|nat$| ?0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x25 (= ?x24 ?0)))
+(let (($x66 (>= ?0 0)))
+(let (($x67 (not $x66)))
+(let (($x70 (or $x67 $x25)))
+(let (($x27 (forall ((?v0 Int) )(let ((?x23 (|nat$| ?v0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x25 (= ?x24 ?v0)))
+(let (($x22 (<= 0 ?v0)))
+(=> $x22 $x25))))))
+))
+(let (($x61 (forall ((?v0 Int) )(let ((?x23 (|nat$| ?v0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x25 (= ?x24 ?v0)))
+(or (not (<= 0 ?v0)) $x25)))))
+))
+(let ((@x69 (monotonicity (rewrite (= (<= 0 ?0) $x66)) (= (not (<= 0 ?0)) $x67))))
+(let ((@x75 (|quant-intro| (monotonicity @x69 (= (or (not (<= 0 ?0)) $x25) $x70)) (= $x61 $x73))))
+(let ((@x60 (rewrite (= (=> (<= 0 ?0) $x25) (or (not (<= 0 ?0)) $x25)))))
+(let ((@x78 (mp (asserted $x27) (trans (|quant-intro| @x60 (= $x27 $x61)) @x75 (= $x27 $x73)) $x73)))
+(let ((@x133 (mp (|mp~| @x78 (|nnf-pos| (refl (|~| $x70 $x70)) (|~| $x73 $x73)) $x73) (|quant-intro| (refl (= $x70 $x70)) (= $x73 $x128)) $x128)))
+(let (($x165 (not $x128)))
+(let (($x219 (or $x165 $x201)))
+(let ((@x204 (rewrite (= (>= 1 0) true))))
+(let ((@x211 (trans (monotonicity @x204 (= (not (>= 1 0)) (not true))) (rewrite (= (not true) false)) (= (not (>= 1 0)) false))))
+(let ((@x214 (monotonicity @x211 (= (or (not (>= 1 0)) $x201) (or false $x201)))))
+(let ((@x218 (trans @x214 (rewrite (= (or false $x201) $x201)) (= (or (not (>= 1 0)) $x201) $x201))))
+(let ((@x223 (monotonicity @x218 (= (or $x165 (or (not (>= 1 0)) $x201)) $x219))))
+(let ((@x226 (trans @x223 (rewrite (= $x219 $x219)) (= (or $x165 (or (not (>= 1 0)) $x201)) $x219))))
+(let ((@x227 (mp ((_ |quant-inst| 1) (or $x165 (or (not (>= 1 0)) $x201))) @x226 $x219)))
+(let (($x12 (= ?x9 ?x11)))
+(let ((@x56 (mp (asserted (not (not $x12))) (rewrite (= (not (not $x12)) $x12)) $x12)))
+(let ((@x252 (trans (monotonicity @x56 (= ?x147 ?x200)) (|unit-resolution| @x227 @x133 $x201) $x237)))
+(let ((@x261 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x239) (not (<= ?x147 0)))) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x237) $x239)) @x252 $x239) (not (<= ?x147 0)))))
+(let ((@x265 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x147 0)) (<= ?x147 0))) @x261 (not (= ?x147 0)))))
+(let (($x179 (= ?x147 0)))
+(let (($x181 (or $x150 $x179)))
+(let (($x134 (forall ((?v0 Int) )(!(let ((?x23 (|nat$| ?v0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x29 (= ?x24 0)))
+(let (($x66 (>= ?v0 0)))
+(or $x66 $x29))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x99 (forall ((?v0 Int) )(let ((?x23 (|nat$| ?v0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x29 (= ?x24 0)))
+(let (($x66 (>= ?v0 0)))
+(or $x66 $x29))))))
+))
+(let ((@x138 (|quant-intro| (refl (= (or $x66 (= ?x24 0)) (or $x66 (= ?x24 0)))) (= $x99 $x134))))
+(let ((@x118 (|nnf-pos| (refl (|~| (or $x66 (= ?x24 0)) (or $x66 (= ?x24 0)))) (|~| $x99 $x99))))
+(let (($x31 (forall ((?v0 Int) )(let ((?x23 (|nat$| ?v0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x29 (= ?x24 0)))
+(let (($x28 (< ?v0 0)))
+(=> $x28 $x29))))))
+))
+(let (($x84 (forall ((?v0 Int) )(let ((?x23 (|nat$| ?v0)))
+(let ((?x24 (|of_nat$| ?x23)))
+(let (($x29 (= ?x24 0)))
+(let (($x28 (< ?v0 0)))
+(let (($x80 (not $x28)))
+(or $x80 $x29)))))))
+))
+(let (($x29 (= ?x24 0)))
+(let (($x96 (or $x66 $x29)))
+(let (($x28 (< ?0 0)))
+(let (($x80 (not $x28)))
+(let (($x81 (or $x80 $x29)))
+(let ((@x95 (trans (monotonicity (rewrite (= $x28 $x67)) (= $x80 (not $x67))) (rewrite (= (not $x67) $x66)) (= $x80 $x66))))
+(let ((@x103 (trans (|quant-intro| (rewrite (= (=> $x28 $x29) $x81)) (= $x31 $x84)) (|quant-intro| (monotonicity @x95 (= $x81 $x96)) (= $x84 $x99)) (= $x31 $x99))))
+(let ((@x139 (mp (|mp~| (mp (asserted $x31) @x103 $x99) @x118 $x99) @x138 $x134)))
+(let (($x184 (not $x134)))
+(let (($x185 (or $x184 $x150 $x179)))
+(let ((@x152 (rewrite (= (>= ?x8 0) $x150))))
+(let ((@x190 (monotonicity (monotonicity @x152 (= (or (>= ?x8 0) $x179) $x181)) (= (or $x184 (or (>= ?x8 0) $x179)) (or $x184 $x181)))))
+(let ((@x194 (trans @x190 (rewrite (= (or $x184 $x181) $x185)) (= (or $x184 (or (>= ?x8 0) $x179)) $x185))))
+(let ((@x195 (mp ((_ |quant-inst| (* 2 ?x7)) (or $x184 (or (>= ?x8 0) $x179))) @x194 $x185)))
+(let (($x153 (not $x150)))
+(let (($x162 (or $x153 $x158)))
+(let (($x166 (or $x165 $x153 $x158)))
+(let (($x148 (= ?x147 ?x8)))
+(let (($x142 (>= ?x8 0)))
+(let (($x143 (not $x142)))
+(let (($x149 (or $x143 $x148)))
+(let (($x167 (or $x165 $x149)))
+(let ((@x164 (monotonicity (monotonicity @x152 (= $x143 $x153)) (rewrite (= $x148 $x158)) (= $x149 $x162))))
+(let ((@x175 (trans (monotonicity @x164 (= $x167 (or $x165 $x162))) (rewrite (= (or $x165 $x162) $x166)) (= $x167 $x166))))
+(let ((@x176 (mp ((_ |quant-inst| (* 2 ?x7)) $x167) @x175 $x166)))
+(let ((@x269 (|unit-resolution| (|unit-resolution| @x176 @x133 $x162) (|unit-resolution| (|unit-resolution| @x195 @x139 $x181) @x265 $x150) $x158)))
+(let (($x178 (>= ?x161 0)))
+(let (($x238 (<= ?x147 1)))
+((_ |th-lemma| arith gcd-test -1/2 -1/2 -1/2 -1/2) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x237) $x239)) @x252 $x239) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x237) $x238)) @x252 $x238) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x158) $x178)) @x269 $x178) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x158) $x177)) @x269 $x177) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+7540f10f61e5a987b0848b309bd25f2a2ae1cd0a 22 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x6 (|of_nat$| |a$|)))
+(let (($x71 (>= ?x6 4)))
+(let (($x78 (not (or (>= ?x6 3) (not $x71)))))
+(let (($x12 (< (* 2 ?x6) 7)))
+(let (($x8 (< ?x6 3)))
+(let (($x52 (not $x8)))
+(let (($x53 (or $x52 $x12)))
+(let ((@x65 (monotonicity (rewrite (= $x8 (not (>= ?x6 3)))) (= $x52 (not (not (>= ?x6 3)))))))
+(let ((@x69 (trans @x65 (rewrite (= (not (not (>= ?x6 3))) (>= ?x6 3))) (= $x52 (>= ?x6 3)))))
+(let ((@x77 (monotonicity @x69 (rewrite (= $x12 (not $x71))) (= $x53 (or (>= ?x6 3) (not $x71))))))
+(let ((@x58 (monotonicity (rewrite (= (=> $x8 $x12) $x53)) (= (not (=> $x8 $x12)) (not $x53)))))
+(let ((@x82 (trans @x58 (monotonicity @x77 (= (not $x53) $x78)) (= (not (=> $x8 $x12)) $x78))))
+(let ((@x85 (|not-or-elim| (mp (asserted (not (=> $x8 $x12))) @x82 $x78) $x71)))
+(let (($x72 (not $x71)))
+(let (($x61 (>= ?x6 3)))
+(let (($x59 (not $x61)))
+(let ((@x84 (|not-or-elim| (mp (asserted (not (=> $x8 $x12))) @x82 $x78) $x59)))
+(|unit-resolution| (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x72 $x61)) @x84 $x72) @x85 false))))))))))))))))))))
+
+3a9a1f0f87885c249813dfb78d14e1062fc20ce3 147 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x8 (|of_nat$| |y$|)))
+(let ((?x9 (+ 1 ?x8)))
+(let ((?x10 (|nat$| ?x9)))
+(let ((?x11 (|of_nat$| ?x10)))
+(let ((?x57 (* (~ 1) ?x8)))
+(let ((?x58 (+ ?x57 ?x11)))
+(let ((?x61 (|nat$| ?x58)))
+(let ((?x64 (|of_nat$| ?x61)))
+(let ((?x195 (* (~ 1) ?x11)))
+(let ((?x246 (+ ?x8 ?x195 ?x64)))
+(let (($x265 (>= ?x246 0)))
+(let (($x247 (= ?x246 0)))
+(let ((?x196 (+ ?x8 ?x195)))
+(let (($x240 (<= ?x196 0)))
+(let (($x215 (<= ?x196 (~ 1))))
+(let (($x197 (= ?x196 (~ 1))))
+(let (($x189 (>= ?x8 (~ 1))))
+(let (($x283 (>= ?x8 0)))
+(let ((?x172 (|nat$| ?x8)))
+(let ((?x284 (|of_nat$| ?x172)))
+(let (($x285 (= ?x284 0)))
+(let (($x286 (or $x283 $x285)))
+(let (($x166 (forall ((?v0 Int) )(!(let ((?x25 (|nat$| ?v0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x31 (= ?x26 0)))
+(let (($x97 (>= ?v0 0)))
+(or $x97 $x31))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x131 (forall ((?v0 Int) )(let ((?x25 (|nat$| ?v0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x31 (= ?x26 0)))
+(let (($x97 (>= ?v0 0)))
+(or $x97 $x31))))))
+))
+(let ((?x25 (|nat$| ?0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x31 (= ?x26 0)))
+(let (($x97 (>= ?0 0)))
+(let (($x128 (or $x97 $x31)))
+(let (($x33 (forall ((?v0 Int) )(let ((?x25 (|nat$| ?v0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x31 (= ?x26 0)))
+(let (($x30 (< ?v0 0)))
+(=> $x30 $x31))))))
+))
+(let (($x116 (forall ((?v0 Int) )(let ((?x25 (|nat$| ?v0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x31 (= ?x26 0)))
+(let (($x30 (< ?v0 0)))
+(let (($x112 (not $x30)))
+(or $x112 $x31)))))))
+))
+(let ((@x123 (monotonicity (rewrite (= (< ?0 0) (not $x97))) (= (not (< ?0 0)) (not (not $x97))))))
+(let ((@x127 (trans @x123 (rewrite (= (not (not $x97)) $x97)) (= (not (< ?0 0)) $x97))))
+(let ((@x133 (|quant-intro| (monotonicity @x127 (= (or (not (< ?0 0)) $x31) $x128)) (= $x116 $x131))))
+(let ((@x115 (rewrite (= (=> (< ?0 0) $x31) (or (not (< ?0 0)) $x31)))))
+(let ((@x136 (mp (asserted $x33) (trans (|quant-intro| @x115 (= $x33 $x116)) @x133 (= $x33 $x131)) $x131)))
+(let ((@x171 (mp (|mp~| @x136 (|nnf-pos| (refl (|~| $x128 $x128)) (|~| $x131 $x131)) $x131) (|quant-intro| (refl (= $x128 $x128)) (= $x131 $x166)) $x166)))
+(let (($x222 (not $x166)))
+(let (($x289 (or $x222 $x283 $x285)))
+(let ((@x294 (mp ((_ |quant-inst| (|of_nat$| |y$|)) (or $x222 $x286)) (rewrite (= (or $x222 $x286) $x289)) $x289)))
+(let ((@x316 (|unit-resolution| (|unit-resolution| @x294 @x171 $x286) (hypothesis (not $x283)) $x285)))
+(let (($x173 (= ?x172 |y$|)))
+(let (($x153 (forall ((?v0 |Nat$|) )(!(= (|nat$| (|of_nat$| ?v0)) ?v0) :pattern ( (|of_nat$| ?v0) )))
+))
+(let (($x22 (forall ((?v0 |Nat$|) )(= (|nat$| (|of_nat$| ?v0)) ?v0))
+))
+(let ((@x155 (refl (= (= (|nat$| (|of_nat$| ?0)) ?0) (= (|nat$| (|of_nat$| ?0)) ?0)))))
+(let ((@x140 (refl (|~| (= (|nat$| (|of_nat$| ?0)) ?0) (= (|nat$| (|of_nat$| ?0)) ?0)))))
+(let ((@x158 (mp (|mp~| (asserted $x22) (|nnf-pos| @x140 (|~| $x22 $x22)) $x22) (|quant-intro| @x155 (= $x22 $x153)) $x153)))
+(let (($x176 (not $x153)))
+(let (($x177 (or $x176 $x173)))
+(let ((@x178 ((_ |quant-inst| |y$|) $x177)))
+(let ((@x321 (monotonicity (symm (|unit-resolution| @x178 @x158 $x173) (= |y$| ?x172)) (= ?x8 ?x284))))
+(let ((@x326 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x8 0)) $x283)) (hypothesis (not $x283)) (trans @x321 @x316 (= ?x8 0)) false)))
+(let ((@x329 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x283) $x189)) (lemma @x326 $x283) $x189)))
+(let (($x192 (not $x189)))
+(let (($x200 (or $x192 $x197)))
+(let (($x160 (forall ((?v0 Int) )(!(let ((?x25 (|nat$| ?v0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x27 (= ?x26 ?v0)))
+(let (($x97 (>= ?v0 0)))
+(let (($x99 (not $x97)))
+(or $x99 $x27)))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x105 (forall ((?v0 Int) )(let ((?x25 (|nat$| ?v0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x27 (= ?x26 ?v0)))
+(let (($x97 (>= ?v0 0)))
+(let (($x99 (not $x97)))
+(or $x99 $x27)))))))
+))
+(let ((@x162 (refl (= (or (not $x97) (= ?x26 ?0)) (or (not $x97) (= ?x26 ?0))))))
+(let ((@x143 (refl (|~| (or (not $x97) (= ?x26 ?0)) (or (not $x97) (= ?x26 ?0))))))
+(let (($x29 (forall ((?v0 Int) )(let ((?x25 (|nat$| ?v0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x27 (= ?x26 ?v0)))
+(let (($x24 (<= 0 ?v0)))
+(=> $x24 $x27))))))
+))
+(let (($x93 (forall ((?v0 Int) )(let ((?x25 (|nat$| ?v0)))
+(let ((?x26 (|of_nat$| ?x25)))
+(let (($x27 (= ?x26 ?v0)))
+(or (not (<= 0 ?v0)) $x27)))))
+))
+(let (($x27 (= ?x26 ?0)))
+(let (($x99 (not $x97)))
+(let (($x102 (or $x99 $x27)))
+(let (($x90 (or (not (<= 0 ?0)) $x27)))
+(let ((@x101 (monotonicity (rewrite (= (<= 0 ?0) $x97)) (= (not (<= 0 ?0)) $x99))))
+(let ((@x95 (|quant-intro| (rewrite (= (=> (<= 0 ?0) $x27) $x90)) (= $x29 $x93))))
+(let ((@x109 (trans @x95 (|quant-intro| (monotonicity @x101 (= $x90 $x102)) (= $x93 $x105)) (= $x29 $x105))))
+(let ((@x146 (|mp~| (mp (asserted $x29) @x109 $x105) (|nnf-pos| @x143 (|~| $x105 $x105)) $x105)))
+(let ((@x165 (mp @x146 (|quant-intro| @x162 (= $x105 $x160)) $x160)))
+(let (($x203 (not $x160)))
+(let (($x204 (or $x203 $x192 $x197)))
+(let (($x188 (or (not (>= ?x9 0)) (= ?x11 ?x9))))
+(let (($x205 (or $x203 $x188)))
+(let ((@x194 (monotonicity (rewrite (= (>= ?x9 0) $x189)) (= (not (>= ?x9 0)) $x192))))
+(let ((@x202 (monotonicity @x194 (rewrite (= (= ?x11 ?x9) $x197)) (= $x188 $x200))))
+(let ((@x213 (trans (monotonicity @x202 (= $x205 (or $x203 $x200))) (rewrite (= (or $x203 $x200) $x204)) (= $x205 $x204))))
+(let ((@x214 (mp ((_ |quant-inst| (+ 1 ?x8)) $x205) @x213 $x204)))
+(let ((@x335 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x197) $x215)) (|unit-resolution| (|unit-resolution| @x214 @x165 $x200) @x329 $x197) $x215)))
+(let (($x243 (not $x240)))
+(let (($x250 (or $x243 $x247)))
+(let (($x253 (or $x203 $x243 $x247)))
+(let (($x239 (or (not (>= ?x58 0)) (= ?x64 ?x58))))
+(let (($x254 (or $x203 $x239)))
+(let ((@x245 (monotonicity (rewrite (= (>= ?x58 0) $x240)) (= (not (>= ?x58 0)) $x243))))
+(let ((@x252 (monotonicity @x245 (rewrite (= (= ?x64 ?x58) $x247)) (= $x239 $x250))))
+(let ((@x262 (trans (monotonicity @x252 (= $x254 (or $x203 $x250))) (rewrite (= (or $x203 $x250) $x253)) (= $x254 $x253))))
+(let ((@x263 (mp ((_ |quant-inst| (+ ?x57 ?x11)) $x254) @x262 $x253)))
+(let ((@x341 (|unit-resolution| (|unit-resolution| @x263 @x165 $x250) (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x215) $x240)) @x335 $x240) $x247)))
+(let (($x73 (<= ?x64 0)))
+(let ((@x79 (monotonicity (rewrite (= (< 0 ?x64) (not $x73))) (= (not (< 0 ?x64)) (not (not $x73))))))
+(let ((@x83 (trans @x79 (rewrite (= (not (not $x73)) $x73)) (= (not (< 0 ?x64)) $x73))))
+(let (($x67 (< 0 ?x64)))
+(let (($x70 (not $x67)))
+(let (($x17 (not (< (* 0 ?x11) (|of_nat$| (|nat$| (- ?x11 ?x8)))))))
+(let ((@x63 (monotonicity (rewrite (= (- ?x11 ?x8) ?x58)) (= (|nat$| (- ?x11 ?x8)) ?x61))))
+(let ((@x69 (monotonicity (rewrite (= (* 0 ?x11) 0)) (monotonicity @x63 (= (|of_nat$| (|nat$| (- ?x11 ?x8))) ?x64)) (= (< (* 0 ?x11) (|of_nat$| (|nat$| (- ?x11 ?x8)))) $x67))))
+(let ((@x86 (mp (asserted $x17) (trans (monotonicity @x69 (= $x17 $x70)) @x83 (= $x17 $x73)) $x73)))
+((_ |th-lemma| arith farkas -1 -1 1) @x86 @x335 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x247) $x265)) @x341 $x265) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+72e646f619a773762ccf2e62425eb512a9cd35f3 144 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x8 (|of_nat$| |y$|)))
+(let ((?x9 (+ 1 ?x8)))
+(let ((?x10 (|nat$| ?x9)))
+(let ((?x11 (|of_nat$| ?x10)))
+(let ((?x62 (+ (~ 1) ?x11)))
+(let ((?x65 (|nat$| ?x62)))
+(let ((?x281 (|of_nat$| ?x65)))
+(let ((?x291 (* (~ 1) ?x281)))
+(let ((?x330 (+ ?x8 ?x291)))
+(let (($x332 (>= ?x330 0)))
+(let (($x329 (= ?x8 ?x281)))
+(let (($x68 (= ?x65 |y$|)))
+(let (($x102 (<= ?x11 0)))
+(let (($x112 (not (or (= (not $x102) $x68) (not $x102)))))
+(let (($x19 (=> (not (ite (< 0 ?x11) true false)) false)))
+(let (($x12 (< 0 ?x11)))
+(let (($x13 (ite $x12 true false)))
+(let (($x17 (= $x13 (= (|nat$| (- ?x11 1)) |y$|))))
+(let (($x21 (or false (or $x17 $x19))))
+(let (($x22 (not $x21)))
+(let (($x74 (= $x12 $x68)))
+(let (($x89 (or $x74 $x12)))
+(let ((@x108 (monotonicity (rewrite (= $x12 (not $x102))) (= $x74 (= (not $x102) $x68)))))
+(let ((@x111 (monotonicity @x108 (rewrite (= $x12 (not $x102))) (= $x89 (or (= (not $x102) $x68) (not $x102))))))
+(let ((@x84 (monotonicity (monotonicity (rewrite (= $x13 $x12)) (= (not $x13) (not $x12))) (= $x19 (=> (not $x12) false)))))
+(let ((@x88 (trans @x84 (rewrite (= (=> (not $x12) false) $x12)) (= $x19 $x12))))
+(let ((@x67 (monotonicity (rewrite (= (- ?x11 1) ?x62)) (= (|nat$| (- ?x11 1)) ?x65))))
+(let ((@x73 (monotonicity (rewrite (= $x13 $x12)) (monotonicity @x67 (= (= (|nat$| (- ?x11 1)) |y$|) $x68)) (= $x17 (= $x12 $x68)))))
+(let ((@x91 (monotonicity (trans @x73 (rewrite (= (= $x12 $x68) $x74)) (= $x17 $x74)) @x88 (= (or $x17 $x19) $x89))))
+(let ((@x98 (trans (monotonicity @x91 (= $x21 (or false $x89))) (rewrite (= (or false $x89) $x89)) (= $x21 $x89))))
+(let ((@x116 (trans (monotonicity @x98 (= $x22 (not $x89))) (monotonicity @x111 (= (not $x89) $x112)) (= $x22 $x112))))
+(let ((@x120 (|not-or-elim| (mp (asserted $x22) @x116 $x112) $x102)))
+(let (($x171 (= $x102 $x68)))
+(let ((@x119 (|not-or-elim| (mp (asserted $x22) @x116 $x112) (not (= (not $x102) $x68)))))
+(let ((@x173 (mp @x119 (rewrite (= (not (= (not $x102) $x68)) $x171)) $x171)))
+(let ((@x219 (|unit-resolution| (|def-axiom| (or (not $x102) $x68 (not $x171))) @x173 (or (not $x102) $x68))))
+(let ((@x345 (monotonicity (symm (|unit-resolution| @x219 @x120 $x68) (= |y$| ?x65)) $x329)))
+(let ((?x241 (* (~ 1) ?x11)))
+(let ((?x242 (+ ?x8 ?x241)))
+(let (($x259 (<= ?x242 (~ 1))))
+(let (($x240 (= ?x242 (~ 1))))
+(let (($x233 (>= ?x8 (~ 1))))
+(let (($x328 (>= ?x281 0)))
+(let (($x311 (= ?x281 0)))
+(let (($x284 (>= ?x11 1)))
+(let (($x287 (not $x284)))
+(let (($x204 (forall ((?v0 Int) )(!(let ((?x30 (|nat$| ?v0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x36 (= ?x31 0)))
+(let (($x131 (>= ?v0 0)))
+(or $x131 $x36))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x165 (forall ((?v0 Int) )(let ((?x30 (|nat$| ?v0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x36 (= ?x31 0)))
+(let (($x131 (>= ?v0 0)))
+(or $x131 $x36))))))
+))
+(let ((?x30 (|nat$| ?0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x36 (= ?x31 0)))
+(let (($x131 (>= ?0 0)))
+(let (($x162 (or $x131 $x36)))
+(let (($x38 (forall ((?v0 Int) )(let ((?x30 (|nat$| ?v0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x36 (= ?x31 0)))
+(let (($x35 (< ?v0 0)))
+(=> $x35 $x36))))))
+))
+(let (($x150 (forall ((?v0 Int) )(let ((?x30 (|nat$| ?v0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x36 (= ?x31 0)))
+(let (($x35 (< ?v0 0)))
+(let (($x146 (not $x35)))
+(or $x146 $x36)))))))
+))
+(let ((@x157 (monotonicity (rewrite (= (< ?0 0) (not $x131))) (= (not (< ?0 0)) (not (not $x131))))))
+(let ((@x161 (trans @x157 (rewrite (= (not (not $x131)) $x131)) (= (not (< ?0 0)) $x131))))
+(let ((@x167 (|quant-intro| (monotonicity @x161 (= (or (not (< ?0 0)) $x36) $x162)) (= $x150 $x165))))
+(let ((@x149 (rewrite (= (=> (< ?0 0) $x36) (or (not (< ?0 0)) $x36)))))
+(let ((@x170 (mp (asserted $x38) (trans (|quant-intro| @x149 (= $x38 $x150)) @x167 (= $x38 $x165)) $x165)))
+(let ((@x209 (mp (|mp~| @x170 (|nnf-pos| (refl (|~| $x162 $x162)) (|~| $x165 $x165)) $x165) (|quant-intro| (refl (= $x162 $x162)) (= $x165 $x204)) $x204)))
+(let (($x266 (not $x204)))
+(let (($x316 (or $x266 $x284 $x311)))
+(let ((@x286 (rewrite (= (>= ?x62 0) $x284))))
+(let ((@x321 (monotonicity (monotonicity @x286 (= (or (>= ?x62 0) $x311) (or $x284 $x311))) (= (or $x266 (or (>= ?x62 0) $x311)) (or $x266 (or $x284 $x311))))))
+(let ((@x325 (trans @x321 (rewrite (= (or $x266 (or $x284 $x311)) $x316)) (= (or $x266 (or (>= ?x62 0) $x311)) $x316))))
+(let ((@x326 (mp ((_ |quant-inst| (+ (~ 1) ?x11)) (or $x266 (or (>= ?x62 0) $x311))) @x325 $x316)))
+(let ((@x353 (|unit-resolution| @x326 @x209 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x287 (not $x102))) @x120 $x287) $x311)))
+(let ((@x362 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x233 (not $x328) (not $x332))) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x311) $x328)) @x353 $x328) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x329) $x332)) @x345 $x332) $x233)))
+(let (($x236 (not $x233)))
+(let (($x244 (or $x236 $x240)))
+(let (($x198 (forall ((?v0 Int) )(!(let ((?x30 (|nat$| ?v0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x32 (= ?x31 ?v0)))
+(let (($x131 (>= ?v0 0)))
+(let (($x133 (not $x131)))
+(or $x133 $x32)))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x139 (forall ((?v0 Int) )(let ((?x30 (|nat$| ?v0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x32 (= ?x31 ?v0)))
+(let (($x131 (>= ?v0 0)))
+(let (($x133 (not $x131)))
+(or $x133 $x32)))))))
+))
+(let ((@x200 (refl (= (or (not $x131) (= ?x31 ?0)) (or (not $x131) (= ?x31 ?0))))))
+(let ((@x181 (refl (|~| (or (not $x131) (= ?x31 ?0)) (or (not $x131) (= ?x31 ?0))))))
+(let (($x34 (forall ((?v0 Int) )(let ((?x30 (|nat$| ?v0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x32 (= ?x31 ?v0)))
+(let (($x29 (<= 0 ?v0)))
+(=> $x29 $x32))))))
+))
+(let (($x127 (forall ((?v0 Int) )(let ((?x30 (|nat$| ?v0)))
+(let ((?x31 (|of_nat$| ?x30)))
+(let (($x32 (= ?x31 ?v0)))
+(or (not (<= 0 ?v0)) $x32)))))
+))
+(let (($x32 (= ?x31 ?0)))
+(let (($x133 (not $x131)))
+(let (($x136 (or $x133 $x32)))
+(let (($x124 (or (not (<= 0 ?0)) $x32)))
+(let ((@x135 (monotonicity (rewrite (= (<= 0 ?0) $x131)) (= (not (<= 0 ?0)) $x133))))
+(let ((@x129 (|quant-intro| (rewrite (= (=> (<= 0 ?0) $x32) $x124)) (= $x34 $x127))))
+(let ((@x143 (trans @x129 (|quant-intro| (monotonicity @x135 (= $x124 $x136)) (= $x127 $x139)) (= $x34 $x139))))
+(let ((@x184 (|mp~| (mp (asserted $x34) @x143 $x139) (|nnf-pos| @x181 (|~| $x139 $x139)) $x139)))
+(let ((@x203 (mp @x184 (|quant-intro| @x200 (= $x139 $x198)) $x198)))
+(let (($x247 (not $x198)))
+(let (($x248 (or $x247 $x236 $x240)))
+(let (($x231 (= ?x11 ?x9)))
+(let (($x227 (>= ?x9 0)))
+(let (($x228 (not $x227)))
+(let (($x232 (or $x228 $x231)))
+(let (($x249 (or $x247 $x232)))
+(let ((@x246 (monotonicity (monotonicity (rewrite (= $x227 $x233)) (= $x228 $x236)) (rewrite (= $x231 $x240)) (= $x232 $x244))))
+(let ((@x257 (trans (monotonicity @x246 (= $x249 (or $x247 $x244))) (rewrite (= (or $x247 $x244) $x248)) (= $x249 $x248))))
+(let ((@x258 (mp ((_ |quant-inst| (+ 1 ?x8)) $x249) @x257 $x248)))
+(let ((@x368 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x240) $x259)) (|unit-resolution| (|unit-resolution| @x258 @x203 $x244) @x362 $x240) $x259)))
+((_ |th-lemma| arith farkas 1 -1 -1 1) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x311) $x328)) @x353 $x328) @x120 @x368 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x329) $x332)) @x345 $x332) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+bda6be21dc699a816acc75c786757ad36dd913c8 78 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x51 (* (~ 1) |x$|)))
+(let (($x69 (>= |x$| 0)))
+(let ((?x76 (ite $x69 |x$| ?x51)))
+(let ((?x213 (* (~ 1) ?x76)))
+(let ((?x216 (+ ?x51 ?x213)))
+(let (($x226 (<= ?x216 0)))
+(let (($x182 (= ?x51 ?x76)))
+(let (($x70 (not $x69)))
+(let (($x181 (= |x$| ?x76)))
+(let ((@x222 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x181) (<= (+ |x$| ?x213) 0))) (|unit-resolution| (|def-axiom| (or $x70 $x181)) (hypothesis $x69) $x181) (<= (+ |x$| ?x213) 0))))
+(let (($x189 (>= ?x76 0)))
+(let (($x190 (not $x189)))
+(let (($x169 (forall ((?v0 Int) )(!(let ((?x21 (|nat$| ?v0)))
+(let ((?x22 (|of_nat$| ?x21)))
+(let (($x23 (= ?x22 ?v0)))
+(let (($x106 (>= ?v0 0)))
+(let (($x108 (not $x106)))
+(or $x108 $x23)))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x114 (forall ((?v0 Int) )(let ((?x21 (|nat$| ?v0)))
+(let ((?x22 (|of_nat$| ?x21)))
+(let (($x23 (= ?x22 ?v0)))
+(let (($x106 (>= ?v0 0)))
+(let (($x108 (not $x106)))
+(or $x108 $x23)))))))
+))
+(let ((?x21 (|nat$| ?0)))
+(let ((?x22 (|of_nat$| ?x21)))
+(let (($x23 (= ?x22 ?0)))
+(let (($x106 (>= ?0 0)))
+(let (($x108 (not $x106)))
+(let (($x111 (or $x108 $x23)))
+(let (($x25 (forall ((?v0 Int) )(let ((?x21 (|nat$| ?v0)))
+(let ((?x22 (|of_nat$| ?x21)))
+(let (($x23 (= ?x22 ?v0)))
+(let (($x20 (<= 0 ?v0)))
+(=> $x20 $x23))))))
+))
+(let (($x102 (forall ((?v0 Int) )(let ((?x21 (|nat$| ?v0)))
+(let ((?x22 (|of_nat$| ?x21)))
+(let (($x23 (= ?x22 ?v0)))
+(or (not (<= 0 ?v0)) $x23)))))
+))
+(let ((@x110 (monotonicity (rewrite (= (<= 0 ?0) $x106)) (= (not (<= 0 ?0)) $x108))))
+(let ((@x116 (|quant-intro| (monotonicity @x110 (= (or (not (<= 0 ?0)) $x23) $x111)) (= $x102 $x114))))
+(let ((@x101 (rewrite (= (=> (<= 0 ?0) $x23) (or (not (<= 0 ?0)) $x23)))))
+(let ((@x119 (mp (asserted $x25) (trans (|quant-intro| @x101 (= $x25 $x102)) @x116 (= $x25 $x114)) $x114)))
+(let ((@x174 (mp (|mp~| @x119 (|nnf-pos| (refl (|~| $x111 $x111)) (|~| $x114 $x114)) $x114) (|quant-intro| (refl (= $x111 $x111)) (= $x114 $x169)) $x169)))
+(let ((?x81 (|nat$| ?x76)))
+(let ((?x84 (|of_nat$| ?x81)))
+(let (($x87 (= ?x84 ?x76)))
+(let (($x90 (not $x87)))
+(let (($x7 (< |x$| 0)))
+(let ((?x9 (ite $x7 (- |x$|) |x$|)))
+(let (($x13 (not (= (|of_nat$| (|nat$| ?x9)) ?x9))))
+(let (($x91 (= (not (= (|of_nat$| (|nat$| (ite $x7 ?x51 |x$|))) (ite $x7 ?x51 |x$|))) $x90)))
+(let ((?x54 (ite $x7 ?x51 |x$|)))
+(let ((?x57 (|nat$| ?x54)))
+(let ((?x60 (|of_nat$| ?x57)))
+(let (($x63 (= ?x60 ?x54)))
+(let ((@x80 (trans (monotonicity (rewrite (= $x7 $x70)) (= ?x54 (ite $x70 ?x51 |x$|))) (rewrite (= (ite $x70 ?x51 |x$|) ?x76)) (= ?x54 ?x76))))
+(let ((@x89 (monotonicity (monotonicity (monotonicity @x80 (= ?x57 ?x81)) (= ?x60 ?x84)) @x80 (= $x63 $x87))))
+(let ((@x59 (monotonicity (monotonicity (rewrite (= (- |x$|) ?x51)) (= ?x9 ?x54)) (= (|nat$| ?x9) ?x57))))
+(let ((@x65 (monotonicity (monotonicity @x59 (= (|of_nat$| (|nat$| ?x9)) ?x60)) (monotonicity (rewrite (= (- |x$|) ?x51)) (= ?x9 ?x54)) (= (= (|of_nat$| (|nat$| ?x9)) ?x9) $x63))))
+(let ((@x94 (trans (monotonicity @x65 (= $x13 (not $x63))) (monotonicity @x89 $x91) (= $x13 $x90))))
+(let ((@x95 (mp (asserted $x13) @x94 $x90)))
+(let (($x198 (or (not $x169) $x190 $x87)))
+(let ((@x203 (mp ((_ |quant-inst| (ite $x69 |x$| ?x51)) (or (not $x169) (or $x190 $x87))) (rewrite (= (or (not $x169) (or $x190 $x87)) $x198)) $x198)))
+(let ((@x224 ((_ |th-lemma| arith farkas -1 1 1) (hypothesis $x69) (|unit-resolution| @x203 @x95 @x174 $x190) @x222 false)))
+(let ((@x225 (lemma @x224 $x70)))
+(let ((@x232 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x182) $x226)) (|unit-resolution| (|def-axiom| (or $x69 $x182)) @x225 $x182) $x226)))
+(let (($x205 (<= ?x76 0)))
+(let ((@x235 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x205 $x189)) (|unit-resolution| @x203 @x95 @x174 $x190) $x205)))
+((_ |th-lemma| arith farkas 1 1 1) @x235 @x225 @x232 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+777f9032b35b7e1c0dce62f13109424c73d5d094 312 0
+unsat
+((set-logic AUFLIA)
+(declare-fun ?v1!0 (|Nat$|) |Nat$|)
+(proof
+(let ((?x23 (|of_nat$| |m$|)))
+(let ((?x24 (* 4 ?x23)))
+(let ((?x110 (+ 1 ?x24)))
+(let ((?x113 (|nat$| ?x110)))
+(let ((?x344 (|of_nat$| ?x113)))
+(let ((?x491 (* (~ 1) ?x344)))
+(let ((?x492 (+ ?x24 ?x491)))
+(let (($x509 (>= ?x492 (~ 1))))
+(let (($x489 (= ?x492 (~ 1))))
+(let (($x481 (>= ?x23 0)))
+(let (($x345 (<= ?x344 1)))
+(let (($x373 (not $x345)))
+(let (($x351 (forall ((?v1 |Nat$|) )(!(let ((?x23 (|of_nat$| |m$|)))
+(let ((?x24 (* 4 ?x23)))
+(let ((?x110 (+ 1 ?x24)))
+(let ((?x113 (|nat$| ?x110)))
+(let (($x348 (= ?v1 ?x113)))
+(let ((?x12 (|nat$| 1)))
+(let (($x13 (= ?v1 ?x12)))
+(let (($x346 (|dvd$| ?v1 ?x113)))
+(let (($x347 (not $x346)))
+(or $x347 $x13 $x348)))))))))) :pattern ( (|dvd$| ?v1 (|nat$| (+ 1 (* 4 (|of_nat$| |m$|))))) )))
+))
+(let (($x352 (not $x351)))
+(let (($x353 (or $x345 $x352)))
+(let (($x354 (not $x353)))
+(let (($x116 (|prime_nat$| ?x113)))
+(let (($x122 (not $x116)))
+(let (($x355 (or $x122 $x354)))
+(let ((?x357 (?v1!0 ?x113)))
+(let (($x361 (= ?x357 ?x113)))
+(let ((?x12 (|nat$| 1)))
+(let (($x360 (= ?x357 ?x12)))
+(let (($x358 (|dvd$| ?x357 ?x113)))
+(let (($x359 (not $x358)))
+(let (($x362 (or $x359 $x360 $x361)))
+(let (($x363 (not $x362)))
+(let (($x364 (or $x116 $x345 $x363)))
+(let (($x365 (not $x364)))
+(let (($x356 (not $x355)))
+(let (($x366 (or $x356 $x365)))
+(let (($x367 (not $x366)))
+(let (($x321 (forall ((?v0 |Nat$|) )(!(let (($x217 (or (not (|dvd$| (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (|nat$| 1)) (= (?v1!0 ?v0) ?v0))))
+(let (($x218 (not $x217)))
+(let ((?x8 (|of_nat$| ?v0)))
+(let (($x87 (<= ?x8 1)))
+(let (($x6 (|prime_nat$| ?v0)))
+(let (($x245 (or $x6 $x87 $x218)))
+(let (($x293 (forall ((?v1 |Nat$|) )(!(let ((?x12 (|nat$| 1)))
+(let (($x13 (= ?v1 ?x12)))
+(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))) :pattern ( (|dvd$| ?v1 ?v0) )))
+))
+(let (($x198 (not $x6)))
+(not (or (not (or $x198 (not (or $x87 (not $x293))))) (not $x245))))))))))) :pattern ( (|prime_nat$| ?v0) ) :pattern ( (|of_nat$| ?v0) )))
+))
+(let (($x288 (forall ((?v0 |Nat$|) )(let (($x217 (or (not (|dvd$| (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (|nat$| 1)) (= (?v1!0 ?v0) ?v0))))
+(let (($x218 (not $x217)))
+(let ((?x8 (|of_nat$| ?v0)))
+(let (($x87 (<= ?x8 1)))
+(let (($x6 (|prime_nat$| ?v0)))
+(let (($x245 (or $x6 $x87 $x218)))
+(let (($x94 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
+(let (($x13 (= ?v1 ?x12)))
+(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
+))
+(let (($x219 (not $x94)))
+(let (($x271 (not (or $x87 $x219))))
+(let (($x198 (not $x6)))
+(let (($x274 (or $x198 $x271)))
+(not (or (not $x274) (not $x245)))))))))))))))
+))
+(let (($x217 (or (not (|dvd$| (?v1!0 ?0) ?0)) (= (?v1!0 ?0) ?x12) (= (?v1!0 ?0) ?0))))
+(let (($x218 (not $x217)))
+(let ((?x8 (|of_nat$| ?0)))
+(let (($x87 (<= ?x8 1)))
+(let (($x6 (|prime_nat$| ?0)))
+(let (($x245 (or $x6 $x87 $x218)))
+(let (($x293 (forall ((?v1 |Nat$|) )(!(let ((?x12 (|nat$| 1)))
+(let (($x13 (= ?v1 ?x12)))
+(or (not (|dvd$| ?v1 ?0)) $x13 (= ?v1 ?0)))) :pattern ( (|dvd$| ?v1 ?0) )))
+))
+(let (($x198 (not $x6)))
+(let (($x94 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
+(let (($x13 (= ?v1 ?x12)))
+(or (not (|dvd$| ?v1 ?0)) $x13 (= ?v1 ?0)))))
+))
+(let (($x219 (not $x94)))
+(let (($x271 (not (or $x87 $x219))))
+(let (($x274 (or $x198 $x271)))
+(let (($x283 (not (or (not $x274) (not $x245)))))
+(let (($x317 (= $x283 (not (or (not (or $x198 (not (or $x87 (not $x293))))) (not $x245))))))
+(let (($x314 (= (or (not $x274) (not $x245)) (or (not (or $x198 (not (or $x87 (not $x293))))) (not $x245)))))
+(let (($x13 (= ?0 ?x12)))
+(let (($x91 (or (not (|dvd$| ?0 ?1)) $x13 (= ?0 ?1))))
+(let ((@x300 (monotonicity (|quant-intro| (refl (= $x91 $x91)) (= $x94 $x293)) (= $x219 (not $x293)))))
+(let ((@x306 (monotonicity (monotonicity @x300 (= (or $x87 $x219) (or $x87 (not $x293)))) (= $x271 (not (or $x87 (not $x293)))))))
+(let ((@x312 (monotonicity (monotonicity @x306 (= $x274 (or $x198 (not (or $x87 (not $x293)))))) (= (not $x274) (not (or $x198 (not (or $x87 (not $x293)))))))))
+(let ((@x323 (|quant-intro| (monotonicity (monotonicity @x312 $x314) $x317) (= $x288 $x321))))
+(let (($x253 (forall ((?v0 |Nat$|) )(let (($x217 (or (not (|dvd$| (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (|nat$| 1)) (= (?v1!0 ?v0) ?v0))))
+(let (($x218 (not $x217)))
+(let ((?x8 (|of_nat$| ?v0)))
+(let (($x87 (<= ?x8 1)))
+(let (($x6 (|prime_nat$| ?v0)))
+(let (($x245 (or $x6 $x87 $x218)))
+(let (($x94 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
+(let (($x13 (= ?v1 ?x12)))
+(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
+))
+(let (($x88 (not $x87)))
+(let (($x97 (and $x88 $x94)))
+(let (($x198 (not $x6)))
+(let (($x227 (or $x198 $x97)))
+(and $x227 $x245)))))))))))))
+))
+(let ((@x276 (monotonicity (rewrite (= (and (not $x87) $x94) $x271)) (= (or $x198 (and (not $x87) $x94)) $x274))))
+(let ((@x279 (monotonicity @x276 (= (and (or $x198 (and (not $x87) $x94)) $x245) (and $x274 $x245)))))
+(let ((@x287 (trans @x279 (rewrite (= (and $x274 $x245) $x283)) (= (and (or $x198 (and (not $x87) $x94)) $x245) $x283))))
+(let (($x231 (forall ((?v0 |Nat$|) )(let (($x217 (or (not (|dvd$| (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (|nat$| 1)) (= (?v1!0 ?v0) ?v0))))
+(let (($x218 (not $x217)))
+(let ((?x8 (|of_nat$| ?v0)))
+(let (($x87 (<= ?x8 1)))
+(let (($x88 (not $x87)))
+(let (($x209 (not $x88)))
+(let (($x222 (or $x209 $x218)))
+(let (($x6 (|prime_nat$| ?v0)))
+(let (($x226 (or $x6 $x222)))
+(let (($x94 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
+(let (($x13 (= ?v1 ?x12)))
+(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
+))
+(let (($x97 (and $x88 $x94)))
+(let (($x198 (not $x6)))
+(let (($x227 (or $x198 $x97)))
+(and $x227 $x226)))))))))))))))
+))
+(let (($x88 (not $x87)))
+(let (($x97 (and $x88 $x94)))
+(let (($x227 (or $x198 $x97)))
+(let (($x250 (and $x227 $x245)))
+(let (($x209 (not $x88)))
+(let (($x222 (or $x209 $x218)))
+(let (($x226 (or $x6 $x222)))
+(let (($x228 (and $x227 $x226)))
+(let ((@x244 (monotonicity (monotonicity (rewrite (= $x209 $x87)) (= $x222 (or $x87 $x218))) (= $x226 (or $x6 (or $x87 $x218))))))
+(let ((@x249 (trans @x244 (rewrite (= (or $x6 (or $x87 $x218)) $x245)) (= $x226 $x245))))
+(let (($x103 (forall ((?v0 |Nat$|) )(let (($x94 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
+(let (($x13 (= ?v1 ?x12)))
+(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
+))
+(let ((?x8 (|of_nat$| ?v0)))
+(let (($x87 (<= ?x8 1)))
+(let (($x88 (not $x87)))
+(let (($x97 (and $x88 $x94)))
+(let (($x6 (|prime_nat$| ?v0)))
+(= $x6 $x97))))))))
+))
+(let ((@x225 (|nnf-neg| (refl (|~| $x209 $x209)) (sk (|~| $x219 $x218)) (|~| (not $x97) $x222))))
+(let ((@x208 (monotonicity (refl (|~| $x88 $x88)) (|nnf-pos| (refl (|~| $x91 $x91)) (|~| $x94 $x94)) (|~| $x97 $x97))))
+(let ((@x230 (|nnf-pos| (refl (|~| $x6 $x6)) (refl (|~| $x198 $x198)) @x208 @x225 (|~| (= $x6 $x97) $x228))))
+(let (($x20 (forall ((?v0 |Nat$|) )(let (($x17 (forall ((?v1 |Nat$|) )(let (($x11 (|dvd$| ?v1 ?v0)))
+(=> $x11 (or (= ?v1 (|nat$| 1)) (= ?v1 ?v0)))))
+))
+(let ((?x8 (|of_nat$| ?v0)))
+(let (($x9 (< 1 ?x8)))
+(let (($x6 (|prime_nat$| ?v0)))
+(= $x6 (and $x9 $x17)))))))
+))
+(let (($x84 (forall ((?v0 |Nat$|) )(let (($x70 (forall ((?v1 |Nat$|) )(or (not (|dvd$| ?v1 ?v0)) (or (= ?v1 (|nat$| 1)) (= ?v1 ?v0))))
+))
+(let ((?x8 (|of_nat$| ?v0)))
+(let (($x9 (< 1 ?x8)))
+(let (($x73 (and $x9 $x70)))
+(let (($x6 (|prime_nat$| ?v0)))
+(= $x6 $x73)))))))
+))
+(let (($x100 (= $x6 $x97)))
+(let (($x70 (forall ((?v1 |Nat$|) )(or (not (|dvd$| ?v1 ?0)) (or (= ?v1 (|nat$| 1)) (= ?v1 ?0))))
+))
+(let (($x9 (< 1 ?x8)))
+(let (($x73 (and $x9 $x70)))
+(let (($x79 (= $x6 $x73)))
+(let ((@x93 (rewrite (= (or (not (|dvd$| ?0 ?1)) (or $x13 (= ?0 ?1))) $x91))))
+(let ((@x99 (monotonicity (rewrite (= $x9 $x88)) (|quant-intro| @x93 (= $x70 $x94)) (= $x73 $x97))))
+(let (($x17 (forall ((?v1 |Nat$|) )(let (($x11 (|dvd$| ?v1 ?0)))
+(=> $x11 (or (= ?v1 (|nat$| 1)) (= ?v1 ?0)))))
+))
+(let (($x19 (= $x6 (and $x9 $x17))))
+(let (($x67 (or (not (|dvd$| ?0 ?1)) (or $x13 (= ?0 ?1)))))
+(let ((@x72 (|quant-intro| (rewrite (= (=> (|dvd$| ?0 ?1) (or $x13 (= ?0 ?1))) $x67)) (= $x17 $x70))))
+(let ((@x78 (monotonicity (monotonicity @x72 (= (and $x9 $x17) $x73)) (= $x19 (= $x6 $x73)))))
+(let ((@x86 (|quant-intro| (trans @x78 (rewrite (= (= $x6 $x73) $x79)) (= $x19 $x79)) (= $x20 $x84))))
+(let ((@x107 (trans @x86 (|quant-intro| (monotonicity @x99 (= $x79 $x100)) (= $x84 $x103)) (= $x20 $x103))))
+(let ((@x234 (|mp~| (mp (asserted $x20) @x107 $x103) (|nnf-pos| @x230 (|~| $x103 $x231)) $x231)))
+(let ((@x235 (mp @x234 (|quant-intro| (monotonicity @x249 (= $x228 $x250)) (= $x231 $x253)) $x253)))
+(let ((@x324 (mp (mp @x235 (|quant-intro| @x287 (= $x253 $x288)) $x288) @x323 $x321)))
+(let (($x371 (or (not $x321) $x367)))
+(let ((@x372 ((_ |quant-inst| (|nat$| ?x110)) $x371)))
+(let ((@x530 (|unit-resolution| (|def-axiom| (or $x366 $x355)) (|unit-resolution| @x372 @x324 $x367) $x355)))
+(let (($x137 (not (or $x122 (>= ?x23 1)))))
+(let (($x28 (<= 1 ?x23)))
+(let (($x29 (=> (|prime_nat$| (|nat$| (+ ?x24 1))) $x28)))
+(let (($x30 (not $x29)))
+(let ((@x136 (monotonicity (rewrite (= $x28 (>= ?x23 1))) (= (or $x122 $x28) (or $x122 (>= ?x23 1))))))
+(let ((@x115 (monotonicity (rewrite (= (+ ?x24 1) ?x110)) (= (|nat$| (+ ?x24 1)) ?x113))))
+(let ((@x121 (monotonicity (monotonicity @x115 (= (|prime_nat$| (|nat$| (+ ?x24 1))) $x116)) (= $x29 (=> $x116 $x28)))))
+(let ((@x127 (trans @x121 (rewrite (= (=> $x116 $x28) (or $x122 $x28))) (= $x29 (or $x122 $x28)))))
+(let ((@x141 (trans (monotonicity @x127 (= $x30 (not (or $x122 $x28)))) (monotonicity @x136 (= (not (or $x122 $x28)) $x137)) (= $x30 $x137))))
+(let ((@x143 (|not-or-elim| (mp (asserted $x30) @x141 $x137) $x116)))
+(let ((@x533 (|unit-resolution| (|unit-resolution| (|def-axiom| (or $x356 $x122 $x354)) @x143 (or $x356 $x354)) @x530 $x354)))
+(let ((@x538 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not (<= ?x344 0)) $x345)) (|unit-resolution| (|def-axiom| (or $x353 $x373)) @x533 $x373) (not (<= ?x344 0)))))
+(let ((@x542 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x344 0)) (<= ?x344 0))) @x538 (not (= ?x344 0)))))
+(let (($x510 (= ?x344 0)))
+(let (($x512 (or $x481 $x510)))
+(let (($x338 (forall ((?v0 Int) )(!(let ((?x37 (|nat$| ?v0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x43 (= ?x38 0)))
+(let (($x157 (>= ?v0 0)))
+(or $x157 $x43))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x190 (forall ((?v0 Int) )(let ((?x37 (|nat$| ?v0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x43 (= ?x38 0)))
+(let (($x157 (>= ?v0 0)))
+(or $x157 $x43))))))
+))
+(let ((?x37 (|nat$| ?0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x43 (= ?x38 0)))
+(let (($x157 (>= ?0 0)))
+(let (($x187 (or $x157 $x43)))
+(let (($x45 (forall ((?v0 Int) )(let ((?x37 (|nat$| ?v0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x43 (= ?x38 0)))
+(let (($x42 (< ?v0 0)))
+(=> $x42 $x43))))))
+))
+(let (($x175 (forall ((?v0 Int) )(let ((?x37 (|nat$| ?v0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x43 (= ?x38 0)))
+(let (($x42 (< ?v0 0)))
+(let (($x171 (not $x42)))
+(or $x171 $x43)))))))
+))
+(let ((@x182 (monotonicity (rewrite (= (< ?0 0) (not $x157))) (= (not (< ?0 0)) (not (not $x157))))))
+(let ((@x186 (trans @x182 (rewrite (= (not (not $x157)) $x157)) (= (not (< ?0 0)) $x157))))
+(let ((@x192 (|quant-intro| (monotonicity @x186 (= (or (not (< ?0 0)) $x43) $x187)) (= $x175 $x190))))
+(let ((@x174 (rewrite (= (=> (< ?0 0) $x43) (or (not (< ?0 0)) $x43)))))
+(let ((@x195 (mp (asserted $x45) (trans (|quant-intro| @x174 (= $x45 $x175)) @x192 (= $x45 $x190)) $x190)))
+(let ((@x343 (mp (|mp~| @x195 (|nnf-pos| (refl (|~| $x187 $x187)) (|~| $x190 $x190)) $x190) (|quant-intro| (refl (= $x187 $x187)) (= $x190 $x338)) $x338)))
+(let (($x515 (not $x338)))
+(let (($x516 (or $x515 $x481 $x510)))
+(let ((@x483 (rewrite (= (>= ?x110 0) $x481))))
+(let ((@x514 (monotonicity @x483 (= (or (>= ?x110 0) $x510) $x512))))
+(let ((@x521 (monotonicity @x514 (= (or $x515 (or (>= ?x110 0) $x510)) (or $x515 $x512)))))
+(let ((@x525 (trans @x521 (rewrite (= (or $x515 $x512) $x516)) (= (or $x515 (or (>= ?x110 0) $x510)) $x516))))
+(let ((@x526 (mp ((_ |quant-inst| (+ 1 ?x24)) (or $x515 (or (>= ?x110 0) $x510))) @x525 $x516)))
+(let (($x484 (not $x481)))
+(let (($x493 (or $x484 $x489)))
+(let (($x332 (forall ((?v0 Int) )(!(let ((?x37 (|nat$| ?v0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x39 (= ?x38 ?v0)))
+(let (($x157 (>= ?v0 0)))
+(let (($x158 (not $x157)))
+(or $x158 $x39)))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x164 (forall ((?v0 Int) )(let ((?x37 (|nat$| ?v0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x39 (= ?x38 ?v0)))
+(let (($x157 (>= ?v0 0)))
+(let (($x158 (not $x157)))
+(or $x158 $x39)))))))
+))
+(let ((@x334 (refl (= (or (not $x157) (= ?x38 ?0)) (or (not $x157) (= ?x38 ?0))))))
+(let ((@x261 (refl (|~| (or (not $x157) (= ?x38 ?0)) (or (not $x157) (= ?x38 ?0))))))
+(let (($x41 (forall ((?v0 Int) )(let ((?x37 (|nat$| ?v0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x39 (= ?x38 ?v0)))
+(let (($x36 (<= 0 ?v0)))
+(=> $x36 $x39))))))
+))
+(let (($x152 (forall ((?v0 Int) )(let ((?x37 (|nat$| ?v0)))
+(let ((?x38 (|of_nat$| ?x37)))
+(let (($x39 (= ?x38 ?v0)))
+(or (not (<= 0 ?v0)) $x39)))))
+))
+(let (($x39 (= ?x38 ?0)))
+(let (($x158 (not $x157)))
+(let (($x161 (or $x158 $x39)))
+(let (($x149 (or (not (<= 0 ?0)) $x39)))
+(let ((@x160 (monotonicity (rewrite (= (<= 0 ?0) $x157)) (= (not (<= 0 ?0)) $x158))))
+(let ((@x154 (|quant-intro| (rewrite (= (=> (<= 0 ?0) $x39) $x149)) (= $x41 $x152))))
+(let ((@x168 (trans @x154 (|quant-intro| (monotonicity @x160 (= $x149 $x161)) (= $x152 $x164)) (= $x41 $x164))))
+(let ((@x264 (|mp~| (mp (asserted $x41) @x168 $x164) (|nnf-pos| @x261 (|~| $x164 $x164)) $x164)))
+(let ((@x337 (mp @x264 (|quant-intro| @x334 (= $x164 $x332)) $x332)))
+(let (($x496 (not $x332)))
+(let (($x497 (or $x496 $x484 $x489)))
+(let (($x479 (= ?x344 ?x110)))
+(let (($x474 (>= ?x110 0)))
+(let (($x475 (not $x474)))
+(let (($x480 (or $x475 $x479)))
+(let (($x498 (or $x496 $x480)))
+(let ((@x495 (monotonicity (monotonicity @x483 (= $x475 $x484)) (rewrite (= $x479 $x489)) (= $x480 $x493))))
+(let ((@x506 (trans (monotonicity @x495 (= $x498 (or $x496 $x493))) (rewrite (= (or $x496 $x493) $x497)) (= $x498 $x497))))
+(let ((@x507 (mp ((_ |quant-inst| (+ 1 ?x24)) $x498) @x506 $x497)))
+(let ((@x546 (|unit-resolution| (|unit-resolution| @x507 @x337 $x493) (|unit-resolution| (|unit-resolution| @x526 @x343 $x512) @x542 $x481) $x489)))
+(let ((@x145 (|not-or-elim| (mp (asserted $x30) @x141 $x137) (not (>= ?x23 1)))))
+((_ |th-lemma| arith farkas -4 1 1) @x145 (|unit-resolution| (|def-axiom| (or $x353 $x373)) @x533 $x373) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x489) $x509)) @x546 $x509) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+c7efedca31e5e8360d3c81014f43c447bc784df3 23 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x17 (= |x$| |a$|)))
+(let ((?x13 (|pair$| |x$| |y$|)))
+(let ((?x14 (|fst$| ?x13)))
+(let (($x16 (= ?x14 |a$|)))
+(let ((@x48 (monotonicity (rewrite (= (=> $x16 $x17) (or (not $x16) $x17))) (= (not (=> $x16 $x17)) (not (or (not $x16) $x17))))))
+(let ((@x49 (|not-or-elim| (mp (asserted (not (=> $x16 $x17))) @x48 (not (or (not $x16) $x17))) $x16)))
+(let (($x65 (= ?x14 |x$|)))
+(let (($x59 (forall ((?v0 |A$|) (?v1 |B$|) )(!(= (|fst$| (|pair$| ?v0 ?v1)) ?v0) :pattern ( (|pair$| ?v0 ?v1) )))
+))
+(let (($x10 (forall ((?v0 |A$|) (?v1 |B$|) )(= (|fst$| (|pair$| ?v0 ?v1)) ?v0))
+))
+(let (($x9 (= (|fst$| (|pair$| ?1 ?0)) ?1)))
+(let ((@x57 (|mp~| (asserted $x10) (|nnf-pos| (refl (|~| $x9 $x9)) (|~| $x10 $x10)) $x10)))
+(let ((@x64 (mp @x57 (|quant-intro| (refl (= $x9 $x9)) (= $x10 $x59)) $x59)))
+(let (($x69 (or (not $x59) $x65)))
+(let ((@x70 ((_ |quant-inst| |x$| |y$|) $x69)))
+(let ((@x72 (trans (symm (|unit-resolution| @x70 @x64 $x65) (= |x$| ?x14)) @x49 $x17)))
+(let ((@x52 (|not-or-elim| (mp (asserted (not (=> $x16 $x17))) @x48 (not (or (not $x16) $x17))) (not $x17))))
+(|unit-resolution| @x52 @x72 false)))))))))))))))))))
+
+aea156a69bb23683148bfccfaa255f874937bce0 42 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x33 (|snd$a| |p2$|)))
+(let ((?x32 (|fst$a| |p1$|)))
+(let (($x34 (= ?x32 ?x33)))
+(let ((?x29 (|pair$| |y$| |x$|)))
+(let (($x30 (= |p2$| ?x29)))
+(let ((?x26 (|pair$a| |x$| |y$|)))
+(let (($x27 (= |p1$| ?x26)))
+(let (($x31 (and $x27 $x30)))
+(let ((@x68 (monotonicity (rewrite (= (=> $x31 $x34) (or (not $x31) $x34))) (= (not (=> $x31 $x34)) (not (or (not $x31) $x34))))))
+(let ((@x69 (|not-or-elim| (mp (asserted (not (=> $x31 $x34))) @x68 (not (or (not $x31) $x34))) $x31)))
+(let ((@x72 (|and-elim| @x69 $x30)))
+(let ((@x150 (symm (monotonicity @x72 (= ?x33 (|snd$a| ?x29))) (= (|snd$a| ?x29) ?x33))))
+(let ((?x123 (|snd$a| ?x29)))
+(let (($x124 (= ?x123 |x$|)))
+(let (($x115 (forall ((?v0 |B$|) (?v1 |A$|) )(!(= (|snd$a| (|pair$| ?v0 ?v1)) ?v1) :pattern ( (|pair$| ?v0 ?v1) )))
+))
+(let (($x22 (forall ((?v0 |B$|) (?v1 |A$|) )(= (|snd$a| (|pair$| ?v0 ?v1)) ?v1))
+))
+(let (($x21 (= (|snd$a| (|pair$| ?1 ?0)) ?0)))
+(let ((@x94 (|mp~| (asserted $x22) (|nnf-pos| (refl (|~| $x21 $x21)) (|~| $x22 $x22)) $x22)))
+(let ((@x120 (mp @x94 (|quant-intro| (refl (= $x21 $x21)) (= $x22 $x115)) $x115)))
+(let (($x131 (or (not $x115) $x124)))
+(let ((@x132 ((_ |quant-inst| |y$| |x$|) $x131)))
+(let ((?x128 (|fst$a| ?x26)))
+(let (($x129 (= ?x128 |x$|)))
+(let (($x103 (forall ((?v0 |A$|) (?v1 |B$|) )(!(= (|fst$a| (|pair$a| ?v0 ?v1)) ?v0) :pattern ( (|pair$a| ?v0 ?v1) )))
+))
+(let (($x16 (forall ((?v0 |A$|) (?v1 |B$|) )(= (|fst$a| (|pair$a| ?v0 ?v1)) ?v0))
+))
+(let (($x15 (= (|fst$a| (|pair$a| ?1 ?0)) ?1)))
+(let ((@x84 (|mp~| (asserted $x16) (|nnf-pos| (refl (|~| $x15 $x15)) (|~| $x16 $x16)) $x16)))
+(let ((@x108 (mp @x84 (|quant-intro| (refl (= $x15 $x15)) (= $x16 $x103)) $x103)))
+(let (($x136 (or (not $x103) $x129)))
+(let ((@x137 ((_ |quant-inst| |x$| |y$|) $x136)))
+(let ((@x152 (trans (monotonicity (|and-elim| @x69 $x27) (= ?x32 ?x128)) (|unit-resolution| @x137 @x108 $x129) (= ?x32 |x$|))))
+(let ((@x154 (trans @x152 (symm (|unit-resolution| @x132 @x120 $x124) (= |x$| ?x123)) (= ?x32 ?x123))))
+(let ((@x74 (|not-or-elim| (mp (asserted (not (=> $x31 $x34))) @x68 (not (or (not $x31) $x34))) (not $x34))))
+(|unit-resolution| @x74 (trans @x154 @x150 $x34) false))))))))))))))))))))))))))))))))))))
+
+9e587b4eedc0dc25b019cb54b54b4a4e643bf93e 49 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x45 (|fun_app$| |f$| |i$|)))
+(let ((?x36 (|fun_upd$| |f$|)))
+(let ((?x37 (|fun_app$b| ?x36 |i1$|)))
+(let ((?x39 (|fun_app$a| ?x37 |v1$|)))
+(let ((?x40 (|fun_upd$| ?x39)))
+(let ((?x41 (|fun_app$b| ?x40 |i2$|)))
+(let ((?x43 (|fun_app$a| ?x41 |v2$|)))
+(let ((?x44 (|fun_app$| ?x43 |i$|)))
+(let (($x46 (= ?x44 ?x45)))
+(let (($x29 (= |i$| |i1$|)))
+(let ((?x178 (ite $x29 |v1$| ?x45)))
+(let (($x185 (= ?x45 ?x178)))
+(let (($x30 (not $x29)))
+(let (($x32 (= |i$| |i2$|)))
+(let (($x33 (not $x32)))
+(let (($x34 (and $x30 $x33)))
+(let ((@x78 (monotonicity (rewrite (= (=> $x34 $x46) (or (not $x34) $x46))) (= (not (=> $x34 $x46)) (not (or (not $x34) $x46))))))
+(let ((@x79 (|not-or-elim| (mp (asserted (not (=> $x34 $x46))) @x78 (not (or (not $x34) $x46))) $x34)))
+(let ((@x80 (|and-elim| @x79 $x30)))
+(let ((@x197 (symm (|unit-resolution| (|def-axiom| (or $x29 $x185)) @x80 $x185) (= ?x178 ?x45))))
+(let ((?x116 (|fun_app$| ?x39 |i$|)))
+(let (($x179 (= ?x116 ?x178)))
+(let (($x103 (forall ((?v0 |A_b_fun$|) (?v1 |A$|) (?v2 |B$|) (?v3 |A$|) )(!(let ((?x21 (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?v0) ?v1) ?v2) ?v3)))
+(= ?x21 (ite (= ?v3 ?v1) ?v2 (|fun_app$| ?v0 ?v3)))) :pattern ( (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?v0) ?v1) ?v2) ?v3) )))
+))
+(let (($x26 (forall ((?v0 |A_b_fun$|) (?v1 |A$|) (?v2 |B$|) (?v3 |A$|) )(let ((?x21 (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?v0) ?v1) ?v2) ?v3)))
+(= ?x21 (ite (= ?v3 ?v1) ?v2 (|fun_app$| ?v0 ?v3)))))
+))
+(let ((?x21 (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?3) ?2) ?1) ?0)))
+(let (($x25 (= ?x21 (ite (= ?0 ?2) ?1 (|fun_app$| ?3 ?0)))))
+(let ((@x94 (|mp~| (asserted $x26) (|nnf-pos| (refl (|~| $x25 $x25)) (|~| $x26 $x26)) $x26)))
+(let ((@x108 (mp @x94 (|quant-intro| (refl (= $x25 $x25)) (= $x26 $x103)) $x103)))
+(let (($x123 (not $x103)))
+(let (($x182 (or $x123 $x179)))
+(let ((@x183 ((_ |quant-inst| |f$| |i1$| |v1$| |i$|) $x182)))
+(let ((?x117 (ite $x32 |v2$| ?x116)))
+(let (($x127 (= ?x116 ?x117)))
+(let ((@x82 (|and-elim| @x79 $x33)))
+(let ((@x195 (symm (|unit-resolution| (|def-axiom| (or $x32 $x127)) @x82 $x127) (= ?x117 ?x116))))
+(let (($x120 (= ?x44 ?x117)))
+(let (($x124 (or $x123 $x120)))
+(let ((@x125 ((_ |quant-inst| (|fun_app$a| ?x37 |v1$|) |i2$| |v2$| |i$|) $x124)))
+(let ((@x201 (trans (trans (|unit-resolution| @x125 @x108 $x120) @x195 (= ?x44 ?x116)) (|unit-resolution| @x183 @x108 $x179) (= ?x44 ?x178))))
+(let ((@x84 (|not-or-elim| (mp (asserted (not (=> $x34 $x46))) @x78 (not (or (not $x34) $x46))) (not $x46))))
+(|unit-resolution| @x84 (trans @x201 @x197 $x46) false)))))))))))))))))))))))))))))))))))))))))))
+
+b3ae8e1fe1d7b019d0bef97ff09cdb8e0a1cd7dd 25 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x7 (|f$| |g$| |x$|)))
+(let (($x71 (not $x7)))
+(let (($x63 (not (or (= $x7 (|fun_app$| |g$| |x$|)) $x7 (|fun_app$| |g$| |x$|)))))
+(let (($x10 (= $x7 (and (|fun_app$| |g$| |x$|) true))))
+(let (($x15 (not (or $x10 (or (= $x7 true) (= (|fun_app$| |g$| |x$|) true))))))
+(let (($x8 (|fun_app$| |g$| |x$|)))
+(let (($x51 (or $x7 $x8)))
+(let (($x42 (= $x7 $x8)))
+(let (($x54 (or $x42 $x51)))
+(let ((@x65 (monotonicity (rewrite (= $x54 (or $x42 $x7 $x8))) (= (not $x54) $x63))))
+(let ((@x53 (monotonicity (rewrite (= (= $x7 true) $x7)) (rewrite (= (= $x8 true) $x8)) (= (or (= $x7 true) (= $x8 true)) $x51))))
+(let ((@x41 (monotonicity (rewrite (= (and $x8 true) $x8)) (= $x10 (= $x7 $x8)))))
+(let ((@x56 (monotonicity (trans @x41 (rewrite (= (= $x7 $x8) $x42)) (= $x10 $x42)) @x53 (= (or $x10 (or (= $x7 true) (= $x8 true))) $x54))))
+(let ((@x67 (trans (monotonicity @x56 (= $x15 (not $x54))) @x65 (= $x15 $x63))))
+(let ((@x68 (mp (asserted $x15) @x67 $x63)))
+(let ((@x72 (|not-or-elim| @x68 $x71)))
+(let (($x73 (not $x8)))
+(let ((@x74 (|not-or-elim| @x68 $x73)))
+(let (($x75 (= $x71 $x8)))
+(let ((@x77 (mp (|not-or-elim| @x68 (not $x42)) (rewrite (= (not $x42) $x75)) $x75)))
+(|unit-resolution| (|unit-resolution| (|def-axiom| (or $x7 $x8 (not $x75))) @x77 $x51) @x74 @x72 false)))))))))))))))))))))))
+
+d9e693c8b48e2988c493bb1e4e83656e750403bf 14 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x7 (exists ((?v0 |A$|) )(|g$| ?v0))
+))
+(let (($x8 (ite $x7 true false)))
+(let (($x9 (|f$| $x8)))
+(let (($x10 (=> $x9 true)))
+(let (($x11 (not $x10)))
+(let ((@x40 (monotonicity (monotonicity (rewrite (= $x8 $x7)) (= $x9 (|f$| $x7))) (= $x10 (=> (|f$| $x7) true)))))
+(let ((@x44 (trans @x40 (rewrite (= (=> (|f$| $x7) true) true)) (= $x10 true))))
+(let ((@x51 (trans (monotonicity @x44 (= $x11 (not true))) (rewrite (= (not true) false)) (= $x11 false))))
+(mp (asserted $x11) @x51 false)))))))))))
+
+389aa7c628b5a2215f1c34b1b3aea4f4becc378c 14 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x7 (forall ((?v0 |A$|) )(|g$| ?v0))
+))
+(let (($x8 (ite $x7 true false)))
+(let (($x9 (|f$| $x8)))
+(let (($x10 (=> $x9 true)))
+(let (($x11 (not $x10)))
+(let ((@x40 (monotonicity (monotonicity (rewrite (= $x8 $x7)) (= $x9 (|f$| $x7))) (= $x10 (=> (|f$| $x7) true)))))
+(let ((@x44 (trans @x40 (rewrite (= (=> (|f$| $x7) true) true)) (= $x10 true))))
+(let ((@x51 (trans (monotonicity @x44 (= $x11 (not true))) (rewrite (= (not true) false)) (= $x11 false))))
+(mp (asserted $x11) @x51 false)))))))))))
+
+53b477f55537542d72fa148413e684cc3ff42e5b 46 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x17 (|fun_app$a| |le$| 3)))
+(let (($x19 (|fun_app$| ?x17 42)))
+(let (($x73 (not $x19)))
+(let (($x15 (= |le$| |uu$|)))
+(let ((@x71 (monotonicity (rewrite (= (=> $x15 $x19) (or (not $x15) $x19))) (= (not (=> $x15 $x19)) (not (or (not $x15) $x19))))))
+(let ((@x72 (|not-or-elim| (mp (asserted (not (=> $x15 $x19))) @x71 (not (or (not $x15) $x19))) $x15)))
+(let ((@x126 (monotonicity (symm @x72 (= |uu$| |le$|)) (= (|fun_app$a| |uu$| 3) ?x17))))
+(let ((@x130 (symm (monotonicity @x126 (= (|fun_app$| (|fun_app$a| |uu$| 3) 42) $x19)) (= $x19 (|fun_app$| (|fun_app$a| |uu$| 3) 42)))))
+(let ((@x133 (monotonicity @x130 (= $x73 (not (|fun_app$| (|fun_app$a| |uu$| 3) 42))))))
+(let ((@x75 (|not-or-elim| (mp (asserted (not (=> $x15 $x19))) @x71 (not (or (not $x15) $x19))) $x73)))
+(let ((?x81 (|fun_app$a| |uu$| 3)))
+(let (($x82 (|fun_app$| ?x81 42)))
+(let (($x58 (forall ((?v0 Int) (?v1 Int) )(!(let (($x52 (<= (+ ?v0 (* (~ 1) ?v1)) 0)))
+(let (($x9 (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1)))
+(= $x9 $x52))) :pattern ( (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1) )))
+))
+(let (($x52 (<= (+ ?1 (* (~ 1) ?0)) 0)))
+(let (($x9 (|fun_app$| (|fun_app$a| |uu$| ?1) ?0)))
+(let (($x55 (= $x9 $x52)))
+(let (($x13 (forall ((?v0 Int) (?v1 Int) )(!(let (($x10 (<= ?v0 ?v1)))
+(let (($x9 (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1)))
+(= $x9 $x10))) :pattern ( (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1) )))
+))
+(let (($x46 (forall ((?v0 Int) (?v1 Int) )(!(let (($x10 (<= ?v0 ?v1)))
+(let (($x9 (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1)))
+(= $x9 $x10))) :pattern ( (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1) )))
+))
+(let ((@x57 (monotonicity (rewrite (= (<= ?1 ?0) $x52)) (= (= $x9 (<= ?1 ?0)) $x55))))
+(let ((@x48 (|quant-intro| (rewrite (= (= $x9 (<= ?1 ?0)) (= $x9 (<= ?1 ?0)))) (= $x13 $x46))))
+(let ((@x63 (mp (asserted $x13) (trans @x48 (|quant-intro| @x57 (= $x46 $x58)) (= $x13 $x58)) $x58)))
+(let ((@x80 (|mp~| @x63 (|nnf-pos| (refl (|~| $x55 $x55)) (|~| $x58 $x58)) $x58)))
+(let (($x113 (or (not $x58) $x82)))
+(let (($x116 (= (or (not $x58) (= $x82 (<= (+ 3 (* (~ 1) 42)) 0))) $x113)))
+(let ((?x83 (* (~ 1) 42)))
+(let ((?x84 (+ 3 ?x83)))
+(let (($x85 (<= ?x84 0)))
+(let (($x86 (= $x82 $x85)))
+(let ((@x97 (trans (monotonicity (rewrite (= ?x83 (~ 42))) (= ?x84 (+ 3 (~ 42)))) (rewrite (= (+ 3 (~ 42)) (~ 39))) (= ?x84 (~ 39)))))
+(let ((@x104 (trans (monotonicity @x97 (= $x85 (<= (~ 39) 0))) (rewrite (= (<= (~ 39) 0) true)) (= $x85 true))))
+(let ((@x111 (trans (monotonicity @x104 (= $x86 (= $x82 true))) (rewrite (= (= $x82 true) $x82)) (= $x86 $x82))))
+(let ((@x121 (mp ((_ |quant-inst| 3 42) (or (not $x58) $x86)) (trans (monotonicity @x111 $x116) (rewrite (= $x113 $x113)) $x116) $x113)))
+(|unit-resolution| (|unit-resolution| @x121 @x80 $x82) (mp @x75 @x133 (not $x82)) false)))))))))))))))))))))))))))))))))))
+
+737e9aeb0ce08125531c37a003d0a11fe8c1aa00 189 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x37 (|nat$| 2)))
+(let ((?x38 (|cons$| ?x37 |nil$|)))
+(let ((?x32 (|nat$| 1)))
+(let ((?x39 (|cons$| ?x32 ?x38)))
+(let ((?x33 (|cons$| ?x32 |nil$|)))
+(let ((?x31 (|nat$| 0)))
+(let ((?x34 (|cons$| ?x31 ?x33)))
+(let ((?x35 (|map$| |uu$| ?x34)))
+(let (($x40 (= ?x35 ?x39)))
+(let ((?x208 (|map$| |uu$| ?x33)))
+(let ((?x326 (|map$| |uu$| |nil$|)))
+(let ((?x325 (|fun_app$| |uu$| ?x32)))
+(let ((?x327 (|cons$| ?x325 ?x326)))
+(let (($x328 (= ?x208 ?x327)))
+(let (($x181 (forall ((?v0 |Nat_nat_fun$|) (?v1 |Nat$|) (?v2 |Nat_list$|) )(!(let ((?x27 (|cons$| (|fun_app$| ?v0 ?v1) (|map$| ?v0 ?v2))))
+(let ((?x24 (|map$| ?v0 (|cons$| ?v1 ?v2))))
+(= ?x24 ?x27))) :pattern ( (|map$| ?v0 (|cons$| ?v1 ?v2)) ) :pattern ( (|cons$| (|fun_app$| ?v0 ?v1) (|map$| ?v0 ?v2)) )))
+))
+(let (($x29 (forall ((?v0 |Nat_nat_fun$|) (?v1 |Nat$|) (?v2 |Nat_list$|) )(let ((?x27 (|cons$| (|fun_app$| ?v0 ?v1) (|map$| ?v0 ?v2))))
+(let ((?x24 (|map$| ?v0 (|cons$| ?v1 ?v2))))
+(= ?x24 ?x27))))
+))
+(let ((?x27 (|cons$| (|fun_app$| ?2 ?1) (|map$| ?2 ?0))))
+(let ((?x24 (|map$| ?2 (|cons$| ?1 ?0))))
+(let (($x28 (= ?x24 ?x27)))
+(let ((@x156 (|mp~| (asserted $x29) (|nnf-pos| (refl (|~| $x28 $x28)) (|~| $x29 $x29)) $x29)))
+(let ((@x186 (mp @x156 (|quant-intro| (refl (= $x28 $x28)) (= $x29 $x181)) $x181)))
+(let (($x213 (not $x181)))
+(let (($x331 (or $x213 $x328)))
+(let ((@x332 ((_ |quant-inst| |uu$| (|nat$| 1) |nil$|) $x331)))
+(let (($x339 (= ?x326 |nil$|)))
+(let (($x173 (forall ((?v0 |Nat_nat_fun$|) )(!(= (|map$| ?v0 |nil$|) |nil$|) :pattern ( (|map$| ?v0 |nil$|) )))
+))
+(let (($x19 (forall ((?v0 |Nat_nat_fun$|) )(= (|map$| ?v0 |nil$|) |nil$|))
+))
+(let ((@x175 (refl (= (= (|map$| ?0 |nil$|) |nil$|) (= (|map$| ?0 |nil$|) |nil$|)))))
+(let ((@x148 (refl (|~| (= (|map$| ?0 |nil$|) |nil$|) (= (|map$| ?0 |nil$|) |nil$|)))))
+(let ((@x178 (mp (|mp~| (asserted $x19) (|nnf-pos| @x148 (|~| $x19 $x19)) $x19) (|quant-intro| @x175 (= $x19 $x173)) $x173)))
+(let (($x343 (or (not $x173) $x339)))
+(let ((@x344 ((_ |quant-inst| |uu$|) $x343)))
+(let ((?x255 (|of_nat$| ?x32)))
+(let ((?x340 (+ 1 ?x255)))
+(let ((?x341 (|nat$| ?x340)))
+(let (($x345 (= ?x325 ?x341)))
+(let (($x85 (forall ((?v0 |Nat$|) )(!(let ((?x7 (|fun_app$| |uu$| ?v0)))
+(= ?x7 (|nat$| (+ 1 (|of_nat$| ?v0))))) :pattern ( (|fun_app$| |uu$| ?v0) )))
+))
+(let ((?x7 (|fun_app$| |uu$| ?0)))
+(let (($x82 (= ?x7 (|nat$| (+ 1 (|of_nat$| ?0))))))
+(let (($x14 (forall ((?v0 |Nat$|) )(!(let ((?x7 (|fun_app$| |uu$| ?v0)))
+(= ?x7 (|nat$| (+ (|of_nat$| ?v0) 1)))) :pattern ( (|fun_app$| |uu$| ?v0) )))
+))
+(let ((@x81 (monotonicity (rewrite (= (+ (|of_nat$| ?0) 1) (+ 1 (|of_nat$| ?0)))) (= (|nat$| (+ (|of_nat$| ?0) 1)) (|nat$| (+ 1 (|of_nat$| ?0)))))))
+(let ((@x84 (monotonicity @x81 (= (= ?x7 (|nat$| (+ (|of_nat$| ?0) 1))) $x82))))
+(let ((@x146 (|mp~| (mp (asserted $x14) (|quant-intro| @x84 (= $x14 $x85)) $x85) (|nnf-pos| (refl (|~| $x82 $x82)) (|~| $x85 $x85)) $x85)))
+(let (($x348 (or (not $x85) $x345)))
+(let ((@x349 ((_ |quant-inst| (|nat$| 1)) $x348)))
+(let ((?x404 (|of_nat$| ?x341)))
+(let ((?x454 (|nat$| ?x404)))
+(let (($x455 (= ?x454 ?x341)))
+(let (($x188 (forall ((?v0 |Nat$|) )(!(= (|nat$| (|of_nat$| ?v0)) ?v0) :pattern ( (|of_nat$| ?v0) )))
+))
+(let (($x44 (forall ((?v0 |Nat$|) )(= (|nat$| (|of_nat$| ?v0)) ?v0))
+))
+(let ((@x190 (refl (= (= (|nat$| (|of_nat$| ?0)) ?0) (= (|nat$| (|of_nat$| ?0)) ?0)))))
+(let ((@x160 (refl (|~| (= (|nat$| (|of_nat$| ?0)) ?0) (= (|nat$| (|of_nat$| ?0)) ?0)))))
+(let ((@x193 (mp (|mp~| (asserted $x44) (|nnf-pos| @x160 (|~| $x44 $x44)) $x44) (|quant-intro| @x190 (= $x44 $x188)) $x188)))
+(let (($x461 (or (not $x188) $x455)))
+(let ((@x462 ((_ |quant-inst| (|nat$| ?x340)) $x461)))
+(let ((?x415 (* (~ 1) ?x404)))
+(let ((?x416 (+ ?x255 ?x415)))
+(let (($x432 (<= ?x416 (~ 1))))
+(let (($x414 (= ?x416 (~ 1))))
+(let (($x407 (>= ?x255 (~ 1))))
+(let (($x401 (>= ?x255 1)))
+(let (($x256 (= ?x255 1)))
+(let (($x195 (forall ((?v0 Int) )(!(let (($x49 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
+(let (($x103 (>= ?v0 0)))
+(let (($x104 (not $x103)))
+(or $x104 $x49)))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x110 (forall ((?v0 Int) )(let (($x49 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
+(let (($x103 (>= ?v0 0)))
+(let (($x104 (not $x103)))
+(or $x104 $x49)))))
+))
+(let (($x49 (= (|of_nat$| (|nat$| ?0)) ?0)))
+(let (($x103 (>= ?0 0)))
+(let (($x104 (not $x103)))
+(let (($x107 (or $x104 $x49)))
+(let (($x51 (forall ((?v0 Int) )(let (($x49 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
+(let (($x46 (<= 0 ?v0)))
+(=> $x46 $x49))))
+))
+(let (($x98 (forall ((?v0 Int) )(let (($x49 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
+(or (not (<= 0 ?v0)) $x49)))
+))
+(let ((@x106 (monotonicity (rewrite (= (<= 0 ?0) $x103)) (= (not (<= 0 ?0)) $x104))))
+(let ((@x112 (|quant-intro| (monotonicity @x106 (= (or (not (<= 0 ?0)) $x49) $x107)) (= $x98 $x110))))
+(let ((@x97 (rewrite (= (=> (<= 0 ?0) $x49) (or (not (<= 0 ?0)) $x49)))))
+(let ((@x115 (mp (asserted $x51) (trans (|quant-intro| @x97 (= $x51 $x98)) @x112 (= $x51 $x110)) $x110)))
+(let ((@x200 (mp (|mp~| @x115 (|nnf-pos| (refl (|~| $x107 $x107)) (|~| $x110 $x110)) $x110) (|quant-intro| (refl (= $x107 $x107)) (= $x110 $x195)) $x195)))
+(let (($x235 (not $x195)))
+(let (($x271 (or $x235 $x256)))
+(let ((@x225 (rewrite (= (not true) false))))
+(let ((@x259 (rewrite (= (>= 1 0) true))))
+(let ((@x263 (trans (monotonicity @x259 (= (not (>= 1 0)) (not true))) @x225 (= (not (>= 1 0)) false))))
+(let ((@x266 (monotonicity @x263 (= (or (not (>= 1 0)) $x256) (or false $x256)))))
+(let ((@x270 (trans @x266 (rewrite (= (or false $x256) $x256)) (= (or (not (>= 1 0)) $x256) $x256))))
+(let ((@x275 (monotonicity @x270 (= (or $x235 (or (not (>= 1 0)) $x256)) $x271))))
+(let ((@x278 (trans @x275 (rewrite (= $x271 $x271)) (= (or $x235 (or (not (>= 1 0)) $x256)) $x271))))
+(let ((@x279 (mp ((_ |quant-inst| 1) (or $x235 (or (not (>= 1 0)) $x256))) @x278 $x271)))
+(let ((@x477 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x256) $x401)) (|unit-resolution| @x279 @x200 $x256) $x401)))
+(let (($x410 (not $x407)))
+(let (($x421 (or $x235 $x410 $x414)))
+(let (($x405 (= ?x404 ?x340)))
+(let (($x402 (>= ?x340 0)))
+(let (($x403 (not $x402)))
+(let (($x406 (or $x403 $x405)))
+(let (($x422 (or $x235 $x406)))
+(let ((@x420 (monotonicity (monotonicity (rewrite (= $x402 $x407)) (= $x403 $x410)) (rewrite (= $x405 $x414)) (= $x406 (or $x410 $x414)))))
+(let ((@x430 (trans (monotonicity @x420 (= $x422 (or $x235 (or $x410 $x414)))) (rewrite (= (or $x235 (or $x410 $x414)) $x421)) (= $x422 $x421))))
+(let ((@x431 (mp ((_ |quant-inst| (+ 1 ?x255)) $x422) @x430 $x421)))
+(let ((@x482 (|unit-resolution| @x431 @x200 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x401) $x407)) @x477 $x407) $x414)))
+(let (($x433 (>= ?x416 (~ 1))))
+(let (($x400 (<= ?x255 1)))
+(let ((@x492 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x256) $x400)) (|unit-resolution| @x279 @x200 $x256) $x400)))
+(let ((@x494 ((_ |th-lemma| arith eq-propagate -1 -1 1 1) @x477 @x492 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x414) $x433)) @x482 $x433) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x414) $x432)) @x482 $x432) (= ?x404 2))))
+(let ((@x502 (trans (monotonicity (symm @x494 (= 2 ?x404)) (= ?x37 ?x454)) (|unit-resolution| @x462 @x193 $x455) (= ?x37 ?x341))))
+(let ((@x504 (trans @x502 (symm (|unit-resolution| @x349 @x146 $x345) (= ?x341 ?x325)) (= ?x37 ?x325))))
+(let ((@x506 (monotonicity @x504 (symm (|unit-resolution| @x344 @x178 $x339) (= |nil$| ?x326)) (= ?x38 ?x327))))
+(let ((@x510 (trans @x506 (symm (|unit-resolution| @x332 @x186 $x328) (= ?x327 ?x208)) (= ?x38 ?x208))))
+(let ((?x216 (|of_nat$| ?x31)))
+(let ((?x329 (+ 1 ?x216)))
+(let ((?x330 (|nat$| ?x329)))
+(let ((?x207 (|fun_app$| |uu$| ?x31)))
+(let (($x333 (= ?x207 ?x330)))
+(let (($x337 (or (not $x85) $x333)))
+(let ((@x338 ((_ |quant-inst| (|nat$| 0)) $x337)))
+(let ((?x350 (|of_nat$| ?x330)))
+(let ((?x452 (|nat$| ?x350)))
+(let (($x453 (= ?x452 ?x330)))
+(let (($x457 (or (not $x188) $x453)))
+(let ((@x458 ((_ |quant-inst| (|nat$| ?x329)) $x457)))
+(let ((?x362 (* (~ 1) ?x350)))
+(let ((?x363 (+ ?x216 ?x362)))
+(let (($x379 (<= ?x363 (~ 1))))
+(let (($x361 (= ?x363 (~ 1))))
+(let (($x354 (>= ?x216 (~ 1))))
+(let (($x335 (>= ?x216 0)))
+(let (($x217 (= ?x216 0)))
+(let (($x236 (or $x235 $x217)))
+(let ((@x220 (rewrite (= (>= 0 0) true))))
+(let ((@x227 (trans (monotonicity @x220 (= (not (>= 0 0)) (not true))) @x225 (= (not (>= 0 0)) false))))
+(let ((@x230 (monotonicity @x227 (= (or (not (>= 0 0)) $x217) (or false $x217)))))
+(let ((@x234 (trans @x230 (rewrite (= (or false $x217) $x217)) (= (or (not (>= 0 0)) $x217) $x217))))
+(let ((@x240 (monotonicity @x234 (= (or $x235 (or (not (>= 0 0)) $x217)) $x236))))
+(let ((@x243 (trans @x240 (rewrite (= $x236 $x236)) (= (or $x235 (or (not (>= 0 0)) $x217)) $x236))))
+(let ((@x244 (mp ((_ |quant-inst| 0) (or $x235 (or (not (>= 0 0)) $x217))) @x243 $x236)))
+(let ((@x517 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x217) $x335)) (|unit-resolution| @x244 @x200 $x217) $x335)))
+(let (($x357 (not $x354)))
+(let (($x368 (or $x235 $x357 $x361)))
+(let (($x351 (= ?x350 ?x329)))
+(let (($x346 (>= ?x329 0)))
+(let (($x347 (not $x346)))
+(let (($x352 (or $x347 $x351)))
+(let (($x369 (or $x235 $x352)))
+(let ((@x367 (monotonicity (monotonicity (rewrite (= $x346 $x354)) (= $x347 $x357)) (rewrite (= $x351 $x361)) (= $x352 (or $x357 $x361)))))
+(let ((@x377 (trans (monotonicity @x367 (= $x369 (or $x235 (or $x357 $x361)))) (rewrite (= (or $x235 (or $x357 $x361)) $x368)) (= $x369 $x368))))
+(let ((@x378 (mp ((_ |quant-inst| (+ 1 ?x216)) $x369) @x377 $x368)))
+(let ((@x522 (|unit-resolution| @x378 @x200 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x335) $x354)) @x517 $x354) $x361)))
+(let (($x380 (>= ?x363 (~ 1))))
+(let (($x334 (<= ?x216 0)))
+(let ((@x532 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x217) $x334)) (|unit-resolution| @x244 @x200 $x217) $x334)))
+(let ((@x534 ((_ |th-lemma| arith eq-propagate -1 -1 1 1) @x517 @x532 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x361) $x380)) @x522 $x380) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x361) $x379)) @x522 $x379) (= ?x350 1))))
+(let ((@x542 (trans (monotonicity (symm @x534 (= 1 ?x350)) (= ?x32 ?x452)) (|unit-resolution| @x458 @x193 $x453) (= ?x32 ?x330))))
+(let ((@x544 (trans @x542 (symm (|unit-resolution| @x338 @x146 $x333) (= ?x330 ?x207)) (= ?x32 ?x207))))
+(let ((@x549 (symm (monotonicity @x544 @x510 (= ?x39 (|cons$| ?x207 ?x208))) (= (|cons$| ?x207 ?x208) ?x39))))
+(let ((?x209 (|cons$| ?x207 ?x208)))
+(let (($x210 (= ?x35 ?x209)))
+(let (($x214 (or $x213 $x210)))
+(let ((@x215 ((_ |quant-inst| |uu$| (|nat$| 0) (|cons$| ?x32 |nil$|)) $x214)))
+(let (($x41 (not $x40)))
+(let ((@x91 (asserted $x41)))
+(|unit-resolution| @x91 (trans (|unit-resolution| @x215 @x186 $x210) @x549 $x40) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+516b38db52977db0759f7a2fb4ee2c61d2623ab0 11 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x7 (forall ((?v0 |A$|) )(|p$| ?v0))
+))
+(let (($x8 (not $x7)))
+(let (($x9 (or $x7 $x8)))
+(let (($x10 (not $x9)))
+(let ((@x40 (trans (monotonicity (rewrite (= $x9 true)) (= $x10 (not true))) (rewrite (= (not true) false)) (= $x10 false))))
+(mp (asserted $x10) @x40 false))))))))
+
+120a595aca724e41775e5a997277b8d456a7e9fe 183 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x24 (|nat$| 6)))
+(let ((?x17 (|nat$| 4)))
+(let ((?x18 (|dec_10$| ?x17)))
+(let ((?x19 (|of_nat$| ?x18)))
+(let ((?x20 (* 4 ?x19)))
+(let ((?x21 (|nat$| ?x20)))
+(let ((?x22 (|dec_10$| ?x21)))
+(let (($x25 (= ?x22 ?x24)))
+(let ((?x348 (|of_nat$| ?x24)))
+(let ((?x393 (+ (~ 10) ?x348)))
+(let ((?x394 (|nat$| ?x393)))
+(let ((?x395 (|dec_10$| ?x394)))
+(let (($x390 (>= ?x348 10)))
+(let ((?x396 (ite $x390 ?x395 ?x24)))
+(let (($x403 (= ?x24 ?x396)))
+(let (($x404 (not $x390)))
+(let (($x398 (<= ?x348 6)))
+(let (($x349 (= ?x348 6)))
+(let (($x188 (forall ((?v0 Int) )(!(let ((?x33 (|nat$| ?v0)))
+(let ((?x34 (|of_nat$| ?x33)))
+(let (($x35 (= ?x34 ?v0)))
+(let (($x114 (>= ?v0 0)))
+(let (($x115 (not $x114)))
+(or $x115 $x35)))))) :pattern ( (|nat$| ?v0) )))
+))
+(let (($x121 (forall ((?v0 Int) )(let ((?x33 (|nat$| ?v0)))
+(let ((?x34 (|of_nat$| ?x33)))
+(let (($x35 (= ?x34 ?v0)))
+(let (($x114 (>= ?v0 0)))
+(let (($x115 (not $x114)))
+(or $x115 $x35)))))))
+))
+(let ((?x33 (|nat$| ?0)))
+(let ((?x34 (|of_nat$| ?x33)))
+(let (($x35 (= ?x34 ?0)))
+(let (($x114 (>= ?0 0)))
+(let (($x115 (not $x114)))
+(let (($x118 (or $x115 $x35)))
+(let (($x37 (forall ((?v0 Int) )(let ((?x33 (|nat$| ?v0)))
+(let ((?x34 (|of_nat$| ?x33)))
+(let (($x35 (= ?x34 ?v0)))
+(let (($x32 (<= 0 ?v0)))
+(=> $x32 $x35))))))
+))
+(let (($x109 (forall ((?v0 Int) )(let ((?x33 (|nat$| ?v0)))
+(let ((?x34 (|of_nat$| ?x33)))
+(let (($x35 (= ?x34 ?v0)))
+(or (not (<= 0 ?v0)) $x35)))))
+))
+(let ((@x117 (monotonicity (rewrite (= (<= 0 ?0) $x114)) (= (not (<= 0 ?0)) $x115))))
+(let ((@x123 (|quant-intro| (monotonicity @x117 (= (or (not (<= 0 ?0)) $x35) $x118)) (= $x109 $x121))))
+(let ((@x108 (rewrite (= (=> (<= 0 ?0) $x35) (or (not (<= 0 ?0)) $x35)))))
+(let ((@x126 (mp (asserted $x37) (trans (|quant-intro| @x108 (= $x37 $x109)) @x123 (= $x37 $x121)) $x121)))
+(let ((@x193 (mp (|mp~| @x126 (|nnf-pos| (refl (|~| $x118 $x118)) (|~| $x121 $x121)) $x121) (|quant-intro| (refl (= $x118 $x118)) (= $x121 $x188)) $x188)))
+(let (($x274 (not $x188)))
+(let (($x364 (or $x274 $x349)))
+(let ((@x352 (rewrite (= (>= 6 0) true))))
+(let ((@x356 (trans (monotonicity @x352 (= (not (>= 6 0)) (not true))) (rewrite (= (not true) false)) (= (not (>= 6 0)) false))))
+(let ((@x359 (monotonicity @x356 (= (or (not (>= 6 0)) $x349) (or false $x349)))))
+(let ((@x363 (trans @x359 (rewrite (= (or false $x349) $x349)) (= (or (not (>= 6 0)) $x349) $x349))))
+(let ((@x368 (monotonicity @x363 (= (or $x274 (or (not (>= 6 0)) $x349)) $x364))))
+(let ((@x371 (trans @x368 (rewrite (= $x364 $x364)) (= (or $x274 (or (not (>= 6 0)) $x349)) $x364))))
+(let ((@x372 (mp ((_ |quant-inst| 6) (or $x274 (or (not (>= 6 0)) $x349))) @x371 $x364)))
+(let ((@x422 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x349) $x398)) (|unit-resolution| @x372 @x193 $x349) $x398)))
+(let ((@x427 (|unit-resolution| (|def-axiom| (or $x390 $x403)) (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x398) $x404)) @x422 $x404) $x403)))
+(let ((?x389 (|dec_10$| ?x24)))
+(let (($x397 (= ?x389 ?x396)))
+(let (($x175 (forall ((?v0 |Nat$|) )(!(let ((?x69 (|dec_10$| (|nat$| (+ (~ 10) (|of_nat$| ?v0))))))
+(let ((?x88 (ite (>= (|of_nat$| ?v0) 10) ?x69 ?v0)))
+(let ((?x6 (|dec_10$| ?v0)))
+(= ?x6 ?x88)))) :pattern ( (|dec_10$| ?v0) ) :pattern ( (|of_nat$| ?v0) )))
+))
+(let (($x96 (forall ((?v0 |Nat$|) )(let ((?x69 (|dec_10$| (|nat$| (+ (~ 10) (|of_nat$| ?v0))))))
+(let ((?x88 (ite (>= (|of_nat$| ?v0) 10) ?x69 ?v0)))
+(let ((?x6 (|dec_10$| ?v0)))
+(= ?x6 ?x88)))))
+))
+(let ((?x69 (|dec_10$| (|nat$| (+ (~ 10) (|of_nat$| ?0))))))
+(let ((?x88 (ite (>= (|of_nat$| ?0) 10) ?x69 ?0)))
+(let ((?x6 (|dec_10$| ?0)))
+(let (($x93 (= ?x6 ?x88)))
+(let (($x15 (forall ((?v0 |Nat$|) )(let ((?x7 (|of_nat$| ?v0)))
+(let (($x9 (< ?x7 10)))
+(let ((?x6 (|dec_10$| ?v0)))
+(= ?x6 (ite $x9 ?v0 (|dec_10$| (|nat$| (- ?x7 10)))))))))
+))
+(let (($x78 (forall ((?v0 |Nat$|) )(let ((?x69 (|dec_10$| (|nat$| (+ (~ 10) (|of_nat$| ?v0))))))
+(let ((?x7 (|of_nat$| ?v0)))
+(let (($x9 (< ?x7 10)))
+(let ((?x72 (ite $x9 ?v0 ?x69)))
+(let ((?x6 (|dec_10$| ?v0)))
+(= ?x6 ?x72)))))))
+))
+(let ((?x7 (|of_nat$| ?0)))
+(let (($x9 (< ?x7 10)))
+(let ((?x72 (ite $x9 ?0 ?x69)))
+(let ((@x87 (monotonicity (rewrite (= $x9 (not (>= ?x7 10)))) (= ?x72 (ite (not (>= ?x7 10)) ?0 ?x69)))))
+(let ((@x92 (trans @x87 (rewrite (= (ite (not (>= ?x7 10)) ?0 ?x69) ?x88)) (= ?x72 ?x88))))
+(let ((@x98 (|quant-intro| (monotonicity @x92 (= (= ?x6 ?x72) $x93)) (= $x78 $x96))))
+(let (($x75 (= ?x6 ?x72)))
+(let ((@x68 (monotonicity (rewrite (= (- ?x7 10) (+ (~ 10) ?x7))) (= (|nat$| (- ?x7 10)) (|nat$| (+ (~ 10) ?x7))))))
+(let ((@x74 (monotonicity (monotonicity @x68 (= (|dec_10$| (|nat$| (- ?x7 10))) ?x69)) (= (ite $x9 ?0 (|dec_10$| (|nat$| (- ?x7 10)))) ?x72))))
+(let ((@x77 (monotonicity @x74 (= (= ?x6 (ite $x9 ?0 (|dec_10$| (|nat$| (- ?x7 10))))) $x75))))
+(let ((@x101 (mp (asserted $x15) (trans (|quant-intro| @x77 (= $x15 $x78)) @x98 (= $x15 $x96)) $x96)))
+(let ((@x180 (mp (|mp~| @x101 (|nnf-pos| (refl (|~| $x93 $x93)) (|~| $x96 $x96)) $x96) (|quant-intro| (refl (= $x93 $x93)) (= $x96 $x175)) $x175)))
+(let (($x209 (not $x175)))
+(let (($x400 (or $x209 $x397)))
+(let ((@x401 ((_ |quant-inst| (|nat$| 6)) $x400)))
+(let ((?x200 (|of_nat$| ?x17)))
+(let ((?x383 (* (~ 1) ?x200)))
+(let ((?x384 (+ ?x19 ?x383)))
+(let (($x385 (<= ?x384 0)))
+(let (($x382 (= ?x19 ?x200)))
+(let ((?x202 (+ (~ 10) ?x200)))
+(let ((?x203 (|nat$| ?x202)))
+(let ((?x204 (|dec_10$| ?x203)))
+(let (($x201 (>= ?x200 10)))
+(let ((?x205 (ite $x201 ?x204 ?x17)))
+(let (($x213 (= ?x17 ?x205)))
+(let (($x214 (not $x201)))
+(let (($x284 (<= ?x200 4)))
+(let (($x256 (= ?x200 4)))
+(let (($x275 (or $x274 $x256)))
+(let ((@x259 (rewrite (= (>= 4 0) true))))
+(let ((@x266 (trans (monotonicity @x259 (= (not (>= 4 0)) (not true))) (rewrite (= (not true) false)) (= (not (>= 4 0)) false))))
+(let ((@x269 (monotonicity @x266 (= (or (not (>= 4 0)) $x256) (or false $x256)))))
+(let ((@x273 (trans @x269 (rewrite (= (or false $x256) $x256)) (= (or (not (>= 4 0)) $x256) $x256))))
+(let ((@x279 (monotonicity @x273 (= (or $x274 (or (not (>= 4 0)) $x256)) $x275))))
+(let ((@x282 (trans @x279 (rewrite (= $x275 $x275)) (= (or $x274 (or (not (>= 4 0)) $x256)) $x275))))
+(let ((@x283 (mp ((_ |quant-inst| 4) (or $x274 (or (not (>= 4 0)) $x256))) @x282 $x275)))
+(let ((@x433 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x256) $x284)) (|unit-resolution| @x283 @x193 $x256) $x284)))
+(let ((@x438 (|unit-resolution| (|def-axiom| (or $x201 $x213)) (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x284) $x214)) @x433 $x214) $x213)))
+(let (($x206 (= ?x18 ?x205)))
+(let (($x210 (or $x209 $x206)))
+(let ((@x211 ((_ |quant-inst| (|nat$| 4)) $x210)))
+(let ((@x443 (trans (|unit-resolution| @x211 @x180 $x206) (symm @x438 (= ?x205 ?x17)) (= ?x18 ?x17))))
+(let ((@x448 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x382) $x385)) (monotonicity @x443 $x382) $x385)))
+(let (($x386 (>= ?x384 0)))
+(let ((@x451 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x382) $x386)) (monotonicity @x443 $x382) $x386)))
+(let (($x285 (>= ?x200 4)))
+(let ((@x454 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x256) $x285)) (|unit-resolution| @x283 @x193 $x256) $x285)))
+(let ((?x207 (|of_nat$| ?x21)))
+(let ((?x309 (* (~ 1) ?x207)))
+(let ((?x310 (+ ?x20 ?x309)))
+(let (($x325 (<= ?x310 0)))
+(let (($x307 (= ?x310 0)))
+(let (($x299 (>= ?x19 0)))
+(let ((@x459 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x299 (not $x285) (not $x386))) @x454 @x451 $x299)))
+(let (($x302 (not $x299)))
+(let (($x311 (or $x302 $x307)))
+(let (($x314 (or $x274 $x302 $x307)))
+(let (($x297 (= ?x207 ?x20)))
+(let (($x295 (>= ?x20 0)))
+(let (($x296 (not $x295)))
+(let (($x298 (or $x296 $x297)))
+(let (($x315 (or $x274 $x298)))
+(let ((@x313 (monotonicity (monotonicity (rewrite (= $x295 $x299)) (= $x296 $x302)) (rewrite (= $x297 $x307)) (= $x298 $x311))))
+(let ((@x323 (trans (monotonicity @x313 (= $x315 (or $x274 $x311))) (rewrite (= (or $x274 $x311) $x314)) (= $x315 $x314))))
+(let ((@x324 (mp ((_ |quant-inst| (* 4 ?x19)) $x315) @x323 $x314)))
+(let ((@x465 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x307) $x325)) (|unit-resolution| (|unit-resolution| @x324 @x193 $x311) @x459 $x307) $x325)))
+(let (($x326 (>= ?x310 0)))
+(let ((@x468 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x307) $x326)) (|unit-resolution| (|unit-resolution| @x324 @x193 $x311) @x459 $x307) $x326)))
+(let ((@x472 (monotonicity ((_ |th-lemma| arith eq-propagate 1 1 -4 -4 -4 -4) @x468 @x465 @x454 @x433 @x451 @x448 (= (+ (~ 10) ?x207) 6)) (= (|nat$| (+ (~ 10) ?x207)) ?x24))))
+(let ((?x219 (+ (~ 10) ?x207)))
+(let ((?x220 (|nat$| ?x219)))
+(let ((?x221 (|dec_10$| ?x220)))
+(let (($x208 (>= ?x207 10)))
+(let ((?x222 (ite $x208 ?x221 ?x21)))
+(let (($x228 (= ?x221 ?x222)))
+(let ((@x476 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 4 4) (or $x208 (not $x325) (not $x285) (not $x386))) @x454 @x465 @x451 $x208)))
+(let ((@x480 (symm (|unit-resolution| (|def-axiom| (or (not $x208) $x228)) @x476 $x228) (= ?x222 ?x221))))
+(let (($x223 (= ?x22 ?x222)))
+(let (($x226 (or $x209 $x223)))
+(let ((@x227 ((_ |quant-inst| (|nat$| ?x20)) $x226)))
+(let ((@x488 (trans (trans (|unit-resolution| @x227 @x180 $x223) @x480 (= ?x22 ?x221)) (monotonicity @x472 (= ?x221 ?x389)) (= ?x22 ?x389))))
+(let ((@x491 (trans (trans @x488 (|unit-resolution| @x401 @x180 $x397) (= ?x22 ?x396)) (symm @x427 (= ?x396 ?x24)) $x25)))
+(let (($x26 (not $x25)))
+(let ((@x102 (asserted $x26)))
+(|unit-resolution| @x102 @x491 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+a25b64a8f04cffe57bd9a525d4bad154c19d2b20 310 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x42 (|map$| |uu$| |xs$|)))
+(let ((?x43 (|eval_dioph$| |ks$| ?x42)))
+(let ((?x145 (* (~ 1) ?x43)))
+(let ((?x146 (+ |l$| ?x145)))
+(let ((?x149 (|div$| ?x146 2)))
+(let ((?x47 (|map$| |uua$| |xs$|)))
+(let ((?x48 (|eval_dioph$| |ks$| ?x47)))
+(let ((?x769 (+ ?x48 (* (~ 1) ?x149))))
+(let (($x771 (>= ?x769 0)))
+(let ((?x452 (* (~ 1) |l$|)))
+(let ((?x39 (|eval_dioph$| |ks$| |xs$|)))
+(let ((?x776 (+ ?x39 ?x452)))
+(let (($x778 (>= ?x776 0)))
+(let (($x41 (= ?x39 |l$|)))
+(let (($x152 (= ?x48 ?x149)))
+(let (($x362 (not $x152)))
+(let ((?x45 (|mod$| |l$| 2)))
+(let ((?x44 (|mod$| ?x43 2)))
+(let (($x46 (= ?x44 ?x45)))
+(let (($x361 (not $x46)))
+(let (($x363 (or $x361 $x362)))
+(let ((?x730 (div ?x43 2)))
+(let ((?x913 (* (~ 1) ?x730)))
+(let ((?x685 (mod ?x43 2)))
+(let ((?x712 (* (~ 1) ?x685)))
+(let ((?x645 (div |l$| 2)))
+(let ((?x671 (* (~ 1) ?x645)))
+(let ((?x599 (mod |l$| 2)))
+(let ((?x626 (* (~ 1) ?x599)))
+(let ((?x656 (* (~ 1) ?x48)))
+(let (($x737 (>= (+ |l$| ?x44 ?x656 ?x626 ?x671 ?x712 ?x913) 1)))
+(let ((?x658 (* (~ 2) ?x645)))
+(let ((?x659 (+ |l$| ?x626 ?x658)))
+(let (($x657 (= ?x659 0)))
+(let ((@x108 (|true-axiom| true)))
+(let ((@x945 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x657) (>= ?x659 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x657)) @x108 $x657) (>= ?x659 0))))
+(let ((?x627 (+ ?x45 ?x626)))
+(let (($x628 (= ?x627 0)))
+(let (($x418 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x83 (mod ?v0 ?v1)))
+(let ((?x230 (* (~ 1) ?v1)))
+(let ((?x227 (* (~ 1) ?v0)))
+(let ((?x273 (mod ?x227 ?x230)))
+(let ((?x279 (* (~ 1) ?x273)))
+(let (($x248 (<= ?v1 0)))
+(let ((?x299 (ite $x248 ?x279 ?x83)))
+(let (($x72 (= ?v1 0)))
+(let ((?x304 (ite $x72 ?v0 ?x299)))
+(let ((?x82 (|mod$| ?v0 ?v1)))
+(= ?x82 ?x304))))))))))) :pattern ( (|mod$| ?v0 ?v1) )))
+))
+(let (($x310 (forall ((?v0 Int) (?v1 Int) )(let ((?x83 (mod ?v0 ?v1)))
+(let ((?x230 (* (~ 1) ?v1)))
+(let ((?x227 (* (~ 1) ?v0)))
+(let ((?x273 (mod ?x227 ?x230)))
+(let ((?x279 (* (~ 1) ?x273)))
+(let (($x248 (<= ?v1 0)))
+(let ((?x299 (ite $x248 ?x279 ?x83)))
+(let (($x72 (= ?v1 0)))
+(let ((?x304 (ite $x72 ?v0 ?x299)))
+(let ((?x82 (|mod$| ?v0 ?v1)))
+(= ?x82 ?x304))))))))))))
+))
+(let ((?x83 (mod ?1 ?0)))
+(let ((?x230 (* (~ 1) ?0)))
+(let ((?x227 (* (~ 1) ?1)))
+(let ((?x273 (mod ?x227 ?x230)))
+(let ((?x279 (* (~ 1) ?x273)))
+(let (($x248 (<= ?0 0)))
+(let ((?x299 (ite $x248 ?x279 ?x83)))
+(let (($x72 (= ?0 0)))
+(let ((?x304 (ite $x72 ?1 ?x299)))
+(let ((?x82 (|mod$| ?1 ?0)))
+(let (($x307 (= ?x82 ?x304)))
+(let (($x89 (forall ((?v0 Int) (?v1 Int) )(let (($x72 (= ?v1 0)))
+(let ((?x87 (ite $x72 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
+(let ((?x82 (|mod$| ?v0 ?v1)))
+(= ?x82 ?x87)))))
+))
+(let (($x293 (forall ((?v0 Int) (?v1 Int) )(let ((?x230 (* (~ 1) ?v1)))
+(let ((?x227 (* (~ 1) ?v0)))
+(let ((?x273 (mod ?x227 ?x230)))
+(let ((?x279 (* (~ 1) ?x273)))
+(let ((?x83 (mod ?v0 ?v1)))
+(let (($x73 (< 0 ?v1)))
+(let ((?x284 (ite $x73 ?x83 ?x279)))
+(let (($x72 (= ?v1 0)))
+(let ((?x287 (ite $x72 ?v0 ?x284)))
+(let ((?x82 (|mod$| ?v0 ?v1)))
+(= ?x82 ?x287))))))))))))
+))
+(let ((@x298 (monotonicity (rewrite (= (< 0 ?0) (not $x248))) (= (ite (< 0 ?0) ?x83 ?x279) (ite (not $x248) ?x83 ?x279)))))
+(let ((@x303 (trans @x298 (rewrite (= (ite (not $x248) ?x83 ?x279) ?x299)) (= (ite (< 0 ?0) ?x83 ?x279) ?x299))))
+(let ((@x306 (monotonicity @x303 (= (ite $x72 ?1 (ite (< 0 ?0) ?x83 ?x279)) ?x304))))
+(let ((@x309 (monotonicity @x306 (= (= ?x82 (ite $x72 ?1 (ite (< 0 ?0) ?x83 ?x279))) $x307))))
+(let (($x73 (< 0 ?0)))
+(let ((?x284 (ite $x73 ?x83 ?x279)))
+(let ((?x287 (ite $x72 ?1 ?x284)))
+(let (($x290 (= ?x82 ?x287)))
+(let (($x291 (= (= ?x82 (ite $x72 ?1 (ite $x73 ?x83 (- (mod (- ?1) (- ?0)))))) $x290)))
+(let ((@x275 (monotonicity (rewrite (= (- ?1) ?x227)) (rewrite (= (- ?0) ?x230)) (= (mod (- ?1) (- ?0)) ?x273))))
+(let ((@x283 (trans (monotonicity @x275 (= (- (mod (- ?1) (- ?0))) (- ?x273))) (rewrite (= (- ?x273) ?x279)) (= (- (mod (- ?1) (- ?0))) ?x279))))
+(let ((@x286 (monotonicity @x283 (= (ite $x73 ?x83 (- (mod (- ?1) (- ?0)))) ?x284))))
+(let ((@x289 (monotonicity @x286 (= (ite $x72 ?1 (ite $x73 ?x83 (- (mod (- ?1) (- ?0))))) ?x287))))
+(let ((@x314 (trans (|quant-intro| (monotonicity @x289 $x291) (= $x89 $x293)) (|quant-intro| @x309 (= $x293 $x310)) (= $x89 $x310))))
+(let ((@x360 (|mp~| (mp (asserted $x89) @x314 $x310) (|nnf-pos| (refl (|~| $x307 $x307)) (|~| $x310 $x310)) $x310)))
+(let ((@x423 (mp @x360 (|quant-intro| (refl (= $x307 $x307)) (= $x310 $x418)) $x418)))
+(let (($x633 (not $x418)))
+(let (($x634 (or $x633 $x628)))
+(let (($x440 (<= 2 0)))
+(let ((?x600 (ite $x440 (* (~ 1) (mod ?x452 (* (~ 1) 2))) ?x599)))
+(let (($x439 (= 2 0)))
+(let ((?x601 (ite $x439 |l$| ?x600)))
+(let (($x602 (= ?x45 ?x601)))
+(let ((@x457 (rewrite (= (* (~ 1) 2) (~ 2)))))
+(let ((@x608 (monotonicity (monotonicity @x457 (= (mod ?x452 (* (~ 1) 2)) (mod ?x452 (~ 2)))) (= (* (~ 1) (mod ?x452 (* (~ 1) 2))) (* (~ 1) (mod ?x452 (~ 2)))))))
+(let ((@x451 (rewrite (= $x440 false))))
+(let ((@x611 (monotonicity @x451 @x608 (= ?x600 (ite false (* (~ 1) (mod ?x452 (~ 2))) ?x599)))))
+(let ((@x615 (trans @x611 (rewrite (= (ite false (* (~ 1) (mod ?x452 (~ 2))) ?x599) ?x599)) (= ?x600 ?x599))))
+(let ((@x449 (rewrite (= $x439 false))))
+(let ((@x622 (trans (monotonicity @x449 @x615 (= ?x601 (ite false |l$| ?x599))) (rewrite (= (ite false |l$| ?x599) ?x599)) (= ?x601 ?x599))))
+(let ((@x632 (trans (monotonicity @x622 (= $x602 (= ?x45 ?x599))) (rewrite (= (= ?x45 ?x599) $x628)) (= $x602 $x628))))
+(let ((@x641 (trans (monotonicity @x632 (= (or $x633 $x602) $x634)) (rewrite (= $x634 $x634)) (= (or $x633 $x602) $x634))))
+(let ((@x950 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x628) (>= ?x627 0))) (|unit-resolution| (mp ((_ |quant-inst| |l$| 2) (or $x633 $x602)) @x641 $x634) @x423 $x628) (>= ?x627 0))))
+(let (($x1021 (not $x778)))
+(let (($x777 (<= ?x776 0)))
+(let (($x770 (<= ?x769 0)))
+(let (($x364 (not $x363)))
+(let ((@x741 (hypothesis $x364)))
+(let ((@x1018 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x362 $x770)) (|unit-resolution| (|def-axiom| (or $x363 $x152)) @x741 $x152) $x770)))
+(let ((?x520 (+ |l$| ?x145 (* (~ 2) (div ?x146 2)) (* (~ 1) (mod (+ |l$| ?x43) 2)))))
+(let (($x517 (= ?x520 0)))
+(let ((@x876 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x517) (>= ?x520 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x517)) @x108 $x517) (>= ?x520 0))))
+(let ((?x584 (* (~ 2) ?x48)))
+(let ((?x585 (+ ?x39 ?x145 ?x584)))
+(let (($x586 (= ?x585 0)))
+(let (($x384 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(!(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
+(let ((?x136 (+ ?x24 (* (~ 1) (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))) (* (~ 2) (|eval_dioph$| ?v0 (|map$| |uua$| ?v1))))))
+(= ?x136 0))) :pattern ( (|eval_dioph$| ?v0 (|map$| |uu$| ?v1)) ) :pattern ( (|eval_dioph$| ?v0 (|map$| |uua$| ?v1)) )))
+))
+(let (($x138 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
+(let ((?x136 (+ ?x24 (* (~ 1) (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))) (* (~ 2) (|eval_dioph$| ?v0 (|map$| |uua$| ?v1))))))
+(= ?x136 0))))
+))
+(let ((?x24 (|eval_dioph$| ?1 ?0)))
+(let ((?x136 (+ ?x24 (* (~ 1) (|eval_dioph$| ?1 (|map$| |uu$| ?0))) (* (~ 2) (|eval_dioph$| ?1 (|map$| |uua$| ?0))))))
+(let (($x132 (= ?x136 0)))
+(let (($x36 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
+(let ((?x27 (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))))
+(let ((?x34 (+ (* (|eval_dioph$| ?v0 (|map$| |uua$| ?v1)) 2) ?x27)))
+(= ?x34 ?x24)))))
+))
+(let (($x127 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
+(let ((?x32 (|eval_dioph$| ?v0 (|map$| |uua$| ?v1))))
+(let ((?x113 (* 2 ?x32)))
+(let ((?x27 (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))))
+(let ((?x119 (+ ?x27 ?x113)))
+(= ?x119 ?x24)))))))
+))
+(let ((?x32 (|eval_dioph$| ?1 (|map$| |uua$| ?0))))
+(let ((?x113 (* 2 ?x32)))
+(let ((?x27 (|eval_dioph$| ?1 (|map$| |uu$| ?0))))
+(let ((?x119 (+ ?x27 ?x113)))
+(let (($x124 (= ?x119 ?x24)))
+(let ((@x118 (monotonicity (rewrite (= (* ?x32 2) ?x113)) (= (+ (* ?x32 2) ?x27) (+ ?x113 ?x27)))))
+(let ((@x123 (trans @x118 (rewrite (= (+ ?x113 ?x27) ?x119)) (= (+ (* ?x32 2) ?x27) ?x119))))
+(let ((@x129 (|quant-intro| (monotonicity @x123 (= (= (+ (* ?x32 2) ?x27) ?x24) $x124)) (= $x36 $x127))))
+(let ((@x142 (trans @x129 (|quant-intro| (rewrite (= $x124 $x132)) (= $x127 $x138)) (= $x36 $x138))))
+(let ((@x335 (|mp~| (mp (asserted $x36) @x142 $x138) (|nnf-pos| (refl (|~| $x132 $x132)) (|~| $x138 $x138)) $x138)))
+(let ((@x389 (mp @x335 (|quant-intro| (refl (= $x132 $x132)) (= $x138 $x384)) $x384)))
+(let ((@x883 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x586) (<= ?x585 0))) (|unit-resolution| ((_ |quant-inst| |ks$| |xs$|) (or (not $x384) $x586)) @x389 $x586) (<= ?x585 0))))
+(let ((?x479 (+ ?x149 (* (~ 1) (div ?x146 2)))))
+(let (($x480 (= ?x479 0)))
+(let (($x411 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x74 (div ?v0 ?v1)))
+(let ((?x230 (* (~ 1) ?v1)))
+(let ((?x227 (* (~ 1) ?v0)))
+(let ((?x233 (div ?x227 ?x230)))
+(let (($x248 (<= ?v1 0)))
+(let ((?x255 (ite $x248 ?x233 ?x74)))
+(let (($x72 (= ?v1 0)))
+(let ((?x71 (|div$| ?v0 ?v1)))
+(= ?x71 (ite $x72 0 ?x255)))))))))) :pattern ( (|div$| ?v0 ?v1) )))
+))
+(let (($x266 (forall ((?v0 Int) (?v1 Int) )(let ((?x74 (div ?v0 ?v1)))
+(let ((?x230 (* (~ 1) ?v1)))
+(let ((?x227 (* (~ 1) ?v0)))
+(let ((?x233 (div ?x227 ?x230)))
+(let (($x248 (<= ?v1 0)))
+(let ((?x255 (ite $x248 ?x233 ?x74)))
+(let (($x72 (= ?v1 0)))
+(let ((?x71 (|div$| ?v0 ?v1)))
+(= ?x71 (ite $x72 0 ?x255)))))))))))
+))
+(let ((?x71 (|div$| ?1 ?0)))
+(let (($x263 (= ?x71 (ite $x72 0 (ite $x248 (div ?x227 ?x230) (div ?1 ?0))))))
+(let (($x81 (forall ((?v0 Int) (?v1 Int) )(let (($x72 (= ?v1 0)))
+(let ((?x79 (ite $x72 0 (ite (< 0 ?v1) (div ?v0 ?v1) (div (- ?v0) (- ?v1))))))
+(let ((?x71 (|div$| ?v0 ?v1)))
+(= ?x71 ?x79)))))
+))
+(let (($x245 (forall ((?v0 Int) (?v1 Int) )(let ((?x230 (* (~ 1) ?v1)))
+(let ((?x227 (* (~ 1) ?v0)))
+(let ((?x233 (div ?x227 ?x230)))
+(let ((?x74 (div ?v0 ?v1)))
+(let (($x73 (< 0 ?v1)))
+(let ((?x236 (ite $x73 ?x74 ?x233)))
+(let (($x72 (= ?v1 0)))
+(let ((?x239 (ite $x72 0 ?x236)))
+(let ((?x71 (|div$| ?v0 ?v1)))
+(= ?x71 ?x239)))))))))))
+))
+(let ((?x233 (div ?x227 ?x230)))
+(let ((?x74 (div ?1 ?0)))
+(let ((?x236 (ite $x73 ?x74 ?x233)))
+(let ((?x239 (ite $x72 0 ?x236)))
+(let (($x242 (= ?x71 ?x239)))
+(let ((@x254 (monotonicity (rewrite (= $x73 (not $x248))) (= ?x236 (ite (not $x248) ?x74 ?x233)))))
+(let ((@x259 (trans @x254 (rewrite (= (ite (not $x248) ?x74 ?x233) (ite $x248 ?x233 ?x74))) (= ?x236 (ite $x248 ?x233 ?x74)))))
+(let ((@x265 (monotonicity (monotonicity @x259 (= ?x239 (ite $x72 0 (ite $x248 ?x233 ?x74)))) (= $x242 $x263))))
+(let (($x243 (= (= ?x71 (ite $x72 0 (ite $x73 ?x74 (div (- ?1) (- ?0))))) $x242)))
+(let ((@x235 (monotonicity (rewrite (= (- ?1) ?x227)) (rewrite (= (- ?0) ?x230)) (= (div (- ?1) (- ?0)) ?x233))))
+(let ((@x241 (monotonicity (monotonicity @x235 (= (ite $x73 ?x74 (div (- ?1) (- ?0))) ?x236)) (= (ite $x72 0 (ite $x73 ?x74 (div (- ?1) (- ?0)))) ?x239))))
+(let ((@x270 (trans (|quant-intro| (monotonicity @x241 $x243) (= $x81 $x245)) (|quant-intro| @x265 (= $x245 $x266)) (= $x81 $x266))))
+(let ((@x355 (|mp~| (mp (asserted $x81) @x270 $x266) (|nnf-pos| (refl (|~| $x263 $x263)) (|~| $x266 $x266)) $x266)))
+(let ((@x416 (mp @x355 (|quant-intro| (refl (= $x263 $x263)) (= $x266 $x411)) $x411)))
+(let (($x486 (or (not $x411) $x480)))
+(let ((?x444 (div ?x146 2)))
+(let ((?x445 (ite $x440 (div (* (~ 1) ?x146) (* (~ 1) 2)) ?x444)))
+(let ((?x446 (ite $x439 0 ?x445)))
+(let (($x447 (= ?x149 ?x446)))
+(let ((@x460 (monotonicity (rewrite (= (* (~ 1) ?x146) (+ ?x452 ?x43))) @x457 (= (div (* (~ 1) ?x146) (* (~ 1) 2)) (div (+ ?x452 ?x43) (~ 2))))))
+(let ((@x463 (monotonicity @x451 @x460 (= ?x445 (ite false (div (+ ?x452 ?x43) (~ 2)) ?x444)))))
+(let ((@x467 (trans @x463 (rewrite (= (ite false (div (+ ?x452 ?x43) (~ 2)) ?x444) ?x444)) (= ?x445 ?x444))))
+(let ((@x474 (trans (monotonicity @x449 @x467 (= ?x446 (ite false 0 ?x444))) (rewrite (= (ite false 0 ?x444) ?x444)) (= ?x446 ?x444))))
+(let ((@x484 (trans (monotonicity @x474 (= $x447 (= ?x149 ?x444))) (rewrite (= (= ?x149 ?x444) $x480)) (= $x447 $x480))))
+(let ((@x493 (trans (monotonicity @x484 (= (or (not $x411) $x447) $x486)) (rewrite (= $x486 $x486)) (= (or (not $x411) $x447) $x486))))
+(let ((@x885 (|unit-resolution| (mp ((_ |quant-inst| (+ |l$| ?x145) 2) (or (not $x411) $x447)) @x493 $x486) @x416 $x480)))
+(let ((@x889 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x480) (<= ?x479 0))) @x885 (<= ?x479 0))))
+(let ((@x892 (|unit-resolution| ((_ |th-lemma| arith) (or false (>= (mod (+ |l$| ?x43) 2) 0))) @x108 (>= (mod (+ |l$| ?x43) 2) 0))))
+(let ((@x893 ((_ |th-lemma| arith farkas 1 -2 -2 -1 1 1) @x892 @x889 (hypothesis $x770) @x883 (hypothesis (not $x777)) @x876 false)))
+(let (($x169 (not $x41)))
+(let (($x370 (= $x41 $x363)))
+(let ((@x369 (monotonicity (rewrite (= (and $x46 $x152) $x364)) (= (= $x169 (and $x46 $x152)) (= $x169 $x364)))))
+(let ((@x374 (trans @x369 (rewrite (= (= $x169 $x364) $x370)) (= (= $x169 (and $x46 $x152)) $x370))))
+(let (($x155 (and $x46 $x152)))
+(let (($x170 (= $x169 $x155)))
+(let (($x53 (= $x41 (and $x46 (= ?x48 (|div$| (- |l$| ?x43) 2))))))
+(let (($x54 (not $x53)))
+(let ((@x151 (monotonicity (rewrite (= (- |l$| ?x43) ?x146)) (= (|div$| (- |l$| ?x43) 2) ?x149))))
+(let ((@x157 (monotonicity (monotonicity @x151 (= (= ?x48 (|div$| (- |l$| ?x43) 2)) $x152)) (= (and $x46 (= ?x48 (|div$| (- |l$| ?x43) 2))) $x155))))
+(let ((@x165 (trans (monotonicity @x157 (= $x53 (= $x41 $x155))) (rewrite (= (= $x41 $x155) (= $x41 $x155))) (= $x53 (= $x41 $x155)))))
+(let ((@x174 (trans (monotonicity @x165 (= $x54 (not (= $x41 $x155)))) (rewrite (= (not (= $x41 $x155)) $x170)) (= $x54 $x170))))
+(let ((@x375 (mp (mp (asserted $x54) @x174 $x170) @x374 $x370)))
+(let ((@x438 (|unit-resolution| (|def-axiom| (or $x169 $x363 (not $x370))) @x375 (or $x169 $x363))))
+(let ((@x1025 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x41 (not $x777) $x1021)) (|unit-resolution| @x438 @x741 $x169) (or (not $x777) $x1021))))
+(let ((@x1026 (|unit-resolution| @x1025 (|unit-resolution| (lemma @x893 (or $x777 (not $x770))) @x1018 $x777) $x1021)))
+(let ((@x1029 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x361 (>= (+ ?x44 (* (~ 1) ?x45)) 0))) (|unit-resolution| (|def-axiom| (or $x363 $x46)) @x741 $x46) (>= (+ ?x44 (* (~ 1) ?x45)) 0))))
+(let ((?x744 (+ ?x43 ?x712 (* (~ 2) ?x730))))
+(let (($x742 (= ?x744 0)))
+(let ((@x1032 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x742) (>= ?x744 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x742)) @x108 $x742) (>= ?x744 0))))
+(let ((?x713 (+ ?x44 ?x712)))
+(let (($x714 (= ?x713 0)))
+(let (($x719 (or $x633 $x714)))
+(let ((?x686 (ite $x440 (* (~ 1) (mod ?x145 (* (~ 1) 2))) ?x685)))
+(let ((?x687 (ite $x439 ?x43 ?x686)))
+(let (($x688 (= ?x44 ?x687)))
+(let ((@x694 (monotonicity (monotonicity @x457 (= (mod ?x145 (* (~ 1) 2)) (mod ?x145 (~ 2)))) (= (* (~ 1) (mod ?x145 (* (~ 1) 2))) (* (~ 1) (mod ?x145 (~ 2)))))))
+(let ((@x697 (monotonicity @x451 @x694 (= ?x686 (ite false (* (~ 1) (mod ?x145 (~ 2))) ?x685)))))
+(let ((@x701 (trans @x697 (rewrite (= (ite false (* (~ 1) (mod ?x145 (~ 2))) ?x685) ?x685)) (= ?x686 ?x685))))
+(let ((@x708 (trans (monotonicity @x449 @x701 (= ?x687 (ite false ?x43 ?x685))) (rewrite (= (ite false ?x43 ?x685) ?x685)) (= ?x687 ?x685))))
+(let ((@x718 (trans (monotonicity @x708 (= $x688 (= ?x44 ?x685))) (rewrite (= (= ?x44 ?x685) $x714)) (= $x688 $x714))))
+(let ((@x726 (trans (monotonicity @x718 (= (or $x633 $x688) $x719)) (rewrite (= $x719 $x719)) (= (or $x633 $x688) $x719))))
+(let ((@x1035 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x714) (>= ?x713 0))) (|unit-resolution| (mp ((_ |quant-inst| (|eval_dioph$| |ks$| ?x42) 2) (or $x633 $x688)) @x726 $x719) @x423 $x714) (>= ?x713 0))))
+(let ((@x992 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x586) (>= ?x585 0))) (|unit-resolution| ((_ |quant-inst| |ks$| |xs$|) (or (not $x384) $x586)) @x389 $x586) (>= ?x585 0))))
+(let ((?x773 (+ ?x44 (* (~ 1) ?x45))))
+(let (($x774 (<= ?x773 0)))
+(let ((@x1010 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x361 $x774)) (|unit-resolution| (|def-axiom| (or $x363 $x46)) @x741 $x46) $x774)))
+(let ((@x1014 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x362 $x771)) (|unit-resolution| (|def-axiom| (or $x363 $x152)) @x741 $x152) $x771)))
+(let ((@x963 (|unit-resolution| ((_ |th-lemma| arith) (or false (not (>= (mod (+ |l$| ?x43) 2) 2)))) @x108 (not (>= (mod (+ |l$| ?x43) 2) 2)))))
+(let ((@x748 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x628) (<= ?x627 0))) (|unit-resolution| (mp ((_ |quant-inst| |l$| 2) (or $x633 $x602)) @x641 $x634) @x423 $x628) (<= ?x627 0))))
+(let ((@x932 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x742) (<= ?x744 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x742)) @x108 $x742) (<= ?x744 0))))
+(let ((@x852 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x657) (<= ?x659 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x657)) @x108 $x657) (<= ?x659 0))))
+(let ((@x937 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x714) (<= ?x713 0))) (|unit-resolution| (mp ((_ |quant-inst| (|eval_dioph$| |ks$| ?x42) 2) (or $x633 $x688)) @x726 $x719) @x423 $x714) (<= ?x713 0))))
+(let ((@x954 (hypothesis $x771)))
+(let ((@x957 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x480) (>= ?x479 0))) @x885 (>= ?x479 0))))
+(let ((@x960 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x517) (<= ?x520 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x517)) @x108 $x517) (<= ?x520 0))))
+(let ((@x515 ((_ |th-lemma| arith farkas 1 -2 -2 -2 1 1 1 1 1 1) @x960 @x957 @x954 (hypothesis $x737) @x937 @x852 @x932 (hypothesis $x774) @x748 @x963 false)))
+(let ((@x1015 (|unit-resolution| (lemma @x515 (or (not $x737) (not $x771) (not $x774))) @x1014 @x1010 (not $x737))))
+(let ((@x1037 (|unit-resolution| @x1015 ((_ |th-lemma| arith) @x992 @x1035 @x1032 @x1029 @x1026 @x950 @x945 $x737) false)))
+(let ((@x1038 (lemma @x1037 $x363)))
+(let ((@x434 (|unit-resolution| (|def-axiom| (or $x41 $x364 (not $x370))) @x375 (or $x41 $x364))))
+(let ((@x1120 (|unit-resolution| @x434 @x1038 $x41)))
+(let ((@x1125 ((_ |th-lemma| arith farkas 2 2 1 1 1 1) (hypothesis (not $x771)) @x889 @x892 @x876 @x883 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x169 $x778)) @x1120 $x778) false)))
+(let ((@x1048 ((_ |th-lemma| arith farkas -1 1 1 -2 -2 1) @x992 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x169 $x777)) @x1120 $x777) @x960 @x957 (hypothesis (not $x770)) @x963 false)))
+(let ((?x587 (|mod$| ?x39 2)))
+(let (($x588 (= ?x587 ?x44)))
+(let (($x377 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(!(= (|mod$| (|eval_dioph$| ?v0 ?v1) 2) (|mod$| (|eval_dioph$| ?v0 (|map$| |uu$| ?v1)) 2)) :pattern ( (|eval_dioph$| ?v0 (|map$| |uu$| ?v1)) )))
+))
+(let (($x30 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(= (|mod$| (|eval_dioph$| ?v0 ?v1) 2) (|mod$| (|eval_dioph$| ?v0 (|map$| |uu$| ?v1)) 2)))
+))
+(let (($x29 (= (|mod$| ?x24 2) (|mod$| ?x27 2))))
+(let ((@x330 (|mp~| (asserted $x30) (|nnf-pos| (refl (|~| $x29 $x29)) (|~| $x30 $x30)) $x30)))
+(let ((@x382 (mp @x330 (|quant-intro| (refl (= $x29 $x29)) (= $x30 $x377)) $x377)))
+(let ((@x1104 (symm (|unit-resolution| ((_ |quant-inst| |ks$| |xs$|) (or (not $x377) $x588)) @x382 $x588) (= ?x44 ?x587))))
+(let ((@x763 (|unit-resolution| (hypothesis $x361) (trans @x1104 (monotonicity @x1120 (= ?x587 ?x45)) $x46) false)))
+(let ((@x1050 (|unit-resolution| (|unit-resolution| (|def-axiom| (or $x364 $x361 $x362)) @x1038 $x363) (lemma @x763 $x46) $x362)))
+(|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x152 (not $x770) (not $x771))) @x1050 (lemma @x1048 $x770) (lemma @x1125 $x771) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+
+d4d0e08ac1741a77a8448ec3a55e48fb2a240ee9 62 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x32 (|collect$| |uu$|)))
+(let ((?x33 (|sup$| ?x32)))
+(let (($x38 (|less_eq$| ?x33 ?x33)))
+(let (($x39 (not $x38)))
+(let ((@x117 (asserted $x39)))
+(let ((?x34 (|collect$| |uua$|)))
+(let ((?x35 (|sup$| ?x34)))
+(let (($x37 (|less_eq$| ?x35 ?x33)))
+(let ((@x115 (asserted $x37)))
+(let (($x36 (|less_eq$| ?x33 ?x35)))
+(let ((@x114 (asserted $x36)))
+(let (($x159 (forall ((?v0 |A$|) (?v1 |A$|) (?v2 |A$|) )(!(let (($x29 (|less_eq$| ?v0 ?v2)))
+(let (($x27 (|less_eq$| ?v1 ?v2)))
+(let (($x136 (not $x27)))
+(let (($x26 (|less_eq$| ?v0 ?v1)))
+(let (($x135 (not $x26)))
+(or $x135 $x136 $x29)))))) :pattern ( (|less_eq$| ?v0 ?v1) (|less_eq$| ?v1 ?v2) )))
+))
+(let (($x154 (forall ((?v0 |A$|) (?v1 |A$|) (?v2 |A$|) )(let (($x29 (|less_eq$| ?v0 ?v2)))
+(let (($x27 (|less_eq$| ?v1 ?v2)))
+(let (($x136 (not $x27)))
+(let (($x26 (|less_eq$| ?v0 ?v1)))
+(let (($x135 (not $x26)))
+(or $x135 $x136 $x29)))))))
+))
+(let (($x29 (|less_eq$| ?2 ?0)))
+(let (($x27 (|less_eq$| ?1 ?0)))
+(let (($x136 (not $x27)))
+(let (($x26 (|less_eq$| ?2 ?1)))
+(let (($x135 (not $x26)))
+(let (($x149 (or $x135 $x136 $x29)))
+(let (($x111 (forall ((?v0 |A$|) (?v1 |A$|) (?v2 |A$|) )(let (($x29 (|less_eq$| ?v0 ?v2)))
+(let (($x27 (|less_eq$| ?v1 ?v2)))
+(let (($x26 (|less_eq$| ?v0 ?v1)))
+(let (($x28 (and $x26 $x27)))
+(let (($x106 (not $x28)))
+(or $x106 $x29)))))))
+))
+(let ((@x141 (monotonicity (rewrite (= (and $x26 $x27) (not (or $x135 $x136)))) (= (not (and $x26 $x27)) (not (not (or $x135 $x136)))))))
+(let ((@x145 (trans @x141 (rewrite (= (not (not (or $x135 $x136))) (or $x135 $x136))) (= (not (and $x26 $x27)) (or $x135 $x136)))))
+(let ((@x148 (monotonicity @x145 (= (or (not (and $x26 $x27)) $x29) (or (or $x135 $x136) $x29)))))
+(let ((@x153 (trans @x148 (rewrite (= (or (or $x135 $x136) $x29) $x149)) (= (or (not (and $x26 $x27)) $x29) $x149))))
+(let ((@x129 (refl (|~| (or (not (and $x26 $x27)) $x29) (or (not (and $x26 $x27)) $x29)))))
+(let (($x31 (forall ((?v0 |A$|) (?v1 |A$|) (?v2 |A$|) )(let (($x29 (|less_eq$| ?v0 ?v2)))
+(let (($x27 (|less_eq$| ?v1 ?v2)))
+(let (($x26 (|less_eq$| ?v0 ?v1)))
+(let (($x28 (and $x26 $x27)))
+(=> $x28 $x29))))))
+))
+(let ((@x110 (rewrite (= (=> (and $x26 $x27) $x29) (or (not (and $x26 $x27)) $x29)))))
+(let ((@x132 (|mp~| (mp (asserted $x31) (|quant-intro| @x110 (= $x31 $x111)) $x111) (|nnf-pos| @x129 (|~| $x111 $x111)) $x111)))
+(let ((@x164 (mp (mp @x132 (|quant-intro| @x153 (= $x111 $x154)) $x154) (|quant-intro| (refl (= $x149 $x149)) (= $x154 $x159)) $x159)))
+(let (($x166 (not $x37)))
+(let (($x165 (not $x36)))
+(let (($x170 (not $x159)))
+(let (($x171 (or $x170 $x165 $x166 $x38)))
+(let ((@x176 (mp ((_ |quant-inst| (|sup$| ?x32) (|sup$| ?x34) (|sup$| ?x32)) (or $x170 (or $x165 $x166 $x38))) (rewrite (= (or $x170 (or $x165 $x166 $x38)) $x171)) $x171)))
+(|unit-resolution| @x176 @x164 @x114 @x115 @x117 false)))))))))))))))))))))))))))))))))))))
+
+ce2ba5128c1bc3cef10c9328de9b15558b908319 25 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x51 (|pred$e| 1)))
+(let (($x52 (not $x51)))
+(let ((@x142 (asserted $x52)))
+(let (($x198 (forall ((?v0 Int) )(!(|pred$e| ?v0) :pattern ( (|pred$e| ?v0) )))
+))
+(let (($x139 (forall ((?v0 Int) )(|pred$e| ?v0))
+))
+(let (($x49 (forall ((?v0 Int) )(let (($x47 (or (|pred$d| (|cons$d| ?v0 |nil$d|)) (not (|pred$d| (|cons$d| ?v0 |nil$d|))))))
+(let (($x42 (|pred$e| ?v0)))
+(and $x42 $x47))))
+))
+(let (($x42 (|pred$e| ?0)))
+(let (($x47 (or (|pred$d| (|cons$d| ?0 |nil$d|)) (not (|pred$d| (|cons$d| ?0 |nil$d|))))))
+(let (($x48 (and $x42 $x47)))
+(let ((@x134 (monotonicity (rewrite (= $x47 true)) (= $x48 (and $x42 true)))))
+(let ((@x141 (|quant-intro| (trans @x134 (rewrite (= (and $x42 true) $x42)) (= $x48 $x42)) (= $x49 $x139))))
+(let ((@x168 (|mp~| (mp (asserted $x49) @x141 $x139) (|nnf-pos| (refl (|~| $x42 $x42)) (|~| $x139 $x139)) $x139)))
+(let ((@x203 (mp @x168 (|quant-intro| (refl (= $x42 $x42)) (= $x139 $x198)) $x198)))
+(let (($x207 (or (not $x198) $x51)))
+(let ((@x208 ((_ |quant-inst| 1) $x207)))
+(|unit-resolution| @x208 @x203 @x142 false))))))))))))))))))
+
--- a/src/HOL/SMT_Examples/SMT_Examples.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy Thu Mar 13 16:39:08 2014 +0100
@@ -11,38 +11,34 @@
declare [[smt_certificates = "SMT_Examples.certs"]]
declare [[smt_read_only_certificates = true]]
+declare [[smt2_certificates = "SMT_Examples.certs2"]]
+declare [[smt2_read_only_certificates = true]]
section {* Propositional and first-order logic *}
-lemma "True" by smt
-
-lemma "p \<or> \<not>p" by smt
-
-lemma "(p \<and> True) = p" by smt
-
-lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q" by smt
-
-lemma "(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)"
- by smt
-
-lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1" by smt
-
-lemma "P=P=P=P=P=P=P=P=P=P" by smt
+lemma "True" by smt2
+lemma "p \<or> \<not>p" by smt2
+lemma "(p \<and> True) = p" by smt2
+lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q" by smt2
+lemma "(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)" by smt2
+lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1" by smt2
+lemma "P = P = P = P = P = P = P = P = P = P" by smt2
lemma
- assumes "a | b | c | d"
- and "e | f | (a & d)"
- and "~(a | (c & ~c)) | b"
- and "~(b & (x | ~x)) | c"
- and "~(d | False) | c"
- and "~(c | (~p & (p | (q & ~q))))"
+ assumes "a \<or> b \<or> c \<or> d"
+ and "e \<or> f \<or> (a \<and> d)"
+ and "\<not> (a \<or> (c \<and> ~c)) \<or> b"
+ and "\<not> (b \<and> (x \<or> \<not> x)) \<or> c"
+ and "\<not> (d \<or> False) \<or> c"
+ and "\<not> (c \<or> (\<not> p \<and> (p \<or> (q \<and> \<not> q))))"
shows False
- using assms by smt
+ using assms by smt2
axiomatization symm_f :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" where
symm_f: "symm_f x y = symm_f y x"
-lemma "a = a \<and> symm_f a b = symm_f b a" by (smt symm_f)
+
+lemma "a = a \<and> symm_f a b = symm_f b a" by (smt2 symm_f)
(*
Taken from ~~/src/HOL/ex/SAT_Examples.thy.
@@ -53,253 +49,246 @@
and "~x30"
and "~x29"
and "~x59"
- and "x1 | x31 | x0"
- and "x2 | x32 | x1"
- and "x3 | x33 | x2"
- and "x4 | x34 | x3"
- and "x35 | x4"
- and "x5 | x36 | x30"
- and "x6 | x37 | x5 | x31"
- and "x7 | x38 | x6 | x32"
- and "x8 | x39 | x7 | x33"
- and "x9 | x40 | x8 | x34"
- and "x41 | x9 | x35"
- and "x10 | x42 | x36"
- and "x11 | x43 | x10 | x37"
- and "x12 | x44 | x11 | x38"
- and "x13 | x45 | x12 | x39"
- and "x14 | x46 | x13 | x40"
- and "x47 | x14 | x41"
- and "x15 | x48 | x42"
- and "x16 | x49 | x15 | x43"
- and "x17 | x50 | x16 | x44"
- and "x18 | x51 | x17 | x45"
- and "x19 | x52 | x18 | x46"
- and "x53 | x19 | x47"
- and "x20 | x54 | x48"
- and "x21 | x55 | x20 | x49"
- and "x22 | x56 | x21 | x50"
- and "x23 | x57 | x22 | x51"
- and "x24 | x58 | x23 | x52"
- and "x59 | x24 | x53"
- and "x25 | x54"
- and "x26 | x25 | x55"
- and "x27 | x26 | x56"
- and "x28 | x27 | x57"
- and "x29 | x28 | x58"
- and "~x1 | ~x31"
- and "~x1 | ~x0"
- and "~x31 | ~x0"
- and "~x2 | ~x32"
- and "~x2 | ~x1"
- and "~x32 | ~x1"
- and "~x3 | ~x33"
- and "~x3 | ~x2"
- and "~x33 | ~x2"
- and "~x4 | ~x34"
- and "~x4 | ~x3"
- and "~x34 | ~x3"
- and "~x35 | ~x4"
- and "~x5 | ~x36"
- and "~x5 | ~x30"
- and "~x36 | ~x30"
- and "~x6 | ~x37"
- and "~x6 | ~x5"
- and "~x6 | ~x31"
- and "~x37 | ~x5"
- and "~x37 | ~x31"
- and "~x5 | ~x31"
- and "~x7 | ~x38"
- and "~x7 | ~x6"
- and "~x7 | ~x32"
- and "~x38 | ~x6"
- and "~x38 | ~x32"
- and "~x6 | ~x32"
- and "~x8 | ~x39"
- and "~x8 | ~x7"
- and "~x8 | ~x33"
- and "~x39 | ~x7"
- and "~x39 | ~x33"
- and "~x7 | ~x33"
- and "~x9 | ~x40"
- and "~x9 | ~x8"
- and "~x9 | ~x34"
- and "~x40 | ~x8"
- and "~x40 | ~x34"
- and "~x8 | ~x34"
- and "~x41 | ~x9"
- and "~x41 | ~x35"
- and "~x9 | ~x35"
- and "~x10 | ~x42"
- and "~x10 | ~x36"
- and "~x42 | ~x36"
- and "~x11 | ~x43"
- and "~x11 | ~x10"
- and "~x11 | ~x37"
- and "~x43 | ~x10"
- and "~x43 | ~x37"
- and "~x10 | ~x37"
- and "~x12 | ~x44"
- and "~x12 | ~x11"
- and "~x12 | ~x38"
- and "~x44 | ~x11"
- and "~x44 | ~x38"
- and "~x11 | ~x38"
- and "~x13 | ~x45"
- and "~x13 | ~x12"
- and "~x13 | ~x39"
- and "~x45 | ~x12"
- and "~x45 | ~x39"
- and "~x12 | ~x39"
- and "~x14 | ~x46"
- and "~x14 | ~x13"
- and "~x14 | ~x40"
- and "~x46 | ~x13"
- and "~x46 | ~x40"
- and "~x13 | ~x40"
- and "~x47 | ~x14"
- and "~x47 | ~x41"
- and "~x14 | ~x41"
- and "~x15 | ~x48"
- and "~x15 | ~x42"
- and "~x48 | ~x42"
- and "~x16 | ~x49"
- and "~x16 | ~x15"
- and "~x16 | ~x43"
- and "~x49 | ~x15"
- and "~x49 | ~x43"
- and "~x15 | ~x43"
- and "~x17 | ~x50"
- and "~x17 | ~x16"
- and "~x17 | ~x44"
- and "~x50 | ~x16"
- and "~x50 | ~x44"
- and "~x16 | ~x44"
- and "~x18 | ~x51"
- and "~x18 | ~x17"
- and "~x18 | ~x45"
- and "~x51 | ~x17"
- and "~x51 | ~x45"
- and "~x17 | ~x45"
- and "~x19 | ~x52"
- and "~x19 | ~x18"
- and "~x19 | ~x46"
- and "~x52 | ~x18"
- and "~x52 | ~x46"
- and "~x18 | ~x46"
- and "~x53 | ~x19"
- and "~x53 | ~x47"
- and "~x19 | ~x47"
- and "~x20 | ~x54"
- and "~x20 | ~x48"
- and "~x54 | ~x48"
- and "~x21 | ~x55"
- and "~x21 | ~x20"
- and "~x21 | ~x49"
- and "~x55 | ~x20"
- and "~x55 | ~x49"
- and "~x20 | ~x49"
- and "~x22 | ~x56"
- and "~x22 | ~x21"
- and "~x22 | ~x50"
- and "~x56 | ~x21"
- and "~x56 | ~x50"
- and "~x21 | ~x50"
- and "~x23 | ~x57"
- and "~x23 | ~x22"
- and "~x23 | ~x51"
- and "~x57 | ~x22"
- and "~x57 | ~x51"
- and "~x22 | ~x51"
- and "~x24 | ~x58"
- and "~x24 | ~x23"
- and "~x24 | ~x52"
- and "~x58 | ~x23"
- and "~x58 | ~x52"
- and "~x23 | ~x52"
- and "~x59 | ~x24"
- and "~x59 | ~x53"
- and "~x24 | ~x53"
- and "~x25 | ~x54"
- and "~x26 | ~x25"
- and "~x26 | ~x55"
- and "~x25 | ~x55"
- and "~x27 | ~x26"
- and "~x27 | ~x56"
- and "~x26 | ~x56"
- and "~x28 | ~x27"
- and "~x28 | ~x57"
- and "~x27 | ~x57"
- and "~x29 | ~x28"
- and "~x29 | ~x58"
- and "~x28 | ~x58"
+ and "x1 \<or> x31 \<or> x0"
+ and "x2 \<or> x32 \<or> x1"
+ and "x3 \<or> x33 \<or> x2"
+ and "x4 \<or> x34 \<or> x3"
+ and "x35 \<or> x4"
+ and "x5 \<or> x36 \<or> x30"
+ and "x6 \<or> x37 \<or> x5 \<or> x31"
+ and "x7 \<or> x38 \<or> x6 \<or> x32"
+ and "x8 \<or> x39 \<or> x7 \<or> x33"
+ and "x9 \<or> x40 \<or> x8 \<or> x34"
+ and "x41 \<or> x9 \<or> x35"
+ and "x10 \<or> x42 \<or> x36"
+ and "x11 \<or> x43 \<or> x10 \<or> x37"
+ and "x12 \<or> x44 \<or> x11 \<or> x38"
+ and "x13 \<or> x45 \<or> x12 \<or> x39"
+ and "x14 \<or> x46 \<or> x13 \<or> x40"
+ and "x47 \<or> x14 \<or> x41"
+ and "x15 \<or> x48 \<or> x42"
+ and "x16 \<or> x49 \<or> x15 \<or> x43"
+ and "x17 \<or> x50 \<or> x16 \<or> x44"
+ and "x18 \<or> x51 \<or> x17 \<or> x45"
+ and "x19 \<or> x52 \<or> x18 \<or> x46"
+ and "x53 \<or> x19 \<or> x47"
+ and "x20 \<or> x54 \<or> x48"
+ and "x21 \<or> x55 \<or> x20 \<or> x49"
+ and "x22 \<or> x56 \<or> x21 \<or> x50"
+ and "x23 \<or> x57 \<or> x22 \<or> x51"
+ and "x24 \<or> x58 \<or> x23 \<or> x52"
+ and "x59 \<or> x24 \<or> x53"
+ and "x25 \<or> x54"
+ and "x26 \<or> x25 \<or> x55"
+ and "x27 \<or> x26 \<or> x56"
+ and "x28 \<or> x27 \<or> x57"
+ and "x29 \<or> x28 \<or> x58"
+ and "~x1 \<or> ~x31"
+ and "~x1 \<or> ~x0"
+ and "~x31 \<or> ~x0"
+ and "~x2 \<or> ~x32"
+ and "~x2 \<or> ~x1"
+ and "~x32 \<or> ~x1"
+ and "~x3 \<or> ~x33"
+ and "~x3 \<or> ~x2"
+ and "~x33 \<or> ~x2"
+ and "~x4 \<or> ~x34"
+ and "~x4 \<or> ~x3"
+ and "~x34 \<or> ~x3"
+ and "~x35 \<or> ~x4"
+ and "~x5 \<or> ~x36"
+ and "~x5 \<or> ~x30"
+ and "~x36 \<or> ~x30"
+ and "~x6 \<or> ~x37"
+ and "~x6 \<or> ~x5"
+ and "~x6 \<or> ~x31"
+ and "~x37 \<or> ~x5"
+ and "~x37 \<or> ~x31"
+ and "~x5 \<or> ~x31"
+ and "~x7 \<or> ~x38"
+ and "~x7 \<or> ~x6"
+ and "~x7 \<or> ~x32"
+ and "~x38 \<or> ~x6"
+ and "~x38 \<or> ~x32"
+ and "~x6 \<or> ~x32"
+ and "~x8 \<or> ~x39"
+ and "~x8 \<or> ~x7"
+ and "~x8 \<or> ~x33"
+ and "~x39 \<or> ~x7"
+ and "~x39 \<or> ~x33"
+ and "~x7 \<or> ~x33"
+ and "~x9 \<or> ~x40"
+ and "~x9 \<or> ~x8"
+ and "~x9 \<or> ~x34"
+ and "~x40 \<or> ~x8"
+ and "~x40 \<or> ~x34"
+ and "~x8 \<or> ~x34"
+ and "~x41 \<or> ~x9"
+ and "~x41 \<or> ~x35"
+ and "~x9 \<or> ~x35"
+ and "~x10 \<or> ~x42"
+ and "~x10 \<or> ~x36"
+ and "~x42 \<or> ~x36"
+ and "~x11 \<or> ~x43"
+ and "~x11 \<or> ~x10"
+ and "~x11 \<or> ~x37"
+ and "~x43 \<or> ~x10"
+ and "~x43 \<or> ~x37"
+ and "~x10 \<or> ~x37"
+ and "~x12 \<or> ~x44"
+ and "~x12 \<or> ~x11"
+ and "~x12 \<or> ~x38"
+ and "~x44 \<or> ~x11"
+ and "~x44 \<or> ~x38"
+ and "~x11 \<or> ~x38"
+ and "~x13 \<or> ~x45"
+ and "~x13 \<or> ~x12"
+ and "~x13 \<or> ~x39"
+ and "~x45 \<or> ~x12"
+ and "~x45 \<or> ~x39"
+ and "~x12 \<or> ~x39"
+ and "~x14 \<or> ~x46"
+ and "~x14 \<or> ~x13"
+ and "~x14 \<or> ~x40"
+ and "~x46 \<or> ~x13"
+ and "~x46 \<or> ~x40"
+ and "~x13 \<or> ~x40"
+ and "~x47 \<or> ~x14"
+ and "~x47 \<or> ~x41"
+ and "~x14 \<or> ~x41"
+ and "~x15 \<or> ~x48"
+ and "~x15 \<or> ~x42"
+ and "~x48 \<or> ~x42"
+ and "~x16 \<or> ~x49"
+ and "~x16 \<or> ~x15"
+ and "~x16 \<or> ~x43"
+ and "~x49 \<or> ~x15"
+ and "~x49 \<or> ~x43"
+ and "~x15 \<or> ~x43"
+ and "~x17 \<or> ~x50"
+ and "~x17 \<or> ~x16"
+ and "~x17 \<or> ~x44"
+ and "~x50 \<or> ~x16"
+ and "~x50 \<or> ~x44"
+ and "~x16 \<or> ~x44"
+ and "~x18 \<or> ~x51"
+ and "~x18 \<or> ~x17"
+ and "~x18 \<or> ~x45"
+ and "~x51 \<or> ~x17"
+ and "~x51 \<or> ~x45"
+ and "~x17 \<or> ~x45"
+ and "~x19 \<or> ~x52"
+ and "~x19 \<or> ~x18"
+ and "~x19 \<or> ~x46"
+ and "~x52 \<or> ~x18"
+ and "~x52 \<or> ~x46"
+ and "~x18 \<or> ~x46"
+ and "~x53 \<or> ~x19"
+ and "~x53 \<or> ~x47"
+ and "~x19 \<or> ~x47"
+ and "~x20 \<or> ~x54"
+ and "~x20 \<or> ~x48"
+ and "~x54 \<or> ~x48"
+ and "~x21 \<or> ~x55"
+ and "~x21 \<or> ~x20"
+ and "~x21 \<or> ~x49"
+ and "~x55 \<or> ~x20"
+ and "~x55 \<or> ~x49"
+ and "~x20 \<or> ~x49"
+ and "~x22 \<or> ~x56"
+ and "~x22 \<or> ~x21"
+ and "~x22 \<or> ~x50"
+ and "~x56 \<or> ~x21"
+ and "~x56 \<or> ~x50"
+ and "~x21 \<or> ~x50"
+ and "~x23 \<or> ~x57"
+ and "~x23 \<or> ~x22"
+ and "~x23 \<or> ~x51"
+ and "~x57 \<or> ~x22"
+ and "~x57 \<or> ~x51"
+ and "~x22 \<or> ~x51"
+ and "~x24 \<or> ~x58"
+ and "~x24 \<or> ~x23"
+ and "~x24 \<or> ~x52"
+ and "~x58 \<or> ~x23"
+ and "~x58 \<or> ~x52"
+ and "~x23 \<or> ~x52"
+ and "~x59 \<or> ~x24"
+ and "~x59 \<or> ~x53"
+ and "~x24 \<or> ~x53"
+ and "~x25 \<or> ~x54"
+ and "~x26 \<or> ~x25"
+ and "~x26 \<or> ~x55"
+ and "~x25 \<or> ~x55"
+ and "~x27 \<or> ~x26"
+ and "~x27 \<or> ~x56"
+ and "~x26 \<or> ~x56"
+ and "~x28 \<or> ~x27"
+ and "~x28 \<or> ~x57"
+ and "~x27 \<or> ~x57"
+ and "~x29 \<or> ~x28"
+ and "~x29 \<or> ~x58"
+ and "~x28 \<or> ~x58"
shows False
- using assms by smt
+ using assms by smt (* smt2 FIXME: THM 0 *)
lemma "\<forall>x::int. P x \<longrightarrow> (\<forall>y::int. P x \<or> P y)"
- by smt
+ by smt2
lemma
assumes "(\<forall>x y. P x y = x)"
shows "(\<exists>y. P x y) = P x c"
- using assms by smt
+ using assms by smt (* smt2 FIXME: Option *)
lemma
assumes "(\<forall>x y. P x y = x)"
and "(\<forall>x. \<exists>y. P x y) = (\<forall>x. P x c)"
shows "(EX y. P x y) = P x c"
- using assms by smt
+ using assms by smt (* smt2 FIXME: Option *)
lemma
assumes "if P x then \<not>(\<exists>y. P y) else (\<forall>y. \<not>P y)"
shows "P x \<longrightarrow> P y"
- using assms by smt
+ using assms by smt2
section {* Arithmetic *}
subsection {* Linear arithmetic over integers and reals *}
-lemma "(3::int) = 3" by smt
-
-lemma "(3::real) = 3" by smt
-
-lemma "(3 :: int) + 1 = 4" by smt
-
-lemma "x + (y + z) = y + (z + (x::int))" by smt
-
-lemma "max (3::int) 8 > 5" by smt
-
-lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt
-
-lemma "P ((2::int) < 3) = P True" by smt
-
-lemma "x + 3 \<ge> 4 \<or> x < (1::int)" by smt
+lemma "(3::int) = 3" by smt2
+lemma "(3::real) = 3" by smt2
+lemma "(3 :: int) + 1 = 4" by smt2
+lemma "x + (y + z) = y + (z + (x::int))" by smt2
+lemma "max (3::int) 8 > 5" by smt2
+lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt2
+lemma "P ((2::int) < 3) = P True" by smt2
+lemma "x + 3 \<ge> 4 \<or> x < (1::int)" by smt2
lemma
assumes "x \<ge> (3::int)" and "y = x + 4"
shows "y - x > 0"
- using assms by smt
+ using assms by smt2
-lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt
+lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt2
lemma
fixes x :: real
assumes "3 * x + 7 * a < 4" and "3 < 2 * x"
shows "a < 0"
- using assms by smt
+ using assms by smt2
-lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)" by smt
+lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)" by smt2
lemma "
- (n < m & m < n') | (n < m & m = n') | (n < n' & n' < m) |
- (n = n' & n' < m) | (n = m & m < n') |
- (n' < m & m < n) | (n' < m & m = n) |
- (n' < n & n < m) | (n' = n & n < m) | (n' = m & m < n) |
- (m < n & n < n') | (m < n & n' = n) | (m < n' & n' < n) |
- (m = n & n < n') | (m = n' & n' < n) |
- (n' = m & m = (n::int))"
- by smt
+ (n < m \<and> m < n') \<or> (n < m \<and> m = n') \<or> (n < n' \<and> n' < m) \<or>
+ (n = n' \<and> n' < m) \<or> (n = m \<and> m < n') \<or>
+ (n' < m \<and> m < n) \<or> (n' < m \<and> m = n) \<or>
+ (n' < n \<and> n < m) \<or> (n' = n \<and> n < m) \<or> (n' = m \<and> m < n) \<or>
+ (m < n \<and> n < n') \<or> (m < n \<and> n' = n) \<or> (m < n' \<and> n' < n) \<or>
+ (m = n \<and> n < n') \<or> (m = n' \<and> n' < n) \<or>
+ (n' = m \<and> m = (n::int))"
+ by smt2
text{*
The following example was taken from HOL/ex/PresburgerEx.thy, where it says:
@@ -320,220 +309,197 @@
lemma "\<lbrakk> x3 = abs x2 - x1; x4 = abs x3 - x2; x5 = abs x4 - x3;
x6 = abs x5 - x4; x7 = abs x6 - x5; x8 = abs x7 - x6;
x9 = abs x8 - x7; x10 = abs x9 - x8; x11 = abs x10 - x9 \<rbrakk>
- \<Longrightarrow> x1 = x10 & x2 = (x11::int)"
- by smt
+ \<Longrightarrow> x1 = x10 \<and> x2 = (x11::int)"
+ by smt2
-lemma "let P = 2 * x + 1 > x + (x::real) in P \<or> False \<or> P" by smt
+lemma "let P = 2 * x + 1 > x + (x::real) in P \<or> False \<or> P" by smt2
lemma "x + (let y = x mod 2 in 2 * y + 1) \<ge> x + (1::int)"
- using [[z3_with_extensions]]
- by smt
+ using [[z3_new_extensions]] by smt2
lemma "x + (let y = x mod 2 in y + y) < x + (3::int)"
- using [[z3_with_extensions]]
- by smt
+ using [[z3_new_extensions]] by smt2
lemma
assumes "x \<noteq> (0::real)"
- shows "x + x \<noteq> (let P = (abs x > 1) in if P \<or> \<not>P then 4 else 2) * x"
- using assms by smt
+ shows "x + x \<noteq> (let P = (abs x > 1) in if P \<or> \<not> P then 4 else 2) * x"
+ using assms [[z3_new_extensions]] by smt2
lemma
assumes "(n + m) mod 2 = 0" and "n mod 4 = 3"
- shows "n mod 2 = 1 & m mod 2 = (1::int)"
- using assms [[z3_with_extensions]] by smt
-
+ shows "n mod 2 = 1 \<and> m mod 2 = (1::int)"
+ using assms [[z3_new_extensions]] by smt2
subsection {* Linear arithmetic with quantifiers *}
-lemma "~ (\<exists>x::int. False)" by smt
-
-lemma "~ (\<exists>x::real. False)" by smt
+lemma "~ (\<exists>x::int. False)" by smt2
+lemma "~ (\<exists>x::real. False)" by smt2
lemma "\<exists>x::int. 0 < x"
using [[smt_oracle=true]] (* no Z3 proof *)
- by smt
+ by smt (* smt2 FIXME: requires Z3 4.3.1 *)
lemma "\<exists>x::real. 0 < x"
using [[smt_oracle=true]] (* no Z3 proof *)
- by smt
+ by smt (* smt2 FIXME: requires Z3 4.3.1 *)
lemma "\<forall>x::int. \<exists>y. y > x"
using [[smt_oracle=true]] (* no Z3 proof *)
- by smt
-
-lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt
-
-lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0" by smt
-
-lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)" by smt
-
-lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)" by smt
-
-lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2" by smt
-
-lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x" by smt
+ by smt (* smt2 FIXME: requires Z3 4.3.1 *)
-lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True" by smt
-
-lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)" by smt
-
-lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt
-
-lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y" by smt
-
-lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x" by smt
-
-lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0" by smt
-
-lemma "\<forall>x::int. SMT.trigger [[SMT.pat x]] (x < a \<longrightarrow> 2 * x < 2 * a)" by smt
-
-lemma "\<forall>(a::int) b::int. 0 < b \<or> b < 1" by smt
+lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt2
+lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0" by smt2
+lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)" by smt2
+lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)" by smt2
+lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2" by smt2
+lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x" by smt2
+lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True" by smt (* smt2 FIXME: requires Z3 4.3.1 *)
+lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)" by smt (* smt2 FIXME: requires Z3 4.3.1 *)
+lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt2
+lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y" by smt2
+lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x" by smt2
+lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0" by smt (* smt2 FIXME: requires Z3 4.3.1 *)
+lemma "\<forall>x::int. SMT2.trigger [[SMT2.pat x]] (x < a \<longrightarrow> 2 * x < 2 * a)" by smt2
+lemma "\<forall>(a::int) b::int. 0 < b \<or> b < 1" by smt2
subsection {* Non-linear arithmetic over integers and reals *}
lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
- using [[smt_oracle, z3_with_extensions]]
- by smt
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2
lemma "(a::int) * (x + 1 + y) = a * x + a * (y + 1)"
- using [[z3_with_extensions]]
- by smt
+ using [[z3_new_extensions]]
+ by smt2
lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)"
- using [[z3_with_extensions]]
- by smt
+ using [[z3_new_extensions]]
+ by smt2
lemma
"(U::int) + (1 + p) * (b + e) + p * d =
U + (2 * (1 + p) * (b + e) + (1 + p) * d + d * p) - (1 + p) * (b + d + e)"
- using [[z3_with_extensions]]
- by smt
+ using [[z3_new_extensions]] by smt2
-lemma [z3_rule]:
+lemma [z3_rule, z3_new_rule]:
fixes x :: "int"
assumes "x * y \<le> 0" and "\<not> y \<le> 0" and "\<not> x \<le> 0"
shows False
using assms by (metis mult_le_0_iff)
lemma "x * y \<le> (0 :: int) \<Longrightarrow> x \<le> 0 \<or> y \<le> 0"
- using [[z3_with_extensions]]
- by smt
-
+ using [[z3_with_extensions]] [[z3_new_extensions]]
+ by smt (* smt2 FIXME: "th-lemma" tactic fails *)
subsection {* Linear arithmetic for natural numbers *}
-lemma "2 * (x::nat) ~= 1" by smt
+lemma "2 * (x::nat) ~= 1" by smt2
-lemma "a < 3 \<Longrightarrow> (7::nat) > 2 * a" by smt
+lemma "a < 3 \<Longrightarrow> (7::nat) > 2 * a" by smt2
-lemma "let x = (1::nat) + y in x - y > 0 * x" by smt
+lemma "let x = (1::nat) + y in x - y > 0 * x" by smt2
lemma
"let x = (1::nat) + y in
let P = (if x > 0 then True else False) in
False \<or> P = (x - 1 = y) \<or> (\<not>P \<longrightarrow> False)"
- by smt
+ by smt2
-lemma "int (nat \<bar>x::int\<bar>) = \<bar>x\<bar>" by smt
+lemma "int (nat \<bar>x::int\<bar>) = \<bar>x\<bar>" by smt2
definition prime_nat :: "nat \<Rightarrow> bool" where
"prime_nat p = (1 < p \<and> (\<forall>m. m dvd p --> m = 1 \<or> m = p))"
-lemma "prime_nat (4*m + 1) \<Longrightarrow> m \<ge> (1::nat)" by (smt prime_nat_def)
+lemma "prime_nat (4*m + 1) \<Longrightarrow> m \<ge> (1::nat)" by (smt2 prime_nat_def)
section {* Pairs *}
lemma "fst (x, y) = a \<Longrightarrow> x = a"
- using fst_conv
- by smt
+ using fst_conv by smt2
lemma "p1 = (x, y) \<and> p2 = (y, x) \<Longrightarrow> fst p1 = snd p2"
- using fst_conv snd_conv
- by smt
+ using fst_conv snd_conv by smt2
section {* Higher-order problems and recursion *}
lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> (f (i1 := v1, i2 := v2)) i = f i"
- using fun_upd_same fun_upd_apply
- by smt
+ using fun_upd_same fun_upd_apply by smt2
lemma "(f g (x::'a::type) = (g x \<and> True)) \<or> (f g x = True) \<or> (g x = True)"
- by smt
+ by smt2
-lemma "id x = x \<and> id True = True" by (smt id_def)
+lemma "id x = x \<and> id True = True"
+ by (smt id_def) (* smt2 FIXME: Option *)
lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> ((f (i1 := v1)) (i2 := v2)) i = f i"
- using fun_upd_same fun_upd_apply
- by smt
+ using fun_upd_same fun_upd_apply by smt2
lemma
"f (\<exists>x. g x) \<Longrightarrow> True"
"f (\<forall>x. g x) \<Longrightarrow> True"
- by smt+
-
-lemma True using let_rsp by smt
+ by smt2+
-lemma "le = op \<le> \<Longrightarrow> le (3::int) 42" by smt
-
-lemma "map (\<lambda>i::nat. i + 1) [0, 1] = [1, 2]" by (smt list.map)
-
-
-lemma "(ALL x. P x) | ~ All P" by smt
+lemma True using let_rsp by smt2
+lemma "le = op \<le> \<Longrightarrow> le (3::int) 42" by smt2
+lemma "map (\<lambda>i::nat. i + 1) [0, 1] = [1, 2]" by (smt2 list.map)
+lemma "(ALL x. P x) \<or> ~ All P" by smt2
fun dec_10 :: "nat \<Rightarrow> nat" where
"dec_10 n = (if n < 10 then n else dec_10 (n - 10))"
-lemma "dec_10 (4 * dec_10 4) = 6" by (smt dec_10.simps)
+lemma "dec_10 (4 * dec_10 4) = 6" by (smt2 dec_10.simps)
axiomatization
eval_dioph :: "int list \<Rightarrow> nat list \<Rightarrow> int"
- where
+where
eval_dioph_mod:
"eval_dioph ks xs mod int n = eval_dioph ks (map (\<lambda>x. x mod n) xs) mod int n"
- and
+and
eval_dioph_div_mult:
"eval_dioph ks (map (\<lambda>x. x div n) xs) * int n +
eval_dioph ks (map (\<lambda>x. x mod n) xs) = eval_dioph ks xs"
+
lemma
"(eval_dioph ks xs = l) =
(eval_dioph ks (map (\<lambda>x. x mod 2) xs) mod 2 = l mod 2 \<and>
eval_dioph ks (map (\<lambda>x. x div 2) xs) =
(l - eval_dioph ks (map (\<lambda>x. x mod 2) xs)) div 2)"
- using [[smt_oracle=true]] (*FIXME*)
- using [[z3_with_extensions]]
- by (smt eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
+ using [[smt2_oracle=true]] (*FIXME*)
+ using [[z3_new_extensions]]
+ by (smt2 eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
context complete_lattice
begin
lemma
- assumes "Sup { a | i::bool . True } \<le> Sup { b | i::bool . True }"
- and "Sup { b | i::bool . True } \<le> Sup { a | i::bool . True }"
- shows "Sup { a | i::bool . True } \<le> Sup { a | i::bool . True }"
- using assms by (smt order_trans)
+ assumes "Sup {a | i::bool. True} \<le> Sup {b | i::bool. True}"
+ and "Sup {b | i::bool. True} \<le> Sup {a | i::bool. True}"
+ shows "Sup {a | i::bool. True} \<le> Sup {a | i::bool. True}"
+ using assms by (smt2 order_trans)
end
-
section {* Monomorphization examples *}
definition Pred :: "'a \<Rightarrow> bool" where "Pred x = True"
-lemma poly_Pred: "Pred x \<and> (Pred [x] \<or> \<not>Pred[x])" by (simp add: Pred_def)
-lemma "Pred (1::int)" by (smt poly_Pred)
+
+lemma poly_Pred: "Pred x \<and> (Pred [x] \<or> \<not> Pred [x])" by (simp add: Pred_def)
+
+lemma "Pred (1::int)" by (smt2 poly_Pred)
axiomatization g :: "'a \<Rightarrow> nat"
axiomatization where
g1: "g (Some x) = g [x]" and
g2: "g None = g []" and
g3: "g xs = length xs"
-lemma "g (Some (3::int)) = g (Some True)" by (smt g1 g2 g3 list.size)
+
+lemma "g (Some (3::int)) = g (Some True)" by (smt g1 g2 g3 list.size) (* smt2 FIXME: Option *)
end
--- a/src/HOL/SMT_Examples/SMT_Tests.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/SMT_Examples/SMT_Tests.thy Thu Mar 13 16:39:08 2014 +0100
@@ -9,11 +9,11 @@
begin
smt_status
+smt2_status
text {* Most examples are taken from various Isabelle theories and from HOL4. *}
-
section {* Propositional logic *}
lemma
@@ -24,7 +24,7 @@
"True \<or> False"
"False \<longrightarrow> True"
"\<not>(False \<longleftrightarrow> True)"
- by smt+
+ by smt2+
lemma
"P \<or> \<not>P"
@@ -63,7 +63,7 @@
"\<not>(P \<longleftrightarrow> \<not>P)"
"(P \<longrightarrow> Q) \<longleftrightarrow> (\<not>Q \<longrightarrow> \<not>P)"
"P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P"
- by smt+
+ by smt2+
lemma
"(if P then Q1 else Q2) \<longleftrightarrow> ((P \<longrightarrow> Q1) \<and> (\<not>P \<longrightarrow> Q2))"
@@ -72,15 +72,14 @@
"(if P1 \<and> P2 then Q1 else Q2) \<longleftrightarrow> (if P1 then if P2 then Q1 else Q2 else Q2)"
"(P1 \<longrightarrow> (if P2 then Q1 else Q2)) \<longleftrightarrow>
(if P1 \<longrightarrow> P2 then P1 \<longrightarrow> Q1 else P1 \<longrightarrow> Q2)"
- by smt+
+ by smt2+
lemma
"case P of True \<Rightarrow> P | False \<Rightarrow> \<not>P"
"case P of False \<Rightarrow> \<not>P | True \<Rightarrow> P"
"case \<not>P of True \<Rightarrow> \<not>P | False \<Rightarrow> P"
"case P of True \<Rightarrow> (Q \<longrightarrow> P) | False \<Rightarrow> (P \<longrightarrow> Q)"
- by smt+
-
+ by smt2+
section {* First-order logic with equality *}
@@ -93,7 +92,7 @@
"x = y \<longrightarrow> g x y = g y x"
"f (f x) = x \<and> f (f (f (f (f x)))) = x \<longrightarrow> f x = x"
"((if a then b else c) = d) = ((a \<longrightarrow> (b = d)) \<and> (\<not> a \<longrightarrow> (c = d)))"
- by smt+
+ by smt2+
lemma
"\<forall>x. x = x"
@@ -106,12 +105,11 @@
"(\<forall>x. P x \<longrightarrow> P (f x)) \<and> P d \<longrightarrow> P (f(f(f(d))))"
"(\<forall>x y. s x y = s y x) \<longrightarrow> a = a \<and> s a b = s b a"
"(\<forall>s. q s \<longrightarrow> r s) \<and> \<not>r s \<and> (\<forall>s. \<not>r s \<and> \<not>q s \<longrightarrow> p t \<or> q t) \<longrightarrow> p t \<or> r t"
- by smt+
+ by smt2+
lemma
"(\<forall>x. P x) \<and> R \<longleftrightarrow> (\<forall>x. P x \<and> R)"
- using [[smt_oracle]] by smt
- (* BUG: Z3 proof parser (line 34): unknown function symbol: "S2!val!0" *)
+ by smt2
lemma
"\<exists>x. x = x"
@@ -120,7 +118,7 @@
"(\<exists>x. P x) \<and> R \<longleftrightarrow> (\<exists>x. P x \<and> R)"
"(\<exists>x y z. S x z) \<longleftrightarrow> (\<exists>x z. S x z)"
"\<not>((\<exists>x. \<not>P x) \<and> ((\<exists>x. P x) \<or> (\<exists>x. P x \<and> Q x)) \<and> \<not>(\<exists>x. P x))"
- by smt+
+ by smt2+
lemma
"\<exists>x y. x = y"
@@ -129,8 +127,7 @@
"\<exists>x. P x \<longrightarrow> P a \<and> P b"
"\<exists>x. (\<exists>y. P y) \<longrightarrow> P x"
"(\<exists>x. Q \<longrightarrow> P x) \<longleftrightarrow> (Q \<longrightarrow> (\<exists>x. P x))"
- using [[smt_oracle]] by smt+
- (* BUG: Z3 proof parser (line 34): unknown function symbol: "S2!val!0" *)
+ oops (* smt2 FIXME: requires Z3 4.3.1 *)
lemma
"(\<not>(\<exists>x. P x)) \<longleftrightarrow> (\<forall>x. \<not> P x)"
@@ -138,7 +135,7 @@
"(\<forall>x y. R x y = x) \<longrightarrow> (\<exists>y. R x y) = R x c"
"(if P x then \<not>(\<exists>y. P y) else (\<forall>y. \<not>P y)) \<longrightarrow> P x \<longrightarrow> P y"
"(\<forall>x y. R x y = x) \<and> (\<forall>x. \<exists>y. R x y) = (\<forall>x. R x c) \<longrightarrow> (\<exists>y. R x y) = R x c"
- by smt+
+ by smt+ (* smt2 FIXME: Option *)
lemma
"\<forall>x. \<exists>y. f x y = f x (g x)"
@@ -149,20 +146,20 @@
"(\<exists>x. \<forall>y. P x \<longleftrightarrow> P y) \<longrightarrow> ((\<exists>x. P x) \<longleftrightarrow> (\<forall>y. P y))"
"\<exists>z. P z \<longrightarrow> (\<forall>x. P x)"
"(\<exists>y. \<forall>x. R x y) \<longrightarrow> (\<forall>x. \<exists>y. R x y)"
- by smt+
+ by smt+ (* smt2 FIXME: requires Z3 4.3.1 *)
lemma
- "(\<exists>! x. P x) \<longrightarrow> (\<exists>x. P x)"
+ "(\<exists>!x. P x) \<longrightarrow> (\<exists>x. P x)"
"(\<exists>!x. P x) \<longleftrightarrow> (\<exists>x. P x \<and> (\<forall>y. y \<noteq> x \<longrightarrow> \<not>P y))"
"P a \<longrightarrow> (\<forall>x. P x \<longrightarrow> x = a) \<longrightarrow> (\<exists>!x. P x)"
"(\<exists>x. P x) \<and> (\<forall>x y. P x \<and> P y \<longrightarrow> x = y) \<longrightarrow> (\<exists>!x. P x)"
"(\<exists>!x. P x) \<and> (\<forall>x. P x \<and> (\<forall>y. P y \<longrightarrow> y = x) \<longrightarrow> R) \<longrightarrow> R"
- by smt+
+ by smt2+
lemma
"(\<forall>x\<in>M. P x) \<and> c \<in> M \<longrightarrow> P c"
"(\<exists>x\<in>M. P x) \<or> \<not>(P c \<and> c \<in> M)"
- by smt+
+ by smt2+
lemma
"let P = True in P"
@@ -173,65 +170,64 @@
"(let x = y1; z = y2 in R x z) \<longleftrightarrow> (let z = y2; x = y1 in R x z)"
"(let x = y1; z = y2 in R x z) \<longleftrightarrow> (let z = y1; x = y2 in R z x)"
"let P = (\<forall>x. Q x) in if P then P else \<not>P"
- by smt+
+ by smt2+
lemma
"a \<noteq> b \<and> a \<noteq> c \<and> b \<noteq> c \<and> (\<forall>x y. f x = f y \<longrightarrow> y = x) \<longrightarrow> f a \<noteq> f b"
- by smt
+ by smt2
lemma
"(\<forall>x y z. f x y = f x z \<longrightarrow> y = z) \<and> b \<noteq> c \<longrightarrow> f a b \<noteq> f a c"
"(\<forall>x y z. f x y = f z y \<longrightarrow> x = z) \<and> a \<noteq> d \<longrightarrow> f a b \<noteq> f d b"
- by smt+
+ by smt2+
section {* Guidance for quantifier heuristics: patterns and weights *}
lemma
- assumes "\<forall>x. SMT.trigger [[SMT.pat (f x)]] (f x = x)"
+ assumes "\<forall>x. SMT2.trigger [[SMT2.pat (f x)]] (f x = x)"
shows "f 1 = 1"
- using assms by smt
+ using assms using [[smt2_trace]] by smt2
lemma
- assumes "\<forall>x y. SMT.trigger [[SMT.pat (f x), SMT.pat (g y)]] (f x = g y)"
+ assumes "\<forall>x y. SMT2.trigger [[SMT2.pat (f x), SMT2.pat (g y)]] (f x = g y)"
shows "f a = g b"
- using assms by smt
+ using assms by smt2
lemma
- assumes "ALL x. SMT.trigger [[SMT.pat (P x)]] (P x --> Q x)"
+ assumes "ALL x. SMT2.trigger [[SMT2.pat (P x)]] (P x --> Q x)"
and "P t"
shows "Q t"
- using assms by smt
+ using assms by smt2
lemma
- assumes "ALL x. SMT.trigger [[SMT.pat (P x), SMT.pat (Q x)]]
+ assumes "ALL x. SMT2.trigger [[SMT2.pat (P x), SMT2.pat (Q x)]]
(P x & Q x --> R x)"
and "P t" and "Q t"
shows "R t"
- using assms by smt
+ using assms by smt2
lemma
- assumes "ALL x. SMT.trigger [[SMT.pat (P x)], [SMT.pat (Q x)]]
+ assumes "ALL x. SMT2.trigger [[SMT2.pat (P x)], [SMT2.pat (Q x)]]
((P x --> R x) & (Q x --> R x))"
and "P t | Q t"
shows "R t"
- using assms by smt
-
-lemma
- assumes "ALL x. SMT.trigger [[SMT.pat (P x)]] (SMT.weight 2 (P x --> Q x))"
- and "P t"
- shows "Q t"
- using assms by smt
+ using assms by smt2
lemma
- assumes "ALL x. SMT.weight 1 (P x --> Q x)"
+ assumes "ALL x. SMT2.trigger [[SMT2.pat (P x)]] (SMT2.weight 2 (P x --> Q x))"
and "P t"
shows "Q t"
- using assms by smt
+ using assms by smt2
+
+lemma
+ assumes "ALL x. SMT2.weight 1 (P x --> Q x)"
+ and "P t"
+ shows "Q t"
+ using assms by smt2
-
-section {* Meta logical connectives *}
+section {* Meta-logical connectives *}
lemma
"True \<Longrightarrow> True"
@@ -252,8 +248,7 @@
"(\<And>x y. h x y \<and> h y x) \<Longrightarrow> \<forall>x. h x x"
"(p \<or> q) \<and> \<not>p \<Longrightarrow> q"
"(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)"
- by smt+
-
+ by smt+ (* smt2 FIXME: Option *)
section {* Natural numbers *}
@@ -264,7 +259,7 @@
"(0::nat) < 1"
"(0::nat) \<le> 1"
"(123456789::nat) < 2345678901"
- by smt+
+ by smt2+
lemma
"Suc 0 = 1"
@@ -272,7 +267,7 @@
"x < Suc x"
"(Suc x = Suc y) = (x = y)"
"Suc (x + y) < Suc x + Suc y"
- by smt+
+ by smt2+
lemma
"(x::nat) + 0 = x"
@@ -280,15 +275,15 @@
"x + y = y + x"
"x + (y + z) = (x + y) + z"
"(x + y = 0) = (x = 0 \<and> y = 0)"
- by smt+
+ by smt2+
-lemma
+lemma
"(x::nat) - 0 = x"
"x < y \<longrightarrow> x - y = 0"
"x - y = 0 \<or> y - x = 0"
"(x - y) + y = (if x < y then y else x)"
- "x - y - z = x - (y + z)"
- by smt+
+ "x - y - z = x - (y + z)"
+ by smt2+
lemma
"(x::nat) * 0 = 0"
@@ -296,7 +291,7 @@
"x * 1 = x"
"1 * x = x"
"3 * x = x * 3"
- by smt+
+ by smt2+
lemma
"(0::nat) div 0 = 0"
@@ -310,8 +305,8 @@
"(3::nat) div 3 = 1"
"(x::nat) div 3 \<le> x"
"(x div 3 = x) = (x = 0)"
- using [[z3_with_extensions]]
- by smt+
+ using [[z3_new_extensions]]
+ by smt2+
lemma
"(0::nat) mod 0 = 0"
@@ -325,14 +320,14 @@
"(3::nat) mod 3 = 0"
"x mod 3 < 3"
"(x mod 3 = x) = (x < 3)"
- using [[z3_with_extensions]]
- by smt+
+ using [[z3_new_extensions]]
+ by smt2+
lemma
"(x::nat) = x div 1 * 1 + x mod 1"
"x = x div 3 * 3 + x mod 3"
- using [[z3_with_extensions]]
- by smt+
+ using [[z3_new_extensions]]
+ by smt2+
lemma
"min (x::nat) y \<le> x"
@@ -341,7 +336,7 @@
"z < x \<and> z < y \<longrightarrow> z < min x y"
"min x y = min y x"
"min x 0 = 0"
- by smt+
+ by smt2+
lemma
"max (x::nat) y \<ge> x"
@@ -350,7 +345,7 @@
"z > x \<and> z > y \<longrightarrow> z > max x y"
"max x y = max y x"
"max x 0 = x"
- by smt+
+ by smt2+
lemma
"0 \<le> (x::nat)"
@@ -366,8 +361,7 @@
"x \<le> y \<longrightarrow> y < z \<longrightarrow> x \<le> z"
"x < y \<longrightarrow> y < z \<longrightarrow> x < z"
"x < y \<and> y < z \<longrightarrow> \<not>(z < x)"
- by smt+
-
+ by smt2+
section {* Integers *}
@@ -382,7 +376,7 @@
"-123 + 345 < (567::int)"
"(123456789::int) < 2345678901"
"(-123456789::int) < 2345678901"
- by smt+
+ by smt2+
lemma
"(x::int) + 0 = x"
@@ -390,7 +384,7 @@
"x + y = y + x"
"x + (y + z) = (x + y) + z"
"(x + y = 0) = (x = -y)"
- by smt+
+ by smt2+
lemma
"(-1::int) = - 1"
@@ -398,16 +392,16 @@
"-(x::int) < 0 \<longleftrightarrow> x > 0"
"x > 0 \<longrightarrow> -x < 0"
"x < 0 \<longrightarrow> -x > 0"
- by smt+
+ by smt2+
-lemma
+lemma
"(x::int) - 0 = x"
"0 - x = -x"
"x < y \<longrightarrow> x - y < 0"
"x - y = -(y - x)"
"x - y = -y + x"
- "x - y - z = x - (y + z)"
- by smt+
+ "x - y - z = x - (y + z)"
+ by smt2+
lemma
"(x::int) * 0 = 0"
@@ -417,7 +411,7 @@
"x * -1 = -x"
"-1 * x = -x"
"3 * x = x * 3"
- by smt+
+ by smt2+
lemma
"(0::int) div 0 = 0"
@@ -444,8 +438,8 @@
"(-1::int) div -3 = 0"
"(-3::int) div -3 = 1"
"(-5::int) div -3 = 1"
- using [[z3_with_extensions]]
- by smt+
+ using [[z3_new_extensions]]
+ by smt2+
lemma
"(0::int) mod 0 = 0"
@@ -474,14 +468,14 @@
"(-5::int) mod -3 = -2"
"x mod 3 < 3"
"(x mod 3 = x) \<longrightarrow> (x < 3)"
- using [[z3_with_extensions]]
- by smt+
+ using [[z3_new_extensions]]
+ by smt2+
lemma
"(x::int) = x div 1 * 1 + x mod 1"
"x = x div 3 * 3 + x mod 3"
- using [[z3_with_extensions]]
- by smt+
+ using [[z3_new_extensions]]
+ by smt2+
lemma
"abs (x::int) \<ge> 0"
@@ -489,7 +483,7 @@
"(x \<ge> 0) = (abs x = x)"
"(x \<le> 0) = (abs x = -x)"
"abs (abs x) = abs x"
- by smt+
+ by smt2+
lemma
"min (x::int) y \<le> x"
@@ -498,7 +492,7 @@
"min x y = min y x"
"x \<ge> 0 \<longrightarrow> min x 0 = 0"
"min x y \<le> abs (x + y)"
- by smt+
+ by smt2+
lemma
"max (x::int) y \<ge> x"
@@ -507,7 +501,7 @@
"max x y = max y x"
"x \<ge> 0 \<longrightarrow> max x 0 = x"
"max x y \<ge> - abs x - abs y"
- by smt+
+ by smt2+
lemma
"0 < (x::int) \<and> x \<le> 1 \<longrightarrow> x = 1"
@@ -522,8 +516,7 @@
"x \<le> y \<longrightarrow> y < z \<longrightarrow> x \<le> z"
"x < y \<longrightarrow> y < z \<longrightarrow> x < z"
"x < y \<and> y < z \<longrightarrow> \<not>(z < x)"
- by smt+
-
+ by smt2+
section {* Reals *}
@@ -539,7 +532,7 @@
"-123 + 345 < (567::real)"
"(123456789::real) < 2345678901"
"(-123456789::real) < 2345678901"
- by smt+
+ by smt2+
lemma
"(x::real) + 0 = x"
@@ -547,7 +540,7 @@
"x + y = y + x"
"x + (y + z) = (x + y) + z"
"(x + y = 0) = (x = -y)"
- by smt+
+ by smt2+
lemma
"(-1::real) = - 1"
@@ -555,7 +548,7 @@
"-(x::real) < 0 \<longleftrightarrow> x > 0"
"x > 0 \<longrightarrow> -x < 0"
"x < 0 \<longrightarrow> -x > 0"
- by smt+
+ by smt2+
lemma
"(x::real) - 0 = x"
@@ -563,8 +556,8 @@
"x < y \<longrightarrow> x - y < 0"
"x - y = -(y - x)"
"x - y = -y + x"
- "x - y - z = x - (y + z)"
- by smt+
+ "x - y - z = x - (y + z)"
+ by smt2+
lemma
"(x::real) * 0 = 0"
@@ -574,7 +567,7 @@
"x * -1 = -x"
"-1 * x = -x"
"3 * x = x * 3"
- by smt+
+ by smt2+
lemma
"(1/2 :: real) < 1"
@@ -585,16 +578,16 @@
"(x::real) / 1 = x"
"x > 0 \<longrightarrow> x / 3 < x"
"x < 0 \<longrightarrow> x / 3 > x"
- using [[z3_with_extensions]]
- by smt+
+ using [[z3_new_extensions]]
+ by smt2+
lemma
"(3::real) * (x / 3) = x"
"(x * 3) / 3 = x"
"x > 0 \<longrightarrow> 2 * x / 3 < x"
"x < 0 \<longrightarrow> 2 * x / 3 > x"
- using [[z3_with_extensions]]
- by smt+
+ using [[z3_new_extensions]]
+ by smt2+
lemma
"abs (x::real) \<ge> 0"
@@ -602,7 +595,7 @@
"(x \<ge> 0) = (abs x = x)"
"(x \<le> 0) = (abs x = -x)"
"abs (abs x) = abs x"
- by smt+
+ by smt2+
lemma
"min (x::real) y \<le> x"
@@ -611,7 +604,7 @@
"min x y = min y x"
"x \<ge> 0 \<longrightarrow> min x 0 = 0"
"min x y \<le> abs (x + y)"
- by smt+
+ by smt2+
lemma
"max (x::real) y \<ge> x"
@@ -620,7 +613,7 @@
"max x y = max y x"
"x \<ge> 0 \<longrightarrow> max x 0 = x"
"max x y \<ge> - abs x - abs y"
- by smt+
+ by smt2+
lemma
"x \<le> (x::real)"
@@ -633,8 +626,7 @@
"x \<le> y \<longrightarrow> y < z \<longrightarrow> x \<le> z"
"x < y \<longrightarrow> y < z \<longrightarrow> x < z"
"x < y \<and> y < z \<longrightarrow> \<not>(z < x)"
- by smt+
-
+ by smt2+
section {* Datatypes, Records, and Typedefs *}
@@ -657,7 +649,7 @@
"(fst (x, y) = snd (x, y)) = (x = y)"
"(fst p = snd p) = (p = (snd p, fst p))"
using fst_conv snd_conv pair_collapse
- by smt+
+ by smt2+
lemma
"[x] \<noteq> Nil"
@@ -670,13 +662,13 @@
"hd (tl [x, y, z]) = y"
"tl (tl [x, y, z]) = [z]"
using list.sel(1,3) list.simps
- by smt+
+ by smt2+
lemma
"fst (hd [(a, b)]) = a"
"snd (hd [(a, b)]) = b"
using fst_conv snd_conv pair_collapse list.sel(1,3) list.simps
- by smt+
+ by smt2+
subsubsection {* Records *}
@@ -694,7 +686,7 @@
"cx p1 \<noteq> cx p2 \<longrightarrow> p1 \<noteq> p2"
"cy p1 \<noteq> cy p2 \<longrightarrow> p1 \<noteq> p2"
using point.simps
- by smt+
+ by smt2+
lemma
"cx \<lparr> cx = 3, cy = 4 \<rparr> = 3"
@@ -705,8 +697,7 @@
"p = \<lparr> cx = 3, cy = 4 \<rparr> \<longrightarrow> p \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p"
"p = \<lparr> cx = 3, cy = 4 \<rparr> \<longrightarrow> p \<lparr> cy := 4 \<rparr> \<lparr> cx := 3 \<rparr> = p"
using point.simps
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt+
+ by smt2+
lemma
"cy (p \<lparr> cx := a \<rparr>) = cy p"
@@ -722,7 +713,7 @@
"cy p1 \<noteq> cy p2 \<longrightarrow> p1 \<noteq> p2"
"black p1 \<noteq> black p2 \<longrightarrow> p1 \<noteq> p2"
using point.simps bw_point.simps
- by smt+
+ by smt2+
lemma
"cx \<lparr> cx = 3, cy = 4, black = b \<rparr> = 3"
@@ -738,8 +729,7 @@
"p = \<lparr> cx = 3, cy = 4, black = True \<rparr> \<longrightarrow>
p \<lparr> black := True \<rparr> \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p"
using point.simps bw_point.simps
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt+
+ by smt+ (* smt2 FIXME: Option *)
lemma
"\<lparr> cx = 3, cy = 4, black = b \<rparr> \<lparr> black := w \<rparr> = \<lparr> cx = 3, cy = 4, black = w \<rparr>"
@@ -773,8 +763,7 @@
"nplus n1 n2 = n3"
using n1_def n2_def n3_def nplus_def
using three_def' Rep_three Abs_three_inverse
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt+
+ by smt2+
subsection {* With support by the SMT solver (but without proofs) *}
@@ -795,8 +784,8 @@
"(fst (x, y) = snd (x, y)) = (x = y)"
"(fst p = snd p) = (p = (snd p, fst p))"
using fst_conv snd_conv pair_collapse
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- by smt+
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
lemma
"[x] \<noteq> Nil"
@@ -809,15 +798,15 @@
"hd (tl [x, y, z]) = y"
"tl (tl [x, y, z]) = [z]"
using list.sel(1,3)
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- by smt+
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
lemma
"fst (hd [(a, b)]) = a"
"snd (hd [(a, b)]) = b"
using fst_conv snd_conv pair_collapse list.sel(1,3)
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- by smt+
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
subsubsection {* Records *}
@@ -828,9 +817,8 @@
"cx p1 \<noteq> cx p2 \<longrightarrow> p1 \<noteq> p2"
"cy p1 \<noteq> cy p2 \<longrightarrow> p1 \<noteq> p2"
using point.simps
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt+
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
lemma
"cx \<lparr> cx = 3, cy = 4 \<rparr> = 3"
@@ -841,18 +829,16 @@
"p = \<lparr> cx = 3, cy = 4 \<rparr> \<longrightarrow> p \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p"
"p = \<lparr> cx = 3, cy = 4 \<rparr> \<longrightarrow> p \<lparr> cy := 4 \<rparr> \<lparr> cx := 3 \<rparr> = p"
using point.simps
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt+
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
lemma
"cy (p \<lparr> cx := a \<rparr>) = cy p"
"cx (p \<lparr> cy := a \<rparr>) = cx p"
"p \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p \<lparr> cy := 4 \<rparr> \<lparr> cx := 3 \<rparr>"
using point.simps
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt+
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
lemma
"p1 = p2 \<longrightarrow> cx p1 = cx p2"
@@ -862,8 +848,8 @@
"cy p1 \<noteq> cy p2 \<longrightarrow> p1 \<noteq> p2"
"black p1 \<noteq> black p2 \<longrightarrow> p1 \<noteq> p2"
using point.simps bw_point.simps
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- by smt+
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
lemma
"cx \<lparr> cx = 3, cy = 4, black = b \<rparr> = 3"
@@ -879,9 +865,8 @@
"p = \<lparr> cx = 3, cy = 4, black = True \<rparr> \<longrightarrow>
p \<lparr> black := True \<rparr> \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p"
using point.simps bw_point.simps
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt+
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
lemma
"\<lparr> cx = 3, cy = 4, black = b \<rparr> \<lparr> black := w \<rparr> = \<lparr> cx = 3, cy = 4, black = w \<rparr>"
@@ -893,9 +878,8 @@
"p \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> \<lparr> black := True \<rparr> =
p \<lparr> black := True \<rparr> \<lparr> cy := 4 \<rparr> \<lparr> cx := 3 \<rparr>"
using point.simps bw_point.simps
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2
subsubsection {* Type definitions *}
@@ -907,10 +891,8 @@
"nplus n1 n1 = n2"
"nplus n1 n2 = n3"
using n1_def n2_def n3_def nplus_def
- using [[smt_datatypes, smt_oracle, z3_with_extensions]]
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt+
-
+ using [[smt2_oracle, z3_new_extensions]]
+ by smt2+
section {* Function updates *}
@@ -924,7 +906,7 @@
"i1 = i2 \<longrightarrow> (f (i1 := v1, i2 := v2)) i1 = v2"
"i1 \<noteq> i2 \<and>i1 \<noteq> i3 \<and> i2 \<noteq> i3 \<longrightarrow> (f (i1 := v1, i2 := v2)) i3 = f i3"
using fun_upd_same fun_upd_apply
- by smt+
+ by smt2+
@@ -932,7 +914,7 @@
lemma Empty: "x \<notin> {}" by simp
-lemmas smt_sets = Empty UNIV_I Un_iff Int_iff
+lemmas smt2_sets = Empty UNIV_I Un_iff Int_iff
lemma
"x \<notin> {}"
@@ -950,6 +932,6 @@
"x \<in> P \<inter> P \<longleftrightarrow> x \<in> P"
"x \<in> P \<inter> (Q \<inter> R) \<longleftrightarrow> x \<in> (P \<inter> Q) \<inter> R"
"{x. x \<in> P} = {y. y \<in> P}"
- by (smt smt_sets)+
+ by (smt2 smt2_sets)+
end
--- a/src/HOL/SMT_Examples/SMT_Word_Examples.certs Thu Mar 13 16:28:25 2014 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,58 +0,0 @@
-ef8166854c461e296fe9c596b7a3fe12065b0c65 1 0
-unsat
-d1ec4aa8c4a5f474e8dbb8a8acbdd12fc33b0cda 1 0
-unsat
-03dee604b20d98218bc88a69efcbf0f1c6dc057a 1 0
-unsat
-6a68bdb5b2a92a239021f6188a807622fe7b8213 1 0
-unsat
-9be3195f24c1786963c05e51e63a24efa7c83141 1 0
-unsat
-608ed753221bdf2f1769ea3686a0f970108a7087 1 0
-unsat
-610484e81fc38952a9a2cb0bfc83d424f7f96ca8 1 0
-unsat
-0a06a4c179bec3512f3dc01e338f246fca223ddb 1 0
-unsat
-dd232118189a55ac7fc80599d2738be8bbaa9333 1 0
-unsat
-8426f9081bd693e21cd8b2e13d07cea1e69e8abd 1 0
-unsat
-8d83ab1c5a55640d0165bbd736d2cc217bcc2efd 1 0
-unsat
-542ef8141028455b42a51f60e3981a74373a60b3 1 0
-unsat
-564709a03da50b938c3b1ab2a8a2f0dc8d8a4749 1 0
-unsat
-c4acaeb4324634878481e3faae3beae53a641067 1 0
-unsat
-873ce0289bcfaf43a446c6ed55bec4289eea0ffd 1 0
-unsat
-8383b80b5e8011f2b51c01ea89c14ce766f5a82b 1 0
-unsat
-6694dc1c5420588e5e48281a8835ac019bfb1aa7 1 0
-unsat
-4094196f5d25f48682e6634b4326469abc38d250 1 0
-unsat
-0597f614ff89c7376d01987b4737ab991b5a321c 1 0
-unsat
-44f955a3f3fab3f5203ec29edc7e00e7cb81bedc 1 0
-unsat
-927e5f0e88fadf6d2f604b1d863a37fc682f942b 1 0
-unsat
-818922160b53f843888d258a1ef7e5d5ddf5129f 1 0
-unsat
-afc6dff121c48475665b0ef064826ffa2cad0e85 1 0
-unsat
-b9ab61d9521faeaa45ec63bff4581742c3e6c550 1 0
-unsat
-8e60769fce6622cdca312aa54d4a77329a99dac2 1 0
-unsat
-bd55726cefc783f8e9ef4ad38596e1f24cca3663 1 0
-unsat
-4e48efd5c9874aedf200e06875d5597b31d98075 1 0
-unsat
-e5c27ae0a583eeafeaa4ef3c59b1b4ec53e06b0f 1 0
-unsat
-7d3ef49480d3ed3a7e5f2d7a12e7108cf7fc7819 1 0
-unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs2 Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,369 @@
+d47653c43412ab1eb54730f2f5a4f4bdf44fcb5a 8 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x36 (monotonicity (rewrite (= (bvneg (_ bv5 4)) (_ bv11 4))) (= (= (_ bv11 4) (bvneg (_ bv5 4))) (= (_ bv11 4) (_ bv11 4))))))
+(let ((@x40 (trans @x36 (rewrite (= (= (_ bv11 4) (_ bv11 4)) true)) (= (= (_ bv11 4) (bvneg (_ bv5 4))) true))))
+(let ((@x47 (trans (monotonicity @x40 (= (not (= (_ bv11 4) (bvneg (_ bv5 4)))) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (bvneg (_ bv5 4)))) false))))
+(mp (asserted (not (= (_ bv11 4) (bvneg (_ bv5 4))))) @x47 false))))))
+
+da258c2a22a4a00129b43deac09b90d379043340 7 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x33 (monotonicity (rewrite (= (= (_ bv11 4) (_ bv11 4)) true)) (= (not (= (_ bv11 4) (_ bv11 4))) (not true)))))
+(let ((@x37 (trans @x33 (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (_ bv11 4))) false))))
+(mp (asserted (not (= (_ bv11 4) (_ bv11 4)))) @x37 false)))))
+
+f2b47b92988d2f0c1404b109b621ba9a6c2b9d1c 7 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x36 (monotonicity (rewrite (= (bvult (_ bv23 8) (_ bv27 8)) true)) (= (not (bvult (_ bv23 8) (_ bv27 8))) (not true)))))
+(let ((@x40 (trans @x36 (rewrite (= (not true) false)) (= (not (bvult (_ bv23 8) (_ bv27 8))) false))))
+(mp (asserted (not (bvult (_ bv23 8) (_ bv27 8)))) @x40 false)))))
+
+1c22485fb98e3caa4d683df39ead427fc3568432 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x36 (monotonicity (rewrite (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5))) (= (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5)) (= (_ bv6 5) (_ bv6 5))))))
+(let ((@x40 (trans @x36 (rewrite (= (= (_ bv6 5) (_ bv6 5)) true)) (= (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5)) true))))
+(let ((@x43 (monotonicity @x40 (= (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5))) (not true)))))
+(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5))) false))))
+(mp (asserted (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5)))) @x47 false)))))))
+
+651f74a079a4aa15d5d621208d8e038db0369475 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x36 (monotonicity (rewrite (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8))) (= (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8)) (= (_ bv21 8) (_ bv21 8))))))
+(let ((@x40 (trans @x36 (rewrite (= (= (_ bv21 8) (_ bv21 8)) true)) (= (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8)) true))))
+(let ((@x43 (monotonicity @x40 (= (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8))) (not true)))))
+(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8))) false))))
+(mp (asserted (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8)))) @x47 false)))))))
+
+eefb4f0a8b690f38fb11c31757b3209b40cfd1c5 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x41 (monotonicity (rewrite (= (bvsub (_ bv11 8) (_ bv27 8)) (_ bv240 8))) (rewrite (= (bvneg (_ bv16 8)) (_ bv240 8))) (= (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))) (= (_ bv240 8) (_ bv240 8))))))
+(let ((@x45 (trans @x41 (rewrite (= (= (_ bv240 8) (_ bv240 8)) true)) (= (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))) true))))
+(let ((@x48 (monotonicity @x45 (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) (not true)))))
+(let ((@x52 (trans @x48 (rewrite (= (not true) false)) (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) false))))
+(mp (asserted (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))))) @x52 false)))))))
+
+e251dcc0ad168cb65c5bc1d32039c72ca2609bb3 7 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x33 (monotonicity (rewrite (= (= (_ bv11 5) (_ bv11 5)) true)) (= (not (= (_ bv11 5) (_ bv11 5))) (not true)))))
+(let ((@x37 (trans @x33 (rewrite (= (not true) false)) (= (not (= (_ bv11 5) (_ bv11 5))) false))))
+(mp (asserted (not (= (_ bv11 5) (_ bv11 5)))) @x37 false)))))
+
+4f488dde65b4a70d1d31d589531d3445a9be689f 11 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x40 (monotonicity (rewrite (= (bvneg (_ bv40 7)) (_ bv88 7))) (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvadd (_ bv88 7) (_ bv1 7))))))
+(let ((@x45 (trans @x40 (rewrite (= (bvadd (_ bv88 7) (_ bv1 7)) (_ bv89 7))) (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (_ bv89 7)))))
+(let ((@x50 (monotonicity @x45 (rewrite (= (bvneg (_ bv39 7)) (_ bv89 7))) (= (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7))) (= (_ bv89 7) (_ bv89 7))))))
+(let ((@x54 (trans @x50 (rewrite (= (= (_ bv89 7) (_ bv89 7)) true)) (= (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7))) true))))
+(let ((@x57 (monotonicity @x54 (= (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7)))) (not true)))))
+(let ((@x61 (trans @x57 (rewrite (= (not true) false)) (= (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7)))) false))))
+(mp (asserted (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7))))) @x61 false)))))))))
+
+2e53bd8b513a3dc9dee350d0d8b1c315cf2b2449 19 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x13 (bvadd |b$| |c$|)))
+(let ((?x14 (bvadd ?x13 |a$|)))
+(let ((?x8 (bvmul (_ bv2 32) |b$|)))
+(let ((?x9 (bvadd |a$| ?x8)))
+(let ((?x11 (bvadd ?x9 |c$|)))
+(let ((?x12 (bvsub ?x11 |b$|)))
+(let (($x15 (= ?x12 ?x14)))
+(let (($x16 (not $x15)))
+(let ((@x56 (rewrite (= (= (bvadd |a$| |b$| |c$|) (bvadd |a$| |b$| |c$|)) true))))
+(let ((@x46 (rewrite (= (bvsub (bvadd |a$| ?x8 |c$|) |b$|) (bvadd |a$| |b$| |c$|)))))
+(let ((@x44 (monotonicity (rewrite (= ?x11 (bvadd |a$| ?x8 |c$|))) (= ?x12 (bvsub (bvadd |a$| ?x8 |c$|) |b$|)))))
+(let ((@x54 (monotonicity (trans @x44 @x46 (= ?x12 (bvadd |a$| |b$| |c$|))) (rewrite (= ?x14 (bvadd |a$| |b$| |c$|))) (= $x15 (= (bvadd |a$| |b$| |c$|) (bvadd |a$| |b$| |c$|))))))
+(let ((@x61 (monotonicity (trans @x54 @x56 (= $x15 true)) (= $x16 (not true)))))
+(let ((@x65 (trans @x61 (rewrite (= (not true) false)) (= $x16 false))))
+(mp (asserted $x16) @x65 false)))))))))))))))))
+
+570be43092e6421d4222501467362afbd680c2e2 18 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x9 (bvmul (_ bv4 4) |x$|)))
+(let (($x10 (= ?x9 (_ bv4 4))))
+(let (($x41 (= (_ bv5 4) |x$|)))
+(let (($x54 (not (or (not $x41) (= (_ bv4 4) ?x9)))))
+(let ((@x46 (monotonicity (rewrite (= (= |x$| (_ bv5 4)) $x41)) (= (not (= |x$| (_ bv5 4))) (not $x41)))))
+(let ((@x53 (monotonicity @x46 (rewrite (= $x10 (= (_ bv4 4) ?x9))) (= (or (not (= |x$| (_ bv5 4))) $x10) (or (not $x41) (= (_ bv4 4) ?x9))))))
+(let (($x12 (not (=> (= |x$| (_ bv5 4)) $x10))))
+(let ((@x37 (rewrite (= (=> (= |x$| (_ bv5 4)) $x10) (or (not (= |x$| (_ bv5 4))) $x10)))))
+(let ((@x58 (trans (monotonicity @x37 (= $x12 (not (or (not (= |x$| (_ bv5 4))) $x10)))) (monotonicity @x53 (= (not (or (not (= |x$| (_ bv5 4))) $x10)) $x54)) (= $x12 $x54))))
+(let ((@x65 (monotonicity (|not-or-elim| (mp (asserted $x12) @x58 $x54) $x41) (= ?x9 (bvmul (_ bv4 4) (_ bv5 4))))))
+(let ((@x71 (monotonicity (trans @x65 (rewrite (= (bvmul (_ bv4 4) (_ bv5 4)) (_ bv4 4))) $x10) (= (= (_ bv4 4) ?x9) (= (_ bv4 4) (_ bv4 4))))))
+(let ((@x75 (trans @x71 (rewrite (= (= (_ bv4 4) (_ bv4 4)) true)) (= (= (_ bv4 4) ?x9) true))))
+(let ((@x82 (trans (monotonicity @x75 (= (not (= (_ bv4 4) ?x9)) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv4 4) ?x9)) false))))
+(mp (|not-or-elim| (mp (asserted $x12) @x58 $x54) (not (= (_ bv4 4) ?x9))) @x82 false))))))))))))))))
+
+2538d74409c652fbc39d33a15f25d18c9bb179bf 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x35 (monotonicity (rewrite (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32))) (= (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32)) (= (_ bv4 32) (_ bv4 32))))))
+(let ((@x39 (trans @x35 (rewrite (= (= (_ bv4 32) (_ bv4 32)) true)) (= (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32)) true))))
+(let ((@x42 (monotonicity @x39 (= (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32))) (not true)))))
+(let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32))) false))))
+(mp (asserted (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32)))) @x46 false)))))))
+
+ea3351a199ecbca8cfc913892024d6ba767f41dc 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x35 (monotonicity (rewrite (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8))) (= (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8)) (= (_ bv7 8) (_ bv7 8))))))
+(let ((@x39 (trans @x35 (rewrite (= (= (_ bv7 8) (_ bv7 8)) true)) (= (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8)) true))))
+(let ((@x42 (monotonicity @x39 (= (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8))) (not true)))))
+(let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8))) false))))
+(mp (asserted (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8)))) @x46 false)))))))
+
+a36393e9d24b671ce68aafbd67bbc7bcd4c32a9f 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x35 (monotonicity (rewrite (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8))) (= (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8)) (= (_ bv15 8) (_ bv15 8))))))
+(let ((@x39 (trans @x35 (rewrite (= (= (_ bv15 8) (_ bv15 8)) true)) (= (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8)) true))))
+(let ((@x42 (monotonicity @x39 (= (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8))) (not true)))))
+(let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8))) false))))
+(mp (asserted (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8)))) @x46 false)))))))
+
+48dba82ab628843121b1cc45b6a662d4282a5dfd 8 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x34 (monotonicity (rewrite (= (bvnot (_ bv240 16)) (_ bv65295 16))) (= (= (bvnot (_ bv240 16)) (_ bv65295 16)) (= (_ bv65295 16) (_ bv65295 16))))))
+(let ((@x38 (trans @x34 (rewrite (= (= (_ bv65295 16) (_ bv65295 16)) true)) (= (= (bvnot (_ bv240 16)) (_ bv65295 16)) true))))
+(let ((@x45 (trans (monotonicity @x38 (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) (not true))) (rewrite (= (not true) false)) (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) false))))
+(mp (asserted (not (= (bvnot (_ bv240 16)) (_ bv65295 16)))) @x45 false))))))
+
+ffdba93b71ca27a7275f33b87244eb12ceb5e9c2 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x35 (monotonicity (rewrite (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12))) (= (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12)) (= (_ bv2843 12) (_ bv2843 12))))))
+(let ((@x39 (trans @x35 (rewrite (= (= (_ bv2843 12) (_ bv2843 12)) true)) (= (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12)) true))))
+(let ((@x42 (monotonicity @x39 (= (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12))) (not true)))))
+(let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12))) false))))
+(mp (asserted (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12)))) @x46 false)))))))
+
+24677a2d05cd59ffe782bea3654e41f124fc1b93 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x35 (monotonicity (rewrite (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) (= (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)) (= (_ bv207 10) (_ bv207 10))))))
+(let ((@x39 (trans @x35 (rewrite (= (= (_ bv207 10) (_ bv207 10)) true)) (= (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)) true))))
+(let ((@x42 (monotonicity @x39 (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) (not true)))))
+(let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) false))))
+(mp (asserted (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)))) @x46 false)))))))
+
+bf709bf2b13e6bf4f9668ad197c5d7a4ca581525 8 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x50 (monotonicity (rewrite (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) (= (_ bv3 2) (_ bv3 2))))))
+(let ((@x54 (trans @x50 (rewrite (= (= (_ bv3 2) (_ bv3 2)) true)) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) true))))
+(let ((@x61 (trans (monotonicity @x54 (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (not true))) (rewrite (= (not true) false)) (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) false))))
+(mp (asserted (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)))) @x61 false))))))
+
+f487669e8e249c60376443304a5a78c58eddd1cc 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x34 (monotonicity (rewrite (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10))) (= (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10)) (= (_ bv10 10) (_ bv10 10))))))
+(let ((@x38 (trans @x34 (rewrite (= (= (_ bv10 10) (_ bv10 10)) true)) (= (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10)) true))))
+(let ((@x41 (monotonicity @x38 (= (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10))) (not true)))))
+(let ((@x45 (trans @x41 (rewrite (= (not true) false)) (= (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10))) false))))
+(mp (asserted (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10)))) @x45 false)))))))
+
+e6179d5000250fb81646a549216cd9ad7b2619a2 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x34 (monotonicity (rewrite (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6))) (= (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6)) (= (_ bv58 6) (_ bv58 6))))))
+(let ((@x38 (trans @x34 (rewrite (= (= (_ bv58 6) (_ bv58 6)) true)) (= (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6)) true))))
+(let ((@x41 (monotonicity @x38 (= (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6))) (not true)))))
+(let ((@x45 (trans @x41 (rewrite (= (not true) false)) (= (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6))) false))))
+(mp (asserted (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6)))) @x45 false)))))))
+
+5ca573788c44ee26ee19907e7d9d9ec1635c9a5b 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x51 (monotonicity (rewrite (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) (= (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)) (= (_ bv76 8) (_ bv76 8))))))
+(let ((@x55 (trans @x51 (rewrite (= (= (_ bv76 8) (_ bv76 8)) true)) (= (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)) true))))
+(let ((@x58 (monotonicity @x55 (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) (not true)))))
+(let ((@x62 (trans @x58 (rewrite (= (not true) false)) (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) false))))
+(mp (asserted (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)))) @x62 false)))))))
+
+b4a2032ff1791888567d8f54fa94d95365cb3255 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x51 (monotonicity (rewrite (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8))) (= (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8)) (= (_ bv6 8) (_ bv6 8))))))
+(let ((@x55 (trans @x51 (rewrite (= (= (_ bv6 8) (_ bv6 8)) true)) (= (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8)) true))))
+(let ((@x58 (monotonicity @x55 (= (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8))) (not true)))))
+(let ((@x62 (trans @x58 (rewrite (= (not true) false)) (= (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8))) false))))
+(mp (asserted (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8)))) @x62 false)))))))
+
+7a4f6966fce99a20413ba9068cef650098d5df66 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x51 (monotonicity (rewrite (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) (= (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)) (= (_ bv4 8) (_ bv4 8))))))
+(let ((@x55 (trans @x51 (rewrite (= (= (_ bv4 8) (_ bv4 8)) true)) (= (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)) true))))
+(let ((@x58 (monotonicity @x55 (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) (not true)))))
+(let ((@x62 (trans @x58 (rewrite (= (not true) false)) (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) false))))
+(mp (asserted (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)))) @x62 false)))))))
+
+17e3ce1c7a7f4469b5b93e126887f9f5cc55a51d 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x50 (monotonicity (rewrite (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4))) (= (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4)) (= (_ bv9 4) (_ bv9 4))))))
+(let ((@x54 (trans @x50 (rewrite (= (= (_ bv9 4) (_ bv9 4)) true)) (= (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4)) true))))
+(let ((@x57 (monotonicity @x54 (= (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4))) (not true)))))
+(let ((@x61 (trans @x57 (rewrite (= (not true) false)) (= (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4))) false))))
+(mp (asserted (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4)))) @x61 false)))))))
+
+070667ff72c73dc8cd9ebb50cc06803d9785fef4 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x50 (monotonicity (rewrite (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) (= (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)) (= (_ bv13 4) (_ bv13 4))))))
+(let ((@x54 (trans @x50 (rewrite (= (= (_ bv13 4) (_ bv13 4)) true)) (= (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)) true))))
+(let ((@x57 (monotonicity @x54 (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) (not true)))))
+(let ((@x61 (trans @x57 (rewrite (= (not true) false)) (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) false))))
+(mp (asserted (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)))) @x61 false)))))))
+
+222d5f4b74cc91bf83cca8b1b96f9cfe0f7db0f7 17 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x9 (bvand |x$| (_ bv255 16))))
+(let ((?x7 (bvand |x$| (_ bv65280 16))))
+(let ((?x10 (bvor ?x7 ?x9)))
+(let (($x11 (= ?x10 |x$|)))
+(let (($x12 (not $x11)))
+(let ((@x57 (symm (commutativity (= (= |x$| ?x10) $x11)) (= $x11 (= |x$| ?x10)))))
+(let ((@x33 (asserted $x12)))
+(let ((@x61 (mp @x33 (monotonicity @x57 (= $x12 (not (= |x$| ?x10)))) (not (= |x$| ?x10)))))
+(let (($x50 (= |x$| ?x10)))
+(let ((@x32 (|true-axiom| true)))
+(let (($x51 (or $x50 false false false false false false false false false false false false false false false false)))
+(let ((@x53 (|unit-resolution| ((_ |th-lemma| bv) $x51) @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 $x50)))
+(|unit-resolution| @x53 @x61 false)))))))))))))))
+
+f856dea62e897c0065d5a1827265d3ff37ee50c8 51 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x9 (bvand |w$| (_ bv255 16))))
+(let (($x10 (= ?x9 |w$|)))
+(let (($x62 (not $x10)))
+(let ((@x316 (symm (commutativity (= (= |w$| ?x9) $x10)) (= $x10 (= |w$| ?x9)))))
+(let (($x55 (not (or (bvule (_ bv256 16) |w$|) $x10))))
+(let ((@x47 (monotonicity (rewrite (= (bvult |w$| (_ bv256 16)) (not (bvule (_ bv256 16) |w$|)))) (= (not (bvult |w$| (_ bv256 16))) (not (not (bvule (_ bv256 16) |w$|)))))))
+(let ((@x51 (trans @x47 (rewrite (= (not (not (bvule (_ bv256 16) |w$|))) (bvule (_ bv256 16) |w$|))) (= (not (bvult |w$| (_ bv256 16))) (bvule (_ bv256 16) |w$|)))))
+(let ((@x54 (monotonicity @x51 (= (or (not (bvult |w$| (_ bv256 16))) $x10) (or (bvule (_ bv256 16) |w$|) $x10)))))
+(let ((@x57 (monotonicity @x54 (= (not (or (not (bvult |w$| (_ bv256 16))) $x10)) $x55))))
+(let (($x12 (not (=> (bvult |w$| (_ bv256 16)) $x10))))
+(let ((@x37 (rewrite (= (=> (bvult |w$| (_ bv256 16)) $x10) (or (not (bvult |w$| (_ bv256 16))) $x10)))))
+(let ((@x40 (monotonicity @x37 (= $x12 (not (or (not (bvult |w$| (_ bv256 16))) $x10))))))
+(let ((@x63 (|not-or-elim| (mp (asserted $x12) (trans @x40 @x57 (= $x12 $x55)) $x55) $x62)))
+(let ((@x320 (mp @x63 (monotonicity @x316 (= $x62 (not (= |w$| ?x9)))) (not (= |w$| ?x9)))))
+(let (($x298 (= |w$| ?x9)))
+(let (($x79 (= ((_ extract 15 15) |w$|) (_ bv1 1))))
+(let (($x262 (not $x79)))
+(let (($x72 (= ((_ extract 8 8) |w$|) (_ bv1 1))))
+(let (($x73 (= ((_ extract 9 9) |w$|) (_ bv1 1))))
+(let (($x80 (and $x73 $x72)))
+(let (($x81 (or $x73 $x72 $x80)))
+(let (($x74 (= ((_ extract 10 10) |w$|) (_ bv1 1))))
+(let (($x82 (and $x74 $x81)))
+(let (($x83 (or $x74 $x73 $x72 $x80 $x82)))
+(let (($x75 (= ((_ extract 11 11) |w$|) (_ bv1 1))))
+(let (($x84 (and $x75 $x83)))
+(let (($x85 (or $x75 $x74 $x73 $x72 $x80 $x82 $x84)))
+(let (($x76 (= ((_ extract 12 12) |w$|) (_ bv1 1))))
+(let (($x86 (and $x76 $x85)))
+(let (($x87 (or $x76 $x75 $x74 $x73 $x72 $x80 $x82 $x84 $x86)))
+(let (($x77 (= ((_ extract 13 13) |w$|) (_ bv1 1))))
+(let (($x88 (and $x77 $x87)))
+(let (($x89 (or $x77 $x76 $x75 $x74 $x73 $x72 $x80 $x82 $x84 $x86 $x88)))
+(let (($x78 (= ((_ extract 14 14) |w$|) (_ bv1 1))))
+(let (($x90 (and $x78 $x89)))
+(let (($x91 (or $x78 $x77 $x76 $x75 $x74 $x73 $x72 $x80 $x82 $x84 $x86 $x88 $x90)))
+(let (($x92 (and $x79 $x91)))
+(let (($x93 (or $x79 $x78 $x77 $x76 $x75 $x74 $x73 $x72 $x80 $x82 $x84 $x86 $x88 $x90 $x92)))
+(let (($x295 (not $x93)))
+(let (($x41 (bvule (_ bv256 16) |w$|)))
+(let (($x42 (not $x41)))
+(let ((@x61 (|not-or-elim| (mp (asserted $x12) (trans @x40 @x57 (= $x12 $x55)) $x55) $x42)))
+(let ((@x301 (|unit-resolution| ((_ |th-lemma| bv) (or $x41 $x295)) @x61 $x295)))
+(let ((@x32 (|true-axiom| true)))
+(let (($x310 (or $x298 false false false false false false false false $x72 $x73 $x74 $x75 $x76 $x77 $x78 $x79)))
+(let ((@x312 (|unit-resolution| ((_ |th-lemma| bv) $x310) @x32 @x32 @x32 @x32 @x32 @x32 @x32 @x32 (|unit-resolution| (|def-axiom| (or $x93 (not $x72))) @x301 (not $x72)) (|unit-resolution| (|def-axiom| (or $x93 (not $x73))) @x301 (not $x73)) (|unit-resolution| (|def-axiom| (or $x93 (not $x74))) @x301 (not $x74)) (|unit-resolution| (|def-axiom| (or $x93 (not $x75))) @x301 (not $x75)) (|unit-resolution| (|def-axiom| (or $x93 (not $x76))) @x301 (not $x76)) (|unit-resolution| (|def-axiom| (or $x93 (not $x77))) @x301 (not $x77)) (|unit-resolution| (|def-axiom| (or $x93 (not $x78))) @x301 (not $x78)) (|unit-resolution| (|def-axiom| (or $x93 $x262)) @x301 $x262) $x298)))
+(|unit-resolution| @x312 @x320 false)))))))))))))))))))))))))))))))))))))))))))))))))
+
+39d6b3ac211187a764a365cb2d10eb3330116060 29 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x6 (|bv2int$| (_ bv0 2))))
+(let (($x181 (<= ?x6 0)))
+(let (($x182 (not $x181)))
+(let (($x173 (forall ((?v0 (_ BitVec 2)) )(!(let ((?x22 (|bv2int$| ?v0)))
+(let (($x59 (<= ?x22 0)))
+(not $x59))) :pattern ( (|bv2int$| ?v0) )))
+))
+(let (($x63 (forall ((?v0 (_ BitVec 2)) )(let ((?x22 (|bv2int$| ?v0)))
+(let (($x59 (<= ?x22 0)))
+(not $x59))))
+))
+(let ((@x175 (refl (= (not (<= (|bv2int$| ?0) 0)) (not (<= (|bv2int$| ?0) 0))))))
+(let ((@x110 (refl (|~| (not (<= (|bv2int$| ?0) 0)) (not (<= (|bv2int$| ?0) 0))))))
+(let (($x24 (forall ((?v0 (_ BitVec 2)) )(let ((?x22 (|bv2int$| ?v0)))
+(< 0 ?x22)))
+))
+(let ((@x62 (rewrite (= (< 0 (|bv2int$| ?0)) (not (<= (|bv2int$| ?0) 0))))))
+(let ((@x113 (|mp~| (mp (asserted $x24) (|quant-intro| @x62 (= $x24 $x63)) $x63) (|nnf-pos| @x110 (|~| $x63 $x63)) $x63)))
+(let ((@x178 (mp @x113 (|quant-intro| @x175 (= $x63 $x173)) $x173)))
+(let (($x185 (not $x173)))
+(let (($x186 (or $x185 $x182)))
+(let ((@x187 ((_ |quant-inst| (_ bv0 2)) $x186)))
+(let (($x8 (= ?x6 0)))
+(let ((@x52 (asserted $x8)))
+(|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x8) $x181)) @x52 (|unit-resolution| @x187 @x178 $x182) false)))))))))))))))))))
+
+f7db43c56c17d090679f2e9727e9eaa7cf84ab8d 16 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x10 (|p$| true)))
+(let (($x7 (bvule (_ bv0 4) |a$|)))
+(let (($x8 (ite $x7 true false)))
+(let ((?x9 (|p$| $x8)))
+(let (($x11 (= ?x9 ?x10)))
+(let (($x12 (not $x11)))
+(let ((@x50 (monotonicity (monotonicity (rewrite (= $x7 true)) (= (|p$| $x7) ?x10)) (= (= (|p$| $x7) ?x10) (= ?x10 ?x10)))))
+(let ((@x54 (trans @x50 (rewrite (= (= ?x10 ?x10) true)) (= (= (|p$| $x7) ?x10) true))))
+(let ((@x61 (trans (monotonicity @x54 (= (not (= (|p$| $x7) ?x10)) (not true))) (rewrite (= (not true) false)) (= (not (= (|p$| $x7) ?x10)) false))))
+(let ((@x41 (monotonicity (monotonicity (rewrite (= $x8 $x7)) (= ?x9 (|p$| $x7))) (= $x11 (= (|p$| $x7) ?x10)))))
+(let ((@x44 (monotonicity @x41 (= $x12 (not (= (|p$| $x7) ?x10))))))
+(mp (asserted $x12) (trans @x44 @x61 (= $x12 false)) false))))))))))))))
+
--- a/src/HOL/SMT_Examples/SMT_Word_Examples.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.thy Thu Mar 13 16:39:08 2014 +0100
@@ -8,11 +8,10 @@
imports "~~/src/HOL/Word/Word"
begin
-declare [[smt_oracle = true]]
-declare [[smt_certificates = "SMT_Word_Examples.certs"]]
-declare [[smt_read_only_certificates = true]]
-
-
+declare [[smt2_oracle = true]]
+declare [[z3_new_extensions = true]]
+declare [[smt2_certificates = "SMT_Word_Examples.certs2"]]
+declare [[smt2_read_only_certificates = true]]
text {*
Currently, there is no proof reconstruction for words.
@@ -20,66 +19,38 @@
*}
-
section {* Bitvector numbers *}
-lemma "(27 :: 4 word) = -5" by smt
-
-lemma "(27 :: 4 word) = 11" by smt
-
-lemma "23 < (27::8 word)" by smt
-
-lemma "27 + 11 = (6::5 word)" by smt
-
-lemma "7 * 3 = (21::8 word)" by smt
-
-lemma "11 - 27 = (-16::8 word)" by smt
-
-lemma "- -11 = (11::5 word)" by smt
-
-lemma "-40 + 1 = (-39::7 word)" by smt
-
-lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by smt
-
-lemma "x = (5 :: 4 word) \<Longrightarrow> 4 * x = 4" by smt
-
+lemma "(27 :: 4 word) = -5" by smt2
+lemma "(27 :: 4 word) = 11" by smt2
+lemma "23 < (27::8 word)" by smt2
+lemma "27 + 11 = (6::5 word)" by smt2
+lemma "7 * 3 = (21::8 word)" by smt2
+lemma "11 - 27 = (-16::8 word)" by smt2
+lemma "- -11 = (11::5 word)" by smt2
+lemma "-40 + 1 = (-39::7 word)" by smt2
+lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by smt2
+lemma "x = (5 :: 4 word) \<Longrightarrow> 4 * x = 4" by smt2
section {* Bit-level logic *}
-lemma "0b110 AND 0b101 = (0b100 :: 32 word)" by smt
-
-lemma "0b110 OR 0b011 = (0b111 :: 8 word)" by smt
-
-lemma "0xF0 XOR 0xFF = (0x0F :: 8 word)" by smt
-
-lemma "NOT (0xF0 :: 16 word) = 0xFF0F" by smt
-
-lemma "word_cat (27::4 word) (27::8 word) = (2843::12 word)" by smt
-
-lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)"
- by smt
-
-lemma "slice 1 (0b10110 :: 4 word) = (0b11 :: 2 word)" by smt
-
-lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by smt
-
-lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt
-
-lemma "0b10011 << 2 = (0b1001100::8 word)" by smt
-
-lemma "0b11001 >> 2 = (0b110::8 word)" by smt
-
-lemma "0b10011 >>> 2 = (0b100::8 word)" by smt
-
-lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt
-
-lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by smt
-
-lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" by smt
-
-lemma "w < 256 \<Longrightarrow> (w :: 16 word) AND 0x00FF = w" by smt
-
+lemma "0b110 AND 0b101 = (0b100 :: 32 word)" by smt2
+lemma "0b110 OR 0b011 = (0b111 :: 8 word)" by smt2
+lemma "0xF0 XOR 0xFF = (0x0F :: 8 word)" by smt2
+lemma "NOT (0xF0 :: 16 word) = 0xFF0F" by smt2
+lemma "word_cat (27::4 word) (27::8 word) = (2843::12 word)" by smt2
+lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)" by smt2
+lemma "slice 1 (0b10110 :: 4 word) = (0b11 :: 2 word)" by smt2
+lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by smt2
+lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt2
+lemma "0b10011 << 2 = (0b1001100::8 word)" by smt2
+lemma "0b11001 >> 2 = (0b110::8 word)" by smt2
+lemma "0b10011 >>> 2 = (0b100::8 word)" by smt2
+lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt2
+lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by smt2
+lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" by smt2
+lemma "w < 256 \<Longrightarrow> (w :: 16 word) AND 0x00FF = w" by smt2
section {* Combined integer-bitvector properties *}
@@ -91,10 +62,8 @@
and "bv2int 3 = 3"
and "\<forall>x::2 word. bv2int x > 0"
shows "\<forall>i::int. i < 0 \<longrightarrow> (\<forall>x::2 word. bv2int x > i)"
- using assms
- using [[z3_options="AUTO_CONFIG=false"]]
- by smt
+ using assms by smt2
-lemma "P (0 \<le> (a :: 4 word)) = P True" by smt
+lemma "P (0 \<le> (a :: 4 word)) = P True" by smt2
end
--- a/src/HOL/Sledgehammer.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Sledgehammer.thy Thu Mar 13 16:39:08 2014 +0100
@@ -7,7 +7,7 @@
header {* Sledgehammer: Isabelle--ATP Linkup *}
theory Sledgehammer
-imports ATP SMT
+imports ATP SMT SMT2
keywords "sledgehammer" :: diag and "sledgehammer_params" :: thy_decl
begin
@@ -27,6 +27,7 @@
ML_file "Tools/Sledgehammer/sledgehammer_prover.ML"
ML_file "Tools/Sledgehammer/sledgehammer_prover_atp.ML"
ML_file "Tools/Sledgehammer/sledgehammer_prover_smt.ML"
+ML_file "Tools/Sledgehammer/sledgehammer_prover_smt2.ML"
ML_file "Tools/Sledgehammer/sledgehammer_prover_minimize.ML"
ML_file "Tools/Sledgehammer/sledgehammer_mepo.ML"
ML_file "Tools/Sledgehammer/sledgehammer_mash.ML"
--- a/src/HOL/Tools/ATP/atp_proof_reconstruct.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/ATP/atp_proof_reconstruct.ML Thu Mar 13 16:39:08 2014 +0100
@@ -377,22 +377,12 @@
union (op =) (filter (fn (_, (_, status)) => status = Non_Rec_Def) facts) facts')
accum fact_names
-val isa_ext = Thm.get_name_hint @{thm ext}
-val isa_short_ext = Long_Name.base_name isa_ext
-
-fun ext_name ctxt =
- if Thm.eq_thm_prop (@{thm ext},
- singleton (Attrib.eval_thms ctxt) (Facts.named isa_short_ext, [])) then
- isa_short_ext
- else
- isa_ext
-
val leo2_extcnf_equal_neg_rule = "extcnf_equal_neg"
val leo2_unfold_def_rule = "unfold_def"
fun add_fact ctxt fact_names ((_, ss), _, _, rule, deps) =
(if rule = leo2_extcnf_equal_neg_rule then
- insert (op =) (ext_name ctxt, (Global, General))
+ insert (op =) (short_thm_name ctxt ext, (Global, General))
else if rule = leo2_unfold_def_rule then
(* LEO 1.3.3 does not record definitions properly, leading to missing dependencies in the TSTP
proof. Remove the next line once this is fixed. *)
@@ -401,7 +391,7 @@
(fn [] =>
(* agsyHOL and Satallax don't include definitions in their unsatisfiable cores, so we
assume the worst and include them all here. *)
- [(ext_name ctxt, (Global, General))] |> add_non_rec_defs fact_names
+ [(short_thm_name ctxt ext, (Global, General))] |> add_non_rec_defs fact_names
| facts => facts)
else
I)
--- a/src/HOL/Tools/ATP/atp_util.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/ATP/atp_util.ML Thu Mar 13 16:39:08 2014 +0100
@@ -48,8 +48,8 @@
val is_legitimate_tptp_def : term -> bool
val transform_elim_prop : term -> term
val specialize_type : theory -> (string * typ) -> term -> term
- val strip_subgoal :
- thm -> int -> Proof.context -> (string * typ) list * term list * term
+ val strip_subgoal : thm -> int -> Proof.context -> (string * typ) list * term list * term
+ val short_thm_name : Proof.context -> thm -> string
end;
structure ATP_Util : ATP_UTIL =
@@ -425,4 +425,13 @@
val concl_t = t |> Logic.strip_assums_concl |> curry subst_bounds frees
in (rev params, hyp_ts, concl_t) end
+fun short_thm_name ctxt th =
+ let
+ val long = Thm.get_name_hint th
+ val short = Long_Name.base_name long
+ in
+ if Thm.eq_thm_prop (th, singleton (Attrib.eval_thms ctxt) (Facts.named short, [])) then short
+ else long
+ end
+
end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_builtin.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,222 @@
+(* Title: HOL/Tools/SMT2/smt2_builtin.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Tables of types and terms directly supported by SMT solvers.
+*)
+
+signature SMT2_BUILTIN =
+sig
+ (*for experiments*)
+ val filter_builtins: (typ -> bool) -> Proof.context -> Proof.context
+
+ (*built-in types*)
+ val add_builtin_typ: SMT2_Util.class ->
+ typ * (typ -> string option) * (typ -> int -> string option) -> Context.generic ->
+ Context.generic
+ val add_builtin_typ_ext: typ * (typ -> bool) -> Context.generic ->
+ Context.generic
+ val dest_builtin_typ: Proof.context -> typ -> string option
+ val is_builtin_typ_ext: Proof.context -> typ -> bool
+
+ (*built-in numbers*)
+ val dest_builtin_num: Proof.context -> term -> (string * typ) option
+ val is_builtin_num: Proof.context -> term -> bool
+ val is_builtin_num_ext: Proof.context -> term -> bool
+
+ (*built-in functions*)
+ type 'a bfun = Proof.context -> typ -> term list -> 'a
+ type bfunr = string * int * term list * (term list -> term)
+ val add_builtin_fun: SMT2_Util.class -> (string * typ) * bfunr option bfun -> Context.generic ->
+ Context.generic
+ val add_builtin_fun': SMT2_Util.class -> term * string -> Context.generic -> Context.generic
+ val add_builtin_fun_ext: (string * typ) * term list bfun -> Context.generic -> Context.generic
+ val add_builtin_fun_ext': string * typ -> Context.generic -> Context.generic
+ val add_builtin_fun_ext'': string -> Context.generic -> Context.generic
+ val dest_builtin_fun: Proof.context -> string * typ -> term list -> bfunr option
+ val dest_builtin_eq: Proof.context -> term -> term -> bfunr option
+ val dest_builtin_pred: Proof.context -> string * typ -> term list -> bfunr option
+ val dest_builtin_conn: Proof.context -> string * typ -> term list -> bfunr option
+ val dest_builtin: Proof.context -> string * typ -> term list -> bfunr option
+ val dest_builtin_ext: Proof.context -> string * typ -> term list -> term list option
+ val is_builtin_fun: Proof.context -> string * typ -> term list -> bool
+ val is_builtin_fun_ext: Proof.context -> string * typ -> term list -> bool
+end
+
+structure SMT2_Builtin: SMT2_BUILTIN =
+struct
+
+
+(* built-in tables *)
+
+datatype ('a, 'b) kind = Ext of 'a | Int of 'b
+
+type ('a, 'b) ttab = ((typ * ('a, 'b) kind) Ord_List.T) SMT2_Util.dict
+
+fun typ_ord ((T, _), (U, _)) =
+ let
+ fun tord (TVar _, Type _) = GREATER
+ | tord (Type _, TVar _) = LESS
+ | tord (Type (n, Ts), Type (m, Us)) =
+ if n = m then list_ord tord (Ts, Us)
+ else Term_Ord.typ_ord (T, U)
+ | tord TU = Term_Ord.typ_ord TU
+ in tord (T, U) end
+
+fun insert_ttab cs T f =
+ SMT2_Util.dict_map_default (cs, [])
+ (Ord_List.insert typ_ord (perhaps (try Logic.varifyT_global) T, f))
+
+fun merge_ttab ttabp = SMT2_Util.dict_merge (Ord_List.merge typ_ord) ttabp
+
+fun lookup_ttab ctxt ttab T =
+ let fun match (U, _) = Sign.typ_instance (Proof_Context.theory_of ctxt) (T, U)
+ in
+ get_first (find_first match) (SMT2_Util.dict_lookup ttab (SMT2_Config.solver_class_of ctxt))
+ end
+
+type ('a, 'b) btab = ('a, 'b) ttab Symtab.table
+
+fun insert_btab cs n T f =
+ Symtab.map_default (n, []) (insert_ttab cs T f)
+
+fun merge_btab btabp = Symtab.join (K merge_ttab) btabp
+
+fun lookup_btab ctxt btab (n, T) =
+ (case Symtab.lookup btab n of
+ NONE => NONE
+ | SOME ttab => lookup_ttab ctxt ttab T)
+
+type 'a bfun = Proof.context -> typ -> term list -> 'a
+
+type bfunr = string * int * term list * (term list -> term)
+
+structure Builtins = Generic_Data
+(
+ type T =
+ (typ -> bool, (typ -> string option) * (typ -> int -> string option)) ttab *
+ (term list bfun, bfunr option bfun) btab
+ val empty = ([], Symtab.empty)
+ val extend = I
+ fun merge ((t1, b1), (t2, b2)) = (merge_ttab (t1, t2), merge_btab (b1, b2))
+)
+
+fun filter_ttab keep_T = map (apsnd (filter (keep_T o fst)))
+
+fun filter_builtins keep_T =
+ Context.proof_map (Builtins.map (fn (ttab, btab) =>
+ (filter_ttab keep_T ttab, Symtab.map (K (filter_ttab keep_T)) btab)))
+
+
+(* built-in types *)
+
+fun add_builtin_typ cs (T, f, g) =
+ Builtins.map (apfst (insert_ttab cs T (Int (f, g))))
+
+fun add_builtin_typ_ext (T, f) = Builtins.map (apfst (insert_ttab SMT2_Util.basicC T (Ext f)))
+
+fun lookup_builtin_typ ctxt =
+ lookup_ttab ctxt (fst (Builtins.get (Context.Proof ctxt)))
+
+fun dest_builtin_typ ctxt T =
+ (case lookup_builtin_typ ctxt T of
+ SOME (_, Int (f, _)) => f T
+ | _ => NONE)
+
+fun is_builtin_typ_ext ctxt T =
+ (case lookup_builtin_typ ctxt T of
+ SOME (_, Int (f, _)) => is_some (f T)
+ | SOME (_, Ext f) => f T
+ | NONE => false)
+
+
+(* built-in numbers *)
+
+fun dest_builtin_num ctxt t =
+ (case try HOLogic.dest_number t of
+ NONE => NONE
+ | SOME (T, i) =>
+ if i < 0 then NONE else
+ (case lookup_builtin_typ ctxt T of
+ SOME (_, Int (_, g)) => g T i |> Option.map (rpair T)
+ | _ => NONE))
+
+val is_builtin_num = is_some oo dest_builtin_num
+
+fun is_builtin_num_ext ctxt t =
+ (case try HOLogic.dest_number t of
+ NONE => false
+ | SOME (T, _) => is_builtin_typ_ext ctxt T)
+
+
+(* built-in functions *)
+
+fun add_builtin_fun cs ((n, T), f) =
+ Builtins.map (apsnd (insert_btab cs n T (Int f)))
+
+fun add_builtin_fun' cs (t, n) =
+ let
+ val c as (m, T) = Term.dest_Const t
+ fun app U ts = Term.list_comb (Const (m, U), ts)
+ fun bfun _ U ts = SOME (n, length (Term.binder_types T), ts, app U)
+ in add_builtin_fun cs (c, bfun) end
+
+fun add_builtin_fun_ext ((n, T), f) =
+ Builtins.map (apsnd (insert_btab SMT2_Util.basicC n T (Ext f)))
+
+fun add_builtin_fun_ext' c = add_builtin_fun_ext (c, fn _ => fn _ => I)
+
+fun add_builtin_fun_ext'' n context =
+ let val thy = Context.theory_of context
+ in add_builtin_fun_ext' (n, Sign.the_const_type thy n) context end
+
+fun lookup_builtin_fun ctxt =
+ lookup_btab ctxt (snd (Builtins.get (Context.Proof ctxt)))
+
+fun dest_builtin_fun ctxt (c as (_, T)) ts =
+ (case lookup_builtin_fun ctxt c of
+ SOME (_, Int f) => f ctxt T ts
+ | _ => NONE)
+
+fun dest_builtin_eq ctxt t u =
+ let
+ val aT = TFree (Name.aT, @{sort type})
+ val c = (@{const_name HOL.eq}, aT --> aT --> @{typ bool})
+ fun mk ts = Term.list_comb (HOLogic.eq_const (Term.fastype_of (hd ts)), ts)
+ in
+ dest_builtin_fun ctxt c []
+ |> Option.map (fn (n, i, _, _) => (n, i, [t, u], mk))
+ end
+
+fun special_builtin_fun pred ctxt (c as (_, T)) ts =
+ if pred (Term.body_type T, Term.binder_types T) then
+ dest_builtin_fun ctxt c ts
+ else NONE
+
+fun dest_builtin_pred ctxt = special_builtin_fun (equal @{typ bool} o fst) ctxt
+
+fun dest_builtin_conn ctxt =
+ special_builtin_fun (forall (equal @{typ bool}) o (op ::)) ctxt
+
+fun dest_builtin ctxt c ts =
+ let val t = Term.list_comb (Const c, ts)
+ in
+ (case dest_builtin_num ctxt t of
+ SOME (n, _) => SOME (n, 0, [], K t)
+ | NONE => dest_builtin_fun ctxt c ts)
+ end
+
+fun dest_builtin_fun_ext ctxt (c as (_, T)) ts =
+ (case lookup_builtin_fun ctxt c of
+ SOME (_, Int f) => f ctxt T ts |> Option.map (fn (_, _, us, _) => us)
+ | SOME (_, Ext f) => SOME (f ctxt T ts)
+ | NONE => NONE)
+
+fun dest_builtin_ext ctxt c ts =
+ if is_builtin_num_ext ctxt (Term.list_comb (Const c, ts)) then SOME []
+ else dest_builtin_fun_ext ctxt c ts
+
+fun is_builtin_fun ctxt c ts = is_some (dest_builtin_fun ctxt c ts)
+
+fun is_builtin_fun_ext ctxt c ts = is_some (dest_builtin_fun_ext ctxt c ts)
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_config.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,250 @@
+(* Title: HOL/Tools/SMT2/smt2_config.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Configuration options and diagnostic tools for SMT.
+*)
+
+signature SMT2_CONFIG =
+sig
+ (*solver*)
+ type solver_info = {
+ name: string,
+ class: Proof.context -> SMT2_Util.class,
+ avail: unit -> bool,
+ options: Proof.context -> string list }
+ val add_solver: solver_info -> Context.generic -> Context.generic
+ val set_solver_options: string * string -> Context.generic -> Context.generic
+ val is_available: Proof.context -> string -> bool
+ val available_solvers_of: Proof.context -> string list
+ val select_solver: string -> Context.generic -> Context.generic
+ val solver_of: Proof.context -> string
+ val solver_class_of: Proof.context -> SMT2_Util.class
+ val solver_options_of: Proof.context -> string list
+
+ (*options*)
+ val oracle: bool Config.T
+ val timeout: real Config.T
+ val random_seed: int Config.T
+ val read_only_certificates: bool Config.T
+ val verbose: bool Config.T
+ val trace: bool Config.T
+ val trace_used_facts: bool Config.T
+ val monomorph_limit: int Config.T
+ val monomorph_instances: int Config.T
+ val infer_triggers: bool Config.T
+ val filter_only_facts: bool Config.T
+ val debug_files: string Config.T
+
+ (*tools*)
+ val with_timeout: Proof.context -> ('a -> 'b) -> 'a -> 'b
+
+ (*diagnostics*)
+ val trace_msg: Proof.context -> ('a -> string) -> 'a -> unit
+ val verbose_msg: Proof.context -> ('a -> string) -> 'a -> unit
+
+ (*certificates*)
+ val select_certificates: string -> Context.generic -> Context.generic
+ val certificates_of: Proof.context -> Cache_IO.cache option
+
+ (*setup*)
+ val print_setup: Proof.context -> unit
+end
+
+structure SMT2_Config: SMT2_CONFIG =
+struct
+
+(* solver *)
+
+type solver_info = {
+ name: string,
+ class: Proof.context -> SMT2_Util.class,
+ avail: unit -> bool,
+ options: Proof.context -> string list}
+
+(* FIXME just one data slot (record) per program unit *)
+structure Solvers = Generic_Data
+(
+ type T = (solver_info * string list) Symtab.table * string option
+ val empty = (Symtab.empty, NONE)
+ val extend = I
+ fun merge ((ss1, s1), (ss2, s2)) =
+ (Symtab.merge (K true) (ss1, ss2), merge_options (s1, s2))
+)
+
+fun set_solver_options (name, options) =
+ let val opts = String.tokens (Symbol.is_ascii_blank o str) options
+ in Solvers.map (apfst (Symtab.map_entry name (apsnd (K opts)))) end
+
+fun add_solver (info as {name, ...} : solver_info) context =
+ if Symtab.defined (fst (Solvers.get context)) name then
+ error ("Solver already registered: " ^ quote name)
+ else
+ context
+ |> Solvers.map (apfst (Symtab.update (name, (info, []))))
+ |> Context.map_theory (Attrib.setup (Binding.name (name ^ "_options"))
+ (Scan.lift (@{keyword "="} |-- Args.name) >>
+ (Thm.declaration_attribute o K o set_solver_options o pair name))
+ ("Additional command line options for SMT solver " ^ quote name))
+
+fun all_solvers_of ctxt = Symtab.keys (fst (Solvers.get (Context.Proof ctxt)))
+
+fun solver_name_of ctxt = snd (Solvers.get (Context.Proof ctxt))
+
+fun is_available ctxt name =
+ (case Symtab.lookup (fst (Solvers.get (Context.Proof ctxt))) name of
+ SOME ({avail, ...}, _) => avail ()
+ | NONE => false)
+
+fun available_solvers_of ctxt =
+ filter (is_available ctxt) (all_solvers_of ctxt)
+
+fun warn_solver (Context.Proof ctxt) name =
+ Context_Position.if_visible ctxt
+ warning ("The SMT solver " ^ quote name ^ " is not installed.")
+ | warn_solver _ _ = ();
+
+fun select_solver name context =
+ let
+ val ctxt = Context.proof_of context
+ val upd = Solvers.map (apsnd (K (SOME name)))
+ in
+ if not (member (op =) (all_solvers_of ctxt) name) then
+ error ("Trying to select unknown solver: " ^ quote name)
+ else if not (is_available ctxt name) then
+ (warn_solver context name; upd context)
+ else upd context
+ end
+
+fun no_solver_err () = error "No SMT solver selected"
+
+fun solver_of ctxt =
+ (case solver_name_of ctxt of
+ SOME name => name
+ | NONE => no_solver_err ())
+
+fun solver_info_of default select ctxt =
+ (case Solvers.get (Context.Proof ctxt) of
+ (solvers, SOME name) => select (Symtab.lookup solvers name)
+ | (_, NONE) => default ())
+
+fun solver_class_of ctxt =
+ let fun class_of ({class, ...}: solver_info, _) = class ctxt
+ in solver_info_of no_solver_err (class_of o the) ctxt end
+
+fun solver_options_of ctxt =
+ let
+ fun all_options NONE = []
+ | all_options (SOME ({options, ...} : solver_info, opts)) =
+ opts @ options ctxt
+ in solver_info_of (K []) all_options ctxt end
+
+val setup_solver =
+ Attrib.setup @{binding smt2_solver}
+ (Scan.lift (@{keyword "="} |-- Args.name) >>
+ (Thm.declaration_attribute o K o select_solver))
+ "SMT solver configuration"
+
+
+(* options *)
+
+val oracle = Attrib.setup_config_bool @{binding smt2_oracle} (K true)
+val timeout = Attrib.setup_config_real @{binding smt2_timeout} (K 30.0)
+val random_seed = Attrib.setup_config_int @{binding smt2_random_seed} (K 1)
+val read_only_certificates = Attrib.setup_config_bool @{binding smt2_read_only_certificates} (K false)
+val verbose = Attrib.setup_config_bool @{binding smt2_verbose} (K true)
+val trace = Attrib.setup_config_bool @{binding smt2_trace} (K false)
+val trace_used_facts = Attrib.setup_config_bool @{binding smt2_trace_used_facts} (K false)
+val monomorph_limit = Attrib.setup_config_int @{binding smt2_monomorph_limit} (K 10)
+val monomorph_instances = Attrib.setup_config_int @{binding smt2_monomorph_instances} (K 500)
+val infer_triggers = Attrib.setup_config_bool @{binding smt2_infer_triggers} (K false)
+val filter_only_facts = Attrib.setup_config_bool @{binding smt2_filter_only_facts} (K false)
+val debug_files = Attrib.setup_config_string @{binding smt2_debug_files} (K "")
+
+
+(* diagnostics *)
+
+fun cond_trace flag f x = if flag then tracing ("SMT: " ^ f x) else ()
+
+fun verbose_msg ctxt = cond_trace (Config.get ctxt verbose)
+
+fun trace_msg ctxt = cond_trace (Config.get ctxt trace)
+
+
+(* tools *)
+
+fun with_timeout ctxt f x =
+ TimeLimit.timeLimit (seconds (Config.get ctxt timeout)) f x
+ handle TimeLimit.TimeOut => raise SMT2_Failure.SMT SMT2_Failure.Time_Out
+
+
+(* certificates *)
+
+(* FIXME just one data slot (record) per program unit *)
+structure Certificates = Generic_Data
+(
+ type T = Cache_IO.cache option
+ val empty = NONE
+ val extend = I
+ fun merge (s, _) = s (* FIXME merge options!? *)
+)
+
+val get_certificates_path =
+ Option.map (Cache_IO.cache_path_of) o Certificates.get o Context.Proof
+
+fun select_certificates name context = context |> Certificates.put (
+ if name = "" then NONE
+ else
+ Path.explode name
+ |> Path.append (Thy_Load.master_directory (Context.theory_of context))
+ |> SOME o Cache_IO.unsynchronized_init)
+
+val certificates_of = Certificates.get o Context.Proof
+
+val setup_certificates =
+ Attrib.setup @{binding smt2_certificates}
+ (Scan.lift (@{keyword "="} |-- Args.name) >>
+ (Thm.declaration_attribute o K o select_certificates))
+ "SMT certificates configuration"
+
+
+(* setup *)
+
+val _ = Theory.setup (
+ setup_solver #>
+ setup_certificates)
+
+fun print_setup ctxt =
+ let
+ fun string_of_bool b = if b then "true" else "false"
+
+ val names = available_solvers_of ctxt
+ val ns = if null names then ["(none)"] else sort_strings names
+ val n = the_default "(none)" (solver_name_of ctxt)
+ val opts = solver_options_of ctxt
+
+ val t = string_of_real (Config.get ctxt timeout)
+
+ val certs_filename =
+ (case get_certificates_path ctxt of
+ SOME path => Path.print path
+ | NONE => "(disabled)")
+ in
+ Pretty.writeln (Pretty.big_list "SMT setup:" [
+ Pretty.str ("Current SMT solver: " ^ n),
+ Pretty.str ("Current SMT solver options: " ^ space_implode " " opts),
+ Pretty.str_list "Available SMT solvers: " "" ns,
+ Pretty.str ("Current timeout: " ^ t ^ " seconds"),
+ Pretty.str ("With proofs: " ^
+ string_of_bool (not (Config.get ctxt oracle))),
+ Pretty.str ("Certificates cache: " ^ certs_filename),
+ Pretty.str ("Fixed certificates: " ^
+ string_of_bool (Config.get ctxt read_only_certificates))])
+ end
+
+val _ =
+ Outer_Syntax.improper_command @{command_spec "smt2_status"}
+ "show the available SMT solvers, the currently selected SMT solver, \
+ \and the values of SMT configuration options"
+ (Scan.succeed (Toplevel.keep (print_setup o Toplevel.context_of)))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_datatypes.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,133 @@
+(* Title: HOL/Tools/SMT2/smt2_datatypes.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Collector functions for common type declarations and their representation
+as algebraic datatypes.
+*)
+
+signature SMT2_DATATYPES =
+sig
+ val add_decls: typ ->
+ (typ * (term * term list) list) list list * Proof.context ->
+ (typ * (term * term list) list) list list * Proof.context
+end
+
+structure SMT2_Datatypes: SMT2_DATATYPES =
+struct
+
+val lhs_head_of = Term.head_of o fst o Logic.dest_equals o Thm.prop_of
+
+fun mk_selectors T Ts ctxt =
+ let
+ val (sels, ctxt') =
+ Variable.variant_fixes (replicate (length Ts) "select") ctxt
+ in (map2 (fn n => fn U => Free (n, T --> U)) sels Ts, ctxt') end
+
+
+(* datatype declarations *)
+
+fun get_datatype_decl ({descr, ...} : Datatype.info) n Ts ctxt =
+ let
+ fun get_vars (_, (m, vs, _)) = if m = n then SOME vs else NONE
+ val vars = the (get_first get_vars descr) ~~ Ts
+ val lookup_var = the o AList.lookup (op =) vars
+
+ fun typ_of (dt as Datatype.DtTFree _) = lookup_var dt
+ | typ_of (Datatype.DtType (m, dts)) = Type (m, map typ_of dts)
+ | typ_of (Datatype.DtRec i) =
+ the (AList.lookup (op =) descr i)
+ |> (fn (m, dts, _) => Type (m, map typ_of dts))
+
+ fun mk_constr T (m, dts) ctxt =
+ let
+ val Ts = map typ_of dts
+ val constr = Const (m, Ts ---> T)
+ val (selects, ctxt') = mk_selectors T Ts ctxt
+ in ((constr, selects), ctxt') end
+
+ fun mk_decl (i, (_, _, constrs)) ctxt =
+ let
+ val T = typ_of (Datatype.DtRec i)
+ val (css, ctxt') = fold_map (mk_constr T) constrs ctxt
+ in ((T, css), ctxt') end
+
+ in fold_map mk_decl descr ctxt end
+
+
+(* record declarations *)
+
+val record_name_of = Long_Name.implode o fst o split_last o Long_Name.explode
+
+fun get_record_decl ({ext_def, ...} : Record.info) T ctxt =
+ let
+ val (con, _) = Term.dest_Const (lhs_head_of ext_def)
+ val (fields, more) = Record.get_extT_fields (Proof_Context.theory_of ctxt) T
+ val fieldTs = map snd fields @ [snd more]
+
+ val constr = Const (con, fieldTs ---> T)
+ val (selects, ctxt') = mk_selectors T fieldTs ctxt
+ in ((T, [(constr, selects)]), ctxt') end
+
+
+(* typedef declarations *)
+
+fun get_typedef_decl (info : Typedef.info) T Ts =
+ let
+ val ({Abs_name, Rep_name, abs_type, rep_type, ...}, _) = info
+
+ val env = snd (Term.dest_Type abs_type) ~~ Ts
+ val instT = Term.map_atyps (perhaps (AList.lookup (op =) env))
+
+ val constr = Const (Abs_name, instT (rep_type --> abs_type))
+ val select = Const (Rep_name, instT (abs_type --> rep_type))
+ in (T, [(constr, [select])]) end
+
+
+(* collection of declarations *)
+
+fun declared declss T = exists (exists (equal T o fst)) declss
+fun declared' dss T = exists (exists (equal T o fst) o snd) dss
+
+fun get_decls T n Ts ctxt =
+ let val thy = Proof_Context.theory_of ctxt
+ in
+ (case Datatype.get_info thy n of
+ SOME info => get_datatype_decl info n Ts ctxt
+ | NONE =>
+ (case Record.get_info thy (record_name_of n) of
+ SOME info => get_record_decl info T ctxt |>> single
+ | NONE =>
+ (case Typedef.get_info ctxt n of
+ [] => ([], ctxt)
+ | info :: _ => ([get_typedef_decl info T Ts], ctxt))))
+ end
+
+fun add_decls T (declss, ctxt) =
+ let
+ fun depends Ts ds = exists (member (op =) (map fst ds)) Ts
+
+ fun add (TFree _) = I
+ | add (TVar _) = I
+ | add (T as Type (@{type_name fun}, _)) =
+ fold add (Term.body_type T :: Term.binder_types T)
+ | add @{typ bool} = I
+ | add (T as Type (n, Ts)) = (fn (dss, ctxt1) =>
+ if declared declss T orelse declared' dss T then (dss, ctxt1)
+ else if SMT2_Builtin.is_builtin_typ_ext ctxt1 T then (dss, ctxt1)
+ else
+ (case get_decls T n Ts ctxt1 of
+ ([], _) => (dss, ctxt1)
+ | (ds, ctxt2) =>
+ let
+ val constrTs =
+ maps (map (snd o Term.dest_Const o fst) o snd) ds
+ val Us = fold (union (op =) o Term.binder_types) constrTs []
+
+ fun ins [] = [(Us, ds)]
+ | ins ((Uds as (Us', _)) :: Udss) =
+ if depends Us' ds then (Us, ds) :: Uds :: Udss
+ else Uds :: ins Udss
+ in fold add Us (ins dss, ctxt2) end))
+ in add T ([], ctxt) |>> append declss o map snd end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_failure.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,61 @@
+(* Title: HOL/Tools/SMT2/smt2_failure.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Failures and exception of SMT.
+*)
+
+signature SMT2_FAILURE =
+sig
+ type counterexample = {
+ is_real_cex: bool,
+ free_constraints: term list,
+ const_defs: term list}
+ datatype failure =
+ Counterexample of counterexample |
+ Time_Out |
+ Out_Of_Memory |
+ Abnormal_Termination of int |
+ Other_Failure of string
+ val pretty_counterexample: Proof.context -> counterexample -> Pretty.T
+ val string_of_failure: Proof.context -> failure -> string
+ exception SMT of failure
+end
+
+structure SMT2_Failure: SMT2_FAILURE =
+struct
+
+type counterexample = {
+ is_real_cex: bool,
+ free_constraints: term list,
+ const_defs: term list}
+
+datatype failure =
+ Counterexample of counterexample |
+ Time_Out |
+ Out_Of_Memory |
+ Abnormal_Termination of int |
+ Other_Failure of string
+
+fun pretty_counterexample ctxt {is_real_cex, free_constraints, const_defs} =
+ let
+ val msg =
+ if is_real_cex then "Counterexample found (possibly spurious)"
+ else "Potential counterexample found"
+ in
+ if null free_constraints andalso null const_defs then Pretty.str msg
+ else
+ Pretty.big_list (msg ^ ":")
+ (map (Syntax.pretty_term ctxt) (free_constraints @ const_defs))
+ end
+
+fun string_of_failure ctxt (Counterexample cex) =
+ Pretty.string_of (pretty_counterexample ctxt cex)
+ | string_of_failure _ Time_Out = "Timed out"
+ | string_of_failure _ Out_Of_Memory = "Ran out of memory"
+ | string_of_failure _ (Abnormal_Termination err) =
+ "Solver terminated abnormally with error code " ^ string_of_int err
+ | string_of_failure _ (Other_Failure msg) = msg
+
+exception SMT of failure
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_normalize.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,577 @@
+(* Title: HOL/Tools/SMT2/smt2_normalize.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Normalization steps on theorems required by SMT solvers.
+*)
+
+signature SMT2_NORMALIZE =
+sig
+ val drop_fact_warning: Proof.context -> thm -> unit
+ val atomize_conv: Proof.context -> conv
+ type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list
+ val add_extra_norm: SMT2_Util.class * extra_norm -> Context.generic -> Context.generic
+ val normalize: Proof.context -> (int option * thm) list -> (int * thm) list
+end
+
+structure SMT2_Normalize: SMT2_NORMALIZE =
+struct
+
+fun drop_fact_warning ctxt =
+ SMT2_Config.verbose_msg ctxt (prefix "Warning: dropping assumption: " o
+ Display.string_of_thm ctxt)
+
+
+(* general theorem normalizations *)
+
+(** instantiate elimination rules **)
+
+local
+ val (cpfalse, cfalse) = `SMT2_Util.mk_cprop (Thm.cterm_of @{theory} @{const False})
+
+ fun inst f ct thm =
+ let val cv = f (Drule.strip_imp_concl (Thm.cprop_of thm))
+ in Thm.instantiate ([], [(cv, ct)]) thm end
+in
+
+fun instantiate_elim thm =
+ (case Thm.concl_of thm of
+ @{const Trueprop} $ Var (_, @{typ bool}) => inst Thm.dest_arg cfalse thm
+ | Var _ => inst I cpfalse thm
+ | _ => thm)
+
+end
+
+
+(** normalize definitions **)
+
+fun norm_def thm =
+ (case Thm.prop_of thm of
+ @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) =>
+ norm_def (thm RS @{thm fun_cong})
+ | Const (@{const_name "=="}, _) $ _ $ Abs _ => norm_def (thm RS @{thm meta_eq_to_obj_eq})
+ | _ => thm)
+
+
+(** atomization **)
+
+fun atomize_conv ctxt ct =
+ (case Thm.term_of ct of
+ @{const "==>"} $ _ $ _ =>
+ Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_imp}
+ | Const (@{const_name "=="}, _) $ _ $ _ =>
+ Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_eq}
+ | Const (@{const_name all}, _) $ Abs _ =>
+ Conv.binder_conv (atomize_conv o snd) ctxt then_conv Conv.rewr_conv @{thm atomize_all}
+ | _ => Conv.all_conv) ct
+
+val setup_atomize =
+ fold SMT2_Builtin.add_builtin_fun_ext'' [@{const_name "==>"}, @{const_name "=="},
+ @{const_name all}, @{const_name Trueprop}]
+
+
+(** unfold special quantifiers **)
+
+local
+ val special_quants = [
+ (@{const_name Ex1}, @{thm Ex1_def_raw}),
+ (@{const_name Ball}, @{thm Ball_def_raw}),
+ (@{const_name Bex}, @{thm Bex_def_raw})]
+
+ fun special_quant (Const (n, _)) = AList.lookup (op =) special_quants n
+ | special_quant _ = NONE
+
+ fun special_quant_conv _ ct =
+ (case special_quant (Thm.term_of ct) of
+ SOME thm => Conv.rewr_conv thm
+ | NONE => Conv.all_conv) ct
+in
+
+fun unfold_special_quants_conv ctxt =
+ SMT2_Util.if_exists_conv (is_some o special_quant) (Conv.top_conv special_quant_conv ctxt)
+
+val setup_unfolded_quants = fold (SMT2_Builtin.add_builtin_fun_ext'' o fst) special_quants
+
+end
+
+
+(** trigger inference **)
+
+local
+ (*** check trigger syntax ***)
+
+ fun dest_trigger (Const (@{const_name pat}, _) $ _) = SOME true
+ | dest_trigger (Const (@{const_name nopat}, _) $ _) = SOME false
+ | dest_trigger _ = NONE
+
+ fun eq_list [] = false
+ | eq_list (b :: bs) = forall (equal b) bs
+
+ fun proper_trigger t =
+ t
+ |> these o try HOLogic.dest_list
+ |> map (map_filter dest_trigger o these o try HOLogic.dest_list)
+ |> (fn [] => false | bss => forall eq_list bss)
+
+ fun proper_quant inside f t =
+ (case t of
+ Const (@{const_name All}, _) $ Abs (_, _, u) => proper_quant true f u
+ | Const (@{const_name Ex}, _) $ Abs (_, _, u) => proper_quant true f u
+ | @{const trigger} $ p $ u =>
+ (if inside then f p else false) andalso proper_quant false f u
+ | Abs (_, _, u) => proper_quant false f u
+ | u1 $ u2 => proper_quant false f u1 andalso proper_quant false f u2
+ | _ => true)
+
+ fun check_trigger_error ctxt t =
+ error ("SMT triggers must only occur under quantifier and multipatterns " ^
+ "must have the same kind: " ^ Syntax.string_of_term ctxt t)
+
+ fun check_trigger_conv ctxt ct =
+ if proper_quant false proper_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct
+ else check_trigger_error ctxt (Thm.term_of ct)
+
+
+ (*** infer simple triggers ***)
+
+ fun dest_cond_eq ct =
+ (case Thm.term_of ct of
+ Const (@{const_name HOL.eq}, _) $ _ $ _ => Thm.dest_binop ct
+ | @{const HOL.implies} $ _ $ _ => dest_cond_eq (Thm.dest_arg ct)
+ | _ => raise CTERM ("no equation", [ct]))
+
+ fun get_constrs thy (Type (n, _)) = these (Datatype.get_constrs thy n)
+ | get_constrs _ _ = []
+
+ fun is_constr thy (n, T) =
+ let fun match (m, U) = m = n andalso Sign.typ_instance thy (T, U)
+ in can (the o find_first match o get_constrs thy o Term.body_type) T end
+
+ fun is_constr_pat thy t =
+ (case Term.strip_comb t of
+ (Free _, []) => true
+ | (Const c, ts) => is_constr thy c andalso forall (is_constr_pat thy) ts
+ | _ => false)
+
+ fun is_simp_lhs ctxt t =
+ (case Term.strip_comb t of
+ (Const c, ts as _ :: _) =>
+ not (SMT2_Builtin.is_builtin_fun_ext ctxt c ts) andalso
+ forall (is_constr_pat (Proof_Context.theory_of ctxt)) ts
+ | _ => false)
+
+ fun has_all_vars vs t =
+ subset (op aconv) (vs, map Free (Term.add_frees t []))
+
+ fun minimal_pats vs ct =
+ if has_all_vars vs (Thm.term_of ct) then
+ (case Thm.term_of ct of
+ _ $ _ =>
+ (case pairself (minimal_pats vs) (Thm.dest_comb ct) of
+ ([], []) => [[ct]]
+ | (ctss, ctss') => union (eq_set (op aconvc)) ctss ctss')
+ | _ => [])
+ else []
+
+ fun proper_mpat _ _ _ [] = false
+ | proper_mpat thy gen u cts =
+ let
+ val tps = (op ~~) (`gen (map Thm.term_of cts))
+ fun some_match u = tps |> exists (fn (t', t) =>
+ Pattern.matches thy (t', u) andalso not (t aconv u))
+ in not (Term.exists_subterm some_match u) end
+
+ val pat = SMT2_Util.mk_const_pat @{theory} @{const_name SMT2.pat} SMT2_Util.destT1
+ fun mk_pat ct = Thm.apply (SMT2_Util.instT' ct pat) ct
+
+ fun mk_clist T = pairself (Thm.cterm_of @{theory}) (HOLogic.cons_const T, HOLogic.nil_const T)
+ fun mk_list (ccons, cnil) f cts = fold_rev (Thm.mk_binop ccons o f) cts cnil
+ val mk_pat_list = mk_list (mk_clist @{typ SMT2.pattern})
+ val mk_mpat_list = mk_list (mk_clist @{typ "SMT2.pattern list"})
+ fun mk_trigger ctss = mk_mpat_list (mk_pat_list mk_pat) ctss
+
+ val trigger_eq = mk_meta_eq @{lemma "p = SMT2.trigger t p" by (simp add: trigger_def)}
+
+ fun insert_trigger_conv [] ct = Conv.all_conv ct
+ | insert_trigger_conv ctss ct =
+ let val (ctr, cp) = Thm.dest_binop (Thm.rhs_of trigger_eq) ||> rpair ct
+ in Thm.instantiate ([], [cp, (ctr, mk_trigger ctss)]) trigger_eq end
+
+ fun infer_trigger_eq_conv outer_ctxt (ctxt, cvs) ct =
+ let
+ val (lhs, rhs) = dest_cond_eq ct
+
+ val vs = map Thm.term_of cvs
+ val thy = Proof_Context.theory_of ctxt
+
+ fun get_mpats ct =
+ if is_simp_lhs ctxt (Thm.term_of ct) then minimal_pats vs ct
+ else []
+ val gen = Variable.export_terms ctxt outer_ctxt
+ val filter_mpats = filter (proper_mpat thy gen (Thm.term_of rhs))
+
+ in insert_trigger_conv (filter_mpats (get_mpats lhs)) ct end
+
+ fun has_trigger (@{const SMT2.trigger} $ _ $ _) = true
+ | has_trigger _ = false
+
+ fun try_trigger_conv cv ct =
+ if SMT2_Util.under_quant has_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct
+ else Conv.try_conv cv ct
+
+ fun infer_trigger_conv ctxt =
+ if Config.get ctxt SMT2_Config.infer_triggers then
+ try_trigger_conv (SMT2_Util.under_quant_conv (infer_trigger_eq_conv ctxt) ctxt)
+ else Conv.all_conv
+in
+
+fun trigger_conv ctxt =
+ SMT2_Util.prop_conv (check_trigger_conv ctxt then_conv infer_trigger_conv ctxt)
+
+val setup_trigger =
+ fold SMT2_Builtin.add_builtin_fun_ext''
+ [@{const_name SMT2.pat}, @{const_name SMT2.nopat}, @{const_name SMT2.trigger}]
+
+end
+
+
+(** adding quantifier weights **)
+
+local
+ (*** check weight syntax ***)
+
+ val has_no_weight =
+ not o Term.exists_subterm (fn @{const SMT2.weight} => true | _ => false)
+
+ fun is_weight (@{const SMT2.weight} $ w $ t) =
+ (case try HOLogic.dest_number w of
+ SOME (_, i) => i >= 0 andalso has_no_weight t
+ | _ => false)
+ | is_weight t = has_no_weight t
+
+ fun proper_trigger (@{const SMT2.trigger} $ _ $ t) = is_weight t
+ | proper_trigger t = is_weight t
+
+ fun check_weight_error ctxt t =
+ error ("SMT weight must be a non-negative number and must only occur " ^
+ "under the top-most quantifier and an optional trigger: " ^
+ Syntax.string_of_term ctxt t)
+
+ fun check_weight_conv ctxt ct =
+ if SMT2_Util.under_quant proper_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct
+ else check_weight_error ctxt (Thm.term_of ct)
+
+
+ (*** insertion of weights ***)
+
+ fun under_trigger_conv cv ct =
+ (case Thm.term_of ct of
+ @{const SMT2.trigger} $ _ $ _ => Conv.arg_conv cv
+ | _ => cv) ct
+
+ val weight_eq = mk_meta_eq @{lemma "p = SMT2.weight i p" by (simp add: weight_def)}
+ fun mk_weight_eq w =
+ let val cv = Thm.dest_arg1 (Thm.rhs_of weight_eq)
+ in Thm.instantiate ([], [(cv, Numeral.mk_cnumber @{ctyp int} w)]) weight_eq end
+
+ fun add_weight_conv NONE _ = Conv.all_conv
+ | add_weight_conv (SOME weight) ctxt =
+ let val cv = Conv.rewr_conv (mk_weight_eq weight)
+ in SMT2_Util.under_quant_conv (K (under_trigger_conv cv)) ctxt end
+in
+
+fun weight_conv weight ctxt =
+ SMT2_Util.prop_conv (check_weight_conv ctxt then_conv add_weight_conv weight ctxt)
+
+val setup_weight = SMT2_Builtin.add_builtin_fun_ext'' @{const_name SMT2.weight}
+
+end
+
+
+(** combined general normalizations **)
+
+fun gen_normalize1_conv ctxt weight =
+ atomize_conv ctxt then_conv
+ unfold_special_quants_conv ctxt then_conv
+ Thm.beta_conversion true then_conv
+ trigger_conv ctxt then_conv
+ weight_conv weight ctxt
+
+fun gen_normalize1 ctxt weight =
+ instantiate_elim #>
+ norm_def #>
+ Conv.fconv_rule (Thm.beta_conversion true then_conv Thm.eta_conversion) #>
+ Drule.forall_intr_vars #>
+ Conv.fconv_rule (gen_normalize1_conv ctxt weight) #>
+ (* Z3 4.3.1 silently normalizes "P --> Q --> R" to "P & Q --> R" *)
+ Raw_Simplifier.rewrite_rule ctxt @{thms HOL.imp_conjL[symmetric, THEN eq_reflection]}
+
+fun gen_norm1_safe ctxt (i, (weight, thm)) =
+ (case try (gen_normalize1 ctxt weight) thm of
+ SOME thm' => SOME (i, thm')
+ | NONE => (drop_fact_warning ctxt thm; NONE))
+
+fun gen_normalize ctxt iwthms = map_filter (gen_norm1_safe ctxt) iwthms
+
+
+
+(* unfolding of definitions and theory-specific rewritings *)
+
+fun expand_head_conv cv ct =
+ (case Thm.term_of ct of
+ _ $ _ =>
+ Conv.fun_conv (expand_head_conv cv) then_conv
+ Conv.try_conv (Thm.beta_conversion false)
+ | _ => cv) ct
+
+
+(** rewrite bool case expressions as if expressions **)
+
+local
+ fun is_case_bool (Const (@{const_name "bool.case_bool"}, _)) = true
+ | is_case_bool _ = false
+
+ fun unfold_conv _ =
+ SMT2_Util.if_true_conv (is_case_bool o Term.head_of)
+ (expand_head_conv (Conv.rewr_conv @{thm case_bool_if}))
+in
+
+fun rewrite_case_bool_conv ctxt =
+ SMT2_Util.if_exists_conv is_case_bool (Conv.top_conv unfold_conv ctxt)
+
+val setup_case_bool = SMT2_Builtin.add_builtin_fun_ext'' @{const_name "bool.case_bool"}
+
+end
+
+
+(** unfold abs, min and max **)
+
+local
+ val defs = [
+ (@{const_name min}, @{thm min_def_raw}),
+ (@{const_name max}, @{thm max_def_raw}),
+ (@{const_name abs}, @{thm abs_if_raw})]
+
+ fun abs_min_max ctxt (Const (n, Type (@{type_name fun}, [T, _]))) =
+ (case AList.lookup (op =) defs n of
+ NONE => NONE
+ | SOME thm => if SMT2_Builtin.is_builtin_typ_ext ctxt T then SOME thm else NONE)
+ | abs_min_max _ _ = NONE
+
+ fun unfold_amm_conv ctxt ct =
+ (case abs_min_max ctxt (Term.head_of (Thm.term_of ct)) of
+ SOME thm => expand_head_conv (Conv.rewr_conv thm)
+ | NONE => Conv.all_conv) ct
+in
+
+fun unfold_abs_min_max_conv ctxt =
+ SMT2_Util.if_exists_conv (is_some o abs_min_max ctxt) (Conv.top_conv unfold_amm_conv ctxt)
+
+val setup_abs_min_max = fold (SMT2_Builtin.add_builtin_fun_ext'' o fst) defs
+
+end
+
+
+(** embedding of standard natural number operations into integer operations **)
+
+local
+ val nat_embedding = @{thms nat_int' int_nat_nneg int_nat_neg}
+
+ val simple_nat_ops = [
+ @{const less (nat)}, @{const less_eq (nat)},
+ @{const Suc}, @{const plus (nat)}, @{const minus (nat)}]
+
+ val mult_nat_ops =
+ [@{const times (nat)}, @{const div (nat)}, @{const mod (nat)}]
+
+ val nat_ops = simple_nat_ops @ mult_nat_ops
+
+ val nat_consts = nat_ops @ [@{const numeral (nat)},
+ @{const zero_class.zero (nat)}, @{const one_class.one (nat)}]
+
+ val nat_int_coercions = [@{const of_nat (int)}, @{const nat}]
+
+ val builtin_nat_ops = nat_int_coercions @ simple_nat_ops
+
+ val is_nat_const = member (op aconv) nat_consts
+
+ fun is_nat_const' @{const of_nat (int)} = true
+ | is_nat_const' t = is_nat_const t
+
+ val expands = map mk_meta_eq @{thms nat_zero_as_int nat_one_as_int nat_numeral_as_int
+ nat_less_as_int nat_leq_as_int Suc_as_int nat_plus_as_int nat_minus_as_int nat_times_as_int
+ nat_div_as_int nat_mod_as_int}
+
+ val ints = map mk_meta_eq @{thms int_0 int_1 int_Suc int_plus int_minus int_mult zdiv_int
+ zmod_int}
+ val int_if = mk_meta_eq @{lemma "int (if P then n else m) = (if P then int n else int m)" by simp}
+
+ fun mk_number_eq ctxt i lhs =
+ let
+ val eq = SMT2_Util.mk_cequals lhs (Numeral.mk_cnumber @{ctyp int} i)
+ val ctxt' = put_simpset HOL_ss ctxt addsimps @{thms Int.int_numeral}
+ val tac = HEADGOAL (Simplifier.simp_tac ctxt')
+ in Goal.norm_result ctxt (Goal.prove_internal ctxt [] eq (K tac)) end
+
+ fun ite_conv cv1 cv2 =
+ Conv.combination_conv (Conv.combination_conv (Conv.arg_conv cv1) cv2) cv2
+
+ fun int_conv ctxt ct =
+ (case Thm.term_of ct of
+ @{const of_nat (int)} $ (n as (@{const numeral (nat)} $ _)) =>
+ Conv.rewr_conv (mk_number_eq ctxt (snd (HOLogic.dest_number n)) ct)
+ | @{const of_nat (int)} $ _ =>
+ (Conv.rewrs_conv ints then_conv Conv.sub_conv ints_conv ctxt) else_conv
+ (Conv.rewr_conv int_if then_conv
+ ite_conv (nat_conv ctxt) (int_conv ctxt)) else_conv
+ Conv.sub_conv (Conv.top_sweep_conv nat_conv) ctxt
+ | _ => Conv.no_conv) ct
+
+ and ints_conv ctxt = Conv.top_sweep_conv int_conv ctxt
+
+ and expand_conv ctxt =
+ SMT2_Util.if_conv (is_nat_const o Term.head_of)
+ (expand_head_conv (Conv.rewrs_conv expands) then_conv ints_conv ctxt) (int_conv ctxt)
+
+ and nat_conv ctxt = SMT2_Util.if_exists_conv is_nat_const' (Conv.top_sweep_conv expand_conv ctxt)
+
+ val uses_nat_int = Term.exists_subterm (member (op aconv) nat_int_coercions)
+in
+
+val nat_as_int_conv = nat_conv
+
+fun add_nat_embedding thms =
+ if exists (uses_nat_int o Thm.prop_of) thms then (thms, nat_embedding) else (thms, [])
+
+val setup_nat_as_int =
+ SMT2_Builtin.add_builtin_typ_ext (@{typ nat}, K true) #>
+ fold (SMT2_Builtin.add_builtin_fun_ext' o Term.dest_Const) builtin_nat_ops
+
+end
+
+
+(** normalize numerals **)
+
+local
+ (*
+ rewrite Numeral1 into 1
+ rewrite - 0 into 0
+ *)
+
+ fun is_irregular_number (Const (@{const_name numeral}, _) $ Const (@{const_name num.One}, _)) =
+ true
+ | is_irregular_number (Const (@{const_name uminus}, _) $ Const (@{const_name Groups.zero}, _)) =
+ true
+ | is_irregular_number _ =
+ false;
+
+ fun is_strange_number ctxt t = is_irregular_number t andalso SMT2_Builtin.is_builtin_num ctxt t;
+
+ val proper_num_ss =
+ simpset_of (put_simpset HOL_ss @{context}
+ addsimps @{thms Num.numeral_One minus_zero})
+
+ fun norm_num_conv ctxt =
+ SMT2_Util.if_conv (is_strange_number ctxt) (Simplifier.rewrite (put_simpset proper_num_ss ctxt))
+ Conv.no_conv
+in
+
+fun normalize_numerals_conv ctxt =
+ SMT2_Util.if_exists_conv (is_strange_number ctxt) (Conv.top_sweep_conv norm_num_conv ctxt)
+
+end
+
+
+(** combined unfoldings and rewritings **)
+
+fun unfold_conv ctxt =
+ rewrite_case_bool_conv ctxt then_conv
+ unfold_abs_min_max_conv ctxt then_conv
+ nat_as_int_conv ctxt then_conv
+ Thm.beta_conversion true
+
+fun unfold1 ctxt = map (apsnd (Conv.fconv_rule (unfold_conv ctxt)))
+
+fun burrow_ids f ithms =
+ let
+ val (is, thms) = split_list ithms
+ val (thms', extra_thms) = f thms
+ in (is ~~ thms') @ map (pair ~1) extra_thms end
+
+fun unfold2 ctxt ithms =
+ ithms
+ |> map (apsnd (Conv.fconv_rule (normalize_numerals_conv ctxt)))
+ |> burrow_ids add_nat_embedding
+
+
+
+(* overall normalization *)
+
+type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list
+
+structure Extra_Norms = Generic_Data
+(
+ type T = extra_norm SMT2_Util.dict
+ val empty = []
+ val extend = I
+ fun merge data = SMT2_Util.dict_merge fst data
+)
+
+fun add_extra_norm (cs, norm) = Extra_Norms.map (SMT2_Util.dict_update (cs, norm))
+
+fun apply_extra_norms ctxt ithms =
+ let
+ val cs = SMT2_Config.solver_class_of ctxt
+ val es = SMT2_Util.dict_lookup (Extra_Norms.get (Context.Proof ctxt)) cs
+ in burrow_ids (fold (fn e => e ctxt) es o rpair []) ithms end
+
+local
+ val ignored = member (op =) [@{const_name All}, @{const_name Ex},
+ @{const_name Let}, @{const_name If}, @{const_name HOL.eq}]
+
+ val schematic_consts_of =
+ let
+ fun collect (@{const SMT2.trigger} $ p $ t) =
+ collect_trigger p #> collect t
+ | collect (t $ u) = collect t #> collect u
+ | collect (Abs (_, _, t)) = collect t
+ | collect (t as Const (n, _)) =
+ if not (ignored n) then Monomorph.add_schematic_consts_of t else I
+ | collect _ = I
+ and collect_trigger t =
+ let val dest = these o try HOLogic.dest_list
+ in fold (fold collect_pat o dest) (dest t) end
+ and collect_pat (Const (@{const_name SMT2.pat}, _) $ t) = collect t
+ | collect_pat (Const (@{const_name SMT2.nopat}, _) $ t) = collect t
+ | collect_pat _ = I
+ in (fn t => collect t Symtab.empty) end
+in
+
+fun monomorph ctxt xthms =
+ let val (xs, thms) = split_list xthms
+ in
+ map (pair 1) thms
+ |> Monomorph.monomorph schematic_consts_of ctxt
+ |> maps (uncurry (map o pair)) o map2 pair xs o map (map snd)
+ end
+
+end
+
+fun normalize ctxt wthms =
+ wthms
+ |> map_index I
+ |> gen_normalize ctxt
+ |> unfold1 ctxt
+ |> monomorph ctxt
+ |> unfold2 ctxt
+ |> apply_extra_norms ctxt
+
+val _ = Theory.setup (Context.theory_map (
+ setup_atomize #>
+ setup_unfolded_quants #>
+ setup_trigger #>
+ setup_weight #>
+ setup_case_bool #>
+ setup_abs_min_max #>
+ setup_nat_as_int))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_real.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,121 @@
+(* Title: HOL/Tools/SMT2/smt2_real.ML
+ Author: Sascha Boehme, TU Muenchen
+
+SMT setup for reals.
+*)
+
+structure SMT2_Real: sig end =
+struct
+
+
+(* SMT-LIB logic *)
+
+fun smtlib_logic ts =
+ if exists (Term.exists_type (Term.exists_subtype (equal @{typ real}))) ts
+ then SOME "AUFLIRA"
+ else NONE
+
+
+(* SMT-LIB and Z3 built-ins *)
+
+local
+ fun real_num _ i = SOME (string_of_int i ^ ".0")
+
+ fun is_linear [t] = SMT2_Util.is_number t
+ | is_linear [t, u] = SMT2_Util.is_number t orelse SMT2_Util.is_number u
+ | is_linear _ = false
+
+ fun mk_times ts = Term.list_comb (@{const times (real)}, ts)
+
+ fun times _ _ ts = if is_linear ts then SOME ("*", 2, ts, mk_times) else NONE
+in
+
+val setup_builtins =
+ SMT2_Builtin.add_builtin_typ SMTLIB2_Interface.smtlib2C
+ (@{typ real}, K (SOME "Real"), real_num) #>
+ fold (SMT2_Builtin.add_builtin_fun' SMTLIB2_Interface.smtlib2C) [
+ (@{const less (real)}, "<"),
+ (@{const less_eq (real)}, "<="),
+ (@{const uminus (real)}, "~"),
+ (@{const plus (real)}, "+"),
+ (@{const minus (real)}, "-") ] #>
+ SMT2_Builtin.add_builtin_fun SMTLIB2_Interface.smtlib2C
+ (Term.dest_Const @{const times (real)}, times) #>
+ SMT2_Builtin.add_builtin_fun' Z3_New_Interface.smtlib2_z3C
+ (@{const times (real)}, "*") #>
+ SMT2_Builtin.add_builtin_fun' Z3_New_Interface.smtlib2_z3C
+ (@{const divide (real)}, "/")
+
+end
+
+
+(* Z3 constructors *)
+
+local
+ fun z3_mk_builtin_typ (Z3_New_Interface.Sym ("Real", _)) = SOME @{typ real}
+ | z3_mk_builtin_typ (Z3_New_Interface.Sym ("real", _)) = SOME @{typ real}
+ (*FIXME: delete*)
+ | z3_mk_builtin_typ _ = NONE
+
+ fun z3_mk_builtin_num _ i T =
+ if T = @{typ real} then SOME (Numeral.mk_cnumber @{ctyp real} i)
+ else NONE
+
+ fun mk_nary _ cu [] = cu
+ | mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts)
+
+ val mk_uminus = Thm.apply (Thm.cterm_of @{theory} @{const uminus (real)})
+ val add = Thm.cterm_of @{theory} @{const plus (real)}
+ val real0 = Numeral.mk_cnumber @{ctyp real} 0
+ val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (real)})
+ val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (real)})
+ val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const divide (real)})
+ val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (real)})
+ val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (real)})
+
+ fun z3_mk_builtin_fun (Z3_New_Interface.Sym ("-", _)) [ct] = SOME (mk_uminus ct)
+ | z3_mk_builtin_fun (Z3_New_Interface.Sym ("+", _)) cts =
+ SOME (mk_nary add real0 cts)
+ | z3_mk_builtin_fun (Z3_New_Interface.Sym ("-", _)) [ct, cu] =
+ SOME (mk_sub ct cu)
+ | z3_mk_builtin_fun (Z3_New_Interface.Sym ("*", _)) [ct, cu] =
+ SOME (mk_mul ct cu)
+ | z3_mk_builtin_fun (Z3_New_Interface.Sym ("/", _)) [ct, cu] =
+ SOME (mk_div ct cu)
+ | z3_mk_builtin_fun (Z3_New_Interface.Sym ("<", _)) [ct, cu] =
+ SOME (mk_lt ct cu)
+ | z3_mk_builtin_fun (Z3_New_Interface.Sym ("<=", _)) [ct, cu] =
+ SOME (mk_le ct cu)
+ | z3_mk_builtin_fun (Z3_New_Interface.Sym (">", _)) [ct, cu] =
+ SOME (mk_lt cu ct)
+ | z3_mk_builtin_fun (Z3_New_Interface.Sym (">=", _)) [ct, cu] =
+ SOME (mk_le cu ct)
+ | z3_mk_builtin_fun _ _ = NONE
+in
+
+val z3_mk_builtins = {
+ mk_builtin_typ = z3_mk_builtin_typ,
+ mk_builtin_num = z3_mk_builtin_num,
+ mk_builtin_fun = (fn _ => fn sym => fn cts =>
+ (case try (#T o Thm.rep_cterm o hd) cts of
+ SOME @{typ real} => z3_mk_builtin_fun sym cts
+ | _ => NONE)) }
+
+end
+
+
+(* Z3 proof replay *)
+
+val real_linarith_proc = Simplifier.simproc_global @{theory} "fast_real_arith" [
+ "(m::real) < n", "(m::real) <= n", "(m::real) = n"] Lin_Arith.simproc
+
+
+(* setup *)
+
+val _ = Theory.setup (Context.theory_map (
+ SMTLIB2_Interface.add_logic (10, smtlib_logic) #>
+ setup_builtins #>
+ Z3_New_Interface.add_mk_builtins z3_mk_builtins #>
+ Z3_New_Replay_Util.add_simproc real_linarith_proc))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_solver.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,346 @@
+(* Title: HOL/Tools/SMT2/smt2_solver.ML
+ Author: Sascha Boehme, TU Muenchen
+
+SMT solvers registry and SMT tactic.
+*)
+
+signature SMT2_SOLVER =
+sig
+ (*configuration*)
+ datatype outcome = Unsat | Sat | Unknown
+ type solver_config = {
+ name: string,
+ class: Proof.context -> SMT2_Util.class,
+ avail: unit -> bool,
+ command: unit -> string list,
+ options: Proof.context -> string list,
+ default_max_relevant: int,
+ supports_filter: bool,
+ outcome: string -> string list -> outcome * string list,
+ cex_parser: (Proof.context -> SMT2_Translate.replay_data -> string list ->
+ term list * term list) option,
+ replay: (Proof.context -> SMT2_Translate.replay_data -> string list ->
+ ((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm) option }
+
+ (*registry*)
+ val add_solver: solver_config -> theory -> theory
+ val solver_name_of: Proof.context -> string
+ val available_solvers_of: Proof.context -> string list
+ val apply_solver: Proof.context -> (int option * thm) list ->
+ ((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm
+ val default_max_relevant: Proof.context -> string -> int
+
+ (*filter*)
+ val smt2_filter: Proof.context -> thm -> ('a * (int option * thm)) list -> int -> Time.time ->
+ {outcome: SMT2_Failure.failure option, conjecture_id: int, helper_ids: (int * thm) list,
+ fact_ids: (int * ('a * thm)) list, z3_proof: Z3_New_Proof.z3_step list}
+
+ (*tactic*)
+ val smt2_tac: Proof.context -> thm list -> int -> tactic
+ val smt2_tac': Proof.context -> thm list -> int -> tactic
+end
+
+structure SMT2_Solver: SMT2_SOLVER =
+struct
+
+
+(* interface to external solvers *)
+
+local
+
+fun make_cmd command options problem_path proof_path = space_implode " " (
+ "(exec 2>&1;" :: map File.shell_quote (command @ options) @
+ [File.shell_path problem_path, ")", ">", File.shell_path proof_path])
+
+fun trace_and ctxt msg f x =
+ let val _ = SMT2_Config.trace_msg ctxt (fn () => msg) ()
+ in f x end
+
+fun run ctxt name mk_cmd input =
+ (case SMT2_Config.certificates_of ctxt of
+ NONE =>
+ if not (SMT2_Config.is_available ctxt name) then
+ error ("The SMT solver " ^ quote name ^ " is not installed.")
+ else if Config.get ctxt SMT2_Config.debug_files = "" then
+ trace_and ctxt ("Invoking SMT solver " ^ quote name ^ " ...")
+ (Cache_IO.run mk_cmd) input
+ else
+ let
+ val base_path = Path.explode (Config.get ctxt SMT2_Config.debug_files)
+ val in_path = Path.ext "smt2_in" base_path
+ val out_path = Path.ext "smt2_out" base_path
+ in Cache_IO.raw_run mk_cmd input in_path out_path end
+ | SOME certs =>
+ (case Cache_IO.lookup certs input of
+ (NONE, key) =>
+ if Config.get ctxt SMT2_Config.read_only_certificates then
+ error ("Bad certificate cache: missing certificate")
+ else
+ Cache_IO.run_and_cache certs key mk_cmd input
+ | (SOME output, _) =>
+ trace_and ctxt ("Using cached certificate from " ^
+ File.shell_path (Cache_IO.cache_path_of certs) ^ " ...")
+ I output))
+
+(* Z3 returns 1 if "get-model" or "get-model" fails *)
+val normal_return_codes = [0, 1]
+
+fun run_solver ctxt name mk_cmd input =
+ let
+ fun pretty tag ls = Pretty.string_of (Pretty.big_list tag (map Pretty.str ls))
+
+ val _ = SMT2_Config.trace_msg ctxt (pretty "Problem:" o split_lines) input
+
+ val {redirected_output=res, output=err, return_code} =
+ SMT2_Config.with_timeout ctxt (run ctxt name mk_cmd) input
+ val _ = SMT2_Config.trace_msg ctxt (pretty "Solver:") err
+
+ val output = fst (take_suffix (equal "") res)
+ val _ = SMT2_Config.trace_msg ctxt (pretty "Result:") output
+
+ val _ = member (op =) normal_return_codes return_code orelse
+ raise SMT2_Failure.SMT (SMT2_Failure.Abnormal_Termination return_code)
+ in output end
+
+fun trace_assms ctxt =
+ SMT2_Config.trace_msg ctxt (Pretty.string_of o
+ Pretty.big_list "Assertions:" o map (Display.pretty_thm ctxt o snd))
+
+fun trace_replay_data ({context=ctxt, typs, terms, ...} : SMT2_Translate.replay_data) =
+ let
+ fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p]
+ fun p_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T)
+ fun p_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t)
+ in
+ SMT2_Config.trace_msg ctxt (fn () =>
+ Pretty.string_of (Pretty.big_list "Names:" [
+ Pretty.big_list "sorts:" (map p_typ (Symtab.dest typs)),
+ Pretty.big_list "functions:" (map p_term (Symtab.dest terms))])) ()
+ end
+
+in
+
+fun invoke name command ithms ctxt =
+ let
+ val options = SMT2_Config.solver_options_of ctxt
+ val cmd = command ()
+ val comments = [space_implode " " options]
+
+ val (str, replay_data as {context=ctxt', ...}) =
+ ithms
+ |> tap (trace_assms ctxt)
+ |> SMT2_Translate.translate ctxt comments
+ ||> tap trace_replay_data
+ in (run_solver ctxt' name (make_cmd cmd options) str, replay_data) end
+
+end
+
+
+(* configuration *)
+
+datatype outcome = Unsat | Sat | Unknown
+
+type solver_config = {
+ name: string,
+ class: Proof.context -> SMT2_Util.class,
+ avail: unit -> bool,
+ command: unit -> string list,
+ options: Proof.context -> string list,
+ default_max_relevant: int,
+ supports_filter: bool,
+ outcome: string -> string list -> outcome * string list,
+ cex_parser: (Proof.context -> SMT2_Translate.replay_data -> string list ->
+ term list * term list) option,
+ replay: (Proof.context -> SMT2_Translate.replay_data -> string list ->
+ ((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm) option }
+
+
+(* check well-sortedness *)
+
+val has_topsort = Term.exists_type (Term.exists_subtype (fn
+ TFree (_, []) => true
+ | TVar (_, []) => true
+ | _ => false))
+
+(* top sorts cause problems with atomization *)
+fun check_topsort ctxt thm =
+ if has_topsort (Thm.prop_of thm) then (SMT2_Normalize.drop_fact_warning ctxt thm; TrueI) else thm
+
+
+(* registry *)
+
+type solver_info = {
+ command: unit -> string list,
+ default_max_relevant: int,
+ supports_filter: bool,
+ replay: Proof.context -> string list * SMT2_Translate.replay_data ->
+ ((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm }
+
+structure Solvers = Generic_Data
+(
+ type T = solver_info Symtab.table
+ val empty = Symtab.empty
+ val extend = I
+ fun merge data = Symtab.merge (K true) data
+)
+
+local
+ fun finish outcome cex_parser replay ocl outer_ctxt
+ (output, (replay_data as {context=ctxt, ...} : SMT2_Translate.replay_data)) =
+ (case outcome output of
+ (Unsat, ls) =>
+ if not (Config.get ctxt SMT2_Config.oracle) andalso is_some replay
+ then the replay outer_ctxt replay_data ls
+ else (([], []), ocl ())
+ | (result, ls) =>
+ let
+ val (ts, us) =
+ (case cex_parser of SOME f => f ctxt replay_data ls | _ => ([], []))
+ in
+ raise SMT2_Failure.SMT (SMT2_Failure.Counterexample {
+ is_real_cex = (result = Sat),
+ free_constraints = ts,
+ const_defs = us})
+ end)
+
+ val cfalse = Thm.cterm_of @{theory} (@{const Trueprop} $ @{const False})
+in
+
+fun add_solver cfg =
+ let
+ val {name, class, avail, command, options, default_max_relevant,
+ supports_filter, outcome, cex_parser, replay} = cfg
+
+ fun core_oracle () = cfalse
+
+ fun solver ocl = {
+ command = command,
+ default_max_relevant = default_max_relevant,
+ supports_filter = supports_filter,
+ replay = finish (outcome name) cex_parser replay ocl }
+
+ val info = {name=name, class=class, avail=avail, options=options}
+ in
+ Thm.add_oracle (Binding.name name, core_oracle) #-> (fn (_, ocl) =>
+ Context.theory_map (Solvers.map (Symtab.update_new (name, solver ocl)))) #>
+ Context.theory_map (SMT2_Config.add_solver info)
+ end
+
+end
+
+fun get_info ctxt name =
+ the (Symtab.lookup (Solvers.get (Context.Proof ctxt)) name)
+
+val solver_name_of = SMT2_Config.solver_of
+
+val available_solvers_of = SMT2_Config.available_solvers_of
+
+fun name_and_info_of ctxt =
+ let val name = solver_name_of ctxt
+ in (name, get_info ctxt name) end
+
+fun apply_solver ctxt wthms0 =
+ let
+ val wthms = map (apsnd (check_topsort ctxt)) wthms0
+ val (name, {command, replay, ...}) = name_and_info_of ctxt
+ in replay ctxt (invoke name command (SMT2_Normalize.normalize ctxt wthms) ctxt) end
+
+val default_max_relevant = #default_max_relevant oo get_info
+val supports_filter = #supports_filter o snd o name_and_info_of
+
+
+(* filter *)
+
+val no_id = ~1
+
+fun smt2_filter ctxt goal xwfacts i time_limit =
+ let
+ val ctxt =
+ ctxt
+ |> Config.put SMT2_Config.oracle false
+ |> Config.put SMT2_Config.filter_only_facts true
+ |> Config.put SMT2_Config.timeout (Time.toReal time_limit)
+
+ val ({context=ctxt, prems, concl, ...}, _) = Subgoal.focus ctxt i goal
+ fun negate ct = Thm.dest_comb ct ||> Thm.apply @{cterm Not} |-> Thm.apply
+ val cprop =
+ (case try negate (Thm.rhs_of (SMT2_Normalize.atomize_conv ctxt concl)) of
+ SOME ct => ct
+ | NONE => raise SMT2_Failure.SMT (SMT2_Failure.Other_Failure "goal is not a HOL term"))
+
+ val wconjecture = (NONE, Thm.assume cprop)
+ val wprems = map (pair NONE) prems
+ val wfacts = map snd xwfacts
+ val wthms = wconjecture :: wprems @ wfacts
+ val iwthms = map_index I wthms
+
+ val conjecture_i = 0
+ val facts_i = 1 + length wprems
+ in
+ wthms
+ |> apply_solver ctxt
+ |> fst
+ |> (fn (iidths0, z3_proof) =>
+ let
+ val iidths = if supports_filter ctxt then iidths0 else map (apsnd (apfst (K no_id))) iwthms
+ in
+ {outcome = NONE,
+ conjecture_id =
+ the_default no_id (Option.map fst (AList.lookup (op =) iidths conjecture_i)),
+ helper_ids = map_filter (try (fn (~1, idth) => idth)) iidths,
+ fact_ids = map_filter (fn (i, (id, _)) =>
+ try (apsnd (apsnd snd o nth xwfacts)) (id, i - facts_i)) iidths,
+ z3_proof = z3_proof}
+ end)
+ end
+ handle SMT2_Failure.SMT fail => {outcome = SOME fail, conjecture_id = no_id, helper_ids = [],
+ fact_ids = [], z3_proof = []}
+
+
+(* SMT tactic *)
+
+local
+ fun trace_assumptions ctxt wfacts iidths =
+ let val used = map_filter (try (snd o nth wfacts) o fst) iidths in
+ if Config.get ctxt SMT2_Config.trace_used_facts andalso length wfacts > 0 then
+ tracing (Pretty.string_of (Pretty.big_list "SMT used facts:"
+ (map (Display.pretty_thm ctxt) used)))
+ else ()
+ end
+
+ fun solve ctxt wfacts =
+ wfacts
+ |> apply_solver ctxt
+ |>> apfst (trace_assumptions ctxt wfacts)
+ |> snd
+
+ fun str_of ctxt fail =
+ SMT2_Failure.string_of_failure ctxt fail
+ |> prefix ("Solver " ^ SMT2_Config.solver_of ctxt ^ ": ")
+
+ fun safe_solve ctxt wfacts = SOME (solve ctxt wfacts)
+ handle
+ SMT2_Failure.SMT (fail as SMT2_Failure.Counterexample _) =>
+ (SMT2_Config.verbose_msg ctxt (str_of ctxt) fail; NONE)
+ | SMT2_Failure.SMT (fail as SMT2_Failure.Time_Out) =>
+ error ("SMT: Solver " ^ quote (SMT2_Config.solver_of ctxt) ^ ": " ^
+ SMT2_Failure.string_of_failure ctxt fail ^ " (setting the " ^
+ "configuration option " ^ quote (Config.name_of SMT2_Config.timeout) ^ " might help)")
+ | SMT2_Failure.SMT fail => error (str_of ctxt fail)
+
+ fun resolve (SOME thm) = rtac thm 1
+ | resolve NONE = no_tac
+
+ fun tac prove ctxt rules =
+ CONVERSION (SMT2_Normalize.atomize_conv ctxt)
+ THEN' rtac @{thm ccontr}
+ THEN' SUBPROOF (fn {context = ctxt, prems, ...} =>
+ resolve (prove ctxt (map (pair NONE) (rules @ prems)))) ctxt
+in
+
+val smt2_tac = tac safe_solve
+val smt2_tac' = tac (SOME oo solve)
+
+end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_systems.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,162 @@
+(* Title: HOL/Tools/SMT2/smt2_systems.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Setup SMT solvers.
+*)
+
+signature SMT2_SYSTEMS =
+sig
+ datatype z3_non_commercial =
+ Z3_Non_Commercial_Unknown |
+ Z3_Non_Commercial_Accepted |
+ Z3_Non_Commercial_Declined
+ val z3_non_commercial: unit -> z3_non_commercial
+ val z3_extensions: bool Config.T
+end
+
+structure SMT2_Systems: SMT2_SYSTEMS =
+struct
+
+(* helper functions *)
+
+fun make_avail name () = getenv (name ^ "_SOLVER") <> ""
+
+fun make_command name () = [getenv (name ^ "_SOLVER")]
+
+fun outcome_of unsat sat unknown solver_name line =
+ if String.isPrefix unsat line then SMT2_Solver.Unsat
+ else if String.isPrefix sat line then SMT2_Solver.Sat
+ else if String.isPrefix unknown line then SMT2_Solver.Unknown
+ else raise SMT2_Failure.SMT (SMT2_Failure.Other_Failure ("Solver " ^ quote solver_name ^
+ " failed -- enable tracing using the " ^ quote (Config.name_of SMT2_Config.trace) ^
+ " option for details"))
+
+fun on_first_line test_outcome solver_name lines =
+ let
+ val empty_line = (fn "" => true | _ => false)
+ val split_first = (fn [] => ("", []) | l :: ls => (l, ls))
+ val (l, ls) = split_first (snd (take_prefix empty_line lines))
+ in (test_outcome solver_name l, ls) end
+
+
+(* CVC3 *)
+
+local
+ fun cvc3_options ctxt = [
+ "-seed", string_of_int (Config.get ctxt SMT2_Config.random_seed),
+ "-lang", "smtlib", "-output-lang", "presentation",
+ "-timeout", string_of_int (Real.ceil (Config.get ctxt SMT2_Config.timeout))]
+in
+
+val cvc3: SMT2_Solver.solver_config = {
+ name = "cvc3_new",
+ class = K SMTLIB2_Interface.smtlib2C,
+ avail = make_avail "CVC3_NEW",
+ command = make_command "CVC3_NEW",
+ options = cvc3_options,
+ default_max_relevant = 400 (* FUDGE *),
+ supports_filter = false,
+ outcome =
+ on_first_line (outcome_of "Unsatisfiable." "Satisfiable." "Unknown."),
+ cex_parser = NONE,
+ replay = NONE }
+
+end
+
+
+(* Yices *)
+
+val yices: SMT2_Solver.solver_config = {
+ name = "yices_new",
+ class = K SMTLIB2_Interface.smtlib2C,
+ avail = make_avail "YICES_NEW",
+ command = make_command "YICES_NEW",
+ options = (fn ctxt => [
+ "--rand-seed=" ^ string_of_int (Config.get ctxt SMT2_Config.random_seed),
+ "--timeout=" ^
+ string_of_int (Real.ceil (Config.get ctxt SMT2_Config.timeout)),
+ "--smtlib"]),
+ default_max_relevant = 350 (* FUDGE *),
+ supports_filter = false,
+ outcome = on_first_line (outcome_of "unsat" "sat" "unknown"),
+ cex_parser = NONE,
+ replay = NONE }
+
+
+(* Z3 *)
+
+datatype z3_non_commercial =
+ Z3_Non_Commercial_Unknown |
+ Z3_Non_Commercial_Accepted |
+ Z3_Non_Commercial_Declined
+
+local
+ val accepted = member (op =) ["yes", "Yes", "YES"]
+ val declined = member (op =) ["no", "No", "NO"]
+in
+
+fun z3_non_commercial () =
+ let
+ val flag1 = Options.default_string @{option z3_non_commercial}
+ val flag2 = getenv "Z3_NON_COMMERCIAL"
+ in
+ if accepted flag1 then Z3_Non_Commercial_Accepted
+ else if declined flag1 then Z3_Non_Commercial_Declined
+ else if accepted flag2 then Z3_Non_Commercial_Accepted
+ else if declined flag2 then Z3_Non_Commercial_Declined
+ else Z3_Non_Commercial_Unknown
+ end
+
+fun if_z3_non_commercial f =
+ (case z3_non_commercial () of
+ Z3_Non_Commercial_Accepted => f ()
+ | Z3_Non_Commercial_Declined =>
+ error (Pretty.string_of (Pretty.para
+ "The SMT solver Z3 may only be used for non-commercial applications."))
+ | Z3_Non_Commercial_Unknown =>
+ error (Pretty.string_of (Pretty.para
+ ("The SMT solver Z3 is not activated. To activate it, set the Isabelle \
+ \system option \"z3_non_commercial\" to \"yes\" (e.g. via \
+ \the Isabelle/jEdit menu Plugin Options / Isabelle / General)."))))
+
+end
+
+val z3_extensions = Attrib.setup_config_bool @{binding z3_new_extensions} (K false)
+
+local
+ fun z3_make_command name () = if_z3_non_commercial (make_command name)
+
+ fun z3_options ctxt =
+ ["REFINE_INJ_AXIOM=false" (* not supported by replay *),
+ "-rs:" ^ string_of_int (Config.get ctxt SMT2_Config.random_seed),
+ "-T:" ^ string_of_int (Real.ceil (Config.get ctxt SMT2_Config.timeout)),
+ "-smt2"]
+
+ fun select_class ctxt =
+ if Config.get ctxt z3_extensions then Z3_New_Interface.smtlib2_z3C
+ else SMTLIB2_Interface.smtlib2C
+in
+
+val z3: SMT2_Solver.solver_config = {
+ name = "z3_new",
+ class = select_class,
+ avail = make_avail "Z3_NEW",
+ command = z3_make_command "Z3_NEW",
+ options = z3_options,
+ default_max_relevant = 350 (* FUDGE *),
+ supports_filter = true,
+ outcome = on_first_line (outcome_of "unsat" "sat" "unknown"),
+ cex_parser = SOME Z3_New_Model.parse_counterex,
+ replay = SOME Z3_New_Replay.replay }
+
+end
+
+
+(* overall setup *)
+
+val _ = Theory.setup (
+ SMT2_Solver.add_solver cvc3 #>
+ SMT2_Solver.add_solver yices #>
+ SMT2_Solver.add_solver z3)
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_translate.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,535 @@
+(* Title: HOL/Tools/SMT2/smt2_translate.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Translate theorems into an SMT intermediate format and serialize them.
+*)
+
+signature SMT2_TRANSLATE =
+sig
+ (*intermediate term structure*)
+ datatype squant = SForall | SExists
+ datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
+ datatype sterm =
+ SVar of int |
+ SApp of string * sterm list |
+ SLet of string * sterm * sterm |
+ SQua of squant * string list * sterm spattern list * int option * sterm
+
+ (*translation configuration*)
+ type sign = {
+ header: string,
+ sorts: string list,
+ dtyps: (string * (string * (string * string) list) list) list list,
+ funcs: (string * (string list * string)) list }
+ type config = {
+ header: term list -> string,
+ has_datatypes: bool,
+ serialize: string list -> sign -> sterm list -> string }
+ type replay_data = {
+ context: Proof.context,
+ typs: typ Symtab.table,
+ terms: term Symtab.table,
+ rewrite_rules: thm list,
+ assms: (int * thm) list }
+
+ (*translation*)
+ val add_config: SMT2_Util.class * (Proof.context -> config) -> Context.generic -> Context.generic
+ val translate: Proof.context -> string list -> (int * thm) list -> string * replay_data
+end
+
+structure SMT2_Translate: SMT2_TRANSLATE =
+struct
+
+
+(* intermediate term structure *)
+
+datatype squant = SForall | SExists
+
+datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
+
+datatype sterm =
+ SVar of int |
+ SApp of string * sterm list |
+ SLet of string * sterm * sterm |
+ SQua of squant * string list * sterm spattern list * int option * sterm
+
+
+
+(* translation configuration *)
+
+type sign = {
+ header: string,
+ sorts: string list,
+ dtyps: (string * (string * (string * string) list) list) list list,
+ funcs: (string * (string list * string)) list }
+
+type config = {
+ header: term list -> string,
+ has_datatypes: bool,
+ serialize: string list -> sign -> sterm list -> string }
+
+type replay_data = {
+ context: Proof.context,
+ typs: typ Symtab.table,
+ terms: term Symtab.table,
+ rewrite_rules: thm list,
+ assms: (int * thm) list }
+
+
+
+(* translation context *)
+
+fun add_components_of_typ (Type (s, Ts)) =
+ cons (Long_Name.base_name s) #> fold_rev add_components_of_typ Ts
+ | add_components_of_typ (TFree (s, _)) = cons (perhaps (try (unprefix "'")) s)
+ | add_components_of_typ _ = I;
+
+fun suggested_name_of_typ T = space_implode "_" (add_components_of_typ T []);
+
+fun suggested_name_of_term (Const (s, _)) = Long_Name.base_name s
+ | suggested_name_of_term (Free (s, _)) = s
+ | suggested_name_of_term _ = Name.uu
+
+val empty_tr_context = (Name.context, Typtab.empty, Termtab.empty)
+val safe_suffix = "$"
+
+fun add_typ T proper (cx as (names, typs, terms)) =
+ (case Typtab.lookup typs T of
+ SOME (name, _) => (name, cx)
+ | NONE =>
+ let
+ val sugg = Name.desymbolize true (suggested_name_of_typ T) ^ safe_suffix
+ val (name, names') = Name.variant sugg names
+ val typs' = Typtab.update (T, (name, proper)) typs
+ in (name, (names', typs', terms)) end)
+
+fun add_fun t sort (cx as (names, typs, terms)) =
+ (case Termtab.lookup terms t of
+ SOME (name, _) => (name, cx)
+ | NONE =>
+ let
+ val sugg = Name.desymbolize false (suggested_name_of_term t) ^ safe_suffix
+ val (name, names') = Name.variant sugg names
+ val terms' = Termtab.update (t, (name, sort)) terms
+ in (name, (names', typs, terms')) end)
+
+fun sign_of header dtyps (_, typs, terms) = {
+ header = header,
+ sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
+ dtyps = dtyps,
+ funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms []}
+
+fun replay_data_of ctxt rules assms (_, typs, terms) =
+ let
+ fun add_typ (T, (n, _)) = Symtab.update (n, T)
+ val typs' = Typtab.fold add_typ typs Symtab.empty
+
+ fun add_fun (t, (n, _)) = Symtab.update (n, t)
+ val terms' = Termtab.fold add_fun terms Symtab.empty
+ in
+ {context=ctxt, typs=typs', terms=terms', rewrite_rules=rules, assms=assms}
+ end
+
+
+
+(* preprocessing *)
+
+(** datatype declarations **)
+
+fun collect_datatypes_and_records (tr_context, ctxt) ts =
+ let
+ val (declss, ctxt') = fold (Term.fold_types SMT2_Datatypes.add_decls) ts ([], ctxt)
+
+ fun is_decl_typ T = exists (exists (equal T o fst)) declss
+
+ fun add_typ' T proper =
+ (case SMT2_Builtin.dest_builtin_typ ctxt' T of
+ SOME n => pair n
+ | NONE => add_typ T proper)
+
+ fun tr_select sel =
+ let val T = Term.range_type (Term.fastype_of sel)
+ in add_fun sel NONE ##>> add_typ' T (not (is_decl_typ T)) end
+ fun tr_constr (constr, selects) =
+ add_fun constr NONE ##>> fold_map tr_select selects
+ fun tr_typ (T, cases) = add_typ' T false ##>> fold_map tr_constr cases
+ val (declss', tr_context') = fold_map (fold_map tr_typ) declss tr_context
+
+ fun add (constr, selects) =
+ Termtab.update (constr, length selects) #>
+ fold (Termtab.update o rpair 1) selects
+ val funcs = fold (fold (fold add o snd)) declss Termtab.empty
+ in ((funcs, declss', tr_context', ctxt'), ts) end
+ (* FIXME: also return necessary datatype and record theorems *)
+
+
+(** eta-expand quantifiers, let expressions and built-ins *)
+
+local
+ fun eta f T t = Abs (Name.uu, T, f (Term.incr_boundvars 1 t $ Bound 0))
+
+ fun exp f T = eta f (Term.domain_type (Term.domain_type T))
+
+ fun exp2 T q =
+ let val U = Term.domain_type T
+ in Abs (Name.uu, U, q $ eta I (Term.domain_type U) (Bound 0)) end
+
+ fun expf k i T t =
+ let val Ts = drop i (fst (SMT2_Util.dest_funT k T))
+ in
+ Term.incr_boundvars (length Ts) t
+ |> fold_rev (fn i => fn u => u $ Bound i) (0 upto length Ts - 1)
+ |> fold_rev (fn T => fn u => Abs (Name.uu, T, u)) Ts
+ end
+in
+
+fun eta_expand ctxt funcs =
+ let
+ fun exp_func t T ts =
+ (case Termtab.lookup funcs t of
+ SOME k => Term.list_comb (t, ts) |> k <> length ts ? expf k (length ts) T
+ | NONE => Term.list_comb (t, ts))
+
+ fun expand ((q as Const (@{const_name All}, _)) $ Abs a) = q $ abs_expand a
+ | expand ((q as Const (@{const_name All}, T)) $ t) = q $ exp expand T t
+ | expand (q as Const (@{const_name All}, T)) = exp2 T q
+ | expand ((q as Const (@{const_name Ex}, _)) $ Abs a) = q $ abs_expand a
+ | expand ((q as Const (@{const_name Ex}, T)) $ t) = q $ exp expand T t
+ | expand (q as Const (@{const_name Ex}, T)) = exp2 T q
+ | expand ((l as Const (@{const_name Let}, _)) $ t $ Abs a) = expand (Term.betapply (Abs a, t))
+ | expand ((l as Const (@{const_name Let}, T)) $ t $ u) = expand (u $ t)
+ | expand ((l as Const (@{const_name Let}, T)) $ t) =
+ let val U = Term.domain_type (Term.range_type T)
+ in Abs (Name.uu, U, Bound 0 $ Term.incr_boundvars 1 t) end
+ | expand (Const (@{const_name Let}, T)) =
+ let val U = Term.domain_type (Term.range_type T)
+ in Abs (Name.uu, Term.domain_type T, Abs (Name.uu, U, Bound 0 $ Bound 1)) end
+ | expand t =
+ (case Term.strip_comb t of
+ (u as Const (c as (_, T)), ts) =>
+ (case SMT2_Builtin.dest_builtin ctxt c ts of
+ SOME (_, k, us, mk) =>
+ if k = length us then mk (map expand us)
+ else if k < length us then chop k (map expand us) |>> mk |> Term.list_comb
+ else expf k (length ts) T (mk (map expand us))
+ | NONE => exp_func u T (map expand ts))
+ | (u as Free (_, T), ts) => exp_func u T (map expand ts)
+ | (Abs a, ts) => Term.list_comb (abs_expand a, map expand ts)
+ | (u, ts) => Term.list_comb (u, map expand ts))
+
+ and abs_expand (n, T, t) = Abs (n, T, expand t)
+
+ in map expand end
+
+end
+
+
+(** introduce explicit applications **)
+
+local
+ (*
+ Make application explicit for functions with varying number of arguments.
+ *)
+
+ fun add t i = apfst (Termtab.map_default (t, i) (Integer.min i))
+ fun add_type T = apsnd (Typtab.update (T, ()))
+
+ fun min_arities t =
+ (case Term.strip_comb t of
+ (u as Const _, ts) => add u (length ts) #> fold min_arities ts
+ | (u as Free _, ts) => add u (length ts) #> fold min_arities ts
+ | (Abs (_, T, u), ts) => (can dest_funT T ? add_type T) #> min_arities u #> fold min_arities ts
+ | (_, ts) => fold min_arities ts)
+
+ fun minimize types t i =
+ let
+ fun find_min j [] _ = j
+ | find_min j (U :: Us) T =
+ if Typtab.defined types T then j else find_min (j + 1) Us (U --> T)
+
+ val (Ts, T) = Term.strip_type (Term.type_of t)
+ in find_min 0 (take i (rev Ts)) T end
+
+ fun app u (t, T) =
+ (Const (@{const_name SMT2.fun_app}, T --> T) $ t $ u, Term.range_type T)
+
+ fun apply i t T ts =
+ let
+ val (ts1, ts2) = chop i ts
+ val (_, U) = SMT2_Util.dest_funT i T
+ in fst (fold app ts2 (Term.list_comb (t, ts1), U)) end
+in
+
+fun intro_explicit_application ctxt funcs ts =
+ let
+ val (arities, types) = fold min_arities ts (Termtab.empty, Typtab.empty)
+ val arities' = Termtab.map (minimize types) arities (* FIXME: highly suspicious *)
+
+ fun app_func t T ts =
+ if is_some (Termtab.lookup funcs t) then Term.list_comb (t, ts)
+ else apply (the (Termtab.lookup arities' t)) t T ts
+
+ fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t))
+
+ fun traverse Ts t =
+ (case Term.strip_comb t of
+ (q as Const (@{const_name All}, _), [Abs (x, T, u)]) =>
+ q $ Abs (x, T, in_trigger (T :: Ts) u)
+ | (q as Const (@{const_name Ex}, _), [Abs (x, T, u)]) =>
+ q $ Abs (x, T, in_trigger (T :: Ts) u)
+ | (q as Const (@{const_name Let}, _), [u1, u2 as Abs _]) =>
+ q $ traverse Ts u1 $ traverse Ts u2
+ | (u as Const (c as (_, T)), ts) =>
+ (case SMT2_Builtin.dest_builtin ctxt c ts of
+ SOME (_, k, us, mk) =>
+ let
+ val (ts1, ts2) = chop k (map (traverse Ts) us)
+ val U = Term.strip_type T |>> snd o chop k |> (op --->)
+ in apply 0 (mk ts1) U ts2 end
+ | NONE => app_func u T (map (traverse Ts) ts))
+ | (u as Free (_, T), ts) => app_func u T (map (traverse Ts) ts)
+ | (u as Bound i, ts) => apply 0 u (nth Ts i) (map (traverse Ts) ts)
+ | (Abs (n, T, u), ts) => traverses Ts (Abs (n, T, traverse (T::Ts) u)) ts
+ | (u, ts) => traverses Ts u ts)
+ and in_trigger Ts ((c as @{const SMT2.trigger}) $ p $ t) = c $ in_pats Ts p $ in_weight Ts t
+ | in_trigger Ts t = in_weight Ts t
+ and in_pats Ts ps =
+ in_list @{typ "SMT2.pattern list"} (in_list @{typ SMT2.pattern} (in_pat Ts)) ps
+ and in_pat Ts ((p as Const (@{const_name SMT2.pat}, _)) $ t) = p $ traverse Ts t
+ | in_pat Ts ((p as Const (@{const_name SMT2.nopat}, _)) $ t) = p $ traverse Ts t
+ | in_pat _ t = raise TERM ("bad pattern", [t])
+ and in_weight Ts ((c as @{const SMT2.weight}) $ w $ t) = c $ w $ traverse Ts t
+ | in_weight Ts t = traverse Ts t
+ and traverses Ts t ts = Term.list_comb (t, map (traverse Ts) ts)
+ in map (traverse []) ts end
+
+val fun_app_eq = mk_meta_eq @{thm SMT2.fun_app_def}
+
+end
+
+
+(** map HOL formulas to FOL formulas (i.e., separate formulas froms terms) **)
+
+local
+ val is_quant = member (op =) [@{const_name All}, @{const_name Ex}]
+
+ val fol_rules = [
+ Let_def,
+ @{lemma "P = True == P" by (rule eq_reflection) simp},
+ @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
+
+ exception BAD_PATTERN of unit
+
+ fun wrap_in_if pat t =
+ if pat then raise BAD_PATTERN () else @{const If (bool)} $ t $ @{const True} $ @{const False}
+
+ fun is_builtin_conn_or_pred ctxt c ts =
+ is_some (SMT2_Builtin.dest_builtin_conn ctxt c ts) orelse
+ is_some (SMT2_Builtin.dest_builtin_pred ctxt c ts)
+in
+
+fun folify ctxt =
+ let
+ fun in_list T f t = HOLogic.mk_list T (map_filter f (HOLogic.dest_list t))
+
+ fun in_term pat t =
+ (case Term.strip_comb t of
+ (@{const True}, []) => t
+ | (@{const False}, []) => t
+ | (u as Const (@{const_name If}, _), [t1, t2, t3]) =>
+ if pat then raise BAD_PATTERN () else u $ in_form t1 $ in_term pat t2 $ in_term pat t3
+ | (Const (c as (n, _)), ts) =>
+ if is_builtin_conn_or_pred ctxt c ts then wrap_in_if pat (in_form t)
+ else if is_quant n then wrap_in_if pat (in_form t)
+ else Term.list_comb (Const c, map (in_term pat) ts)
+ | (Free c, ts) => Term.list_comb (Free c, map (in_term pat) ts)
+ | _ => t)
+
+ and in_weight ((c as @{const SMT2.weight}) $ w $ t) = c $ w $ in_form t
+ | in_weight t = in_form t
+
+ and in_pat ((p as Const (@{const_name SMT2.pat}, _)) $ t) =
+ p $ in_term true t
+ | in_pat ((p as Const (@{const_name SMT2.nopat}, _)) $ t) =
+ p $ in_term true t
+ | in_pat t = raise TERM ("bad pattern", [t])
+
+ and in_pats ps =
+ in_list @{typ "SMT2.pattern list"} (SOME o in_list @{typ SMT2.pattern} (try in_pat)) ps
+
+ and in_trigger ((c as @{const SMT2.trigger}) $ p $ t) = c $ in_pats p $ in_weight t
+ | in_trigger t = in_weight t
+
+ and in_form t =
+ (case Term.strip_comb t of
+ (q as Const (qn, _), [Abs (n, T, u)]) =>
+ if is_quant qn then q $ Abs (n, T, in_trigger u)
+ else in_term false t
+ | (Const c, ts) =>
+ (case SMT2_Builtin.dest_builtin_conn ctxt c ts of
+ SOME (_, _, us, mk) => mk (map in_form us)
+ | NONE =>
+ (case SMT2_Builtin.dest_builtin_pred ctxt c ts of
+ SOME (_, _, us, mk) => mk (map (in_term false) us)
+ | NONE => in_term false t))
+ | _ => in_term false t)
+ in
+ map in_form #>
+ pair (fol_rules, I)
+ end
+
+end
+
+
+(* translation into intermediate format *)
+
+(** utility functions **)
+
+val quantifier = (fn
+ @{const_name All} => SOME SForall
+ | @{const_name Ex} => SOME SExists
+ | _ => NONE)
+
+fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) =
+ if q = qname then group_quant qname (T :: Ts) u else (Ts, t)
+ | group_quant _ Ts t = (Ts, t)
+
+fun dest_weight (@{const SMT2.weight} $ w $ t) = (SOME (snd (HOLogic.dest_number w)), t)
+ | dest_weight t = (NONE, t)
+
+fun dest_pat (Const (@{const_name SMT2.pat}, _) $ t) = (t, true)
+ | dest_pat (Const (@{const_name SMT2.nopat}, _) $ t) = (t, false)
+ | dest_pat t = raise TERM ("bad pattern", [t])
+
+fun dest_pats [] = I
+ | dest_pats ts =
+ (case map dest_pat ts |> split_list ||> distinct (op =) of
+ (ps, [true]) => cons (SPat ps)
+ | (ps, [false]) => cons (SNoPat ps)
+ | _ => raise TERM ("bad multi-pattern", ts))
+
+fun dest_trigger (@{const SMT2.trigger} $ tl $ t) =
+ (rev (fold (dest_pats o HOLogic.dest_list) (HOLogic.dest_list tl) []), t)
+ | dest_trigger t = ([], t)
+
+fun dest_quant qn T t = quantifier qn |> Option.map (fn q =>
+ let
+ val (Ts, u) = group_quant qn [T] t
+ val (ps, p) = dest_trigger u
+ val (w, b) = dest_weight p
+ in (q, rev Ts, ps, w, b) end)
+
+fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
+ | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
+
+
+(** translation from Isabelle terms into SMT intermediate terms **)
+
+fun intermediate header dtyps builtin ctxt ts trx =
+ let
+ fun transT (T as TFree _) = add_typ T true
+ | transT (T as TVar _) = (fn _ => raise TYPE ("bad SMT type", [T], []))
+ | transT (T as Type _) =
+ (case SMT2_Builtin.dest_builtin_typ ctxt T of
+ SOME n => pair n
+ | NONE => add_typ T true)
+
+ fun app n ts = SApp (n, ts)
+
+ fun trans t =
+ (case Term.strip_comb t of
+ (Const (qn, _), [Abs (_, T, t1)]) =>
+ (case dest_quant qn T t1 of
+ SOME (q, Ts, ps, w, b) =>
+ fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
+ trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', w, b'))
+ | NONE => raise TERM ("unsupported quantifier", [t]))
+ | (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) =>
+ transT T ##>> trans t1 ##>> trans t2 #>> (fn ((U, u1), u2) => SLet (U, u1, u2))
+ | (u as Const (c as (_, T)), ts) =>
+ (case builtin ctxt c ts of
+ SOME (n, _, us, _) => fold_map trans us #>> app n
+ | NONE => transs u T ts)
+ | (u as Free (_, T), ts) => transs u T ts
+ | (Bound i, []) => pair (SVar i)
+ | _ => raise TERM ("bad SMT term", [t]))
+
+ and transs t T ts =
+ let val (Us, U) = SMT2_Util.dest_funT (length ts) T
+ in
+ fold_map transT Us ##>> transT U #-> (fn Up =>
+ add_fun t (SOME Up) ##>> fold_map trans ts #>> SApp)
+ end
+
+ val (us, trx') = fold_map trans ts trx
+ in ((sign_of (header ts) dtyps trx', us), trx') end
+
+
+
+(* translation *)
+
+structure Configs = Generic_Data
+(
+ type T = (Proof.context -> config) SMT2_Util.dict
+ val empty = []
+ val extend = I
+ fun merge data = SMT2_Util.dict_merge fst data
+)
+
+fun add_config (cs, cfg) = Configs.map (SMT2_Util.dict_update (cs, cfg))
+
+fun get_config ctxt =
+ let val cs = SMT2_Config.solver_class_of ctxt
+ in
+ (case SMT2_Util.dict_get (Configs.get (Context.Proof ctxt)) cs of
+ SOME cfg => cfg ctxt
+ | NONE => error ("SMT: no translation configuration found " ^
+ "for solver class " ^ quote (SMT2_Util.string_of_class cs)))
+ end
+
+fun translate ctxt comments ithms =
+ let
+ val {header, has_datatypes, serialize} = get_config ctxt
+
+ fun no_dtyps (tr_context, ctxt) ts =
+ ((Termtab.empty, [], tr_context, ctxt), ts)
+
+ val ts1 = map (Envir.beta_eta_contract o SMT2_Util.prop_of o snd) ithms
+
+ val ((funcs, dtyps, tr_context, ctxt1), ts2) =
+ ((empty_tr_context, ctxt), ts1)
+ |-> (if has_datatypes then collect_datatypes_and_records else no_dtyps)
+
+ fun is_binder (Const (@{const_name Let}, _) $ _) = true
+ | is_binder t = Lambda_Lifting.is_quantifier t
+
+ fun mk_trigger ((q as Const (@{const_name All}, _)) $ Abs (n, T, t)) =
+ q $ Abs (n, T, mk_trigger t)
+ | mk_trigger (eq as (Const (@{const_name HOL.eq}, T) $ lhs $ _)) =
+ Term.domain_type T --> @{typ SMT2.pattern}
+ |> (fn T => Const (@{const_name SMT2.pat}, T) $ lhs)
+ |> HOLogic.mk_list @{typ SMT2.pattern} o single
+ |> HOLogic.mk_list @{typ "SMT2.pattern list"} o single
+ |> (fn t => @{const SMT2.trigger} $ t $ eq)
+ | mk_trigger t = t
+
+ val (ctxt2, ts3) =
+ ts2
+ |> eta_expand ctxt1 funcs
+ |> rpair ctxt1
+ |-> Lambda_Lifting.lift_lambdas NONE is_binder
+ |-> (fn (ts', defs) => fn ctxt' =>
+ map mk_trigger defs @ ts'
+ |> intro_explicit_application ctxt' funcs
+ |> pair ctxt')
+
+ val ((rewrite_rules, builtin), ts4) = folify ctxt2 ts3
+ |>> apfst (cons fun_app_eq)
+ in
+ (ts4, tr_context)
+ |-> intermediate header dtyps (builtin SMT2_Builtin.dest_builtin) ctxt2
+ |>> uncurry (serialize comments)
+ ||> replay_data_of ctxt2 rewrite_rules ithms
+ end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smt2_util.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,224 @@
+(* Title: HOL/Tools/SMT2/smt2_util.ML
+ Author: Sascha Boehme, TU Muenchen
+
+General utility functions.
+*)
+
+signature SMT2_UTIL =
+sig
+ (*basic combinators*)
+ val repeat: ('a -> 'a option) -> 'a -> 'a
+ val repeat_yield: ('a -> 'b -> ('a * 'b) option) -> 'a -> 'b -> 'a * 'b
+
+ (*class dictionaries*)
+ type class = string list
+ val basicC: class
+ val string_of_class: class -> string
+ type 'a dict = (class * 'a) Ord_List.T
+ val dict_map_default: class * 'a -> ('a -> 'a) -> 'a dict -> 'a dict
+ val dict_update: class * 'a -> 'a dict -> 'a dict
+ val dict_merge: ('a * 'a -> 'a) -> 'a dict * 'a dict -> 'a dict
+ val dict_lookup: 'a dict -> class -> 'a list
+ val dict_get: 'a dict -> class -> 'a option
+
+ (*types*)
+ val dest_funT: int -> typ -> typ list * typ
+
+ (*terms*)
+ val dest_conj: term -> term * term
+ val dest_disj: term -> term * term
+ val under_quant: (term -> 'a) -> term -> 'a
+ val is_number: term -> bool
+
+ (*patterns and instantiations*)
+ val mk_const_pat: theory -> string -> (ctyp -> 'a) -> 'a * cterm
+ val destT1: ctyp -> ctyp
+ val destT2: ctyp -> ctyp
+ val instTs: ctyp list -> ctyp list * cterm -> cterm
+ val instT: ctyp -> ctyp * cterm -> cterm
+ val instT': cterm -> ctyp * cterm -> cterm
+
+ (*certified terms*)
+ val certify: Proof.context -> term -> cterm
+ val typ_of: cterm -> typ
+ val dest_cabs: cterm -> Proof.context -> cterm * Proof.context
+ val dest_all_cabs: cterm -> Proof.context -> cterm * Proof.context
+ val dest_cbinder: cterm -> Proof.context -> cterm * Proof.context
+ val dest_all_cbinders: cterm -> Proof.context -> cterm * Proof.context
+ val mk_cprop: cterm -> cterm
+ val dest_cprop: cterm -> cterm
+ val mk_cequals: cterm -> cterm -> cterm
+ val term_of: cterm -> term
+ val prop_of: thm -> term
+
+ (*conversions*)
+ val if_conv: (term -> bool) -> conv -> conv -> conv
+ val if_true_conv: (term -> bool) -> conv -> conv
+ val if_exists_conv: (term -> bool) -> conv -> conv
+ val binders_conv: (Proof.context -> conv) -> Proof.context -> conv
+ val under_quant_conv: (Proof.context * cterm list -> conv) ->
+ Proof.context -> conv
+ val prop_conv: conv -> conv
+end
+
+structure SMT2_Util: SMT2_UTIL =
+struct
+
+(* basic combinators *)
+
+fun repeat f =
+ let fun rep x = (case f x of SOME y => rep y | NONE => x)
+ in rep end
+
+fun repeat_yield f =
+ let fun rep x y = (case f x y of SOME (x', y') => rep x' y' | NONE => (x, y))
+ in rep end
+
+
+(* class dictionaries *)
+
+type class = string list
+
+val basicC = []
+
+fun string_of_class [] = "basic"
+ | string_of_class cs = "basic." ^ space_implode "." cs
+
+type 'a dict = (class * 'a) Ord_List.T
+
+fun class_ord ((cs1, _), (cs2, _)) =
+ rev_order (list_ord fast_string_ord (cs1, cs2))
+
+fun dict_insert (cs, x) d =
+ if AList.defined (op =) d cs then d
+ else Ord_List.insert class_ord (cs, x) d
+
+fun dict_map_default (cs, x) f =
+ dict_insert (cs, x) #> AList.map_entry (op =) cs f
+
+fun dict_update (e as (_, x)) = dict_map_default e (K x)
+
+fun dict_merge val_merge = sort class_ord o AList.join (op =) (K val_merge)
+
+fun dict_lookup d cs =
+ let fun match (cs', x) = if is_prefix (op =) cs' cs then SOME x else NONE
+ in map_filter match d end
+
+fun dict_get d cs =
+ (case AList.lookup (op =) d cs of
+ NONE => (case cs of [] => NONE | _ => dict_get d (take (length cs - 1) cs))
+ | SOME x => SOME x)
+
+
+(* types *)
+
+val dest_funT =
+ let
+ fun dest Ts 0 T = (rev Ts, T)
+ | dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U
+ | dest _ _ T = raise TYPE ("not a function type", [T], [])
+ in dest [] end
+
+
+(* terms *)
+
+fun dest_conj (@{const HOL.conj} $ t $ u) = (t, u)
+ | dest_conj t = raise TERM ("not a conjunction", [t])
+
+fun dest_disj (@{const HOL.disj} $ t $ u) = (t, u)
+ | dest_disj t = raise TERM ("not a disjunction", [t])
+
+fun under_quant f t =
+ (case t of
+ Const (@{const_name All}, _) $ Abs (_, _, u) => under_quant f u
+ | Const (@{const_name Ex}, _) $ Abs (_, _, u) => under_quant f u
+ | _ => f t)
+
+val is_number =
+ let
+ fun is_num env (Const (@{const_name Let}, _) $ t $ Abs (_, _, u)) = is_num (t :: env) u
+ | is_num env (Bound i) = i < length env andalso is_num env (nth env i)
+ | is_num _ t = can HOLogic.dest_number t
+ in is_num [] end
+
+
+(* patterns and instantiations *)
+
+fun mk_const_pat thy name destT =
+ let val cpat = Thm.cterm_of thy (Const (name, Sign.the_const_type thy name))
+ in (destT (Thm.ctyp_of_term cpat), cpat) end
+
+val destT1 = hd o Thm.dest_ctyp
+val destT2 = hd o tl o Thm.dest_ctyp
+
+fun instTs cUs (cTs, ct) = Thm.instantiate_cterm (cTs ~~ cUs, []) ct
+fun instT cU (cT, ct) = instTs [cU] ([cT], ct)
+fun instT' ct = instT (Thm.ctyp_of_term ct)
+
+
+(* certified terms *)
+
+fun certify ctxt = Thm.cterm_of (Proof_Context.theory_of ctxt)
+
+fun typ_of ct = #T (Thm.rep_cterm ct)
+
+fun dest_cabs ct ctxt =
+ (case Thm.term_of ct of
+ Abs _ =>
+ let val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
+ in (snd (Thm.dest_abs (SOME n) ct), ctxt') end
+ | _ => raise CTERM ("no abstraction", [ct]))
+
+val dest_all_cabs = repeat_yield (try o dest_cabs)
+
+fun dest_cbinder ct ctxt =
+ (case Thm.term_of ct of
+ Const _ $ Abs _ => dest_cabs (Thm.dest_arg ct) ctxt
+ | _ => raise CTERM ("not a binder", [ct]))
+
+val dest_all_cbinders = repeat_yield (try o dest_cbinder)
+
+val mk_cprop = Thm.apply (Thm.cterm_of @{theory} @{const Trueprop})
+
+fun dest_cprop ct =
+ (case Thm.term_of ct of
+ @{const Trueprop} $ _ => Thm.dest_arg ct
+ | _ => raise CTERM ("not a property", [ct]))
+
+val equals = mk_const_pat @{theory} @{const_name "=="} destT1
+fun mk_cequals ct cu = Thm.mk_binop (instT' ct equals) ct cu
+
+val dest_prop = (fn @{const Trueprop} $ t => t | t => t)
+fun term_of ct = dest_prop (Thm.term_of ct)
+fun prop_of thm = dest_prop (Thm.prop_of thm)
+
+
+(* conversions *)
+
+fun if_conv pred cv1 cv2 ct = if pred (Thm.term_of ct) then cv1 ct else cv2 ct
+
+fun if_true_conv pred cv = if_conv pred cv Conv.all_conv
+
+fun if_exists_conv pred = if_true_conv (Term.exists_subterm pred)
+
+fun binders_conv cv ctxt =
+ Conv.binder_conv (binders_conv cv o snd) ctxt else_conv cv ctxt
+
+fun under_quant_conv cv ctxt =
+ let
+ fun quant_conv inside ctxt cvs ct =
+ (case Thm.term_of ct of
+ Const (@{const_name All}, _) $ Abs _ =>
+ Conv.binder_conv (under_conv cvs) ctxt
+ | Const (@{const_name Ex}, _) $ Abs _ =>
+ Conv.binder_conv (under_conv cvs) ctxt
+ | _ => if inside then cv (ctxt, cvs) else Conv.all_conv) ct
+ and under_conv cvs (cv, ctxt) = quant_conv true ctxt (cv :: cvs)
+ in quant_conv false ctxt [] end
+
+fun prop_conv cv ct =
+ (case Thm.term_of ct of
+ @{const Trueprop} $ _ => Conv.arg_conv cv ct
+ | _ => raise CTERM ("not a property", [ct]))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smtlib2.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,199 @@
+(* Title: HOL/Tools/SMT2/smtlib2.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Parsing and generating SMT-LIB 2.
+*)
+
+signature SMTLIB2 =
+sig
+ exception PARSE of int * string
+ datatype tree =
+ Num of int |
+ Dec of int * int |
+ Str of string |
+ Sym of string |
+ Key of string |
+ S of tree list
+ val parse: string list -> tree
+ val pretty_tree: tree -> Pretty.T
+ val str_of: tree -> string
+end
+
+structure SMTLIB2: SMTLIB2 =
+struct
+
+(* data structures *)
+
+exception PARSE of int * string
+
+datatype tree =
+ Num of int |
+ Dec of int * int |
+ Str of string |
+ Sym of string |
+ Key of string |
+ S of tree list
+
+datatype unfinished = None | String of string | Symbol of string
+
+
+
+(* utilities *)
+
+fun read_raw pred l cs =
+ (case take_prefix pred cs of
+ ([], []) => raise PARSE (l, "empty token")
+ | ([], c :: _) => raise PARSE (l, "unexpected character " ^ quote c)
+ | x => x)
+
+
+
+(* numerals and decimals *)
+
+fun int_of cs = fst (read_int cs)
+
+fun read_num l cs =
+ (case read_raw Symbol.is_ascii_digit l cs of
+ (cs1, "." :: cs') =>
+ let val (cs2, cs'') = read_raw Symbol.is_ascii_digit l cs'
+ in (Dec (int_of cs1, int_of cs2), cs'') end
+ | (cs1, cs2) => (Num (int_of cs1), cs2))
+
+
+
+(* binary numbers *)
+
+fun is_bin c = (c = "0" orelse c = "1")
+
+fun read_bin l cs = read_raw is_bin l cs |>> Num o fst o read_radix_int 2
+
+
+
+(* hex numbers *)
+
+val is_hex = member (op =) (raw_explode "0123456789abcdefABCDEF")
+
+fun within c1 c2 c = (ord c1 <= ord c andalso ord c <= ord c2)
+
+fun unhex i [] = i
+ | unhex i (c :: cs) =
+ if within "0" "9" c then unhex (i * 16 + (ord c - ord "0")) cs
+ else if within "a" "f" c then unhex (i * 16 + (ord c - ord "a" + 10)) cs
+ else if within "A" "F" c then unhex (i * 16 + (ord c - ord "A" + 10)) cs
+ else raise Fail ("bad hex character " ^ quote c)
+
+fun read_hex l cs = read_raw is_hex l cs |>> Num o unhex 0
+
+
+
+(* symbols *)
+
+val symbol_chars = raw_explode "~!@$%^&*_+=<>.?/-"
+
+fun is_sym c =
+ Symbol.is_ascii_letter c orelse
+ Symbol.is_ascii_digit c orelse
+ member (op =) symbol_chars c
+
+fun read_sym f l cs = read_raw is_sym l cs |>> f o implode
+
+
+
+(* quoted tokens *)
+
+fun read_quoted stop (escape, replacement) cs =
+ let
+ fun read _ [] = NONE
+ | read rs (cs as (c :: cs')) =
+ if is_prefix (op =) stop cs then
+ SOME (implode (rev rs), drop (length stop) cs)
+ else if not (null escape) andalso is_prefix (op =) escape cs then
+ read (replacement :: rs) (drop (length escape) cs)
+ else read (c :: rs) cs'
+ in read [] cs end
+
+fun read_string cs = read_quoted ["\\", "\""] (["\\", "\\"], "\\") cs
+fun read_symbol cs = read_quoted ["|"] ([], "") cs
+
+
+
+(* core parser *)
+
+fun read _ [] rest tss = (rest, tss)
+ | read l ("(" :: cs) None tss = read l cs None ([] :: tss)
+ | read l (")" :: cs) None (ts1 :: ts2 :: tss) =
+ read l cs None ((S (rev ts1) :: ts2) :: tss)
+ | read l ("#" :: "x" :: cs) None (ts :: tss) =
+ token read_hex l cs ts tss
+ | read l ("#" :: cs) None (ts :: tss) =
+ token read_bin l cs ts tss
+ | read l (":" :: cs) None (ts :: tss) =
+ token (read_sym Key) l cs ts tss
+ | read l ("\"" :: cs) None (ts :: tss) =
+ quoted read_string String Str l "" cs ts tss
+ | read l ("|" :: cs) None (ts :: tss) =
+ quoted read_symbol Symbol Sym l "" cs ts tss
+ | read l ((c as "!") :: cs) None (ts :: tss) =
+ token (fn _ => pair (Sym c)) l cs ts tss
+ | read l (c :: cs) None (ts :: tss) =
+ if Symbol.is_ascii_blank c then read l cs None (ts :: tss)
+ else if Symbol.is_digit c then token read_num l (c :: cs) ts tss
+ else token (read_sym Sym) l (c :: cs) ts tss
+ | read l cs (String s) (ts :: tss) =
+ quoted read_string String Str l s cs ts tss
+ | read l cs (Symbol s) (ts :: tss) =
+ quoted read_symbol Symbol Sym l s cs ts tss
+ | read l _ _ [] = raise PARSE (l, "bad parser state")
+
+and token f l cs ts tss =
+ let val (t, cs') = f l cs
+ in read l cs' None ((t :: ts) :: tss) end
+
+and quoted r f g l s cs ts tss =
+ (case r cs of
+ NONE => (f (s ^ implode cs), ts :: tss)
+ | SOME (s', cs') => read l cs' None ((g (s ^ s') :: ts) :: tss))
+
+
+
+(* overall parser *)
+
+fun read_line l line = read l (raw_explode line)
+
+fun add_line line (l, (None, tss)) =
+ if size line = 0 orelse nth_string line 0 = ";" then (l + 1, (None, tss))
+ else (l + 1, read_line l line None tss)
+ | add_line line (l, (unfinished, tss)) =
+ (l + 1, read_line l line unfinished tss)
+
+fun finish (_, (None, [[t]])) = t
+ | finish (l, _) = raise PARSE (l, "bad nesting")
+
+fun parse lines = finish (fold add_line lines (1, (None, [[]])))
+
+
+
+(* pretty printer *)
+
+fun pretty_tree (Num i) = Pretty.str (string_of_int i)
+ | pretty_tree (Dec (i, j)) =
+ Pretty.str (string_of_int i ^ "." ^ string_of_int j)
+ | pretty_tree (Str s) =
+ raw_explode s
+ |> maps (fn "\"" => ["\\", "\""] | "\\" => ["\\", "\\"] | c => [c])
+ |> implode
+ |> enclose "\"" "\""
+ |> Pretty.str
+ | pretty_tree (Sym s) =
+ if String.isPrefix "(" s (* for bit vector functions *) orelse
+ forall is_sym (raw_explode s) then
+ Pretty.str s
+ else
+ Pretty.str ("|" ^ s ^ "|")
+ | pretty_tree (Key s) = Pretty.str (":" ^ s)
+ | pretty_tree (S trees) =
+ Pretty.enclose "(" ")" (Pretty.separate "" (map pretty_tree trees))
+
+val str_of = Pretty.str_of o pretty_tree
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/smtlib2_interface.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,154 @@
+(* Title: HOL/Tools/SMT2/smtlib2_interface.ML
+ Author: Sascha Boehme, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+Interface to SMT solvers based on the SMT-LIB 2 format.
+*)
+
+signature SMTLIB2_INTERFACE =
+sig
+ val smtlib2C: SMT2_Util.class
+ val add_logic: int * (term list -> string option) -> Context.generic -> Context.generic
+ val translate_config: Proof.context -> SMT2_Translate.config
+end
+
+structure SMTLIB2_Interface: SMTLIB2_INTERFACE =
+struct
+
+val smtlib2C = ["smtlib2"]
+
+
+(* builtins *)
+
+local
+ fun int_num _ i = SOME (string_of_int i)
+
+ fun is_linear [t] = SMT2_Util.is_number t
+ | is_linear [t, u] = SMT2_Util.is_number t orelse SMT2_Util.is_number u
+ | is_linear _ = false
+
+ fun times _ _ ts =
+ let val mk = Term.list_comb o pair @{const times (int)}
+ in if is_linear ts then SOME ("*", 2, ts, mk) else NONE end
+in
+
+val setup_builtins =
+ fold (SMT2_Builtin.add_builtin_typ smtlib2C) [
+ (@{typ bool}, K (SOME "Bool"), K (K NONE)),
+ (@{typ int}, K (SOME "Int"), int_num)] #>
+ fold (SMT2_Builtin.add_builtin_fun' smtlib2C) [
+ (@{const True}, "true"),
+ (@{const False}, "false"),
+ (@{const Not}, "not"),
+ (@{const HOL.conj}, "and"),
+ (@{const HOL.disj}, "or"),
+ (@{const HOL.implies}, "=>"),
+ (@{const HOL.eq ('a)}, "="),
+ (@{const If ('a)}, "ite"),
+ (@{const less (int)}, "<"),
+ (@{const less_eq (int)}, "<="),
+ (@{const uminus (int)}, "~"),
+ (@{const plus (int)}, "+"),
+ (@{const minus (int)}, "-")] #>
+ SMT2_Builtin.add_builtin_fun smtlib2C
+ (Term.dest_Const @{const times (int)}, times)
+
+end
+
+
+(* serialization *)
+
+(** header **)
+
+fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2)
+
+structure Logics = Generic_Data
+(
+ type T = (int * (term list -> string option)) list
+ val empty = []
+ val extend = I
+ fun merge data = Ord_List.merge fst_int_ord data
+)
+
+fun add_logic pf = Logics.map (Ord_List.insert fst_int_ord pf)
+
+fun choose_logic ctxt ts =
+ let
+ fun choose [] = "AUFLIA"
+ | choose ((_, f) :: fs) = (case f ts of SOME s => s | NONE => choose fs)
+ in "(set-logic " ^ choose (Logics.get (Context.Proof ctxt)) ^ ")\n" end
+
+
+(** serialization **)
+
+fun var i = "?v" ^ string_of_int i
+
+fun tree_of_sterm l (SMT2_Translate.SVar i) = SMTLIB2.Sym (var (l - i - 1))
+ | tree_of_sterm _ (SMT2_Translate.SApp (n, [])) = SMTLIB2.Sym n
+ | tree_of_sterm l (SMT2_Translate.SApp (n, ts)) =
+ SMTLIB2.S (SMTLIB2.Sym n :: map (tree_of_sterm l) ts)
+ | tree_of_sterm _ (SMT2_Translate.SLet _) =
+ raise Fail "SMT-LIB: unsupported let expression"
+ | tree_of_sterm l (SMT2_Translate.SQua (q, ss, pats, w, t)) =
+ let
+ val l' = l + length ss
+
+ fun quant_name SMT2_Translate.SForall = "forall"
+ | quant_name SMT2_Translate.SExists = "exists"
+
+ fun gen_trees_of_pat keyword ps =
+ [SMTLIB2.Key keyword, (case map (tree_of_sterm l') ps of [t] => t | ts => SMTLIB2.S ts)]
+ fun trees_of_pat (SMT2_Translate.SPat ps) = gen_trees_of_pat "pattern" ps
+ | trees_of_pat (SMT2_Translate.SNoPat ps) = gen_trees_of_pat "no-pattern" ps
+ fun trees_of_weight NONE = []
+ | trees_of_weight (SOME i) = [SMTLIB2.Key "weight", SMTLIB2.Num i]
+ fun tree_of_pats_weight [] NONE t = t
+ | tree_of_pats_weight pats w t =
+ SMTLIB2.S (SMTLIB2.Sym "!" :: t :: maps trees_of_pat pats @ trees_of_weight w)
+
+ val vs = map_index (fn (i, ty) =>
+ SMTLIB2.S [SMTLIB2.Sym (var (l + i)), SMTLIB2.Sym ty]) ss
+
+ val body = t
+ |> tree_of_sterm l'
+ |> tree_of_pats_weight pats w
+ in
+ SMTLIB2.S [SMTLIB2.Sym (quant_name q), SMTLIB2.S vs, body]
+ end
+
+
+fun sctrarg (sel, typ) = "(" ^ sel ^ " " ^ typ ^ ")"
+fun sctr (name, args) = enclose "(" ")" (space_implode " " (name :: map sctrarg args))
+fun sdatatype (name, ctrs) = enclose "(" ")" (space_implode " " (name :: map sctr ctrs))
+
+fun string_of_fun (f, (ss, s)) = f ^ " (" ^ space_implode " " ss ^ ") " ^ s
+
+fun serialize comments {header, sorts, dtyps, funcs} ts =
+ Buffer.empty
+ |> fold (Buffer.add o enclose "; " "\n") comments
+ |> Buffer.add "(set-option :produce-proofs true)\n"
+ |> Buffer.add header
+ |> fold (Buffer.add o enclose "(declare-sort " " 0)\n")
+ (sort fast_string_ord sorts)
+ |> (if null dtyps then I
+ else Buffer.add (enclose "(declare-datatypes () (" "))\n"
+ (space_implode "\n " (maps (map sdatatype) dtyps))))
+ |> fold (Buffer.add o enclose "(declare-fun " ")\n" o string_of_fun)
+ (sort (fast_string_ord o pairself fst) funcs)
+ |> fold (Buffer.add o enclose "(assert " ")\n" o SMTLIB2.str_of o
+ tree_of_sterm 0) ts
+ |> Buffer.add "(check-sat)\n(get-proof)\n" (* FIXME: (get-model)\n" *)
+ |> Buffer.content
+
+(* interface *)
+
+fun translate_config ctxt = {
+ header = choose_logic ctxt,
+ has_datatypes = false,
+ serialize = serialize}
+
+val _ = Theory.setup (Context.theory_map
+ (setup_builtins #>
+ SMT2_Translate.add_config (smtlib2C, translate_config)))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_interface.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,198 @@
+(* Title: HOL/Tools/SMT2/z3_new_interface.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Interface to Z3 based on a relaxed version of SMT-LIB.
+*)
+
+signature Z3_NEW_INTERFACE =
+sig
+ val smtlib2_z3C: SMT2_Util.class
+
+ datatype sym = Sym of string * sym list
+ type mk_builtins = {
+ mk_builtin_typ: sym -> typ option,
+ mk_builtin_num: theory -> int -> typ -> cterm option,
+ mk_builtin_fun: theory -> sym -> cterm list -> cterm option }
+ val add_mk_builtins: mk_builtins -> Context.generic -> Context.generic
+ val mk_builtin_typ: Proof.context -> sym -> typ option
+ val mk_builtin_num: Proof.context -> int -> typ -> cterm option
+ val mk_builtin_fun: Proof.context -> sym -> cterm list -> cterm option
+
+ val is_builtin_theory_term: Proof.context -> term -> bool
+end
+
+structure Z3_New_Interface: Z3_NEW_INTERFACE =
+struct
+
+val smtlib2_z3C = SMTLIB2_Interface.smtlib2C @ ["z3"]
+
+
+
+(* interface *)
+
+local
+ fun translate_config ctxt =
+ let
+ val {serialize, ...} = SMTLIB2_Interface.translate_config ctxt
+ in
+ {header=K "", serialize=serialize, has_datatypes=true}
+ end
+
+ fun is_div_mod @{const div (int)} = true
+ | is_div_mod @{const mod (int)} = true
+ | is_div_mod _ = false
+
+ val have_int_div_mod = exists (Term.exists_subterm is_div_mod o Thm.prop_of)
+
+ fun add_div_mod _ (thms, extra_thms) =
+ if have_int_div_mod thms orelse have_int_div_mod extra_thms then
+ (thms, @{thms div_as_z3div mod_as_z3mod} @ extra_thms)
+ else (thms, extra_thms)
+
+ val setup_builtins =
+ SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const times (int)}, "*") #>
+ SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const z3div}, "div") #>
+ SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const z3mod}, "mod")
+in
+
+val _ = Theory.setup (Context.theory_map (
+ setup_builtins #>
+ SMT2_Normalize.add_extra_norm (smtlib2_z3C, add_div_mod) #>
+ SMT2_Translate.add_config (smtlib2_z3C, translate_config)))
+
+end
+
+
+
+(* constructors *)
+
+datatype sym = Sym of string * sym list
+
+
+(** additional constructors **)
+
+type mk_builtins = {
+ mk_builtin_typ: sym -> typ option,
+ mk_builtin_num: theory -> int -> typ -> cterm option,
+ mk_builtin_fun: theory -> sym -> cterm list -> cterm option }
+
+fun chained _ [] = NONE
+ | chained f (b :: bs) = (case f b of SOME y => SOME y | NONE => chained f bs)
+
+fun chained_mk_builtin_typ bs sym =
+ chained (fn {mk_builtin_typ=mk, ...} : mk_builtins => mk sym) bs
+
+fun chained_mk_builtin_num ctxt bs i T =
+ let val thy = Proof_Context.theory_of ctxt
+ in chained (fn {mk_builtin_num=mk, ...} : mk_builtins => mk thy i T) bs end
+
+fun chained_mk_builtin_fun ctxt bs s cts =
+ let val thy = Proof_Context.theory_of ctxt
+ in chained (fn {mk_builtin_fun=mk, ...} : mk_builtins => mk thy s cts) bs end
+
+fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2)
+
+structure Mk_Builtins = Generic_Data
+(
+ type T = (int * mk_builtins) list
+ val empty = []
+ val extend = I
+ fun merge data = Ord_List.merge fst_int_ord data
+)
+
+fun add_mk_builtins mk = Mk_Builtins.map (Ord_List.insert fst_int_ord (serial (), mk))
+
+fun get_mk_builtins ctxt = map snd (Mk_Builtins.get (Context.Proof ctxt))
+
+
+(** basic and additional constructors **)
+
+fun mk_builtin_typ _ (Sym ("Bool", _)) = SOME @{typ bool}
+ | mk_builtin_typ _ (Sym ("Int", _)) = SOME @{typ int}
+ | mk_builtin_typ _ (Sym ("bool", _)) = SOME @{typ bool} (*FIXME: legacy*)
+ | mk_builtin_typ _ (Sym ("int", _)) = SOME @{typ int} (*FIXME: legacy*)
+ | mk_builtin_typ ctxt sym = chained_mk_builtin_typ (get_mk_builtins ctxt) sym
+
+fun mk_builtin_num _ i @{typ int} = SOME (Numeral.mk_cnumber @{ctyp int} i)
+ | mk_builtin_num ctxt i T =
+ chained_mk_builtin_num ctxt (get_mk_builtins ctxt) i T
+
+val mk_true = Thm.cterm_of @{theory} (@{const Not} $ @{const False})
+val mk_false = Thm.cterm_of @{theory} @{const False}
+val mk_not = Thm.apply (Thm.cterm_of @{theory} @{const Not})
+val mk_implies = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.implies})
+val mk_iff = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.eq (bool)})
+val conj = Thm.cterm_of @{theory} @{const HOL.conj}
+val disj = Thm.cterm_of @{theory} @{const HOL.disj}
+
+fun mk_nary _ cu [] = cu
+ | mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts)
+
+val eq = SMT2_Util.mk_const_pat @{theory} @{const_name HOL.eq} SMT2_Util.destT1
+fun mk_eq ct cu = Thm.mk_binop (SMT2_Util.instT' ct eq) ct cu
+
+val if_term =
+ SMT2_Util.mk_const_pat @{theory} @{const_name If} (SMT2_Util.destT1 o SMT2_Util.destT2)
+fun mk_if cc ct = Thm.mk_binop (Thm.apply (SMT2_Util.instT' ct if_term) cc) ct
+
+val access = SMT2_Util.mk_const_pat @{theory} @{const_name fun_app} SMT2_Util.destT1
+fun mk_access array = Thm.apply (SMT2_Util.instT' array access) array
+
+val update =
+ SMT2_Util.mk_const_pat @{theory} @{const_name fun_upd} (Thm.dest_ctyp o SMT2_Util.destT1)
+fun mk_update array index value =
+ let val cTs = Thm.dest_ctyp (Thm.ctyp_of_term array)
+ in Thm.apply (Thm.mk_binop (SMT2_Util.instTs cTs update) array index) value end
+
+val mk_uminus = Thm.apply (Thm.cterm_of @{theory} @{const uminus (int)})
+val add = Thm.cterm_of @{theory} @{const plus (int)}
+val int0 = Numeral.mk_cnumber @{ctyp int} 0
+val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (int)})
+val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (int)})
+val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3div})
+val mk_mod = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3mod})
+val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (int)})
+val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (int)})
+
+fun mk_builtin_fun ctxt sym cts =
+ (case (sym, cts) of
+ (Sym ("true", _), []) => SOME mk_true
+ | (Sym ("false", _), []) => SOME mk_false
+ | (Sym ("not", _), [ct]) => SOME (mk_not ct)
+ | (Sym ("and", _), _) => SOME (mk_nary conj mk_true cts)
+ | (Sym ("or", _), _) => SOME (mk_nary disj mk_false cts)
+ | (Sym ("implies", _), [ct, cu]) => SOME (mk_implies ct cu)
+ | (Sym ("iff", _), [ct, cu]) => SOME (mk_iff ct cu)
+ | (Sym ("~", _), [ct, cu]) => SOME (mk_iff ct cu)
+ | (Sym ("xor", _), [ct, cu]) => SOME (mk_not (mk_iff ct cu))
+ | (Sym ("if", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3)
+ | (Sym ("ite", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3) (* FIXME: remove *)
+ | (Sym ("=", _), [ct, cu]) => SOME (mk_eq ct cu)
+ | (Sym ("select", _), [ca, ck]) => SOME (Thm.apply (mk_access ca) ck)
+ | (Sym ("store", _), [ca, ck, cv]) => SOME (mk_update ca ck cv)
+ | _ =>
+ (case (sym, try (#T o Thm.rep_cterm o hd) cts, cts) of
+ (Sym ("+", _), SOME @{typ int}, _) => SOME (mk_nary add int0 cts)
+ | (Sym ("-", _), SOME @{typ int}, [ct]) => SOME (mk_uminus ct)
+ | (Sym ("-", _), SOME @{typ int}, [ct, cu]) => SOME (mk_sub ct cu)
+ | (Sym ("*", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mul ct cu)
+ | (Sym ("div", _), SOME @{typ int}, [ct, cu]) => SOME (mk_div ct cu)
+ | (Sym ("mod", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mod ct cu)
+ | (Sym ("<", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt ct cu)
+ | (Sym ("<=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le ct cu)
+ | (Sym (">", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt cu ct)
+ | (Sym (">=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le cu ct)
+ | _ => chained_mk_builtin_fun ctxt (get_mk_builtins ctxt) sym cts))
+
+
+
+(* abstraction *)
+
+fun is_builtin_theory_term ctxt t =
+ if SMT2_Builtin.is_builtin_num ctxt t then true
+ else
+ (case Term.strip_comb t of
+ (Const c, ts) => SMT2_Builtin.is_builtin_fun ctxt c ts
+ | _ => false)
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_isar.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,107 @@
+(* Title: HOL/Tools/SMT2/z3_new_isar.ML
+ Author: Jasmin Blanchette, TU Muenchen
+
+Z3 proofs as generic ATP proofs for Isar proof reconstruction.
+*)
+
+signature Z3_NEW_ISAR =
+sig
+ type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
+
+ val atp_proof_of_z3_proof: theory -> int -> (int * string) list -> Z3_New_Proof.z3_step list ->
+ (term, string) atp_step list
+end;
+
+structure Z3_New_Isar: Z3_NEW_ISAR =
+struct
+
+open ATP_Util
+open ATP_Problem
+open ATP_Proof
+open ATP_Proof_Reconstruct
+
+val z3_apply_def_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Apply_Def
+val z3_hypothesis_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Hypothesis
+val z3_intro_def_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Intro_Def
+val z3_lemma_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Lemma
+
+fun inline_z3_defs _ [] = []
+ | inline_z3_defs defs ((name, role, t, rule, deps) :: lines) =
+ if rule = z3_intro_def_rule then
+ let val def = t |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> swap in
+ inline_z3_defs (insert (op =) def defs)
+ (map (replace_dependencies_in_line (name, [])) lines)
+ end
+ else if rule = z3_apply_def_rule then
+ inline_z3_defs defs (map (replace_dependencies_in_line (name, [])) lines)
+ else
+ (name, role, Term.subst_atomic defs t, rule, deps) :: inline_z3_defs defs lines
+
+fun add_z3_hypotheses [] = I
+ | add_z3_hypotheses hyps =
+ HOLogic.dest_Trueprop
+ #> curry s_imp (Library.foldr1 s_conj (map HOLogic.dest_Trueprop hyps))
+ #> HOLogic.mk_Trueprop
+
+fun inline_z3_hypotheses _ _ [] = []
+ | inline_z3_hypotheses hyp_names hyps ((name, role, t, rule, deps) :: lines) =
+ if rule = z3_hypothesis_rule then
+ inline_z3_hypotheses (name :: hyp_names) (AList.map_default (op =) (t, []) (cons name) hyps)
+ lines
+ else
+ let val deps' = subtract (op =) hyp_names deps in
+ if rule = z3_lemma_rule then
+ (name, role, t, rule, deps') :: inline_z3_hypotheses hyp_names hyps lines
+ else
+ let
+ val add_hyps = filter_out (null o inter (op =) deps o snd) hyps
+ val t' = add_z3_hypotheses (map fst add_hyps) t
+ val deps' = subtract (op =) hyp_names deps
+ val hyps' = fold (AList.update (op =) o apsnd (insert (op =) name)) add_hyps hyps
+ in
+ (name, role, t', rule, deps') :: inline_z3_hypotheses hyp_names hyps' lines
+ end
+ end
+
+fun simplify_prop (@{const Not} $ t) = s_not (simplify_prop t)
+ | simplify_prop (@{const conj} $ t $ u) = s_conj (simplify_prop t, simplify_prop u)
+ | simplify_prop (@{const disj} $ t $ u) = s_disj (simplify_prop t, simplify_prop u)
+ | simplify_prop (@{const implies} $ t $ u) = s_imp (simplify_prop t, simplify_prop u)
+ | simplify_prop (@{const HOL.eq (bool)} $ t $ u) = s_iff (simplify_prop t, simplify_prop u)
+ | simplify_prop (t $ u) = simplify_prop t $ simplify_prop u
+ | simplify_prop (Abs (s, T, t)) = Abs (s, T, simplify_prop t)
+ | simplify_prop t = t
+
+fun simplify_line (name, role, t, rule, deps) = (name, role, simplify_prop t, rule, deps)
+
+fun atp_proof_of_z3_proof thy conjecture_id fact_ids proof =
+ let
+ fun step_of (Z3_New_Proof.Z3_Step {id, rule, prems, concl, ...}) =
+ let
+ fun step_name_of id = (string_of_int id, the_list (AList.lookup (op =) fact_ids id))
+
+ val name as (_, ss) = step_name_of id
+ val role =
+ (case rule of
+ Z3_New_Proof.Asserted =>
+ if not (null ss) then Axiom
+ else if id = conjecture_id then Negated_Conjecture
+ else Hypothesis
+ | Z3_New_Proof.Rewrite => Lemma
+ | Z3_New_Proof.Rewrite_Star => Lemma
+ | Z3_New_Proof.Skolemize => Lemma
+ | Z3_New_Proof.Th_Lemma _ => Lemma
+ | _ => Plain)
+ in
+ (name, role, HOLogic.mk_Trueprop (Object_Logic.atomize_term thy concl),
+ Z3_New_Proof.string_of_rule rule, map step_name_of prems)
+ end
+ in
+ proof
+ |> map step_of
+ |> inline_z3_defs []
+ |> inline_z3_hypotheses [] []
+ |> map simplify_line
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_model.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,334 @@
+(* Title: HOL/Tools/SMT2/z3_new_model.ML
+ Author: Sascha Boehme and Philipp Meyer, TU Muenchen
+
+Parser for counterexamples generated by Z3.
+*)
+
+signature Z3_NEW_MODEL =
+sig
+ val parse_counterex: Proof.context -> SMT2_Translate.replay_data -> string list ->
+ term list * term list
+end
+
+structure Z3_New_Model: Z3_NEW_MODEL =
+struct
+
+(* counterexample expressions *)
+
+datatype expr = True | False | Number of int * int option | Value of int |
+ Array of array | App of string * expr list
+and array = Fresh of expr | Store of (array * expr) * expr
+
+
+(* parsing *)
+
+val space = Scan.many Symbol.is_ascii_blank
+fun spaced p = p --| space
+fun in_parens p = spaced (Scan.$$ "(") |-- p --| spaced (Scan.$$ ")")
+fun in_braces p = spaced (Scan.$$ "{") |-- p --| spaced (Scan.$$ "}")
+
+val digit = (fn
+ "0" => SOME 0 | "1" => SOME 1 | "2" => SOME 2 | "3" => SOME 3 |
+ "4" => SOME 4 | "5" => SOME 5 | "6" => SOME 6 | "7" => SOME 7 |
+ "8" => SOME 8 | "9" => SOME 9 | _ => NONE)
+
+val nat_num = spaced (Scan.repeat1 (Scan.some digit) >>
+ (fn ds => fold (fn d => fn i => i * 10 + d) ds 0))
+val int_num = spaced (Scan.optional ($$ "-" >> K (fn i => ~i)) I :|--
+ (fn sign => nat_num >> sign))
+
+val is_char = Symbol.is_ascii_letter orf Symbol.is_ascii_digit orf
+ member (op =) (raw_explode "_+*-/%~=<>$&|?!.@^#")
+val name = spaced (Scan.many1 is_char >> implode)
+
+fun $$$ s = spaced (Scan.this_string s)
+
+fun array_expr st = st |> in_parens (
+ $$$ "const" |-- expr >> Fresh ||
+ $$$ "store" |-- array_expr -- expr -- expr >> Store)
+
+and expr st = st |> (
+ $$$ "true" >> K True ||
+ $$$ "false" >> K False ||
+ int_num -- Scan.option ($$$ "/" |-- int_num) >> Number ||
+ $$$ "val!" |-- nat_num >> Value ||
+ name >> (App o rpair []) ||
+ array_expr >> Array ||
+ in_parens (name -- Scan.repeat1 expr) >> App)
+
+fun args st = ($$$ "->" >> K [] || expr ::: args) st
+val args_case = args -- expr
+val else_case = $$$ "else" -- $$$ "->" |-- expr >> pair ([] : expr list)
+
+val func =
+ let fun cases st = (else_case >> single || args_case ::: cases) st
+ in in_braces cases end
+
+val cex = space |--
+ Scan.repeat (name --| $$$ "->" -- (func || expr >> (single o pair [])))
+
+fun resolve terms ((n, k), cases) =
+ (case Symtab.lookup terms n of
+ NONE => NONE
+ | SOME t => SOME ((t, k), cases))
+
+fun annotate _ (_, []) = NONE
+ | annotate terms (n, [([], c)]) = resolve terms ((n, 0), (c, []))
+ | annotate _ (_, [_]) = NONE
+ | annotate terms (n, cases as (args, _) :: _) =
+ let val (cases', (_, else_case)) = split_last cases
+ in resolve terms ((n, length args), (else_case, cases')) end
+
+fun read_cex terms ls =
+ maps (cons "\n" o raw_explode) ls
+ |> try (fst o Scan.finite Symbol.stopper cex)
+ |> the_default []
+ |> map_filter (annotate terms)
+
+
+(* translation into terms *)
+
+fun max_value vs =
+ let
+ fun max_val_expr (Value i) = Integer.max i
+ | max_val_expr (App (_, es)) = fold max_val_expr es
+ | max_val_expr (Array a) = max_val_array a
+ | max_val_expr _ = I
+
+ and max_val_array (Fresh e) = max_val_expr e
+ | max_val_array (Store ((a, e1), e2)) =
+ max_val_array a #> max_val_expr e1 #> max_val_expr e2
+
+ fun max_val (_, (ec, cs)) =
+ max_val_expr ec #> fold (fn (es, e) => fold max_val_expr (e :: es)) cs
+
+ in fold max_val vs ~1 end
+
+fun with_context terms f vs = fst (fold_map f vs (terms, max_value vs + 1))
+
+fun get_term n T es (cx as (terms, next_val)) =
+ (case Symtab.lookup terms n of
+ SOME t => ((t, es), cx)
+ | NONE =>
+ let val t = Var (("skolem", next_val), T)
+ in ((t, []), (Symtab.update (n, t) terms, next_val + 1)) end)
+
+fun trans_expr _ True = pair @{const True}
+ | trans_expr _ False = pair @{const False}
+ | trans_expr T (Number (i, NONE)) = pair (HOLogic.mk_number T i)
+ | trans_expr T (Number (i, SOME j)) =
+ pair (Const (@{const_name divide}, [T, T] ---> T) $
+ HOLogic.mk_number T i $ HOLogic.mk_number T j)
+ | trans_expr T (Value i) = pair (Var (("value", i), T))
+ | trans_expr T (Array a) = trans_array T a
+ | trans_expr T (App (n, es)) = get_term n T es #-> (fn (t, es') =>
+ let val Ts = fst (SMT2_Util.dest_funT (length es') (Term.fastype_of t))
+ in fold_map (uncurry trans_expr) (Ts ~~ es') #>> Term.list_comb o pair t end)
+
+and trans_array T a =
+ let val (dT, rT) = Term.dest_funT T
+ in
+ (case a of
+ Fresh e => trans_expr rT e #>> (fn t => Abs ("x", dT, t))
+ | Store ((a', e1), e2) =>
+ trans_array T a' ##>> trans_expr dT e1 ##>> trans_expr rT e2 #>>
+ (fn ((m, k), v) =>
+ Const (@{const_name fun_upd}, [T, dT, rT] ---> T) $ m $ k $ v))
+ end
+
+fun trans_pattern T ([], e) = trans_expr T e #>> pair []
+ | trans_pattern T (arg :: args, e) =
+ trans_expr (Term.domain_type T) arg ##>>
+ trans_pattern (Term.range_type T) (args, e) #>>
+ (fn (arg', (args', e')) => (arg' :: args', e'))
+
+fun mk_fun_upd T U = Const (@{const_name fun_upd}, [T --> U, T, U, T] ---> U)
+
+fun mk_update ([], u) _ = u
+ | mk_update ([t], u) f =
+ uncurry mk_fun_upd (Term.dest_funT (Term.fastype_of f)) $ f $ t $ u
+ | mk_update (t :: ts, u) f =
+ let
+ val (dT, rT) = Term.dest_funT (Term.fastype_of f)
+ val (dT', rT') = Term.dest_funT rT
+ in
+ mk_fun_upd dT rT $ f $ t $
+ mk_update (ts, u) (absdummy dT' (Const ("_", rT')))
+ end
+
+fun mk_lambda Ts (t, pats) =
+ fold_rev absdummy Ts t |> fold mk_update pats
+
+fun translate ((t, k), (e, cs)) =
+ let
+ val T = Term.fastype_of t
+ val (Us, U) = SMT2_Util.dest_funT k (Term.fastype_of t)
+
+ fun mk_full_def u' pats =
+ pats
+ |> filter_out (fn (_, u) => u aconv u')
+ |> HOLogic.mk_eq o pair t o mk_lambda Us o pair u'
+
+ fun mk_eq (us, u) = HOLogic.mk_eq (Term.list_comb (t, us), u)
+ fun mk_eqs u' [] = [HOLogic.mk_eq (t, u')]
+ | mk_eqs _ pats = map mk_eq pats
+ in
+ trans_expr U e ##>>
+ (if k = 0 then pair [] else fold_map (trans_pattern T) cs) #>>
+ (fn (u', pats) => (mk_eqs u' pats, mk_full_def u' pats))
+ end
+
+
+(* normalization *)
+
+fun partition_eqs f =
+ let
+ fun part t (xs, ts) =
+ (case try HOLogic.dest_eq t of
+ SOME (l, r) => (case f l r of SOME x => (x::xs, ts) | _ => (xs, t::ts))
+ | NONE => (xs, t :: ts))
+ in (fn ts => fold part ts ([], [])) end
+
+fun first_eq pred =
+ let
+ fun part _ [] = NONE
+ | part us (t :: ts) =
+ (case try (pred o HOLogic.dest_eq) t of
+ SOME (SOME lr) => SOME (lr, fold cons us ts)
+ | _ => part (t :: us) ts)
+ in (fn ts => part [] ts) end
+
+fun replace_vars tab =
+ let
+ fun repl v = the_default v (AList.lookup (op aconv) tab v)
+ fun replace (v as Var _) = repl v
+ | replace (v as Free _) = repl v
+ | replace t = t
+ in map (Term.map_aterms replace) end
+
+fun remove_int_nat_coercions (eqs, defs) =
+ let
+ fun mk_nat_num t i =
+ (case try HOLogic.dest_number i of
+ SOME (_, n) => SOME (t, HOLogic.mk_number @{typ nat} n)
+ | NONE => NONE)
+ fun nat_of (@{const of_nat (int)} $ (t as Var _)) i = mk_nat_num t i
+ | nat_of (@{const nat} $ i) (t as Var _) = mk_nat_num t i
+ | nat_of _ _ = NONE
+ val (nats, eqs') = partition_eqs nat_of eqs
+
+ fun is_coercion t =
+ (case try HOLogic.dest_eq t of
+ SOME (@{const of_nat (int)}, _) => true
+ | SOME (@{const nat}, _) => true
+ | _ => false)
+ in pairself (replace_vars nats) (eqs', filter_out is_coercion defs) end
+
+fun unfold_funapp (eqs, defs) =
+ let
+ fun unfold_app (Const (@{const_name SMT2.fun_app}, _) $ f $ t) = f $ t
+ | unfold_app t = t
+ fun unfold_eq ((eq as Const (@{const_name HOL.eq}, _)) $ t $ u) =
+ eq $ unfold_app t $ u
+ | unfold_eq t = t
+
+ fun is_fun_app t =
+ (case try HOLogic.dest_eq t of
+ SOME (Const (@{const_name SMT2.fun_app}, _), _) => true
+ | _ => false)
+
+ in (map unfold_eq eqs, filter_out is_fun_app defs) end
+
+val unfold_eqs =
+ let
+ val is_ground = not o Term.exists_subterm Term.is_Var
+ fun is_non_rec (v, t) = not (Term.exists_subterm (equal v) t)
+
+ fun rewr_var (l as Var _, r) = if is_ground r then SOME (l, r) else NONE
+ | rewr_var (r, l as Var _) = if is_ground r then SOME (l, r) else NONE
+ | rewr_var _ = NONE
+
+ fun rewr_free' e = if is_non_rec e then SOME e else NONE
+ fun rewr_free (e as (Free _, _)) = rewr_free' e
+ | rewr_free (e as (_, Free _)) = rewr_free' (swap e)
+ | rewr_free _ = NONE
+
+ fun is_trivial (Const (@{const_name HOL.eq}, _) $ t $ u) = t aconv u
+ | is_trivial _ = false
+
+ fun replace r = replace_vars [r] #> filter_out is_trivial
+
+ fun unfold_vars (es, ds) =
+ (case first_eq rewr_var es of
+ SOME (lr, es') => unfold_vars (pairself (replace lr) (es', ds))
+ | NONE => (es, ds))
+
+ fun unfold_frees ues (es, ds) =
+ (case first_eq rewr_free es of
+ SOME (lr, es') =>
+ pairself (replace lr) (es', ds)
+ |> unfold_frees (HOLogic.mk_eq lr :: replace lr ues)
+ | NONE => (ues @ es, ds))
+
+ in unfold_vars #> unfold_frees [] end
+
+fun swap_free ((eq as Const (@{const_name HOL.eq}, _)) $ t $ (u as Free _)) =
+ eq $ u $ t
+ | swap_free t = t
+
+fun frees_for_vars ctxt (eqs, defs) =
+ let
+ fun fresh_free i T (cx as (frees, ctxt)) =
+ (case Inttab.lookup frees i of
+ SOME t => (t, cx)
+ | NONE =>
+ let
+ val (n, ctxt') = yield_singleton Variable.variant_fixes "" ctxt
+ val t = Free (n, T)
+ in (t, (Inttab.update (i, t) frees, ctxt')) end)
+
+ fun repl_var (Var ((_, i), T)) = fresh_free i T
+ | repl_var (t $ u) = repl_var t ##>> repl_var u #>> op $
+ | repl_var (Abs (n, T, t)) = repl_var t #>> (fn t' => Abs (n, T, t'))
+ | repl_var t = pair t
+ in
+ (Inttab.empty, ctxt)
+ |> fold_map repl_var eqs
+ ||>> fold_map repl_var defs
+ |> fst
+ end
+
+
+(* overall procedure *)
+
+val is_free_constraint = Term.exists_subterm (fn Free _ => true | _ => false)
+
+fun is_free_def (Const (@{const_name HOL.eq}, _) $ Free _ $ _) = true
+ | is_free_def _ = false
+
+fun defined tp =
+ try (pairself (fst o HOLogic.dest_eq)) tp
+ |> the_default false o Option.map (op aconv)
+
+fun add_free_defs free_cs defs =
+ let val (free_defs, defs') = List.partition is_free_def defs
+ in (free_cs @ filter_out (member defined free_cs) free_defs, defs') end
+
+fun is_const_def (Const (@{const_name HOL.eq}, _) $ Const _ $ _) = true
+ | is_const_def _ = false
+
+(* TODO: Adapt parser to SMT-LIB 2 format for models *)
+fun parse_counterex ctxt ({terms, ...} : SMT2_Translate.replay_data) ls =
+ read_cex terms ls
+ |> with_context terms translate
+ |> apfst flat o split_list
+ |> remove_int_nat_coercions
+ |> unfold_funapp
+ |> unfold_eqs
+ |>> map swap_free
+ |>> filter is_free_constraint
+ |-> add_free_defs
+ |> frees_for_vars ctxt
+ ||> filter is_const_def
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_proof.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,563 @@
+(* Title: HOL/Tools/SMT2/z3_new_proof.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Z3 proofs: parsing and abstract syntax tree.
+*)
+
+signature Z3_NEW_PROOF =
+sig
+ (*proof rules*)
+ datatype z3_rule = True_Axiom | Asserted | Goal | Modus_Ponens | Reflexivity |
+ Symmetry | Transitivity | Transitivity_Star | Monotonicity | Quant_Intro |
+ Distributivity | And_Elim | Not_Or_Elim | Rewrite | Rewrite_Star |
+ Pull_Quant | Pull_Quant_Star | Push_Quant | Elim_Unused_Vars |
+ Dest_Eq_Res | Quant_Inst | Hypothesis | Lemma | Unit_Resolution |
+ Iff_True | Iff_False | Commutativity | Def_Axiom | Intro_Def | Apply_Def |
+ Iff_Oeq | Nnf_Pos | Nnf_Neg | Nnf_Star | Cnf_Star | Skolemize |
+ Modus_Ponens_Oeq | Th_Lemma of string
+ val string_of_rule: z3_rule -> string
+
+ (*proofs*)
+ datatype z3_step = Z3_Step of {
+ id: int,
+ rule: z3_rule,
+ prems: int list,
+ concl: term,
+ fixes: string list,
+ is_fix_step: bool}
+
+ (*type and term parsers*)
+ type type_parser = SMTLIB2.tree * typ list -> typ option
+ type term_parser = SMTLIB2.tree * term list -> term option
+ val add_type_parser: type_parser -> Context.generic -> Context.generic
+ val add_term_parser: term_parser -> Context.generic -> Context.generic
+
+ (*proof parser*)
+ val parse: typ Symtab.table -> term Symtab.table -> string list ->
+ Proof.context -> z3_step list * Proof.context
+end
+
+structure Z3_New_Proof: Z3_NEW_PROOF =
+struct
+
+(* proof rules *)
+
+datatype z3_rule = True_Axiom | Asserted | Goal | Modus_Ponens | Reflexivity |
+ Symmetry | Transitivity | Transitivity_Star | Monotonicity | Quant_Intro |
+ Distributivity | And_Elim | Not_Or_Elim | Rewrite | Rewrite_Star |
+ Pull_Quant | Pull_Quant_Star | Push_Quant | Elim_Unused_Vars | Dest_Eq_Res |
+ Quant_Inst | Hypothesis | Lemma | Unit_Resolution | Iff_True | Iff_False |
+ Commutativity | Def_Axiom | Intro_Def | Apply_Def | Iff_Oeq | Nnf_Pos |
+ Nnf_Neg | Nnf_Star | Cnf_Star | Skolemize | Modus_Ponens_Oeq |
+ Th_Lemma of string
+ (* TODO: some proof rules come with further information
+ that is currently dropped by the parser *)
+
+val rule_names = Symtab.make [
+ ("true-axiom", True_Axiom),
+ ("asserted", Asserted),
+ ("goal", Goal),
+ ("mp", Modus_Ponens),
+ ("refl", Reflexivity),
+ ("symm", Symmetry),
+ ("trans", Transitivity),
+ ("trans*", Transitivity_Star),
+ ("monotonicity", Monotonicity),
+ ("quant-intro", Quant_Intro),
+ ("distributivity", Distributivity),
+ ("and-elim", And_Elim),
+ ("not-or-elim", Not_Or_Elim),
+ ("rewrite", Rewrite),
+ ("rewrite*", Rewrite_Star),
+ ("pull-quant", Pull_Quant),
+ ("pull-quant*", Pull_Quant_Star),
+ ("push-quant", Push_Quant),
+ ("elim-unused", Elim_Unused_Vars),
+ ("der", Dest_Eq_Res),
+ ("quant-inst", Quant_Inst),
+ ("hypothesis", Hypothesis),
+ ("lemma", Lemma),
+ ("unit-resolution", Unit_Resolution),
+ ("iff-true", Iff_True),
+ ("iff-false", Iff_False),
+ ("commutativity", Commutativity),
+ ("def-axiom", Def_Axiom),
+ ("intro-def", Intro_Def),
+ ("apply-def", Apply_Def),
+ ("iff~", Iff_Oeq),
+ ("nnf-pos", Nnf_Pos),
+ ("nnf-neg", Nnf_Neg),
+ ("nnf*", Nnf_Star),
+ ("cnf*", Cnf_Star),
+ ("sk", Skolemize),
+ ("mp~", Modus_Ponens_Oeq)]
+
+fun rule_of_string name =
+ (case Symtab.lookup rule_names name of
+ SOME rule => rule
+ | NONE => error ("unknown Z3 proof rule " ^ quote name))
+
+fun string_of_rule (Th_Lemma kind) = "th-lemma " ^ kind
+ | string_of_rule r =
+ let fun eq_rule (s, r') = if r = r' then SOME s else NONE
+ in the (Symtab.get_first eq_rule rule_names) end
+
+
+
+(* proofs *)
+
+datatype z3_node = Z3_Node of {
+ id: int,
+ rule: z3_rule,
+ prems: z3_node list,
+ concl: term,
+ bounds: string list}
+
+fun mk_node id rule prems concl bounds =
+ Z3_Node {id=id, rule=rule, prems=prems, concl=concl, bounds=bounds}
+
+datatype z3_step = Z3_Step of {
+ id: int,
+ rule: z3_rule,
+ prems: int list,
+ concl: term,
+ fixes: string list,
+ is_fix_step: bool}
+
+fun mk_step id rule prems concl fixes is_fix_step =
+ Z3_Step {id=id, rule=rule, prems=prems, concl=concl, fixes=fixes,
+ is_fix_step=is_fix_step}
+
+
+
+(* core type and term parser *)
+
+fun core_type_parser (SMTLIB2.Sym "Bool", []) = SOME @{typ HOL.bool}
+ | core_type_parser (SMTLIB2.Sym "Int", []) = SOME @{typ Int.int}
+ | core_type_parser _ = NONE
+
+fun mk_unary n t =
+ let val T = fastype_of t
+ in Const (n, T --> T) $ t end
+
+fun mk_binary' n T U t1 t2 = Const (n, [T, T] ---> U) $ t1 $ t2
+
+fun mk_binary n t1 t2 =
+ let val T = fastype_of t1
+ in mk_binary' n T T t1 t2 end
+
+fun mk_rassoc f t ts =
+ let val us = rev (t :: ts)
+ in fold f (tl us) (hd us) end
+
+fun mk_lassoc f t ts = fold (fn u1 => fn u2 => f u2 u1) ts t
+
+fun mk_lassoc' n = mk_lassoc (mk_binary n)
+
+fun mk_binary_pred n S t1 t2 =
+ let
+ val T1 = fastype_of t1
+ val T2 = fastype_of t2
+ val T =
+ if T1 <> Term.dummyT then T1
+ else if T2 <> Term.dummyT then T2
+ else TVar (("?a", serial ()), S)
+ in mk_binary' n T @{typ HOL.bool} t1 t2 end
+
+fun mk_less t1 t2 = mk_binary_pred @{const_name ord_class.less} @{sort linorder} t1 t2
+fun mk_less_eq t1 t2 = mk_binary_pred @{const_name ord_class.less_eq} @{sort linorder} t1 t2
+
+fun core_term_parser (SMTLIB2.Sym "true", _) = SOME @{const HOL.True}
+ | core_term_parser (SMTLIB2.Sym "false", _) = SOME @{const HOL.False}
+ | core_term_parser (SMTLIB2.Sym "not", [t]) = SOME (HOLogic.mk_not t)
+ | core_term_parser (SMTLIB2.Sym "and", t :: ts) = SOME (mk_rassoc (curry HOLogic.mk_conj) t ts)
+ | core_term_parser (SMTLIB2.Sym "or", t :: ts) = SOME (mk_rassoc (curry HOLogic.mk_disj) t ts)
+ | core_term_parser (SMTLIB2.Sym "=>", [t1, t2]) = SOME (HOLogic.mk_imp (t1, t2))
+ | core_term_parser (SMTLIB2.Sym "implies", [t1, t2]) = SOME (HOLogic.mk_imp (t1, t2))
+ | core_term_parser (SMTLIB2.Sym "=", [t1, t2]) = SOME (HOLogic.mk_eq (t1, t2))
+ | core_term_parser (SMTLIB2.Sym "~", [t1, t2]) = SOME (HOLogic.mk_eq (t1, t2))
+ | core_term_parser (SMTLIB2.Sym "ite", [t1, t2, t3]) =
+ let
+ val T = fastype_of t2
+ val c = Const (@{const_name HOL.If}, [@{typ HOL.bool}, T, T] ---> T)
+ in SOME (c $ t1 $ t2 $ t3) end
+ | core_term_parser (SMTLIB2.Num i, []) = SOME (HOLogic.mk_number @{typ Int.int} i)
+ | core_term_parser (SMTLIB2.Sym "-", [t]) = SOME (mk_unary @{const_name uminus_class.uminus} t)
+ | core_term_parser (SMTLIB2.Sym "~", [t]) = SOME (mk_unary @{const_name uminus_class.uminus} t)
+ | core_term_parser (SMTLIB2.Sym "+", t :: ts) =
+ SOME (mk_lassoc' @{const_name plus_class.plus} t ts)
+ | core_term_parser (SMTLIB2.Sym "-", t :: ts) =
+ SOME (mk_lassoc' @{const_name minus_class.minus} t ts)
+ | core_term_parser (SMTLIB2.Sym "*", t :: ts) =
+ SOME (mk_lassoc' @{const_name times_class.times} t ts)
+ | core_term_parser (SMTLIB2.Sym "div", [t1, t2]) = SOME (mk_binary @{const_name SMT2.z3div} t1 t2)
+ | core_term_parser (SMTLIB2.Sym "mod", [t1, t2]) = SOME (mk_binary @{const_name SMT2.z3mod} t1 t2)
+ | core_term_parser (SMTLIB2.Sym "<", [t1, t2]) = SOME (mk_less t1 t2)
+ | core_term_parser (SMTLIB2.Sym ">", [t1, t2]) = SOME (mk_less t2 t1)
+ | core_term_parser (SMTLIB2.Sym "<=", [t1, t2]) = SOME (mk_less_eq t1 t2)
+ | core_term_parser (SMTLIB2.Sym ">=", [t1, t2]) = SOME (mk_less_eq t2 t1)
+ | core_term_parser _ = NONE
+
+
+
+(* type and term parsers *)
+
+type type_parser = SMTLIB2.tree * typ list -> typ option
+
+type term_parser = SMTLIB2.tree * term list -> term option
+
+fun id_ord ((id1, _), (id2, _)) = int_ord (id1, id2)
+
+structure Parsers = Generic_Data
+(
+ type T = (int * type_parser) list * (int * term_parser) list
+ val empty = ([(serial (), core_type_parser)], [(serial (), core_term_parser)])
+ val extend = I
+ fun merge ((tys1, ts1), (tys2, ts2)) =
+ (Ord_List.merge id_ord (tys1, tys2), Ord_List.merge id_ord (ts1, ts2))
+)
+
+fun add_type_parser type_parser =
+ Parsers.map (apfst (Ord_List.insert id_ord (serial (), type_parser)))
+
+fun add_term_parser term_parser =
+ Parsers.map (apsnd (Ord_List.insert id_ord (serial (), term_parser)))
+
+fun get_type_parsers ctxt = map snd (fst (Parsers.get (Context.Proof ctxt)))
+fun get_term_parsers ctxt = map snd (snd (Parsers.get (Context.Proof ctxt)))
+
+fun apply_parsers parsers x =
+ let
+ fun apply [] = NONE
+ | apply (parser :: parsers) =
+ (case parser x of
+ SOME y => SOME y
+ | NONE => apply parsers)
+ in apply parsers end
+
+
+
+(* proof parser context *)
+
+datatype shared = Tree of SMTLIB2.tree | Term of term | Proof of z3_node | None
+
+type 'a context = {
+ ctxt: Proof.context,
+ id: int,
+ syms: shared Symtab.table,
+ typs: typ Symtab.table,
+ funs: term Symtab.table,
+ extra: 'a}
+
+fun mk_context ctxt id syms typs funs extra: 'a context =
+ {ctxt=ctxt, id=id, syms=syms, typs=typs, funs=funs, extra=extra}
+
+fun empty_context ctxt typs funs = mk_context ctxt 1 Symtab.empty typs funs []
+
+fun ctxt_of ({ctxt, ...}: 'a context) = ctxt
+
+fun next_id ({ctxt, id, syms, typs, funs, extra}: 'a context) =
+ (id, mk_context ctxt (id + 1) syms typs funs extra)
+
+fun lookup_binding ({syms, ...}: 'a context) =
+ the_default None o Symtab.lookup syms
+
+fun map_syms f ({ctxt, id, syms, typs, funs, extra}: 'a context) =
+ mk_context ctxt id (f syms) typs funs extra
+
+fun update_binding b = map_syms (Symtab.update b)
+
+fun with_bindings bs f cx =
+ let val bs' = map (lookup_binding cx o fst) bs
+ in
+ cx
+ |> fold update_binding bs
+ |> f
+ ||> fold2 (fn (name, _) => update_binding o pair name) bs bs'
+ end
+
+fun lookup_typ ({typs, ...}: 'a context) = Symtab.lookup typs
+fun lookup_fun ({funs, ...}: 'a context) = Symtab.lookup funs
+
+fun fresh_fun add name n T ({ctxt, id, syms, typs, funs, extra}: 'a context) =
+ let
+ val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
+ val t = Free (n', T)
+ val funs' = Symtab.update (name, t) funs
+ in (t, mk_context ctxt' id syms typs funs' (add (n', T) extra)) end
+
+fun declare_fun name n T = snd o fresh_fun cons name n T
+fun declare_free name n T = fresh_fun (cons o pair name) name n T
+
+fun with_fresh_names f ({ctxt, id, syms, typs, funs, extra}: 'a context) =
+ let
+ fun bind (_, v as (_, T)) t = Logic.all_const T $ Term.absfree v t
+
+ val needs_inferT = equal Term.dummyT orf Term.is_TVar
+ val needs_infer = Term.exists_type (Term.exists_subtype needs_inferT)
+ fun infer_types ctxt =
+ singleton (Type_Infer_Context.infer_types ctxt) #>
+ singleton (Proof_Context.standard_term_check_finish ctxt)
+ fun infer ctxt t = if needs_infer t then infer_types ctxt t else t
+
+ type bindings = (string * (string * typ)) list
+ val (t, {ctxt=ctxt', extra=names, ...}: bindings context) =
+ f (mk_context ctxt id syms typs funs [])
+ val t' = infer ctxt' (fold_rev bind names (HOLogic.mk_Trueprop t))
+
+ in ((t', map fst names), mk_context ctxt id syms typs funs extra) end
+
+
+
+(* proof parser *)
+
+exception Z3_PARSE of string * SMTLIB2.tree
+
+val desymbolize = Name.desymbolize false o perhaps (try (unprefix "?"))
+
+fun parse_type cx ty Ts =
+ (case apply_parsers (get_type_parsers (ctxt_of cx)) (ty, Ts) of
+ SOME T => T
+ | NONE =>
+ (case ty of
+ SMTLIB2.Sym name =>
+ (case lookup_typ cx name of
+ SOME T => T
+ | NONE => raise Z3_PARSE ("unknown Z3 type", ty))
+ | _ => raise Z3_PARSE ("bad Z3 type format", ty)))
+
+fun parse_term t ts cx =
+ (case apply_parsers (get_term_parsers (ctxt_of cx)) (t, ts) of
+ SOME u => (u, cx)
+ | NONE =>
+ (case t of
+ SMTLIB2.Sym name =>
+ (case lookup_fun cx name of
+ SOME u => (Term.list_comb (u, ts), cx)
+ | NONE =>
+ if null ts then declare_free name (desymbolize name) Term.dummyT cx
+ else raise Z3_PARSE ("bad Z3 term", t))
+ | _ => raise Z3_PARSE ("bad Z3 term format", t)))
+
+fun type_of cx ty =
+ (case try (parse_type cx ty) [] of
+ SOME T => T
+ | NONE =>
+ (case ty of
+ SMTLIB2.S (ty' :: tys) => parse_type cx ty' (map (type_of cx) tys)
+ | _ => raise Z3_PARSE ("bad Z3 type", ty)))
+
+fun dest_var cx (SMTLIB2.S [SMTLIB2.Sym name, ty]) = (name, (desymbolize name, type_of cx ty))
+ | dest_var _ v = raise Z3_PARSE ("bad Z3 quantifier variable format", v)
+
+fun dest_body (SMTLIB2.S (SMTLIB2.Sym "!" :: body :: _)) = dest_body body
+ | dest_body body = body
+
+fun dest_binding (SMTLIB2.S [SMTLIB2.Sym name, t]) = (name, Tree t)
+ | dest_binding b = raise Z3_PARSE ("bad Z3 let binding format", b)
+
+fun term_of t cx =
+ (case t of
+ SMTLIB2.S [SMTLIB2.Sym "forall", SMTLIB2.S vars, body] =>
+ quant HOLogic.mk_all vars body cx
+ | SMTLIB2.S [SMTLIB2.Sym "exists", SMTLIB2.S vars, body] =>
+ quant HOLogic.mk_exists vars body cx
+ | SMTLIB2.S [SMTLIB2.Sym "let", SMTLIB2.S bindings, body] =>
+ with_bindings (map dest_binding bindings) (term_of body) cx
+ | SMTLIB2.S (SMTLIB2.Sym "!" :: t :: _) => term_of t cx
+ | SMTLIB2.S (f :: args) =>
+ cx
+ |> fold_map term_of args
+ |-> parse_term f
+ | SMTLIB2.Sym name =>
+ (case lookup_binding cx name of
+ Tree u =>
+ cx
+ |> term_of u
+ |-> (fn u' => pair u' o update_binding (name, Term u'))
+ | Term u => (u, cx)
+ | None => parse_term t [] cx
+ | _ => raise Z3_PARSE ("bad Z3 term format", t))
+ | _ => parse_term t [] cx)
+
+and quant q vars body cx =
+ let val vs = map (dest_var cx) vars
+ in
+ cx
+ |> with_bindings (map (apsnd (Term o Free)) vs) (term_of (dest_body body))
+ |>> fold_rev (fn (_, (n, T)) => fn t => q (n, T, t)) vs
+ end
+
+fun rule_of (SMTLIB2.Sym name) = rule_of_string name
+ | rule_of (SMTLIB2.S (SMTLIB2.Sym "_" :: SMTLIB2.Sym name :: args)) =
+ (case (name, args) of
+ ("th-lemma", SMTLIB2.Sym kind :: _) => Th_Lemma kind
+ | _ => rule_of_string name)
+ | rule_of r = raise Z3_PARSE ("bad Z3 proof rule format", r)
+
+fun node_of p cx =
+ (case p of
+ SMTLIB2.Sym name =>
+ (case lookup_binding cx name of
+ Proof node => (node, cx)
+ | Tree p' =>
+ cx
+ |> node_of p'
+ |-> (fn node => pair node o update_binding (name, Proof node))
+ | _ => raise Z3_PARSE ("bad Z3 proof format", p))
+ | SMTLIB2.S [SMTLIB2.Sym "let", SMTLIB2.S bindings, p] =>
+ with_bindings (map dest_binding bindings) (node_of p) cx
+ | SMTLIB2.S (name :: parts) =>
+ let
+ val (ps, p) = split_last parts
+ val r = rule_of name
+ in
+ cx
+ |> fold_map node_of ps
+ ||>> with_fresh_names (term_of p)
+ ||>> next_id
+ |>> (fn ((prems, (t, ns)), id) => mk_node id r prems t ns)
+ end
+ | _ => raise Z3_PARSE ("bad Z3 proof format", p))
+
+fun dest_name (SMTLIB2.Sym name) = name
+ | dest_name t = raise Z3_PARSE ("bad name", t)
+
+fun dest_seq (SMTLIB2.S ts) = ts
+ | dest_seq t = raise Z3_PARSE ("bad Z3 proof format", t)
+
+fun parse' (SMTLIB2.S (SMTLIB2.Sym "set-logic" :: _) :: ts) cx = parse' ts cx
+ | parse' (SMTLIB2.S [SMTLIB2.Sym "declare-fun", n, tys, ty] :: ts) cx =
+ let
+ val name = dest_name n
+ val Ts = map (type_of cx) (dest_seq tys)
+ val T = type_of cx ty
+ in parse' ts (declare_fun name (desymbolize name) (Ts ---> T) cx) end
+ | parse' (SMTLIB2.S [SMTLIB2.Sym "proof", p] :: _) cx = node_of p cx
+ | parse' ts _ = raise Z3_PARSE ("bad Z3 proof declarations", SMTLIB2.S ts)
+
+fun parse_proof typs funs lines ctxt =
+ let
+ val ts = dest_seq (SMTLIB2.parse lines)
+ val (node, cx) = parse' ts (empty_context ctxt typs funs)
+ in (node, ctxt_of cx) end
+ handle SMTLIB2.PARSE (l, msg) =>
+ error ("parsing error at line " ^ string_of_int l ^ ": " ^ msg)
+ | Z3_PARSE (msg, t) =>
+ error (msg ^ ": " ^ SMTLIB2.str_of t)
+
+
+
+(* handling of bound variables *)
+
+fun subst_of tyenv =
+ let fun add (ix, (S, T)) = cons (TVar (ix, S), T)
+ in Vartab.fold add tyenv [] end
+
+fun substTs_same subst =
+ let val applyT = Same.function (AList.lookup (op =) subst)
+ in Term_Subst.map_atypsT_same applyT end
+
+fun subst_types ctxt env bounds t =
+ let
+ val match = Sign.typ_match (Proof_Context.theory_of ctxt)
+
+ val t' = singleton (Variable.polymorphic ctxt) t
+ val patTs = map snd (Term.strip_qnt_vars @{const_name all} t')
+ val objTs = map (the o Symtab.lookup env) bounds
+ val subst = subst_of (fold match (patTs ~~ objTs) Vartab.empty)
+ in Same.commit (Term_Subst.map_types_same (substTs_same subst)) t' end
+
+fun eq_quant (@{const_name HOL.All}, _) (@{const_name HOL.All}, _) = true
+ | eq_quant (@{const_name HOL.Ex}, _) (@{const_name HOL.Ex}, _) = true
+ | eq_quant _ _ = false
+
+fun opp_quant (@{const_name HOL.All}, _) (@{const_name HOL.Ex}, _) = true
+ | opp_quant (@{const_name HOL.Ex}, _) (@{const_name HOL.All}, _) = true
+ | opp_quant _ _ = false
+
+fun with_quant pred i (Const q1 $ Abs (_, T1, t1), Const q2 $ Abs (_, T2, t2)) =
+ if pred q1 q2 andalso T1 = T2 then
+ let val t = Var (("", i), T1)
+ in SOME (pairself Term.subst_bound ((t, t1), (t, t2))) end
+ else NONE
+ | with_quant _ _ _ = NONE
+
+fun dest_quant_pair i (@{term HOL.Not} $ t1, t2) =
+ Option.map (apfst HOLogic.mk_not) (with_quant opp_quant i (t1, t2))
+ | dest_quant_pair i (t1, t2) = with_quant eq_quant i (t1, t2)
+
+fun dest_quant i t =
+ (case dest_quant_pair i (HOLogic.dest_eq (HOLogic.dest_Trueprop t)) of
+ SOME (t1, t2) => HOLogic.mk_Trueprop (HOLogic.mk_eq (t1, t2))
+ | NONE => raise TERM ("lift_quant", [t]))
+
+fun match_types ctxt pat obj =
+ (Vartab.empty, Vartab.empty)
+ |> Pattern.first_order_match (Proof_Context.theory_of ctxt) (pat, obj)
+
+fun strip_match ctxt pat i obj =
+ (case try (match_types ctxt pat) obj of
+ SOME (tyenv, _) => subst_of tyenv
+ | NONE => strip_match ctxt pat (i + 1) (dest_quant i obj))
+
+fun dest_all i (Const (@{const_name all}, _) $ (a as Abs (_, T, _))) =
+ dest_all (i + 1) (Term.betapply (a, Var (("", i), T)))
+ | dest_all i t = (i, t)
+
+fun dest_alls t = dest_all (Term.maxidx_of_term t + 1) t
+
+fun match_rule ctxt env (Z3_Node {bounds=bs', concl=t', ...}) bs t =
+ let
+ val t'' = singleton (Variable.polymorphic ctxt) t'
+ val (i, obj) = dest_alls (subst_types ctxt env bs t)
+ in
+ (case try (strip_match ctxt (snd (dest_alls t'')) i) obj of
+ NONE => NONE
+ | SOME subst =>
+ let
+ val applyT = Same.commit (substTs_same subst)
+ val patTs = map snd (Term.strip_qnt_vars @{const_name all} t'')
+ in SOME (Symtab.make (bs' ~~ map applyT patTs)) end)
+ end
+
+
+
+(* linearizing proofs and resolving types of bound variables *)
+
+fun has_step (tab, _) = Inttab.defined tab
+
+fun add_step id rule bounds concl is_fix_step ids (tab, sts) =
+ let val step = mk_step id rule ids concl bounds is_fix_step
+ in (id, (Inttab.update (id, ()) tab, step :: sts)) end
+
+fun is_fix_rule rule prems =
+ member (op =) [Quant_Intro, Nnf_Pos, Nnf_Neg] rule andalso length prems = 1
+
+fun lin_proof ctxt env (Z3_Node {id, rule, prems, concl, bounds}) steps =
+ if has_step steps id then (id, steps)
+ else
+ let
+ val t = subst_types ctxt env bounds concl
+ val add = add_step id rule bounds t
+ fun rec_apply e b = fold_map (lin_proof ctxt e) prems #-> add b
+ in
+ if is_fix_rule rule prems then
+ (case match_rule ctxt env (hd prems) bounds t of
+ NONE => rec_apply env false steps
+ | SOME env' => rec_apply env' true steps)
+ else rec_apply env false steps
+ end
+
+fun linearize ctxt node =
+ rev (snd (snd (lin_proof ctxt Symtab.empty node (Inttab.empty, []))))
+
+
+
+(* overall proof parser *)
+
+fun parse typs funs lines ctxt =
+ let val (node, ctxt') = parse_proof typs funs lines ctxt
+ in (linearize ctxt' node, ctxt') end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_real.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,32 @@
+(* Title: HOL/Tools/SMT2/z3_new_real.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Z3 setup for reals.
+*)
+
+structure Z3_New_Real: sig end =
+struct
+
+fun real_type_parser (SMTLIB2.Sym "Real", []) = SOME @{typ Real.real}
+ | real_type_parser _ = NONE
+
+fun real_term_parser (SMTLIB2.Dec (i, 0), []) = SOME (HOLogic.mk_number @{typ Real.real} i)
+ | real_term_parser (SMTLIB2.Sym "/", [t1, t2]) =
+ SOME (@{term "inverse_class.divide :: real => _"} $ t1 $ t2)
+ | real_term_parser (SMTLIB2.Sym "to_real", [t]) = SOME (@{term "Real.real :: int => _"} $ t)
+ | real_term_parser _ = NONE
+
+fun abstract abs t =
+ (case t of
+ (c as @{term "inverse_class.divide :: real => _"}) $ t1 $ t2 =>
+ abs t1 ##>> abs t2 #>> (fn (u1, u2) => SOME (c $ u1 $ u2))
+ | (c as @{term "Real.real :: int => _"}) $ t =>
+ abs t #>> (fn u => SOME (c $ u))
+ | _ => pair NONE)
+
+val _ = Theory.setup (Context.theory_map (
+ Z3_New_Proof.add_type_parser real_type_parser #>
+ Z3_New_Proof.add_term_parser real_term_parser #>
+ Z3_New_Replay_Methods.add_arith_abstracter abstract))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_replay.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,192 @@
+(* Title: HOL/Tools/SMT2/z3_new_replay.ML
+ Author: Sascha Boehme, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+Z3 proof replay.
+*)
+
+signature Z3_NEW_REPLAY =
+sig
+ val replay: Proof.context -> SMT2_Translate.replay_data -> string list ->
+ ((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm
+end
+
+structure Z3_New_Replay: Z3_NEW_REPLAY =
+struct
+
+fun params_of t = Term.strip_qnt_vars @{const_name all} t
+
+fun varify ctxt thm =
+ let
+ val maxidx = Thm.maxidx_of thm + 1
+ val vs = params_of (Thm.prop_of thm)
+ val vars = map_index (fn (i, (n, T)) => Var ((n, i + maxidx), T)) vs
+ in Drule.forall_elim_list (map (SMT2_Util.certify ctxt) vars) thm end
+
+fun add_paramTs names t =
+ fold2 (fn n => fn (_, T) => AList.update (op =) (n, T)) names (params_of t)
+
+fun new_fixes ctxt nTs =
+ let
+ val (ns, ctxt') = Variable.variant_fixes (replicate (length nTs) "") ctxt
+ fun mk (n, T) n' = (n, SMT2_Util.certify ctxt' (Free (n', T)))
+ in (ctxt', Symtab.make (map2 mk nTs ns)) end
+
+fun forall_elim_term ct (Const (@{const_name all}, _) $ (a as Abs _)) =
+ Term.betapply (a, Thm.term_of ct)
+ | forall_elim_term _ qt = raise TERM ("forall_elim'", [qt])
+
+fun apply_fixes elim env = fold (elim o the o Symtab.lookup env)
+
+val apply_fixes_prem = uncurry o apply_fixes Thm.forall_elim
+val apply_fixes_concl = apply_fixes forall_elim_term
+
+fun export_fixes env names = Drule.forall_intr_list (map (the o Symtab.lookup env) names)
+
+fun under_fixes f ctxt (prems, nthms) names concl =
+ let
+ val thms1 = map (varify ctxt) prems
+ val (ctxt', env) =
+ add_paramTs names concl []
+ |> fold (uncurry add_paramTs o apsnd Thm.prop_of) nthms
+ |> new_fixes ctxt
+ val thms2 = map (apply_fixes_prem env) nthms
+ val t = apply_fixes_concl env names concl
+ in export_fixes env names (f ctxt' (thms1 @ thms2) t) end
+
+fun replay_thm ctxt assumed nthms
+ (Z3_New_Proof.Z3_Step {id, rule, concl, fixes, is_fix_step, ...}) =
+ if Z3_New_Replay_Methods.is_assumption rule then
+ (case Inttab.lookup assumed id of
+ SOME (_, thm) => thm
+ | NONE => Thm.assume (SMT2_Util.certify ctxt concl))
+ else
+ under_fixes (Z3_New_Replay_Methods.method_for rule) ctxt
+ (if is_fix_step then (map snd nthms, []) else ([], nthms)) fixes concl
+
+fun replay_step ctxt assumed (step as Z3_New_Proof.Z3_Step {id, prems, fixes, ...}) proofs =
+ let val nthms = map (the o Inttab.lookup proofs) prems
+ in Inttab.update (id, (fixes, replay_thm ctxt assumed nthms step)) proofs end
+
+local
+ val remove_trigger = mk_meta_eq @{thm SMT2.trigger_def}
+ val remove_weight = mk_meta_eq @{thm SMT2.weight_def}
+ val remove_fun_app = mk_meta_eq @{thm SMT2.fun_app_def}
+
+ fun rewrite_conv _ [] = Conv.all_conv
+ | rewrite_conv ctxt eqs = Simplifier.full_rewrite (empty_simpset ctxt addsimps eqs)
+
+ val prep_rules = [@{thm Let_def}, remove_trigger, remove_weight,
+ remove_fun_app, Z3_New_Replay_Literals.rewrite_true]
+
+ fun rewrite _ [] = I
+ | rewrite ctxt eqs = Conv.fconv_rule (rewrite_conv ctxt eqs)
+
+ fun lookup_assm assms_net ct =
+ Z3_New_Replay_Util.net_instances assms_net ct
+ |> map (fn ithm as (_, thm) => (ithm, Thm.cprop_of thm aconvc ct))
+in
+
+fun add_asserted outer_ctxt rewrite_rules assms steps ctxt =
+ let
+ val eqs = map (rewrite ctxt [Z3_New_Replay_Literals.rewrite_true]) rewrite_rules
+ val eqs' = union Thm.eq_thm eqs prep_rules
+
+ val assms_net =
+ assms
+ |> map (apsnd (rewrite ctxt eqs'))
+ |> map (apsnd (Conv.fconv_rule Thm.eta_conversion))
+ |> Z3_New_Replay_Util.thm_net_of snd
+
+ fun revert_conv ctxt = rewrite_conv ctxt eqs' then_conv Thm.eta_conversion
+
+ fun assume thm ctxt =
+ let
+ val ct = Thm.cprem_of thm 1
+ val (thm', ctxt') = yield_singleton Assumption.add_assumes ct ctxt
+ in (thm' RS thm, ctxt') end
+
+ fun add1 id fixes thm1 ((i, th), exact) ((iidths, thms), (ctxt, ptab)) =
+ let
+ val (thm, ctxt') = if exact then (Thm.implies_elim thm1 th, ctxt) else assume thm1 ctxt
+ val thms' = if exact then thms else th :: thms
+ in (((i, (id, th)) :: iidths, thms'), (ctxt', Inttab.update (id, (fixes, thm)) ptab)) end
+
+ fun add (Z3_New_Proof.Z3_Step {id, rule, concl, fixes, ...})
+ (cx as ((iidths, thms), (ctxt, ptab))) =
+ if Z3_New_Replay_Methods.is_assumption rule andalso rule <> Z3_New_Proof.Hypothesis then
+ let
+ val ct = SMT2_Util.certify ctxt concl
+ val thm1 = Thm.trivial ct |> Conv.fconv_rule (Conv.arg1_conv (revert_conv outer_ctxt))
+ val thm2 = singleton (Variable.export ctxt outer_ctxt) thm1
+ in
+ (case lookup_assm assms_net (Thm.cprem_of thm2 1) of
+ [] =>
+ let val (thm, ctxt') = assume thm1 ctxt
+ in ((iidths, thms), (ctxt', Inttab.update (id, (fixes, thm)) ptab)) end
+ | ithms => fold (add1 id fixes thm1) ithms cx)
+ end
+ else
+ cx
+ in fold add steps (([], []), (ctxt, Inttab.empty)) end
+
+end
+
+(* |- (EX x. P x) = P c |- ~ (ALL x. P x) = ~ P c *)
+local
+ val sk_rules = @{lemma
+ "c = (SOME x. P x) ==> (EX x. P x) = P c"
+ "c = (SOME x. ~ P x) ==> (~ (ALL x. P x)) = (~ P c)"
+ by (metis someI_ex)+}
+in
+
+fun discharge_sk_tac i st =
+ (rtac @{thm trans} i
+ THEN resolve_tac sk_rules i
+ THEN (rtac @{thm refl} ORELSE' discharge_sk_tac) (i+1)
+ THEN rtac @{thm refl} i) st
+
+end
+
+fun make_discharge_rules rules = rules @ [@{thm allI}, @{thm refl},
+ @{thm reflexive}, Z3_New_Replay_Literals.true_thm]
+
+val intro_def_rules = @{lemma
+ "(~ P | P) & (P | ~ P)"
+ "(P | ~ P) & (~ P | P)"
+ by fast+}
+
+fun discharge_assms_tac rules =
+ REPEAT (HEADGOAL (resolve_tac (intro_def_rules @ rules) ORELSE' SOLVED' discharge_sk_tac))
+
+fun discharge_assms ctxt rules thm =
+ (if Thm.nprems_of thm = 0 then
+ thm
+ else
+ (case Seq.pull (discharge_assms_tac rules thm) of
+ SOME (thm', _) => thm'
+ | NONE => raise THM ("failed to discharge premise", 1, [thm])))
+ |> Goal.norm_result ctxt
+
+fun discharge rules outer_ctxt inner_ctxt =
+ singleton (Proof_Context.export inner_ctxt outer_ctxt)
+ #> discharge_assms outer_ctxt (make_discharge_rules rules)
+
+fun replay outer_ctxt
+ ({context=ctxt, typs, terms, rewrite_rules, assms} : SMT2_Translate.replay_data) output =
+ let
+ val (steps, ctxt2) = Z3_New_Proof.parse typs terms output ctxt
+ val ((iidths, rules), (ctxt3, assumed)) = add_asserted outer_ctxt rewrite_rules assms steps ctxt2
+ in
+ if Config.get ctxt3 SMT2_Config.filter_only_facts then
+ ((iidths, steps), TrueI)
+ else
+ let
+ val ctxt4 = put_simpset (Z3_New_Replay_Util.make_simpset ctxt3 []) ctxt3
+ val proofs = fold (replay_step ctxt4 assumed) steps assumed
+ val (_, Z3_New_Proof.Z3_Step {id, ...}) = split_last steps
+ val thm = Inttab.lookup proofs id |> the |> snd |> discharge rules outer_ctxt ctxt4
+ in (([], steps), thm) end
+ end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_replay_literals.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,356 @@
+(* Title: HOL/Tools/SMT2/z3_new_replay_literals.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Proof tools related to conjunctions and disjunctions.
+*)
+
+signature Z3_NEW_REPLAY_LITERALS =
+sig
+ (*literal table*)
+ type littab = thm Termtab.table
+ val make_littab: thm list -> littab
+ val insert_lit: thm -> littab -> littab
+ val delete_lit: thm -> littab -> littab
+ val lookup_lit: littab -> term -> thm option
+ val get_first_lit: (term -> bool) -> littab -> thm option
+
+ (*rules*)
+ val true_thm: thm
+ val rewrite_true: thm
+
+ (*properties*)
+ val is_conj: term -> bool
+ val is_disj: term -> bool
+ val exists_lit: bool -> (term -> bool) -> term -> bool
+ val negate: cterm -> cterm
+
+ (*proof tools*)
+ val explode: bool -> bool -> bool -> term list -> thm -> thm list
+ val join: bool -> littab -> term -> thm
+ val prove_conj_disj_eq: cterm -> thm
+end
+
+structure Z3_New_Replay_Literals: Z3_NEW_REPLAY_LITERALS =
+struct
+
+
+
+(* literal table *)
+
+type littab = thm Termtab.table
+
+fun make_littab thms = fold (Termtab.update o `SMT2_Util.prop_of) thms Termtab.empty
+
+fun insert_lit thm = Termtab.update (`SMT2_Util.prop_of thm)
+fun delete_lit thm = Termtab.delete (SMT2_Util.prop_of thm)
+fun lookup_lit lits = Termtab.lookup lits
+fun get_first_lit f =
+ Termtab.get_first (fn (t, thm) => if f t then SOME thm else NONE)
+
+
+
+(* rules *)
+
+val true_thm = @{lemma "~False" by simp}
+val rewrite_true = @{lemma "True == ~ False" by simp}
+
+
+
+(* properties and term operations *)
+
+val is_neg = (fn @{const Not} $ _ => true | _ => false)
+fun is_neg' f = (fn @{const Not} $ t => f t | _ => false)
+val is_dneg = is_neg' is_neg
+val is_conj = (fn @{const HOL.conj} $ _ $ _ => true | _ => false)
+val is_disj = (fn @{const HOL.disj} $ _ $ _ => true | _ => false)
+
+fun dest_disj_term' f = (fn
+ @{const Not} $ (@{const HOL.disj} $ t $ u) => SOME (f t, f u)
+ | _ => NONE)
+
+val dest_conj_term = (fn @{const HOL.conj} $ t $ u => SOME (t, u) | _ => NONE)
+val dest_disj_term =
+ dest_disj_term' (fn @{const Not} $ t => t | t => @{const Not} $ t)
+
+fun exists_lit is_conj P =
+ let
+ val dest = if is_conj then dest_conj_term else dest_disj_term
+ fun exists t = P t orelse
+ (case dest t of
+ SOME (t1, t2) => exists t1 orelse exists t2
+ | NONE => false)
+ in exists end
+
+val negate = Thm.apply (Thm.cterm_of @{theory} @{const Not})
+
+
+
+(* proof tools *)
+
+(** explosion of conjunctions and disjunctions **)
+
+local
+ val precomp = Z3_New_Replay_Util.precompose2
+
+ fun destc ct = Thm.dest_binop (Thm.dest_arg ct)
+ val dest_conj1 = precomp destc @{thm conjunct1}
+ val dest_conj2 = precomp destc @{thm conjunct2}
+ fun dest_conj_rules t =
+ dest_conj_term t |> Option.map (K (dest_conj1, dest_conj2))
+
+ fun destd f ct = f (Thm.dest_binop (Thm.dest_arg (Thm.dest_arg ct)))
+ val dn1 = apfst Thm.dest_arg and dn2 = apsnd Thm.dest_arg
+ val dest_disj1 = precomp (destd I) @{lemma "~(P | Q) ==> ~P" by fast}
+ val dest_disj2 = precomp (destd dn1) @{lemma "~(~P | Q) ==> P" by fast}
+ val dest_disj3 = precomp (destd I) @{lemma "~(P | Q) ==> ~Q" by fast}
+ val dest_disj4 = precomp (destd dn2) @{lemma "~(P | ~Q) ==> Q" by fast}
+
+ fun dest_disj_rules t =
+ (case dest_disj_term' is_neg t of
+ SOME (true, true) => SOME (dest_disj2, dest_disj4)
+ | SOME (true, false) => SOME (dest_disj2, dest_disj3)
+ | SOME (false, true) => SOME (dest_disj1, dest_disj4)
+ | SOME (false, false) => SOME (dest_disj1, dest_disj3)
+ | NONE => NONE)
+
+ fun destn ct = [Thm.dest_arg (Thm.dest_arg (Thm.dest_arg ct))]
+ val dneg_rule = Z3_New_Replay_Util.precompose destn @{thm notnotD}
+in
+
+(*
+ explode a term into literals and collect all rules to be able to deduce
+ particular literals afterwards
+*)
+fun explode_term is_conj =
+ let
+ val dest = if is_conj then dest_conj_term else dest_disj_term
+ val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
+
+ fun add (t, rs) = Termtab.map_default (t, rs)
+ (fn rs' => if length rs' < length rs then rs' else rs)
+
+ fun explode1 rules t =
+ (case dest t of
+ SOME (t1, t2) =>
+ let val (rule1, rule2) = the (dest_rules t)
+ in
+ explode1 (rule1 :: rules) t1 #>
+ explode1 (rule2 :: rules) t2 #>
+ add (t, rev rules)
+ end
+ | NONE => add (t, rev rules))
+
+ fun explode0 (@{const Not} $ (@{const Not} $ t)) =
+ Termtab.make [(t, [dneg_rule])]
+ | explode0 t = explode1 [] t Termtab.empty
+
+ in explode0 end
+
+(*
+ extract a literal by applying previously collected rules
+*)
+fun extract_lit thm rules = fold Z3_New_Replay_Util.compose rules thm
+
+
+(*
+ explode a theorem into its literals
+*)
+fun explode is_conj full keep_intermediate stop_lits =
+ let
+ val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
+ val tab = fold (Termtab.update o rpair ()) stop_lits Termtab.empty
+
+ fun explode1 thm =
+ if Termtab.defined tab (SMT2_Util.prop_of thm) then cons thm
+ else
+ (case dest_rules (SMT2_Util.prop_of thm) of
+ SOME (rule1, rule2) =>
+ explode2 rule1 thm #>
+ explode2 rule2 thm #>
+ keep_intermediate ? cons thm
+ | NONE => cons thm)
+
+ and explode2 dest_rule thm =
+ if full orelse
+ exists_lit is_conj (Termtab.defined tab) (SMT2_Util.prop_of thm)
+ then explode1 (Z3_New_Replay_Util.compose dest_rule thm)
+ else cons (Z3_New_Replay_Util.compose dest_rule thm)
+
+ fun explode0 thm =
+ if not is_conj andalso is_dneg (SMT2_Util.prop_of thm)
+ then [Z3_New_Replay_Util.compose dneg_rule thm]
+ else explode1 thm []
+
+ in explode0 end
+
+end
+
+
+(** joining of literals to conjunctions or disjunctions **)
+
+local
+ fun on_cprem i f thm = f (Thm.cprem_of thm i)
+ fun on_cprop f thm = f (Thm.cprop_of thm)
+ fun precomp2 f g thm = (on_cprem 1 f thm, on_cprem 2 g thm, f, g, thm)
+ fun comp2 (cv1, cv2, f, g, rule) thm1 thm2 =
+ Thm.instantiate ([], [(cv1, on_cprop f thm1), (cv2, on_cprop g thm2)]) rule
+ |> Z3_New_Replay_Util.discharge thm1 |> Z3_New_Replay_Util.discharge thm2
+
+ fun d1 ct = Thm.dest_arg ct and d2 ct = Thm.dest_arg (Thm.dest_arg ct)
+
+ val conj_rule = precomp2 d1 d1 @{thm conjI}
+ fun comp_conj ((_, thm1), (_, thm2)) = comp2 conj_rule thm1 thm2
+
+ val disj1 = precomp2 d2 d2 @{lemma "~P ==> ~Q ==> ~(P | Q)" by fast}
+ val disj2 = precomp2 d2 d1 @{lemma "~P ==> Q ==> ~(P | ~Q)" by fast}
+ val disj3 = precomp2 d1 d2 @{lemma "P ==> ~Q ==> ~(~P | Q)" by fast}
+ val disj4 = precomp2 d1 d1 @{lemma "P ==> Q ==> ~(~P | ~Q)" by fast}
+
+ fun comp_disj ((false, thm1), (false, thm2)) = comp2 disj1 thm1 thm2
+ | comp_disj ((false, thm1), (true, thm2)) = comp2 disj2 thm1 thm2
+ | comp_disj ((true, thm1), (false, thm2)) = comp2 disj3 thm1 thm2
+ | comp_disj ((true, thm1), (true, thm2)) = comp2 disj4 thm1 thm2
+
+ fun dest_conj (@{const HOL.conj} $ t $ u) = ((false, t), (false, u))
+ | dest_conj t = raise TERM ("dest_conj", [t])
+
+ val neg = (fn @{const Not} $ t => (true, t) | t => (false, @{const Not} $ t))
+ fun dest_disj (@{const Not} $ (@{const HOL.disj} $ t $ u)) = (neg t, neg u)
+ | dest_disj t = raise TERM ("dest_disj", [t])
+
+ val precomp = Z3_New_Replay_Util.precompose
+ val dnegE = precomp (single o d2 o d1) @{thm notnotD}
+ val dnegI = precomp (single o d1) @{lemma "P ==> ~~P" by fast}
+ fun as_dneg f t = f (@{const Not} $ (@{const Not} $ t))
+
+ val precomp2 = Z3_New_Replay_Util.precompose2
+ fun dni f = apsnd f o Thm.dest_binop o f o d1
+ val negIffE = precomp2 (dni d1) @{lemma "~(P = (~Q)) ==> Q = P" by fast}
+ val negIffI = precomp2 (dni I) @{lemma "P = Q ==> ~(Q = (~P))" by fast}
+ val iff_const = @{const HOL.eq (bool)}
+ fun as_negIff f (@{const HOL.eq (bool)} $ t $ u) =
+ f (@{const Not} $ (iff_const $ u $ (@{const Not} $ t)))
+ | as_negIff _ _ = NONE
+in
+
+fun join is_conj littab t =
+ let
+ val comp = if is_conj then comp_conj else comp_disj
+ val dest = if is_conj then dest_conj else dest_disj
+
+ val lookup = lookup_lit littab
+
+ fun lookup_rule t =
+ (case t of
+ @{const Not} $ (@{const Not} $ t) => (Z3_New_Replay_Util.compose dnegI, lookup t)
+ | @{const Not} $ (@{const HOL.eq (bool)} $ t $ (@{const Not} $ u)) =>
+ (Z3_New_Replay_Util.compose negIffI, lookup (iff_const $ u $ t))
+ | @{const Not} $ ((eq as Const (@{const_name HOL.eq}, _)) $ t $ u) =>
+ let fun rewr lit = lit COMP @{thm not_sym}
+ in (rewr, lookup (@{const Not} $ (eq $ u $ t))) end
+ | _ =>
+ (case as_dneg lookup t of
+ NONE => (Z3_New_Replay_Util.compose negIffE, as_negIff lookup t)
+ | x => (Z3_New_Replay_Util.compose dnegE, x)))
+
+ fun join1 (s, t) =
+ (case lookup t of
+ SOME lit => (s, lit)
+ | NONE =>
+ (case lookup_rule t of
+ (rewrite, SOME lit) => (s, rewrite lit)
+ | (_, NONE) => (s, comp (pairself join1 (dest t)))))
+
+ in snd (join1 (if is_conj then (false, t) else (true, t))) end
+
+end
+
+
+(** proving equality of conjunctions or disjunctions **)
+
+fun iff_intro thm1 thm2 = thm2 COMP (thm1 COMP @{thm iffI})
+
+local
+ val cp1 = @{lemma "(~P) = (~Q) ==> P = Q" by simp}
+ val cp2 = @{lemma "(~P) = Q ==> P = (~Q)" by fastforce}
+ val cp3 = @{lemma "P = (~Q) ==> (~P) = Q" by simp}
+in
+fun contrapos1 prove (ct, cu) = prove (negate ct, negate cu) COMP cp1
+fun contrapos2 prove (ct, cu) = prove (negate ct, Thm.dest_arg cu) COMP cp2
+fun contrapos3 prove (ct, cu) = prove (Thm.dest_arg ct, negate cu) COMP cp3
+end
+
+local
+ val contra_rule = @{lemma "P ==> ~P ==> False" by (rule notE)}
+ fun contra_left conj thm =
+ let
+ val rules = explode_term conj (SMT2_Util.prop_of thm)
+ fun contra_lits (t, rs) =
+ (case t of
+ @{const Not} $ u => Termtab.lookup rules u |> Option.map (pair rs)
+ | _ => NONE)
+ in
+ (case Termtab.lookup rules @{const False} of
+ SOME rs => extract_lit thm rs
+ | NONE =>
+ the (Termtab.get_first contra_lits rules)
+ |> pairself (extract_lit thm)
+ |> (fn (nlit, plit) => nlit COMP (plit COMP contra_rule)))
+ end
+
+ val falseE_v = Thm.dest_arg (Thm.dest_arg (Thm.cprop_of @{thm FalseE}))
+ fun contra_right ct = Thm.instantiate ([], [(falseE_v, ct)]) @{thm FalseE}
+in
+
+fun contradict conj ct =
+ iff_intro (Z3_New_Replay_Util.under_assumption (contra_left conj) ct) (contra_right ct)
+
+end
+
+local
+ fun prove_eq l r (cl, cr) =
+ let
+ fun explode' is_conj = explode is_conj true (l <> r) []
+ fun make_tab is_conj thm = make_littab (true_thm :: explode' is_conj thm)
+ fun prove is_conj ct tab = join is_conj tab (Thm.term_of ct)
+
+ val thm1 = Z3_New_Replay_Util.under_assumption (prove r cr o make_tab l) cl
+ val thm2 = Z3_New_Replay_Util.under_assumption (prove l cl o make_tab r) cr
+ in iff_intro thm1 thm2 end
+
+ datatype conj_disj = CONJ | DISJ | NCON | NDIS
+ fun kind_of t =
+ if is_conj t then SOME CONJ
+ else if is_disj t then SOME DISJ
+ else if is_neg' is_conj t then SOME NCON
+ else if is_neg' is_disj t then SOME NDIS
+ else NONE
+in
+
+fun prove_conj_disj_eq ct =
+ let val cp as (cl, cr) = Thm.dest_binop (Thm.dest_arg ct)
+ in
+ (case (kind_of (Thm.term_of cl), Thm.term_of cr) of
+ (SOME CONJ, @{const False}) => contradict true cl
+ | (SOME DISJ, @{const Not} $ @{const False}) =>
+ contrapos2 (contradict false o fst) cp
+ | (kl, _) =>
+ (case (kl, kind_of (Thm.term_of cr)) of
+ (SOME CONJ, SOME CONJ) => prove_eq true true cp
+ | (SOME CONJ, SOME NDIS) => prove_eq true false cp
+ | (SOME CONJ, _) => prove_eq true true cp
+ | (SOME DISJ, SOME DISJ) => contrapos1 (prove_eq false false) cp
+ | (SOME DISJ, SOME NCON) => contrapos2 (prove_eq false true) cp
+ | (SOME DISJ, _) => contrapos1 (prove_eq false false) cp
+ | (SOME NCON, SOME NCON) => contrapos1 (prove_eq true true) cp
+ | (SOME NCON, SOME DISJ) => contrapos3 (prove_eq true false) cp
+ | (SOME NCON, NONE) => contrapos3 (prove_eq true false) cp
+ | (SOME NDIS, SOME NDIS) => prove_eq false false cp
+ | (SOME NDIS, SOME CONJ) => prove_eq false true cp
+ | (SOME NDIS, NONE) => prove_eq false true cp
+ | _ => raise CTERM ("prove_conj_disj_eq", [ct])))
+ end
+
+end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_replay_methods.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,667 @@
+(* Title: HOL/Tools/SMT2/z3_new_replay_methods.ML
+ Author: Sascha Boehme, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+Proof methods for replaying Z3 proofs.
+*)
+
+signature Z3_NEW_REPLAY_METHODS =
+sig
+ (*abstraction*)
+ type abs_context = int * term Termtab.table
+ type 'a abstracter = term -> abs_context -> 'a * abs_context
+ val add_arith_abstracter: (term abstracter -> term option abstracter) ->
+ Context.generic -> Context.generic
+
+ (*theory lemma methods*)
+ type th_lemma_method = Proof.context -> thm list -> term -> thm
+ val add_th_lemma_method: string * th_lemma_method -> Context.generic ->
+ Context.generic
+
+ (*methods for Z3 proof rules*)
+ type z3_method = Proof.context -> thm list -> term -> thm
+ val true_axiom: z3_method
+ val mp: z3_method
+ val refl: z3_method
+ val symm: z3_method
+ val trans: z3_method
+ val cong: z3_method
+ val quant_intro: z3_method
+ val distrib: z3_method
+ val and_elim: z3_method
+ val not_or_elim: z3_method
+ val rewrite: z3_method
+ val rewrite_star: z3_method
+ val pull_quant: z3_method
+ val push_quant: z3_method
+ val elim_unused: z3_method
+ val dest_eq_res: z3_method
+ val quant_inst: z3_method
+ val lemma: z3_method
+ val unit_res: z3_method
+ val iff_true: z3_method
+ val iff_false: z3_method
+ val comm: z3_method
+ val def_axiom: z3_method
+ val apply_def: z3_method
+ val iff_oeq: z3_method
+ val nnf_pos: z3_method
+ val nnf_neg: z3_method
+ val mp_oeq: z3_method
+ val th_lemma: string -> z3_method
+ val is_assumption: Z3_New_Proof.z3_rule -> bool
+ val method_for: Z3_New_Proof.z3_rule -> z3_method
+end
+
+structure Z3_New_Replay_Methods: Z3_NEW_REPLAY_METHODS =
+struct
+
+type z3_method = Proof.context -> thm list -> term -> thm
+
+
+
+(* utility functions *)
+
+val trace = SMT2_Config.trace_msg
+
+fun pretty_thm ctxt thm = Syntax.pretty_term ctxt (Thm.concl_of thm)
+
+fun pretty_goal ctxt msg rule thms t =
+ let
+ val full_msg = msg ^ ": " ^ quote (Z3_New_Proof.string_of_rule rule)
+ val assms =
+ if null thms then []
+ else [Pretty.big_list "assumptions:" (map (pretty_thm ctxt) thms)]
+ val concl = Pretty.big_list "proposition:" [Syntax.pretty_term ctxt t]
+ in Pretty.big_list full_msg (assms @ [concl]) end
+
+fun replay_error ctxt msg rule thms t = error (Pretty.string_of (pretty_goal ctxt msg rule thms t))
+
+fun replay_rule_error ctxt = replay_error ctxt "Failed to replay Z3 proof step"
+
+fun trace_goal ctxt rule thms t =
+ trace ctxt (fn () => Pretty.string_of (pretty_goal ctxt "Goal" rule thms t))
+
+fun as_prop (t as Const (@{const_name Trueprop}, _) $ _) = t
+ | as_prop t = HOLogic.mk_Trueprop t
+
+fun dest_prop (Const (@{const_name Trueprop}, _) $ t) = t
+ | dest_prop t = t
+
+fun dest_thm thm = dest_prop (Thm.concl_of thm)
+
+fun certify_prop ctxt t = SMT2_Util.certify ctxt (as_prop t)
+
+fun try_provers ctxt rule [] thms t = replay_rule_error ctxt rule thms t
+ | try_provers ctxt rule ((name, prover) :: named_provers) thms t =
+ (case (trace ctxt (K ("Trying prover " ^ quote name)); try prover t) of
+ SOME thm => thm
+ | NONE => try_provers ctxt rule named_provers thms t)
+
+fun match ctxt pat t =
+ (Vartab.empty, Vartab.empty)
+ |> Pattern.first_order_match (Proof_Context.theory_of ctxt) (pat, t)
+
+fun gen_certify_inst sel mk cert ctxt thm t =
+ let
+ val inst = match ctxt (dest_thm thm) (dest_prop t)
+ fun cert_inst (ix, (a, b)) = (cert (mk (ix, a)), cert b)
+ in Vartab.fold (cons o cert_inst) (sel inst) [] end
+
+fun match_instantiateT ctxt t thm =
+ if Term.exists_type (Term.exists_subtype Term.is_TVar) (dest_thm thm) then
+ let val certT = Thm.ctyp_of (Proof_Context.theory_of ctxt)
+ in Thm.instantiate (gen_certify_inst fst TVar certT ctxt thm t, []) thm end
+ else thm
+
+fun match_instantiate ctxt t thm =
+ let
+ val cert = SMT2_Util.certify ctxt
+ val thm' = match_instantiateT ctxt t thm
+ in Thm.instantiate ([], gen_certify_inst snd Var cert ctxt thm' t) thm' end
+
+fun apply_rule ctxt t =
+ (case Z3_New_Replay_Rules.apply ctxt (certify_prop ctxt t) of
+ SOME thm => thm
+ | NONE => raise Fail "apply_rule")
+
+fun discharge _ [] thm = thm
+ | discharge i (rule :: rules) thm = discharge (i + Thm.nprems_of rule) rules (rule RSN (i, thm))
+
+fun by_tac ctxt thms ns ts t tac =
+ Goal.prove ctxt [] (map as_prop ts) (as_prop t)
+ (fn {context, prems} => HEADGOAL (tac context prems))
+ |> Drule.generalize ([], ns)
+ |> discharge 1 thms
+
+fun prove ctxt t tac = by_tac ctxt [] [] [] t (K o tac)
+
+fun prop_tac ctxt prems =
+ Method.insert_tac prems THEN' (Classical.fast_tac ctxt ORELSE' Clasimp.force_tac ctxt)
+
+fun quant_tac ctxt = Blast.blast_tac ctxt
+
+
+
+(* plug-ins *)
+
+type abs_context = int * term Termtab.table
+
+type 'a abstracter = term -> abs_context -> 'a * abs_context
+
+type th_lemma_method = Proof.context -> thm list -> term -> thm
+
+fun id_ord ((id1, _), (id2, _)) = int_ord (id1, id2)
+
+structure Plugins = Generic_Data
+(
+ type T =
+ (int * (term abstracter -> term option abstracter)) list *
+ th_lemma_method Symtab.table
+ val empty = ([], Symtab.empty)
+ val extend = I
+ fun merge ((abss1, ths1), (abss2, ths2)) = (
+ Ord_List.merge id_ord (abss1, abss2),
+ Symtab.merge (K true) (ths1, ths2))
+)
+
+fun add_arith_abstracter abs = Plugins.map (apfst (Ord_List.insert id_ord (serial (), abs)))
+fun get_arith_abstracters ctxt = map snd (fst (Plugins.get (Context.Proof ctxt)))
+
+fun add_th_lemma_method method = Plugins.map (apsnd (Symtab.update_new method))
+fun get_th_lemma_method ctxt = snd (Plugins.get (Context.Proof ctxt))
+
+
+
+(* abstraction *)
+
+fun prove_abstract ctxt thms t tac f =
+ let
+ val ((prems, concl), (_, ts)) = f (1, Termtab.empty)
+ val ns = Termtab.fold (fn (_, v) => cons (fst (Term.dest_Free v))) ts []
+ in
+ by_tac ctxt [] ns prems concl tac
+ |> match_instantiate ctxt t
+ |> discharge 1 thms
+ end
+
+fun prove_abstract' ctxt t tac f =
+ prove_abstract ctxt [] t tac (f #>> pair [])
+
+fun lookup_term (_, terms) t = Termtab.lookup terms t
+
+fun abstract_sub t f cx =
+ (case lookup_term cx t of
+ SOME v => (v, cx)
+ | NONE => f cx)
+
+fun mk_fresh_free t (i, terms) =
+ let val v = Free ("t" ^ string_of_int i, fastype_of t)
+ in (v, (i + 1, Termtab.update (t, v) terms)) end
+
+fun apply_abstracters _ [] _ cx = (NONE, cx)
+ | apply_abstracters abs (abstracter :: abstracters) t cx =
+ (case abstracter abs t cx of
+ (NONE, _) => apply_abstracters abs abstracters t cx
+ | x as (SOME _, _) => x)
+
+fun abstract_term (t as _ $ _) = abstract_sub t (mk_fresh_free t)
+ | abstract_term (t as Abs _) = abstract_sub t (mk_fresh_free t)
+ | abstract_term t = pair t
+
+fun abstract_bin abs f t t1 t2 = abstract_sub t (abs t1 ##>> abs t2 #>> f)
+
+fun abstract_ter abs f t t1 t2 t3 =
+ abstract_sub t (abs t1 ##>> abs t2 ##>> abs t3 #>> (Parse.triple1 #> f))
+
+fun abstract_lit (@{const HOL.Not} $ t) = abstract_term t #>> HOLogic.mk_not
+ | abstract_lit t = abstract_term t
+
+fun abstract_not abs (t as @{const HOL.Not} $ t1) =
+ abstract_sub t (abs t1 #>> HOLogic.mk_not)
+ | abstract_not _ t = abstract_lit t
+
+fun abstract_conj (t as @{const HOL.conj} $ t1 $ t2) =
+ abstract_bin abstract_conj HOLogic.mk_conj t t1 t2
+ | abstract_conj t = abstract_lit t
+
+fun abstract_disj (t as @{const HOL.disj} $ t1 $ t2) =
+ abstract_bin abstract_disj HOLogic.mk_disj t t1 t2
+ | abstract_disj t = abstract_lit t
+
+fun abstract_prop (t as (c as @{const If (bool)}) $ t1 $ t2 $ t3) =
+ abstract_ter abstract_prop (fn (t1, t2, t3) => c $ t1 $ t2 $ t3) t t1 t2 t3
+ | abstract_prop (t as @{const HOL.disj} $ t1 $ t2) =
+ abstract_bin abstract_prop HOLogic.mk_disj t t1 t2
+ | abstract_prop (t as @{const HOL.conj} $ t1 $ t2) =
+ abstract_bin abstract_prop HOLogic.mk_conj t t1 t2
+ | abstract_prop (t as @{const HOL.implies} $ t1 $ t2) =
+ abstract_bin abstract_prop HOLogic.mk_imp t t1 t2
+ | abstract_prop (t as @{term "HOL.eq :: bool => _"} $ t1 $ t2) =
+ abstract_bin abstract_prop HOLogic.mk_eq t t1 t2
+ | abstract_prop t = abstract_not abstract_prop t
+
+fun abstract_arith ctxt u =
+ let
+ fun abs (t as (c as Const _) $ Abs (s, T, t')) =
+ abstract_sub t (abs t' #>> (fn u' => c $ Abs (s, T, u')))
+ | abs (t as (c as Const (@{const_name If}, _)) $ t1 $ t2 $ t3) =
+ abstract_ter abs (fn (t1, t2, t3) => c $ t1 $ t2 $ t3) t t1 t2 t3
+ | abs (t as @{const HOL.Not} $ t1) = abstract_sub t (abs t1 #>> HOLogic.mk_not)
+ | abs (t as @{const HOL.disj} $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> HOLogic.mk_disj)
+ | abs (t as (c as Const (@{const_name uminus_class.uminus}, _)) $ t1) =
+ abstract_sub t (abs t1 #>> (fn u => c $ u))
+ | abs (t as (c as Const (@{const_name plus_class.plus}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name minus_class.minus}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name times_class.times}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name z3div}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name z3mod}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name HOL.eq}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name ord_class.less}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name ord_class.less_eq}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs t = abstract_sub t (fn cx =>
+ if can HOLogic.dest_number t then (t, cx)
+ else
+ (case apply_abstracters abs (get_arith_abstracters ctxt) t cx of
+ (SOME u, cx') => (u, cx')
+ | (NONE, _) => abstract_term t cx))
+ in abs u end
+
+
+
+(* truth axiom *)
+
+fun true_axiom _ _ _ = @{thm TrueI}
+
+
+
+(* modus ponens *)
+
+fun mp _ [p, p_eq_q] _ = discharge 1 [p_eq_q, p] iffD1
+ | mp ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Modus_Ponens thms t
+
+val mp_oeq = mp
+
+
+
+(* reflexivity *)
+
+fun refl ctxt _ t = match_instantiate ctxt t @{thm refl}
+
+
+
+(* symmetry *)
+
+fun symm _ [thm] _ = thm RS @{thm sym}
+ | symm ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Reflexivity thms t
+
+
+
+(* transitivity *)
+
+fun trans _ [thm1, thm2] _ = thm1 RSN (1, thm2 RSN (2, @{thm trans}))
+ | trans ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Transitivity thms t
+
+
+
+(* congruence *)
+
+fun ctac prems i st = st |> (
+ resolve_tac (@{thm refl} :: prems) i
+ ORELSE (cong_tac i THEN ctac prems (i + 1) THEN ctac prems i))
+
+fun cong_basic ctxt thms t =
+ let val st = Thm.trivial (certify_prop ctxt t)
+ in
+ (case Seq.pull (ctac thms 1 st) of
+ SOME (thm, _) => thm
+ | NONE => raise THM ("cong", 0, thms @ [st]))
+ end
+
+val cong_dest_rules = @{lemma
+ "(~ P | Q) & (P | ~ Q) ==> P = Q"
+ "(P | ~ Q) & (~ P | Q) ==> P = Q"
+ by fast+}
+
+fun cong_full ctxt thms t = prove ctxt t (fn ctxt' =>
+ Method.insert_tac thms
+ THEN' (Classical.fast_tac ctxt'
+ ORELSE' dresolve_tac cong_dest_rules
+ THEN' Classical.fast_tac ctxt'))
+
+fun cong ctxt thms = try_provers ctxt Z3_New_Proof.Monotonicity [
+ ("basic", cong_basic ctxt thms),
+ ("full", cong_full ctxt thms)] thms
+
+
+
+(* quantifier introduction *)
+
+val quant_intro_rules = @{lemma
+ "(!!x. P x = Q x) ==> (ALL x. P x) = (ALL x. Q x)"
+ "(!!x. P x = Q x) ==> (EX x. P x) = (EX x. Q x)"
+ "(!!x. (~ P x) = Q x) ==> (~ (EX x. P x)) = (ALL x. Q x)"
+ "(!!x. (~ P x) = Q x) ==> (~ (ALL x. P x)) = (EX x. Q x)"
+ by fast+}
+
+fun quant_intro ctxt [thm] t =
+ prove ctxt t (K (REPEAT_ALL_NEW (resolve_tac (thm :: quant_intro_rules))))
+ | quant_intro ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Quant_Intro thms t
+
+
+
+(* distributivity of conjunctions and disjunctions *)
+
+(* TODO: there are no tests with this proof rule *)
+fun distrib ctxt _ t =
+ prove_abstract' ctxt t prop_tac (abstract_prop (dest_prop t))
+
+
+
+(* elimination of conjunctions *)
+
+fun and_elim ctxt [thm] t =
+ prove_abstract ctxt [thm] t prop_tac (
+ abstract_lit (dest_prop t) ##>>
+ abstract_conj (dest_thm thm) #>>
+ apfst single o swap)
+ | and_elim ctxt thms t = replay_rule_error ctxt Z3_New_Proof.And_Elim thms t
+
+
+
+(* elimination of negated disjunctions *)
+
+fun not_or_elim ctxt [thm] t =
+ prove_abstract ctxt [thm] t prop_tac (
+ abstract_lit (dest_prop t) ##>>
+ abstract_not abstract_disj (dest_thm thm) #>>
+ apfst single o swap)
+ | not_or_elim ctxt thms t =
+ replay_rule_error ctxt Z3_New_Proof.Not_Or_Elim thms t
+
+
+
+(* rewriting *)
+
+fun abstract_eq f1 f2 (Const (@{const_name HOL.eq}, _) $ t1 $ t2) =
+ f1 t1 ##>> f2 t2 #>> HOLogic.mk_eq
+ | abstract_eq _ _ t = abstract_term t
+
+fun prove_prop_rewrite ctxt t =
+ prove_abstract' ctxt t prop_tac (
+ abstract_eq abstract_prop abstract_prop (dest_prop t))
+
+fun arith_rewrite_tac ctxt _ =
+ TRY o Simplifier.simp_tac ctxt
+ THEN_ALL_NEW (Arith_Data.arith_tac ctxt ORELSE' Clasimp.force_tac ctxt)
+
+fun prove_arith_rewrite ctxt t =
+ prove_abstract' ctxt t arith_rewrite_tac (
+ abstract_eq (abstract_arith ctxt) (abstract_arith ctxt) (dest_prop t))
+
+fun rewrite ctxt _ = try_provers ctxt Z3_New_Proof.Rewrite [
+ ("rules", apply_rule ctxt),
+ ("prop_rewrite", prove_prop_rewrite ctxt),
+ ("arith_rewrite", prove_arith_rewrite ctxt)] []
+
+fun rewrite_star ctxt = rewrite ctxt
+
+
+
+(* pulling quantifiers *)
+
+fun pull_quant ctxt _ t = prove ctxt t quant_tac
+
+
+
+(* pushing quantifiers *)
+
+fun push_quant _ _ _ = raise Fail "unsupported" (* FIXME *)
+
+
+
+(* elimination of unused bound variables *)
+
+val elim_all = @{lemma "P = Q ==> (ALL x. P) = Q" by fast}
+val elim_ex = @{lemma "P = Q ==> (EX x. P) = Q" by fast}
+
+fun elim_unused_tac i st = (
+ match_tac [@{thm refl}]
+ ORELSE' (match_tac [elim_all, elim_ex] THEN' elim_unused_tac)
+ ORELSE' (
+ match_tac [@{thm iff_allI}, @{thm iff_exI}]
+ THEN' elim_unused_tac)) i st
+
+fun elim_unused ctxt _ t = prove ctxt t (fn _ => elim_unused_tac)
+
+
+
+(* destructive equality resolution *)
+
+fun dest_eq_res _ _ _ = raise Fail "dest_eq_res" (* FIXME *)
+
+
+
+(* quantifier instantiation *)
+
+val quant_inst_rule = @{lemma "~P x | Q ==> ~(ALL x. P x) | Q" by fast}
+
+fun quant_inst ctxt _ t = prove ctxt t (fn _ =>
+ REPEAT_ALL_NEW (rtac quant_inst_rule)
+ THEN' rtac @{thm excluded_middle})
+
+
+
+(* propositional lemma *)
+
+exception LEMMA of unit
+
+val intro_hyp_rule1 = @{lemma "(~P ==> Q) ==> P | Q" by fast}
+val intro_hyp_rule2 = @{lemma "(P ==> Q) ==> ~P | Q" by fast}
+
+fun norm_lemma thm =
+ (thm COMP_INCR intro_hyp_rule1)
+ handle THM _ => thm COMP_INCR intro_hyp_rule2
+
+fun negated_prop (@{const HOL.Not} $ t) = HOLogic.mk_Trueprop t
+ | negated_prop t = HOLogic.mk_Trueprop (HOLogic.mk_not t)
+
+fun intro_hyps tab (t as @{const HOL.disj} $ t1 $ t2) cx =
+ lookup_intro_hyps tab t (fold (intro_hyps tab) [t1, t2]) cx
+ | intro_hyps tab t cx =
+ lookup_intro_hyps tab t (fn _ => raise LEMMA ()) cx
+
+and lookup_intro_hyps tab t f (cx as (thm, terms)) =
+ (case Termtab.lookup tab (negated_prop t) of
+ NONE => f cx
+ | SOME hyp => (norm_lemma (Thm.implies_intr hyp thm), t :: terms))
+
+fun lemma ctxt (thms as [thm]) t =
+ (let
+ val tab = Termtab.make (map (`Thm.term_of) (#hyps (Thm.crep_thm thm)))
+ val (thm', terms) = intro_hyps tab (dest_prop t) (thm, [])
+ in
+ prove_abstract ctxt [thm'] t prop_tac (
+ fold (snd oo abstract_lit) terms #>
+ abstract_disj (dest_thm thm') #>> single ##>>
+ abstract_disj (dest_prop t))
+ end
+ handle LEMMA () => replay_error ctxt "Bad proof state" Z3_New_Proof.Lemma thms t)
+ | lemma ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Lemma thms t
+
+
+
+(* unit resolution *)
+
+fun abstract_unit (t as (@{const HOL.Not} $ (@{const HOL.disj} $ t1 $ t2))) =
+ abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
+ HOLogic.mk_not o HOLogic.mk_disj)
+ | abstract_unit (t as (@{const HOL.disj} $ t1 $ t2)) =
+ abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
+ HOLogic.mk_disj)
+ | abstract_unit t = abstract_lit t
+
+fun unit_res ctxt thms t =
+ prove_abstract ctxt thms t prop_tac (
+ fold_map (abstract_unit o dest_thm) thms ##>>
+ abstract_unit (dest_prop t) #>>
+ (fn (prems, concl) => (prems, concl)))
+
+
+
+(* iff-true *)
+
+val iff_true_rule = @{lemma "P ==> P = True" by fast}
+
+fun iff_true _ [thm] _ = thm RS iff_true_rule
+ | iff_true ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Iff_True thms t
+
+
+
+(* iff-false *)
+
+val iff_false_rule = @{lemma "~P ==> P = False" by fast}
+
+fun iff_false _ [thm] _ = thm RS iff_false_rule
+ | iff_false ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Iff_False thms t
+
+
+
+(* commutativity *)
+
+fun comm ctxt _ t = match_instantiate ctxt t @{thm eq_commute}
+
+
+
+(* definitional axioms *)
+
+fun def_axiom_disj ctxt t =
+ (case dest_prop t of
+ @{const HOL.disj} $ u1 $ u2 =>
+ prove_abstract' ctxt t prop_tac (
+ abstract_prop u2 ##>> abstract_prop u1 #>> HOLogic.mk_disj o swap)
+ | u => prove_abstract' ctxt t prop_tac (abstract_prop u))
+
+fun def_axiom ctxt _ = try_provers ctxt Z3_New_Proof.Def_Axiom [
+ ("rules", apply_rule ctxt),
+ ("disj", def_axiom_disj ctxt)] []
+
+
+
+(* application of definitions *)
+
+fun apply_def _ [thm] _ = thm (* TODO: cover also the missing cases *)
+ | apply_def ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Apply_Def thms t
+
+
+
+(* iff-oeq *)
+
+fun iff_oeq _ _ _ = raise Fail "iff_oeq" (* FIXME *)
+
+
+
+(* negation normal form *)
+
+fun nnf_prop ctxt thms t =
+ prove_abstract ctxt thms t prop_tac (
+ fold_map (abstract_prop o dest_thm) thms ##>>
+ abstract_prop (dest_prop t))
+
+fun nnf ctxt rule thms = try_provers ctxt rule [
+ ("prop", nnf_prop ctxt thms),
+ ("quant", quant_intro ctxt [hd thms])] thms
+
+fun nnf_pos ctxt = nnf ctxt Z3_New_Proof.Nnf_Pos
+fun nnf_neg ctxt = nnf ctxt Z3_New_Proof.Nnf_Neg
+
+
+
+(* theory lemmas *)
+
+fun arith_th_lemma_tac ctxt prems =
+ Method.insert_tac prems
+ THEN' SELECT_GOAL (Local_Defs.unfold_tac ctxt @{thms z3div_def z3mod_def})
+ THEN' Arith_Data.arith_tac ctxt
+
+fun arith_th_lemma ctxt thms t =
+ prove_abstract ctxt thms t arith_th_lemma_tac (
+ fold_map (abstract_arith ctxt o dest_thm) thms ##>>
+ abstract_arith ctxt (dest_prop t))
+
+val _ = Theory.setup (Context.theory_map (add_th_lemma_method ("arith", arith_th_lemma)))
+
+fun th_lemma name ctxt thms =
+ (case Symtab.lookup (get_th_lemma_method ctxt) name of
+ SOME method => method ctxt thms
+ | NONE => replay_error ctxt "Bad theory" (Z3_New_Proof.Th_Lemma name) thms)
+
+
+
+(* mapping of rules to methods *)
+
+fun is_assumption Z3_New_Proof.Asserted = true
+ | is_assumption Z3_New_Proof.Goal = true
+ | is_assumption Z3_New_Proof.Hypothesis = true
+ | is_assumption Z3_New_Proof.Intro_Def = true
+ | is_assumption Z3_New_Proof.Skolemize = true
+ | is_assumption _ = false
+
+fun unsupported rule ctxt = replay_error ctxt "Unsupported" rule
+fun assumed rule ctxt = replay_error ctxt "Assumed" rule
+
+fun choose Z3_New_Proof.True_Axiom = true_axiom
+ | choose (r as Z3_New_Proof.Asserted) = assumed r
+ | choose (r as Z3_New_Proof.Goal) = assumed r
+ | choose Z3_New_Proof.Modus_Ponens = mp
+ | choose Z3_New_Proof.Reflexivity = refl
+ | choose Z3_New_Proof.Symmetry = symm
+ | choose Z3_New_Proof.Transitivity = trans
+ | choose (r as Z3_New_Proof.Transitivity_Star) = unsupported r
+ | choose Z3_New_Proof.Monotonicity = cong
+ | choose Z3_New_Proof.Quant_Intro = quant_intro
+ | choose Z3_New_Proof.Distributivity = distrib
+ | choose Z3_New_Proof.And_Elim = and_elim
+ | choose Z3_New_Proof.Not_Or_Elim = not_or_elim
+ | choose Z3_New_Proof.Rewrite = rewrite
+ | choose Z3_New_Proof.Rewrite_Star = rewrite_star
+ | choose Z3_New_Proof.Pull_Quant = pull_quant
+ | choose (r as Z3_New_Proof.Pull_Quant_Star) = unsupported r
+ | choose Z3_New_Proof.Push_Quant = push_quant
+ | choose Z3_New_Proof.Elim_Unused_Vars = elim_unused
+ | choose Z3_New_Proof.Dest_Eq_Res = dest_eq_res
+ | choose Z3_New_Proof.Quant_Inst = quant_inst
+ | choose (r as Z3_New_Proof.Hypothesis) = assumed r
+ | choose Z3_New_Proof.Lemma = lemma
+ | choose Z3_New_Proof.Unit_Resolution = unit_res
+ | choose Z3_New_Proof.Iff_True = iff_true
+ | choose Z3_New_Proof.Iff_False = iff_false
+ | choose Z3_New_Proof.Commutativity = comm
+ | choose Z3_New_Proof.Def_Axiom = def_axiom
+ | choose (r as Z3_New_Proof.Intro_Def) = assumed r
+ | choose Z3_New_Proof.Apply_Def = apply_def
+ | choose Z3_New_Proof.Iff_Oeq = iff_oeq
+ | choose Z3_New_Proof.Nnf_Pos = nnf_pos
+ | choose Z3_New_Proof.Nnf_Neg = nnf_neg
+ | choose (r as Z3_New_Proof.Nnf_Star) = unsupported r
+ | choose (r as Z3_New_Proof.Cnf_Star) = unsupported r
+ | choose (r as Z3_New_Proof.Skolemize) = assumed r
+ | choose Z3_New_Proof.Modus_Ponens_Oeq = mp_oeq
+ | choose (Z3_New_Proof.Th_Lemma name) = th_lemma name
+
+fun with_tracing rule method ctxt thms t =
+ let val _ = trace_goal ctxt rule thms t
+ in method ctxt thms t end
+
+fun method_for rule = with_tracing rule (choose rule)
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_replay_rules.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,54 @@
+(* Title: HOL/Tools/SMT2/z3_new_replay_rules.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Custom rules for Z3 proof replay.
+*)
+
+signature Z3_NEW_REPLAY_RULES =
+sig
+ val apply: Proof.context -> cterm -> thm option
+end
+
+structure Z3_New_Replay_Rules: Z3_NEW_REPLAY_RULES =
+struct
+
+structure Data = Generic_Data
+(
+ type T = thm Net.net
+ val empty = Net.empty
+ val extend = I
+ val merge = Net.merge Thm.eq_thm
+)
+
+fun maybe_instantiate ct thm =
+ try Thm.first_order_match (Thm.cprop_of thm, ct)
+ |> Option.map (fn inst => Thm.instantiate inst thm)
+
+fun apply ctxt ct =
+ let
+ val net = Data.get (Context.Proof ctxt)
+ val xthms = Net.match_term net (Thm.term_of ct)
+
+ fun select ct = map_filter (maybe_instantiate ct) xthms
+ fun select' ct =
+ let val thm = Thm.trivial ct
+ in map_filter (try (fn rule => rule COMP thm)) xthms end
+
+ in try hd (case select ct of [] => select' ct | xthms' => xthms') end
+
+val prep = `Thm.prop_of
+
+fun ins thm net = Net.insert_term Thm.eq_thm (prep thm) net handle Net.INSERT => net
+fun del thm net = Net.delete_term Thm.eq_thm (prep thm) net handle Net.DELETE => net
+
+val add = Thm.declaration_attribute (Data.map o ins)
+val del = Thm.declaration_attribute (Data.map o del)
+
+val name = Binding.name "z3_new_rule"
+
+val description = "declaration of Z3 proof rules"
+
+val _ = Theory.setup (Attrib.setup name (Attrib.add_del add del) description #>
+ Global_Theory.add_thms_dynamic (name, Net.content o Data.get))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT2/z3_new_replay_util.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,155 @@
+(* Title: HOL/Tools/SMT2/z3_new_replay_util.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Helper functions required for Z3 proof replay.
+*)
+
+signature Z3_NEW_REPLAY_UTIL =
+sig
+ (*theorem nets*)
+ val thm_net_of: ('a -> thm) -> 'a list -> 'a Net.net
+ val net_instances: (int * thm) Net.net -> cterm -> (int * thm) list
+
+ (*proof combinators*)
+ val under_assumption: (thm -> thm) -> cterm -> thm
+ val discharge: thm -> thm -> thm
+
+ (*a faster COMP*)
+ type compose_data
+ val precompose: (cterm -> cterm list) -> thm -> compose_data
+ val precompose2: (cterm -> cterm * cterm) -> thm -> compose_data
+ val compose: compose_data -> thm -> thm
+
+ (*simpset*)
+ val add_simproc: Simplifier.simproc -> Context.generic -> Context.generic
+ val make_simpset: Proof.context -> thm list -> simpset
+end
+
+structure Z3_New_Replay_Util: Z3_NEW_REPLAY_UTIL =
+struct
+
+
+
+(* theorem nets *)
+
+fun thm_net_of f xthms =
+ let fun insert xthm = Net.insert_term (K false) (Thm.prop_of (f xthm), xthm)
+ in fold insert xthms Net.empty end
+
+fun maybe_instantiate ct thm =
+ try Thm.first_order_match (Thm.cprop_of thm, ct)
+ |> Option.map (fn inst => Thm.instantiate inst thm)
+
+local
+ fun instances_from_net match f net ct =
+ let
+ val lookup = if match then Net.match_term else Net.unify_term
+ val xthms = lookup net (Thm.term_of ct)
+ fun select ct = map_filter (f (maybe_instantiate ct)) xthms
+ fun select' ct =
+ let val thm = Thm.trivial ct
+ in map_filter (f (try (fn rule => rule COMP thm))) xthms end
+ in (case select ct of [] => select' ct | xthms' => xthms') end
+in
+
+fun net_instances net =
+ instances_from_net false (fn f => fn (i, thm) => Option.map (pair i) (f thm))
+ net
+
+end
+
+
+
+(* proof combinators *)
+
+fun under_assumption f ct =
+ let val ct' = SMT2_Util.mk_cprop ct in Thm.implies_intr ct' (f (Thm.assume ct')) end
+
+fun discharge p pq = Thm.implies_elim pq p
+
+
+
+(* a faster COMP *)
+
+type compose_data = cterm list * (cterm -> cterm list) * thm
+
+fun list2 (x, y) = [x, y]
+
+fun precompose f rule = (f (Thm.cprem_of rule 1), f, rule)
+fun precompose2 f rule = precompose (list2 o f) rule
+
+fun compose (cvs, f, rule) thm =
+ discharge thm (Thm.instantiate ([], cvs ~~ f (Thm.cprop_of thm)) rule)
+
+
+
+(* simpset *)
+
+local
+ val antisym_le1 = mk_meta_eq @{thm order_class.antisym_conv}
+ val antisym_le2 = mk_meta_eq @{thm linorder_class.antisym_conv2}
+ val antisym_less1 = mk_meta_eq @{thm linorder_class.antisym_conv1}
+ val antisym_less2 = mk_meta_eq @{thm linorder_class.antisym_conv3}
+
+ fun eq_prop t thm = HOLogic.mk_Trueprop t aconv Thm.prop_of thm
+ fun dest_binop ((c as Const _) $ t $ u) = (c, t, u)
+ | dest_binop t = raise TERM ("dest_binop", [t])
+
+ fun prove_antisym_le ctxt t =
+ let
+ val (le, r, s) = dest_binop t
+ val less = Const (@{const_name less}, Term.fastype_of le)
+ val prems = Simplifier.prems_of ctxt
+ in
+ (case find_first (eq_prop (le $ s $ r)) prems of
+ NONE =>
+ find_first (eq_prop (HOLogic.mk_not (less $ r $ s))) prems
+ |> Option.map (fn thm => thm RS antisym_less1)
+ | SOME thm => SOME (thm RS antisym_le1))
+ end
+ handle THM _ => NONE
+
+ fun prove_antisym_less ctxt t =
+ let
+ val (less, r, s) = dest_binop (HOLogic.dest_not t)
+ val le = Const (@{const_name less_eq}, Term.fastype_of less)
+ val prems = Simplifier.prems_of ctxt
+ in
+ (case find_first (eq_prop (le $ r $ s)) prems of
+ NONE =>
+ find_first (eq_prop (HOLogic.mk_not (less $ s $ r))) prems
+ |> Option.map (fn thm => thm RS antisym_less2)
+ | SOME thm => SOME (thm RS antisym_le2))
+ end
+ handle THM _ => NONE
+
+ val basic_simpset =
+ simpset_of (put_simpset HOL_ss @{context}
+ addsimps @{thms field_simps times_divide_eq_right times_divide_eq_left arith_special
+ arith_simps rel_simps array_rules z3div_def z3mod_def}
+ addsimprocs [@{simproc binary_int_div}, @{simproc binary_int_mod},
+ Simplifier.simproc_global @{theory} "fast_int_arith" [
+ "(m::int) < n", "(m::int) <= n", "(m::int) = n"] Lin_Arith.simproc,
+ Simplifier.simproc_global @{theory} "antisym_le" ["(x::'a::order) <= y"] prove_antisym_le,
+ Simplifier.simproc_global @{theory} "antisym_less" ["~ (x::'a::linorder) < y"]
+ prove_antisym_less])
+
+ structure Simpset = Generic_Data
+ (
+ type T = simpset
+ val empty = basic_simpset
+ val extend = I
+ val merge = Simplifier.merge_ss
+ )
+in
+
+fun add_simproc simproc context =
+ Simpset.map (simpset_map (Context.proof_of context)
+ (fn ctxt => ctxt addsimprocs [simproc])) context
+
+fun make_simpset ctxt rules =
+ simpset_of (put_simpset (Simpset.get (Context.Proof ctxt)) ctxt addsimps rules)
+
+end
+
+end
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_commands.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_commands.ML Thu Mar 13 16:39:08 2014 +0100
@@ -29,7 +29,7 @@
(* val cvc3N = "cvc3" *)
val yicesN = "yices"
-val z3N = "z3"
+val z3_newN = "z3_new"
val runN = "run"
val minN = "min"
@@ -195,14 +195,6 @@
fun merge data : T = AList.merge (op =) (K true) data
)
-fun is_prover_supported ctxt =
- let val thy = Proof_Context.theory_of ctxt in
- is_proof_method orf is_atp thy orf is_smt_prover ctxt
- end
-
-fun is_prover_installed ctxt =
- is_proof_method orf is_smt_prover ctxt orf is_atp_installed (Proof_Context.theory_of ctxt)
-
fun remotify_prover_if_supported_and_not_already_remote ctxt name =
if String.isPrefix remote_prefix name then
SOME name
@@ -220,7 +212,7 @@
(* The first ATP of the list is used by Auto Sledgehammer. Because of the low
timeout, it makes sense to put E first. *)
fun default_provers_param_value mode ctxt =
- [eN, spassN, z3N, e_sineN, vampireN, yicesN]
+ [eN, spassN, z3_newN, e_sineN, vampireN, yicesN]
|> map_filter (remotify_prover_if_not_installed ctxt)
(* In "try" mode, leave at least one thread to another slow tool (e.g. Nitpick) *)
|> take (Multithreading.max_threads_value () - (if mode = Try then 1 else 0))
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_isar.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_isar.ML Thu Mar 13 16:39:08 2014 +0100
@@ -112,7 +112,7 @@
* (term, string) atp_step list * thm
val basic_systematic_methods = [Metis_Method (NONE, NONE), Meson_Method, Blast_Method]
-val simp_based_methods = [Simp_Method, Auto_Method, Fastforce_Method, Force_Method]
+val simp_based_methods = [Auto_Method, Simp_Method, Fastforce_Method, Force_Method]
val basic_arith_methods = [Linarith_Method, Presburger_Method, Algebra_Method]
val arith_methods = basic_arith_methods @ simp_based_methods @ basic_systematic_methods
@@ -125,6 +125,8 @@
fun isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
(one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
let
+ val _ = if debug then Output.urgent_message "Constructing Isar proof..." else ()
+
fun isar_proof_of () =
let
val SOME (verbose, alt_metis_args, preplay_timeout, compress_isar, try0_isar, minimize,
@@ -134,7 +136,7 @@
fun massage_methods (meths as meth :: _) =
if not try0_isar then [meth]
- else if smt_proofs = SOME true then SMT_Method :: meths
+ else if smt_proofs = SOME true then SMT2_Method :: meths
else meths
val (params, _, concl_t) = strip_subgoal goal subgoal ctxt
@@ -272,8 +274,6 @@
and isar_proof outer fix assms lems infs =
Proof (fix, assms, lems @ isar_steps outer NONE [] infs)
- val string_of_isar_proof = string_of_isar_proof ctxt subgoal subgoal_count
-
val trace = Config.get ctxt trace
val canonical_isar_proof =
@@ -303,7 +303,8 @@
fun trace_isar_proof label proof =
if trace then
tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^
- string_of_isar_proof (comment_isar_proof comment_of proof) ^ "\n")
+ string_of_isar_proof ctxt subgoal subgoal_count
+ (comment_isar_proof comment_of proof) ^ "\n")
else
()
@@ -335,7 +336,7 @@
#> kill_useless_labels_in_isar_proof
#> relabel_isar_proof_nicely)
in
- (case string_of_isar_proof isar_proof of
+ (case string_of_isar_proof ctxt subgoal subgoal_count isar_proof of
"" =>
if isar_proofs = SOME true then "\nNo structured proof available (proof too simple)."
else ""
@@ -363,15 +364,14 @@
(case try isar_proof_of () of
SOME s => s
| NONE =>
- if isar_proofs = SOME true then "\nWarning: The Isar proof construction failed." else "")
+ if isar_proofs = SOME true then "\nWarning: Isar proof construction failed." else "")
in one_line_proof ^ isar_proof end
fun isar_proof_would_be_a_good_idea smt_proofs (meth, play) =
(case play of
- Played _ => meth = SMT_Method andalso smt_proofs <> SOME true
- | Play_Timed_Out _ => true
- | Play_Failed => true
- | Not_Played => false)
+ Played _ => meth = SMT2_Method andalso smt_proofs <> SOME true
+ | Play_Timed_Out time => Time.> (time, Time.zeroTime)
+ | Play_Failed => true)
fun proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained
(one_line_params as (preplay, _, _, _, _, _)) =
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_isar_preplay.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_isar_preplay.ML Thu Mar 13 16:39:08 2014 +0100
@@ -178,7 +178,8 @@
end
| set_preplay_outcomes_of_isar_step _ _ _ _ _ _ = ()
-fun peek_at_outcome outcome = if Lazy.is_finished outcome then Lazy.force outcome else Not_Played
+fun peek_at_outcome outcome =
+ if Lazy.is_finished outcome then Lazy.force outcome else Play_Timed_Out Time.zeroTime
fun get_best_method_outcome force =
tap (List.app (K () o Lazy.future Future.default_params o snd)) (* optional parallelism *)
@@ -195,14 +196,17 @@
outcome as Played _ => outcome
| _ => snd (get_best_method_outcome Lazy.force meths_outcomes))
else
- (case get_best_method_outcome peek_at_outcome meths_outcomes of
- (_, Not_Played) => snd (get_best_method_outcome Lazy.force meths_outcomes)
- | (_, outcome) => outcome)
+ let val outcome = snd (get_best_method_outcome peek_at_outcome meths_outcomes) in
+ if outcome = Play_Timed_Out Time.zeroTime then
+ snd (get_best_method_outcome Lazy.force meths_outcomes)
+ else
+ outcome
+ end
end
fun preplay_outcome_of_isar_step_for_method preplay_data l =
AList.lookup (op =) (the (Canonical_Label_Tab.lookup preplay_data l))
- #> the_default (Lazy.value Not_Played)
+ #> the_default (Lazy.value (Play_Timed_Out Time.zeroTime))
fun fastest_method_of_isar_step preplay_data =
the o Canonical_Label_Tab.lookup preplay_data
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_isar_proof.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_isar_proof.ML Thu Mar 13 16:39:08 2014 +0100
@@ -259,7 +259,7 @@
fun is_direct_method (Metis_Method _) = true
| is_direct_method Meson_Method = true
- | is_direct_method SMT_Method = true
+ | is_direct_method SMT2_Method = true
| is_direct_method _ = false
(* Local facts are always passed via "using", which affects "meson" and "metis". This is
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_proof_methods.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_proof_methods.ML Thu Mar 13 16:39:08 2014 +0100
@@ -12,7 +12,7 @@
datatype proof_method =
Metis_Method of string option * string option |
Meson_Method |
- SMT_Method |
+ SMT2_Method |
Blast_Method |
Simp_Method |
Simp_Size_Method |
@@ -26,8 +26,7 @@
datatype play_outcome =
Played of Time.time |
Play_Timed_Out of Time.time |
- Play_Failed |
- Not_Played
+ Play_Failed
type minimize_command = string list -> string
type one_line_params =
@@ -51,7 +50,7 @@
datatype proof_method =
Metis_Method of string option * string option |
Meson_Method |
- SMT_Method |
+ SMT2_Method |
Blast_Method |
Simp_Method |
Simp_Size_Method |
@@ -65,8 +64,7 @@
datatype play_outcome =
Played of Time.time |
Play_Timed_Out of Time.time |
- Play_Failed |
- Not_Played
+ Play_Failed
type minimize_command = string list -> string
type one_line_params =
@@ -78,7 +76,7 @@
| Metis_Method (type_enc_opt, lam_trans_opt) =>
"metis (" ^ commas (map_filter I [type_enc_opt, lam_trans_opt]) ^ ")"
| Meson_Method => "meson"
- | SMT_Method => "smt"
+ | SMT2_Method => "smt2"
| Blast_Method => "blast"
| Simp_Method => "simp"
| Simp_Size_Method => "simp add: size_ne_size_imp_ne"
@@ -93,7 +91,7 @@
exceeded" warnings and the like. *)
fun silence_proof_methods debug =
Try0.silence_methods debug
- #> Config.put SMT_Config.verbose debug
+ #> Config.put SMT2_Config.verbose debug
fun tac_of_proof_method ctxt0 debug (local_facts, global_facts) meth =
let val ctxt = silence_proof_methods debug ctxt0 in
@@ -103,8 +101,7 @@
Metis_Tactic.metis_tac [type_enc_opt |> the_default (hd partial_type_encs)]
(lam_trans_opt |> the_default default_metis_lam_trans) ctxt global_facts
| Meson_Method => Meson.meson_tac ctxt global_facts
-
- | SMT_Method => SMT_Solver.smt_tac ctxt global_facts
+ | SMT2_Method => SMT2_Solver.smt2_tac ctxt global_facts
| _ =>
Method.insert_tac global_facts THEN'
(case meth of
@@ -121,17 +118,14 @@
end
fun string_of_play_outcome (Played time) = string_of_ext_time (false, time)
- | string_of_play_outcome (Play_Timed_Out time) = string_of_ext_time (true, time) ^ ", timed out"
+ | string_of_play_outcome (Play_Timed_Out time) =
+ if time = Time.zeroTime then "" else string_of_ext_time (true, time) ^ ", timed out"
| string_of_play_outcome Play_Failed = "failed"
- | string_of_play_outcome _ = "unknown"
fun play_outcome_ord (Played time1, Played time2) =
int_ord (pairself Time.toMilliseconds (time1, time2))
| play_outcome_ord (Played _, _) = LESS
| play_outcome_ord (_, Played _) = GREATER
- | play_outcome_ord (Not_Played, Not_Played) = EQUAL
- | play_outcome_ord (Not_Played, _) = LESS
- | play_outcome_ord (_, Not_Played) = GREATER
| play_outcome_ord (Play_Timed_Out time1, Play_Timed_Out time2) =
int_ord (pairself Time.toMilliseconds (time1, time2))
| play_outcome_ord (Play_Timed_Out _, _) = LESS
@@ -160,11 +154,11 @@
(* unusing_chained_facts used_chaineds num_chained ^ *)
apply_on_subgoal i n ^ command_call (string_of_proof_method meth) ss
-fun show_time NONE = ""
- | show_time (SOME ext_time) = " (" ^ string_of_ext_time ext_time ^ ")"
-
-fun try_command_line banner time command =
- banner ^ ": " ^ Active.sendback_markup [Markup.padding_command] command ^ show_time time ^ "."
+fun try_command_line banner play command =
+ let val s = string_of_play_outcome play in
+ banner ^ ": " ^ Active.sendback_markup [Markup.padding_command] command ^
+ (s |> s <> "" ? enclose " (" ")") ^ "."
+ end
fun minimize_line _ [] = ""
| minimize_line minimize_command ss =
@@ -182,18 +176,11 @@
let
val (chained, extra) = split_used_facts used_facts
- val (failed, ext_time) =
- (case play of
- Played time => (false, (SOME (false, time)))
- | Play_Timed_Out time => (false, SOME (true, time))
- | Play_Failed => (true, NONE)
- | Not_Played => (false, NONE))
-
val try_line =
map fst extra
|> proof_method_command meth subgoal subgoal_count (map fst chained) num_chained
- |> (if failed then enclose "One-line proof reconstruction failed: " "."
- else try_command_line banner ext_time)
+ |> (if play = Play_Failed then enclose "One-line proof reconstruction failed: " "."
+ else try_command_line banner play)
in
try_line ^ minimize_line minimize_command (map fst (extra @ chained))
end
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover.ML Thu Mar 13 16:39:08 2014 +0100
@@ -184,7 +184,7 @@
Metis_Method (SOME full_typesN, NONE),
Metis_Method (SOME no_typesN, SOME desperate_lam_trans),
Metis_Method (SOME really_full_type_enc, SOME desperate_lam_trans)]) @
- (if smt_proofs then [SMT_Method] else [])
+ (if smt_proofs then [SMT2_Method] else [])
fun extract_proof_method ({type_enc, lam_trans, ...} : params)
(Metis_Method (type_enc', lam_trans')) =
@@ -195,7 +195,7 @@
(if is_none lam_trans' andalso is_none lam_trans then []
else [("lam_trans", [lam_trans' |> the_default default_metis_lam_trans])])
in (metisN, override_params) end
- | extract_proof_method _ SMT_Method = (smtN, [])
+ | extract_proof_method _ SMT2_Method = (smtN, [])
(* based on "Mirabelle.can_apply" and generalized *)
fun timed_apply timeout tac state i =
@@ -219,7 +219,7 @@
fun get_preferred meths = if member (op =) meths preferred then preferred else meth
in
if timeout = Time.zeroTime then
- (get_preferred meths, Not_Played)
+ (get_preferred meths, Play_Timed_Out Time.zeroTime)
else
let
val _ = if mode = Minimize then Output.urgent_message "Preplaying proof..." else ()
@@ -247,9 +247,10 @@
end
val canonical_isar_supported_prover = eN
+val z3_newN = "z3_new"
fun isar_supported_prover_of thy name =
- if is_atp thy name then name
+ if is_atp thy name orelse name = z3_newN then name
else if is_atp_installed thy canonical_isar_supported_prover then canonical_isar_supported_prover
else name
@@ -260,7 +261,7 @@
val maybe_isar_name = name |> isar_proofs = SOME true ? isar_supported_prover_of thy
val (min_name, override_params) =
(case preplay of
- (meth, Played _) =>
+ (meth as Metis_Method _, Played _) =>
if isar_proofs = SOME true then (maybe_isar_name, []) else extract_proof_method params meth
| _ => (maybe_isar_name, []))
in minimize_command override_params min_name end
@@ -279,7 +280,8 @@
val (remote_provers, local_provers) =
proof_method_names @
sort_strings (supported_atps thy) @
- sort_strings (SMT_Solver.available_solvers_of ctxt)
+ sort_strings (SMT_Solver.available_solvers_of ctxt) @
+ sort_strings (SMT2_Solver.available_solvers_of ctxt)
|> List.partition (String.isPrefix remote_prefix)
in
Output.urgent_message ("Supported provers: " ^
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover_minimize.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover_minimize.ML Thu Mar 13 16:39:08 2014 +0100
@@ -49,6 +49,7 @@
open Sledgehammer_Prover
open Sledgehammer_Prover_ATP
open Sledgehammer_Prover_SMT
+open Sledgehammer_Prover_SMT2
fun run_proof_method mode name (params as {debug, verbose, timeout, type_enc, lam_trans, ...})
minimize_command
@@ -56,7 +57,7 @@
let
val meth =
if name = metisN then Metis_Method (type_enc, lam_trans)
- else if name = smtN then SMT_Method
+ else if name = smtN then SMT2_Method
else raise Fail ("unknown proof_method: " ^ quote name)
val used_facts = facts |> map fst
in
@@ -89,11 +90,12 @@
fun is_prover_supported ctxt =
let val thy = Proof_Context.theory_of ctxt in
- is_proof_method orf is_atp thy orf is_smt_prover ctxt
+ is_proof_method orf is_atp thy orf is_smt_prover ctxt orf is_smt2_prover ctxt
end
fun is_prover_installed ctxt =
- is_proof_method orf is_smt_prover ctxt orf is_atp_installed (Proof_Context.theory_of ctxt)
+ is_proof_method orf is_smt_prover ctxt orf is_smt2_prover ctxt orf
+ is_atp_installed (Proof_Context.theory_of ctxt)
val proof_method_default_max_facts = 20
@@ -103,8 +105,12 @@
proof_method_default_max_facts
else if is_atp thy name then
fold (Integer.max o fst o #1 o fst o snd) (#best_slices (get_atp thy name ()) ctxt) 0
- else (* is_smt_prover ctxt name *)
+ else if is_smt_prover ctxt name then
SMT_Solver.default_max_relevant ctxt name
+ else if is_smt2_prover ctxt name then
+ SMT2_Solver.default_max_relevant ctxt name
+ else
+ error ("No such prover: " ^ name ^ ".")
end
fun get_prover ctxt mode name =
@@ -112,6 +118,7 @@
if is_proof_method name then run_proof_method mode name
else if is_atp thy name then run_atp mode name
else if is_smt_prover ctxt name then run_smt_solver mode name
+ else if is_smt2_prover ctxt name then run_smt2_solver mode name
else error ("No such prover: " ^ name ^ ".")
end
@@ -344,7 +351,7 @@
adjust_proof_method_params override_params params))
else
(prover_fast_enough (), (name, params))
- | (SMT_Method, Played timeout) =>
+ | (SMT2_Method, Played timeout) =>
(* Cheat: Assume the original prover is as fast as "smt" for the goal it proved
itself. *)
(can_min_fast_enough timeout, (name, params))
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover_smt.ML Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover_smt.ML Thu Mar 13 16:39:08 2014 +0100
@@ -234,7 +234,7 @@
NONE =>
(Lazy.lazy (fn () =>
play_one_line_proof mode debug verbose preplay_timeout used_pairs state subgoal
- SMT_Method (bunch_of_proof_methods (smt_proofs <> SOME false) false liftingN)),
+ SMT2_Method (bunch_of_proof_methods (smt_proofs <> SOME false) false liftingN)),
fn preplay =>
let
val one_line_params =
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover_smt2.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,267 @@
+(* Title: HOL/Tools/Sledgehammer/sledgehammer_prover_smt2.ML
+ Author: Fabian Immler, TU Muenchen
+ Author: Makarius
+ Author: Jasmin Blanchette, TU Muenchen
+
+SMT solvers as Sledgehammer provers.
+*)
+
+signature SLEDGEHAMMER_PROVER_SMT2 =
+sig
+ type stature = ATP_Problem_Generate.stature
+ type mode = Sledgehammer_Prover.mode
+ type prover = Sledgehammer_Prover.prover
+
+ val smt2_builtins : bool Config.T
+ val smt2_triggers : bool Config.T
+ val smt2_weights : bool Config.T
+ val smt2_weight_min_facts : int Config.T
+ val smt2_min_weight : int Config.T
+ val smt2_max_weight : int Config.T
+ val smt2_max_weight_index : int Config.T
+ val smt2_weight_curve : (int -> int) Unsynchronized.ref
+ val smt2_max_slices : int Config.T
+ val smt2_slice_fact_frac : real Config.T
+ val smt2_slice_time_frac : real Config.T
+ val smt2_slice_min_secs : int Config.T
+
+ val is_smt2_prover : Proof.context -> string -> bool
+ val run_smt2_solver : mode -> string -> prover
+end;
+
+structure Sledgehammer_Prover_SMT2 : SLEDGEHAMMER_PROVER_SMT2 =
+struct
+
+open ATP_Util
+open ATP_Proof
+open ATP_Systems
+open ATP_Problem_Generate
+open ATP_Proof_Reconstruct
+open Sledgehammer_Util
+open Sledgehammer_Proof_Methods
+open Sledgehammer_Isar
+open Sledgehammer_Prover
+
+val smt2_builtins = Attrib.setup_config_bool @{binding sledgehammer_smt2_builtins} (K true)
+val smt2_triggers = Attrib.setup_config_bool @{binding sledgehammer_smt2_triggers} (K true)
+val smt2_weights = Attrib.setup_config_bool @{binding sledgehammer_smt2_weights} (K true)
+val smt2_weight_min_facts =
+ Attrib.setup_config_int @{binding sledgehammer_smt2_weight_min_facts} (K 20)
+
+fun is_smt2_prover ctxt = member (op =) (SMT2_Solver.available_solvers_of ctxt)
+
+(* FUDGE *)
+val smt2_min_weight = Attrib.setup_config_int @{binding sledgehammer_smt2_min_weight} (K 0)
+val smt2_max_weight = Attrib.setup_config_int @{binding sledgehammer_smt2_max_weight} (K 10)
+val smt2_max_weight_index =
+ Attrib.setup_config_int @{binding sledgehammer_smt2_max_weight_index} (K 200)
+val smt2_weight_curve = Unsynchronized.ref (fn x : int => x * x)
+
+fun smt2_fact_weight ctxt j num_facts =
+ if Config.get ctxt smt2_weights andalso num_facts >= Config.get ctxt smt2_weight_min_facts then
+ let
+ val min = Config.get ctxt smt2_min_weight
+ val max = Config.get ctxt smt2_max_weight
+ val max_index = Config.get ctxt smt2_max_weight_index
+ val curve = !smt2_weight_curve
+ in
+ SOME (max - (max - min + 1) * curve (Int.max (0, max_index - j - 1)) div curve max_index)
+ end
+ else
+ NONE
+
+fun weight_smt2_fact ctxt num_facts ((info, th), j) =
+ let val thy = Proof_Context.theory_of ctxt in
+ (info, (smt2_fact_weight ctxt j num_facts, Thm.transfer thy th (* TODO: needed? *)))
+ end
+
+(* "SMT2_Failure.Abnormal_Termination" carries the solver's return code. Until these are sorted out
+ properly in the SMT module, we must interpret these here. *)
+val z3_failures =
+ [(101, OutOfResources),
+ (103, MalformedInput),
+ (110, MalformedInput),
+ (112, TimedOut)]
+val unix_failures =
+ [(138, Crashed),
+ (139, Crashed)]
+val smt2_failures = z3_failures @ unix_failures
+
+fun failure_of_smt2_failure (SMT2_Failure.Counterexample {is_real_cex, ...}) =
+ if is_real_cex then Unprovable else GaveUp
+ | failure_of_smt2_failure SMT2_Failure.Time_Out = TimedOut
+ | failure_of_smt2_failure (SMT2_Failure.Abnormal_Termination code) =
+ (case AList.lookup (op =) smt2_failures code of
+ SOME failure => failure
+ | NONE => UnknownError ("Abnormal termination with exit code " ^ string_of_int code ^ "."))
+ | failure_of_smt2_failure SMT2_Failure.Out_Of_Memory = OutOfResources
+ | failure_of_smt2_failure (SMT2_Failure.Other_Failure s) = UnknownError s
+
+(* FUDGE *)
+val smt2_max_slices = Attrib.setup_config_int @{binding sledgehammer_smt2_max_slices} (K 8)
+val smt2_slice_fact_frac =
+ Attrib.setup_config_real @{binding sledgehammer_smt2_slice_fact_frac} (K 0.667)
+val smt2_slice_time_frac =
+ Attrib.setup_config_real @{binding sledgehammer_smt2_slice_time_frac} (K 0.333)
+val smt2_slice_min_secs = Attrib.setup_config_int @{binding sledgehammer_smt2_slice_min_secs} (K 3)
+
+val is_boring_builtin_typ =
+ not o exists_subtype (member (op =) [@{typ nat}, @{typ int}, HOLogic.realT])
+
+fun smt2_filter_loop name ({debug, overlord, max_mono_iters, max_new_mono_instances, timeout, slice,
+ ...} : params) state goal i =
+ let
+ fun repair_context ctxt =
+ ctxt |> Context.proof_map (SMT2_Config.select_solver name)
+ |> Config.put SMT2_Config.verbose debug
+ |> (if overlord then
+ Config.put SMT2_Config.debug_files
+ (overlord_file_location_of_prover name |> (fn (path, name) => path ^ "/" ^ name))
+ else
+ I)
+ |> Config.put SMT2_Config.infer_triggers (Config.get ctxt smt2_triggers)
+ |> not (Config.get ctxt smt2_builtins)
+ ? (SMT2_Builtin.filter_builtins is_boring_builtin_typ
+ #> Config.put SMT2_Systems.z3_extensions false)
+ |> repair_monomorph_context max_mono_iters default_max_mono_iters max_new_mono_instances
+ default_max_new_mono_instances
+
+ val state = Proof.map_context (repair_context) state
+ val ctxt = Proof.context_of state
+ val max_slices = if slice then Config.get ctxt smt2_max_slices else 1
+
+ fun do_slice timeout slice outcome0 time_so_far
+ (weighted_factss as (fact_filter, weighted_facts) :: _) =
+ let
+ val timer = Timer.startRealTimer ()
+ val slice_timeout =
+ if slice < max_slices then
+ let val ms = Time.toMilliseconds timeout in
+ Int.min (ms, Int.max (1000 * Config.get ctxt smt2_slice_min_secs,
+ Real.ceil (Config.get ctxt smt2_slice_time_frac * Real.fromInt ms)))
+ |> Time.fromMilliseconds
+ end
+ else
+ timeout
+ val num_facts = length weighted_facts
+ val _ =
+ if debug then
+ quote name ^ " slice " ^ string_of_int slice ^ " with " ^ string_of_int num_facts ^
+ " fact" ^ plural_s num_facts ^ " for " ^ string_of_time slice_timeout
+ |> Output.urgent_message
+ else
+ ()
+ val birth = Timer.checkRealTimer timer
+ val _ = if debug then Output.urgent_message "Invoking SMT solver..." else ()
+
+ val filter_result as {outcome, ...} =
+ SMT2_Solver.smt2_filter ctxt goal weighted_facts i slice_timeout
+ handle exn =>
+ if Exn.is_interrupt exn orelse debug then
+ reraise exn
+ else
+ {outcome = SOME (SMT2_Failure.Other_Failure (ML_Compiler.exn_message exn)),
+ conjecture_id = ~1, helper_ids = [], fact_ids = [], z3_proof = []}
+
+ val death = Timer.checkRealTimer timer
+ val outcome0 = if is_none outcome0 then SOME outcome else outcome0
+ val time_so_far = Time.+ (time_so_far, Time.- (death, birth))
+ val timeout = Time.- (timeout, Timer.checkRealTimer timer)
+
+ val too_many_facts_perhaps =
+ (case outcome of
+ NONE => false
+ | SOME (SMT2_Failure.Counterexample _) => false
+ | SOME SMT2_Failure.Time_Out => slice_timeout <> timeout
+ | SOME (SMT2_Failure.Abnormal_Termination _) => true (* kind of *)
+ | SOME SMT2_Failure.Out_Of_Memory => true
+ | SOME (SMT2_Failure.Other_Failure _) => true)
+ in
+ if too_many_facts_perhaps andalso slice < max_slices andalso num_facts > 0 andalso
+ Time.> (timeout, Time.zeroTime) then
+ let
+ val new_num_facts =
+ Real.ceil (Config.get ctxt smt2_slice_fact_frac * Real.fromInt num_facts)
+ val weighted_factss as (new_fact_filter, _) :: _ =
+ weighted_factss
+ |> (fn (x :: xs) => xs @ [x])
+ |> app_hd (apsnd (take new_num_facts))
+ val show_filter = fact_filter <> new_fact_filter
+
+ fun num_of_facts fact_filter num_facts =
+ string_of_int num_facts ^ (if show_filter then " " ^ quote fact_filter else "") ^
+ " fact" ^ plural_s num_facts
+
+ val _ =
+ if debug then
+ quote name ^ " invoked with " ^
+ num_of_facts fact_filter num_facts ^ ": " ^
+ string_of_atp_failure (failure_of_smt2_failure (the outcome)) ^
+ " Retrying with " ^ num_of_facts new_fact_filter new_num_facts ^
+ "..."
+ |> Output.urgent_message
+ else
+ ()
+ in
+ do_slice timeout (slice + 1) outcome0 time_so_far weighted_factss
+ end
+ else
+ {outcome = if is_none outcome then NONE else the outcome0, filter_result = filter_result,
+ used_from = map (apsnd snd) weighted_facts, run_time = time_so_far}
+ end
+ in
+ do_slice timeout 1 NONE Time.zeroTime
+ end
+
+fun run_smt2_solver mode name (params as {debug, verbose, isar_proofs, compress_isar,
+ try0_isar, smt_proofs, minimize, preplay_timeout, ...})
+ minimize_command ({state, goal, subgoal, subgoal_count, factss, ...} : prover_problem) =
+ let
+ val thy = Proof.theory_of state
+ val ctxt = Proof.context_of state
+
+ fun weight_facts facts =
+ let val num_facts = length facts in
+ map (weight_smt2_fact ctxt num_facts) (facts ~~ (0 upto num_facts - 1))
+ end
+
+ val weighted_factss = map (apsnd weight_facts) factss
+ val {outcome, filter_result = {conjecture_id, helper_ids, fact_ids, z3_proof, ...},
+ used_from, run_time} = smt2_filter_loop name params state goal subgoal weighted_factss
+ val used_named_facts = map snd fact_ids
+ val used_facts = map fst used_named_facts
+ val outcome = Option.map failure_of_smt2_failure outcome
+
+ val (preplay, message, message_tail) =
+ (case outcome of
+ NONE =>
+ (Lazy.lazy (fn () =>
+ play_one_line_proof mode debug verbose preplay_timeout used_named_facts state subgoal
+ SMT2_Method (bunch_of_proof_methods (smt_proofs <> SOME false) false liftingN)),
+ fn preplay =>
+ let
+ val fact_ids =
+ map (fn (id, th) => (id, short_thm_name ctxt th)) helper_ids @
+ map (fn (id, ((name, _), _)) => (id, name)) fact_ids
+ val atp_proof = Z3_New_Isar.atp_proof_of_z3_proof thy conjecture_id fact_ids z3_proof
+ val isar_params =
+ K (verbose, (NONE, NONE), preplay_timeout, compress_isar, try0_isar,
+ minimize <> SOME false, atp_proof, goal)
+ val one_line_params =
+ (preplay, proof_banner mode name, used_facts,
+ choose_minimize_command thy params minimize_command name preplay, subgoal,
+ subgoal_count)
+ val num_chained = length (#facts (Proof.goal state))
+ in
+ proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained one_line_params
+ end,
+ if verbose then "\nSMT solver real CPU time: " ^ string_of_time run_time ^ "." else "")
+ | SOME failure =>
+ (Lazy.value (Metis_Method (NONE, NONE), Play_Failed),
+ fn _ => string_of_atp_failure failure, ""))
+ in
+ {outcome = outcome, used_facts = used_facts, used_from = used_from, run_time = run_time,
+ preplay = preplay, message = message, message_tail = message_tail}
+ end
+
+end;
--- a/src/HOL/Transfer.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Transfer.thy Thu Mar 13 16:39:08 2014 +0100
@@ -156,10 +156,10 @@
by(simp add: bi_unique_def)
lemma right_uniqueI: "(\<And>x y z. \<lbrakk> A x y; A x z \<rbrakk> \<Longrightarrow> y = z) \<Longrightarrow> right_unique A"
-unfolding right_unique_def by blast
+unfolding right_unique_def by fast
lemma right_uniqueD: "\<lbrakk> right_unique A; A x y; A x z \<rbrakk> \<Longrightarrow> y = z"
-unfolding right_unique_def by blast
+unfolding right_unique_def by fast
lemma right_total_alt_def:
"right_total R \<longleftrightarrow> ((R ===> op \<longrightarrow>) ===> op \<longrightarrow>) All All"
@@ -204,18 +204,18 @@
by auto
lemma bi_total_OO: "\<lbrakk>bi_total A; bi_total B\<rbrakk> \<Longrightarrow> bi_total (A OO B)"
- unfolding bi_total_def OO_def by metis
+ unfolding bi_total_def OO_def by fast
lemma bi_unique_OO: "\<lbrakk>bi_unique A; bi_unique B\<rbrakk> \<Longrightarrow> bi_unique (A OO B)"
- unfolding bi_unique_def OO_def by metis
+ unfolding bi_unique_def OO_def by blast
lemma right_total_OO:
"\<lbrakk>right_total A; right_total B\<rbrakk> \<Longrightarrow> right_total (A OO B)"
- unfolding right_total_def OO_def by metis
+ unfolding right_total_def OO_def by fast
lemma right_unique_OO:
"\<lbrakk>right_unique A; right_unique B\<rbrakk> \<Longrightarrow> right_unique (A OO B)"
- unfolding right_unique_def OO_def by metis
+ unfolding right_unique_def OO_def by fast
subsection {* Properties of relators *}
@@ -278,7 +278,7 @@
lemma bi_unique_fun [transfer_rule]:
"\<lbrakk>bi_total A; bi_unique B\<rbrakk> \<Longrightarrow> bi_unique (A ===> B)"
unfolding bi_total_def bi_unique_def rel_fun_def fun_eq_iff
- by (safe, metis, fast)
+ by fast+
subsection {* Transfer rules *}
@@ -289,7 +289,7 @@
(transfer_bforall (Domainp A)) transfer_forall"
using assms unfolding right_total_def
unfolding transfer_forall_def transfer_bforall_def rel_fun_def Domainp_iff
- by metis
+ by fast
text {* Transfer rules using implication instead of equality on booleans. *}
@@ -300,7 +300,7 @@
"bi_total A \<Longrightarrow> ((A ===> op =) ===> rev_implies) transfer_forall transfer_forall"
"bi_total A \<Longrightarrow> ((A ===> rev_implies) ===> rev_implies) transfer_forall transfer_forall"
unfolding transfer_forall_def rev_implies_def rel_fun_def right_total_def bi_total_def
- by metis+
+ by fast+
lemma transfer_implies_transfer [transfer_rule]:
"(op = ===> op = ===> op = ) transfer_implies transfer_implies"
@@ -327,13 +327,13 @@
assumes "right_total A"
shows "((A ===> op=) ===> op=) (Bex (Collect (Domainp A))) Ex"
using assms unfolding right_total_def Bex_def rel_fun_def Domainp_iff[abs_def]
-by blast
+by fast
lemma right_total_All_transfer[transfer_rule]:
assumes "right_total A"
shows "((A ===> op =) ===> op =) (Ball (Collect (Domainp A))) All"
using assms unfolding right_total_def Ball_def rel_fun_def Domainp_iff[abs_def]
-by blast
+by fast
lemma All_transfer [transfer_rule]:
assumes "bi_total A"
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Word/Tools/smt2_word.ML Thu Mar 13 16:39:08 2014 +0100
@@ -0,0 +1,144 @@
+(* Title: HOL/Word/Tools/smt2_word.ML
+ Author: Sascha Boehme, TU Muenchen
+
+SMT setup for words.
+*)
+
+structure SMT2_Word: sig end =
+struct
+
+open Word_Lib
+
+(* SMT-LIB logic *)
+
+fun smtlib_logic ts =
+ if exists (Term.exists_type (Term.exists_subtype is_wordT)) ts
+ then SOME "QF_AUFBV"
+ else NONE
+
+
+(* SMT-LIB builtins *)
+
+local
+ val smtlib2C = SMTLIB2_Interface.smtlib2C
+
+ val wordT = @{typ "'a::len word"}
+
+ fun index1 s i = "(_ " ^ s ^ " " ^ string_of_int i ^ ")"
+ fun index2 s i j = "(_ " ^ s ^ " " ^ string_of_int i ^ " " ^ string_of_int j ^ ")"
+
+ fun word_typ (Type (@{type_name word}, [T])) = Option.map (index1 "BitVec") (try dest_binT T)
+ | word_typ _ = NONE
+
+ fun word_num (Type (@{type_name word}, [T])) k =
+ Option.map (index1 ("bv" ^ string_of_int k)) (try dest_binT T)
+ | word_num _ _ = NONE
+
+ fun if_fixed pred m n T ts =
+ let val (Us, U) = Term.strip_type T
+ in
+ if pred (U, Us) then
+ SOME (n, length Us, ts, Term.list_comb o pair (Const (m, T)))
+ else NONE
+ end
+
+ fun if_fixed_all m = if_fixed (forall (can dest_wordT) o (op ::)) m
+ fun if_fixed_args m = if_fixed (forall (can dest_wordT) o snd) m
+
+ fun add_word_fun f (t, n) =
+ let val (m, _) = Term.dest_Const t
+ in SMT2_Builtin.add_builtin_fun smtlib2C (Term.dest_Const t, K (f m n)) end
+
+ fun hd2 xs = hd (tl xs)
+
+ fun mk_nat i = @{const nat} $ HOLogic.mk_number @{typ nat} i
+
+ fun dest_nat (@{const nat} $ n) = snd (HOLogic.dest_number n)
+ | dest_nat t = raise TERM ("not a natural number", [t])
+
+ fun mk_shift c [t, u] = Const c $ t $ mk_nat (snd (HOLogic.dest_number u))
+ | mk_shift c ts = raise TERM ("bad arguments", Const c :: ts)
+
+ fun shift m n T ts =
+ let val U = Term.domain_type T
+ in
+ (case (can dest_wordT U, try (dest_nat o hd2) ts) of
+ (true, SOME i) =>
+ SOME (n, 2, [hd ts, HOLogic.mk_number U i], mk_shift (m, T))
+ | _ => NONE) (* FIXME: also support non-numerical shifts *)
+ end
+
+ fun mk_extract c i ts = Term.list_comb (Const c, mk_nat i :: ts)
+
+ fun extract m n T ts =
+ let val U = Term.range_type (Term.range_type T)
+ in
+ (case (try (dest_nat o hd) ts, try dest_wordT U) of
+ (SOME lb, SOME i) =>
+ SOME (index2 n (i + lb - 1) lb, 1, tl ts, mk_extract (m, T) lb)
+ | _ => NONE)
+ end
+
+ fun mk_extend c ts = Term.list_comb (Const c, ts)
+
+ fun extend m n T ts =
+ let val (U1, U2) = Term.dest_funT T
+ in
+ (case (try dest_wordT U1, try dest_wordT U2) of
+ (SOME i, SOME j) =>
+ if j-i >= 0 then SOME (index1 n (j-i), 1, ts, mk_extend (m, T))
+ else NONE
+ | _ => NONE)
+ end
+
+ fun mk_rotate c i ts = Term.list_comb (Const c, mk_nat i :: ts)
+
+ fun rotate m n T ts =
+ let val U = Term.domain_type (Term.range_type T)
+ in
+ (case (can dest_wordT U, try (dest_nat o hd) ts) of
+ (true, SOME i) => SOME (index1 n i, 1, tl ts, mk_rotate (m, T) i)
+ | _ => NONE)
+ end
+in
+
+val setup_builtins =
+ SMT2_Builtin.add_builtin_typ smtlib2C (wordT, word_typ, word_num) #>
+ fold (add_word_fun if_fixed_all) [
+ (@{term "uminus :: 'a::len word => _"}, "bvneg"),
+ (@{term "plus :: 'a::len word => _"}, "bvadd"),
+ (@{term "minus :: 'a::len word => _"}, "bvsub"),
+ (@{term "times :: 'a::len word => _"}, "bvmul"),
+ (@{term "bitNOT :: 'a::len word => _"}, "bvnot"),
+ (@{term "bitAND :: 'a::len word => _"}, "bvand"),
+ (@{term "bitOR :: 'a::len word => _"}, "bvor"),
+ (@{term "bitXOR :: 'a::len word => _"}, "bvxor"),
+ (@{term "word_cat :: 'a::len word => _"}, "concat") ] #>
+ fold (add_word_fun shift) [
+ (@{term "shiftl :: 'a::len word => _ "}, "bvshl"),
+ (@{term "shiftr :: 'a::len word => _"}, "bvlshr"),
+ (@{term "sshiftr :: 'a::len word => _"}, "bvashr") ] #>
+ add_word_fun extract
+ (@{term "slice :: _ => 'a::len word => _"}, "extract") #>
+ fold (add_word_fun extend) [
+ (@{term "ucast :: 'a::len word => _"}, "zero_extend"),
+ (@{term "scast :: 'a::len word => _"}, "sign_extend") ] #>
+ fold (add_word_fun rotate) [
+ (@{term word_rotl}, "rotate_left"),
+ (@{term word_rotr}, "rotate_right") ] #>
+ fold (add_word_fun if_fixed_args) [
+ (@{term "less :: 'a::len word => _"}, "bvult"),
+ (@{term "less_eq :: 'a::len word => _"}, "bvule"),
+ (@{term word_sless}, "bvslt"),
+ (@{term word_sle}, "bvsle") ]
+
+end
+
+
+(* setup *)
+
+val _ = Theory.setup (Context.theory_map (
+ SMTLIB2_Interface.add_logic (20, smtlib_logic) #>
+ setup_builtins))
+
+end
--- a/src/HOL/Word/Word.thy Thu Mar 13 16:28:25 2014 +0100
+++ b/src/HOL/Word/Word.thy Thu Mar 13 16:39:08 2014 +0100
@@ -4738,6 +4738,7 @@
ML_file "Tools/word_lib.ML"
ML_file "Tools/smt_word.ML"
setup SMT_Word.setup
+ML_file "Tools/smt2_word.ML"
hide_const (open) Word