added proof reconstructon for Z3,
added certificates for simpler re-checking of proofs (no need to invoke external solvers),
added examples and certificates for all examples,
removed Unsynchronized.ref (in smt_normalize.ML)
--- a/CONTRIBUTORS Tue Oct 20 08:10:47 2009 +0200
+++ b/CONTRIBUTORS Tue Oct 20 10:11:30 2009 +0200
@@ -7,10 +7,13 @@
Contributions to this Isabelle version
--------------------------------------
-* Oktober 2009: Florian Haftmann, TUM
+* October 2009: Sascha Boehme, TUM
+ Extension of SMT method: proof-reconstruction for the SMT solver Z3
+
+* October 2009: Florian Haftmann, TUM
Refinement of parts of the HOL datatype package
-* Oktober 2009: Florian Haftmann, TUM
+* October 2009: Florian Haftmann, TUM
Generic term styles for term antiquotations
* September 2009: Thomas Sewell, NICTA
--- a/NEWS Tue Oct 20 08:10:47 2009 +0200
+++ b/NEWS Tue Oct 20 10:11:30 2009 +0200
@@ -46,7 +46,9 @@
arithmetic, and fixed-size bitvectors; there is also basic
support for higher-order features (esp. lambda abstractions).
It is an incomplete decision procedure based on external SMT
-solvers using the oracle mechanism.
+solvers using the oracle mechanism; for the SMT solver Z3,
+this method is proof-producing. Certificates are provided to
+avoid calling the external solvers solely for re-checking proofs.
* Reorganization of number theory:
* former session NumberTheory now named Old_Number_Theory
--- a/src/HOL/IsaMakefile Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/IsaMakefile Tue Oct 20 10:11:30 2009 +0200
@@ -6,7 +6,7 @@
default: HOL
generate: HOL-Generate-HOL HOL-Generate-HOLLight
-images: HOL HOL-Base HOL-Plain HOL-Main HOL-Algebra HOL-Nominal HOL-NSA HOL-Word TLA HOL4
+images: HOL HOL-Base HOL-Plain HOL-Main HOL-Algebra HOL-Nominal HOL-NSA HOL-SMT HOL-Word TLA HOL4
#Note: keep targets sorted (except for HOL-Library and HOL-ex)
test: \
@@ -40,7 +40,7 @@
HOL-Prolog \
HOL-SET-Protocol \
HOL-SizeChange \
- HOL-SMT \
+ HOL-SMT-Examples \
HOL-Statespace \
HOL-Subst \
TLA-Buffer \
@@ -1146,15 +1146,222 @@
HOL-SMT: HOL-Word $(LOG)/HOL-SMT.gz
-$(LOG)/HOL-SMT.gz: $(OUT)/HOL-Word SMT/SMT_Definitions.thy SMT/SMT.thy \
+$(LOG)/HOL-SMT.gz: $(OUT)/HOL-Word SMT/SMT_Base.thy SMT/Z3.thy SMT/SMT.thy \
SMT/Tools/smt_normalize.ML SMT/Tools/smt_monomorph.ML \
SMT/Tools/smt_translate.ML SMT/Tools/smt_builtin.ML \
SMT/Tools/smtlib_interface.ML SMT/Tools/smt_solver.ML \
SMT/Tools/cvc3_solver.ML SMT/Tools/yices_solver.ML \
- SMT/Tools/z3_interface.ML SMT/Tools/z3_solver.ML SMT/Tools/z3_model.ML
+ SMT/Tools/z3_proof_terms.ML SMT/Tools/z3_proof_rules.ML \
+ SMT/Tools/z3_proof.ML SMT/Tools/z3_model.ML SMT/Tools/z3_interface.ML \
+ SMT/Tools/z3_solver.ML
@cd SMT; $(ISABELLE_TOOL) usedir -b -g true $(OUT)/HOL-Word HOL-SMT
+## HOL-SMT-Examples
+
+HOL-SMT-Examples: HOL-SMT $(LOG)/HOL-SMT-Examples.gz
+
+$(LOG)/HOL-SMT-Examples.gz: $(OUT)/HOL-SMT SMT/Examples/ROOT.ML \
+ SMT/Examples/SMT_Examples.thy \
+ SMT/Examples/cert/z3_arith_quant_01 \
+ SMT/Examples/cert/z3_arith_quant_01.proof \
+ SMT/Examples/cert/z3_arith_quant_02 \
+ SMT/Examples/cert/z3_arith_quant_02.proof \
+ SMT/Examples/cert/z3_arith_quant_03 \
+ SMT/Examples/cert/z3_arith_quant_03.proof \
+ SMT/Examples/cert/z3_arith_quant_04 \
+ SMT/Examples/cert/z3_arith_quant_04.proof \
+ SMT/Examples/cert/z3_arith_quant_05 \
+ SMT/Examples/cert/z3_arith_quant_05.proof \
+ SMT/Examples/cert/z3_arith_quant_06 \
+ SMT/Examples/cert/z3_arith_quant_06.proof \
+ SMT/Examples/cert/z3_arith_quant_07 \
+ SMT/Examples/cert/z3_arith_quant_07.proof \
+ SMT/Examples/cert/z3_arith_quant_08 \
+ SMT/Examples/cert/z3_arith_quant_08.proof \
+ SMT/Examples/cert/z3_arith_quant_09 \
+ SMT/Examples/cert/z3_arith_quant_09.proof \
+ SMT/Examples/cert/z3_arith_quant_10 \
+ SMT/Examples/cert/z3_arith_quant_10.proof \
+ SMT/Examples/cert/z3_arith_quant_11 \
+ SMT/Examples/cert/z3_arith_quant_11.proof \
+ SMT/Examples/cert/z3_arith_quant_12 \
+ SMT/Examples/cert/z3_arith_quant_12.proof \
+ SMT/Examples/cert/z3_arith_quant_13 \
+ SMT/Examples/cert/z3_arith_quant_13.proof \
+ SMT/Examples/cert/z3_arith_quant_14 \
+ SMT/Examples/cert/z3_arith_quant_14.proof \
+ SMT/Examples/cert/z3_arith_quant_15 \
+ SMT/Examples/cert/z3_arith_quant_15.proof \
+ SMT/Examples/cert/z3_arith_quant_16 \
+ SMT/Examples/cert/z3_arith_quant_16.proof \
+ SMT/Examples/cert/z3_arith_quant_17 \
+ SMT/Examples/cert/z3_arith_quant_17.proof \
+ SMT/Examples/cert/z3_arith_quant_18 \
+ SMT/Examples/cert/z3_arith_quant_18.proof \
+ SMT/Examples/cert/z3_bv_01 \
+ SMT/Examples/cert/z3_bv_01.proof \
+ SMT/Examples/cert/z3_bv_02 \
+ SMT/Examples/cert/z3_bv_02.proof \
+ SMT/Examples/cert/z3_bv_arith_01 \
+ SMT/Examples/cert/z3_bv_arith_01.proof \
+ SMT/Examples/cert/z3_bv_arith_02 \
+ SMT/Examples/cert/z3_bv_arith_02.proof \
+ SMT/Examples/cert/z3_bv_arith_03 \
+ SMT/Examples/cert/z3_bv_arith_03.proof \
+ SMT/Examples/cert/z3_bv_arith_04 \
+ SMT/Examples/cert/z3_bv_arith_04.proof \
+ SMT/Examples/cert/z3_bv_arith_05 \
+ SMT/Examples/cert/z3_bv_arith_05.proof \
+ SMT/Examples/cert/z3_bv_arith_06 \
+ SMT/Examples/cert/z3_bv_arith_06.proof \
+ SMT/Examples/cert/z3_bv_arith_07 \
+ SMT/Examples/cert/z3_bv_arith_07.proof \
+ SMT/Examples/cert/z3_bv_arith_08 \
+ SMT/Examples/cert/z3_bv_arith_08.proof \
+ SMT/Examples/cert/z3_bv_arith_09 \
+ SMT/Examples/cert/z3_bv_arith_09.proof \
+ SMT/Examples/cert/z3_bv_arith_10 \
+ SMT/Examples/cert/z3_bv_arith_10.proof \
+ SMT/Examples/cert/z3_bv_bit_01 \
+ SMT/Examples/cert/z3_bv_bit_01.proof \
+ SMT/Examples/cert/z3_bv_bit_02 \
+ SMT/Examples/cert/z3_bv_bit_02.proof \
+ SMT/Examples/cert/z3_bv_bit_03 \
+ SMT/Examples/cert/z3_bv_bit_03.proof \
+ SMT/Examples/cert/z3_bv_bit_04 \
+ SMT/Examples/cert/z3_bv_bit_04.proof \
+ SMT/Examples/cert/z3_bv_bit_05 \
+ SMT/Examples/cert/z3_bv_bit_05.proof \
+ SMT/Examples/cert/z3_bv_bit_06 \
+ SMT/Examples/cert/z3_bv_bit_06.proof \
+ SMT/Examples/cert/z3_bv_bit_07 \
+ SMT/Examples/cert/z3_bv_bit_07.proof \
+ SMT/Examples/cert/z3_bv_bit_08 \
+ SMT/Examples/cert/z3_bv_bit_08.proof \
+ SMT/Examples/cert/z3_bv_bit_09 \
+ SMT/Examples/cert/z3_bv_bit_09.proof \
+ SMT/Examples/cert/z3_bv_bit_10 \
+ SMT/Examples/cert/z3_bv_bit_10.proof \
+ SMT/Examples/cert/z3_bv_bit_11 \
+ SMT/Examples/cert/z3_bv_bit_11.proof \
+ SMT/Examples/cert/z3_bv_bit_12 \
+ SMT/Examples/cert/z3_bv_bit_12.proof \
+ SMT/Examples/cert/z3_bv_bit_13 \
+ SMT/Examples/cert/z3_bv_bit_13.proof \
+ SMT/Examples/cert/z3_bv_bit_14 \
+ SMT/Examples/cert/z3_bv_bit_14.proof \
+ SMT/Examples/cert/z3_bv_bit_15 \
+ SMT/Examples/cert/z3_bv_bit_15.proof \
+ SMT/Examples/cert/z3_fol_01 \
+ SMT/Examples/cert/z3_fol_01.proof \
+ SMT/Examples/cert/z3_fol_02 \
+ SMT/Examples/cert/z3_fol_02.proof \
+ SMT/Examples/cert/z3_fol_03 \
+ SMT/Examples/cert/z3_fol_03.proof \
+ SMT/Examples/cert/z3_fol_04 \
+ SMT/Examples/cert/z3_fol_04.proof \
+ SMT/Examples/cert/z3_hol_01 \
+ SMT/Examples/cert/z3_hol_01.proof \
+ SMT/Examples/cert/z3_hol_02 \
+ SMT/Examples/cert/z3_hol_02.proof \
+ SMT/Examples/cert/z3_hol_03 \
+ SMT/Examples/cert/z3_hol_03.proof \
+ SMT/Examples/cert/z3_hol_04 \
+ SMT/Examples/cert/z3_hol_04.proof \
+ SMT/Examples/cert/z3_hol_05 \
+ SMT/Examples/cert/z3_hol_05.proof \
+ SMT/Examples/cert/z3_hol_06 \
+ SMT/Examples/cert/z3_hol_06.proof \
+ SMT/Examples/cert/z3_hol_07 \
+ SMT/Examples/cert/z3_hol_07.proof \
+ SMT/Examples/cert/z3_hol_08 \
+ SMT/Examples/cert/z3_hol_08.proof \
+ SMT/Examples/cert/z3_linarith_01 \
+ SMT/Examples/cert/z3_linarith_01.proof \
+ SMT/Examples/cert/z3_linarith_02 \
+ SMT/Examples/cert/z3_linarith_02.proof \
+ SMT/Examples/cert/z3_linarith_03 \
+ SMT/Examples/cert/z3_linarith_03.proof \
+ SMT/Examples/cert/z3_linarith_04 \
+ SMT/Examples/cert/z3_linarith_04.proof \
+ SMT/Examples/cert/z3_linarith_05 \
+ SMT/Examples/cert/z3_linarith_05.proof \
+ SMT/Examples/cert/z3_linarith_06 \
+ SMT/Examples/cert/z3_linarith_06.proof \
+ SMT/Examples/cert/z3_linarith_07 \
+ SMT/Examples/cert/z3_linarith_07.proof \
+ SMT/Examples/cert/z3_linarith_08 \
+ SMT/Examples/cert/z3_linarith_08.proof \
+ SMT/Examples/cert/z3_linarith_09 \
+ SMT/Examples/cert/z3_linarith_09.proof \
+ SMT/Examples/cert/z3_linarith_10 \
+ SMT/Examples/cert/z3_linarith_10.proof \
+ SMT/Examples/cert/z3_linarith_11 \
+ SMT/Examples/cert/z3_linarith_11.proof \
+ SMT/Examples/cert/z3_linarith_12 \
+ SMT/Examples/cert/z3_linarith_12.proof \
+ SMT/Examples/cert/z3_linarith_13 \
+ SMT/Examples/cert/z3_linarith_13.proof \
+ SMT/Examples/cert/z3_linarith_14 \
+ SMT/Examples/cert/z3_linarith_14.proof \
+ SMT/Examples/cert/z3_linarith_15 \
+ SMT/Examples/cert/z3_linarith_15.proof \
+ SMT/Examples/cert/z3_linarith_16 \
+ SMT/Examples/cert/z3_linarith_16.proof \
+ SMT/Examples/cert/z3_mono_01 \
+ SMT/Examples/cert/z3_mono_01.proof \
+ SMT/Examples/cert/z3_mono_02 \
+ SMT/Examples/cert/z3_mono_02.proof \
+ SMT/Examples/cert/z3_nat_arith_01 \
+ SMT/Examples/cert/z3_nat_arith_01.proof \
+ SMT/Examples/cert/z3_nat_arith_02 \
+ SMT/Examples/cert/z3_nat_arith_02.proof \
+ SMT/Examples/cert/z3_nat_arith_03 \
+ SMT/Examples/cert/z3_nat_arith_03.proof \
+ SMT/Examples/cert/z3_nat_arith_04 \
+ SMT/Examples/cert/z3_nat_arith_04.proof \
+ SMT/Examples/cert/z3_nat_arith_05 \
+ SMT/Examples/cert/z3_nat_arith_05.proof \
+ SMT/Examples/cert/z3_nat_arith_06 \
+ SMT/Examples/cert/z3_nat_arith_06.proof \
+ SMT/Examples/cert/z3_nat_arith_07 \
+ SMT/Examples/cert/z3_nat_arith_07.proof \
+ SMT/Examples/cert/z3_nlarith_01 \
+ SMT/Examples/cert/z3_nlarith_01.proof \
+ SMT/Examples/cert/z3_nlarith_02 \
+ SMT/Examples/cert/z3_nlarith_02.proof \
+ SMT/Examples/cert/z3_nlarith_03 \
+ SMT/Examples/cert/z3_nlarith_03.proof \
+ SMT/Examples/cert/z3_nlarith_04 \
+ SMT/Examples/cert/z3_nlarith_04.proof \
+ SMT/Examples/cert/z3_pair_01 \
+ SMT/Examples/cert/z3_pair_01.proof \
+ SMT/Examples/cert/z3_pair_02 \
+ SMT/Examples/cert/z3_pair_02.proof \
+ SMT/Examples/cert/z3_prop_01 \
+ SMT/Examples/cert/z3_prop_01.proof \
+ SMT/Examples/cert/z3_prop_02 \
+ SMT/Examples/cert/z3_prop_02.proof \
+ SMT/Examples/cert/z3_prop_03 \
+ SMT/Examples/cert/z3_prop_03.proof \
+ SMT/Examples/cert/z3_prop_04 \
+ SMT/Examples/cert/z3_prop_04.proof \
+ SMT/Examples/cert/z3_prop_05 \
+ SMT/Examples/cert/z3_prop_05.proof \
+ SMT/Examples/cert/z3_prop_06 \
+ SMT/Examples/cert/z3_prop_06.proof \
+ SMT/Examples/cert/z3_prop_07 \
+ SMT/Examples/cert/z3_prop_07.proof \
+ SMT/Examples/cert/z3_prop_08 \
+ SMT/Examples/cert/z3_prop_08.proof \
+ SMT/Examples/cert/z3_prop_09 \
+ SMT/Examples/cert/z3_prop_09.proof \
+ SMT/Examples/cert/z3_prop_10 \
+ SMT/Examples/cert/z3_prop_10.proof
+ @cd SMT; $(ISABELLE_TOOL) usedir $(OUT)/HOL-SMT Examples
+
+
## clean
clean:
@@ -1177,4 +1384,6 @@
$(LOG)/HOL-Unix.gz $(OUT)/HOL-Word $(LOG)/HOL-Word.gz \
$(LOG)/HOL-Word-Examples.gz $(OUT)/HOL-NSA \
$(LOG)/HOL-NSA.gz $(LOG)/HOL-NSA-Examples.gz \
- $(LOG)/HOL-Mirabelle.gz $(LOG)/HOL-SMT.gz
+ $(LOG)/HOL-Mirabelle.gz $(LOG)/HOL-SMT.gz \
+ $(LOG)/HOL-SMT-Examples.gz
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/ROOT.ML Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+use_thy "SMT_Examples";
--- a/src/HOL/SMT/Examples/SMT_Examples.thy Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/Examples/SMT_Examples.thy Tue Oct 20 10:11:30 2009 +0200
@@ -5,35 +5,361 @@
header {* Examples for the 'smt' tactic. *}
theory SMT_Examples
-imports "../SMT"
+imports SMT
begin
-declare [[smt_solver=z3, z3_proofs=false]]
-declare [[smt_trace=false]]
+declare [[smt_solver=z3, z3_proofs=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 "P=P=P=P=P=P=P=P=P=P" by smt
+lemma "True"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_01"]]
+ by smt
+
+lemma "p \<or> \<not>p"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_02"]]
+ by smt
+
+lemma "(p \<and> True) = p"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_03"]]
+ by smt
+
+lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_04"]]
+ by smt
+
+lemma "(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_05"]]
+ using [[z3_proofs=false]] (* no Z3 proof *)
+ by smt
+
+lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_06"]]
+ by smt
+
+lemma "P=P=P=P=P=P=P=P=P=P"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_07"]]
+ by smt
+
+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))))"
+ shows False
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_08"]]
+ using assms by smt
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 add: symm_f)
+lemma "a = a \<and> symm_f a b = symm_f b a"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_09"]]
+ by (smt add: symm_f)
+
+(*
+Taken from ~~/src/HOL/ex/SAT_Examples.thy.
+Translated from TPTP problem library: PUZ015-2.006.dimacs
+*)
+lemma
+ assumes "~x0"
+ 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"
+ shows False
+ using assms
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_prop_10"]]
+ by smt
+
+lemma "\<forall>x::int. P x \<longrightarrow> (\<forall>y::int. P x \<or> P y)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_fol_01"]]
+ by smt
+
+lemma
+ assumes "(\<forall>x y. P x y = x)"
+ shows "(\<exists>y. P x y) = P x c"
+ using assms
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_fol_02"]]
+ by smt
+
+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
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_fol_03"]]
+ by smt
+
+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
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_fol_04"]]
+ by smt
-section {* Linear arithmetic *}
+section {* Arithmetic *}
+
+subsection {* Linear arithmetic over integers and reals *}
+
+lemma "(3::int) = 3"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_01"]]
+ by smt
+
+lemma "(3::real) = 3"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_02"]]
+ by smt
+
+lemma "(3 :: int) + 1 = 4"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_03"]]
+ by smt
+
+lemma "x + (y + z) = y + (z + (x::int))"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_04"]]
+ by smt
+
+lemma "max (3::int) 8 > 5"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_05"]]
+ by smt
+
+lemma "abs (x :: real) + abs y \<ge> abs (x + y)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_06"]]
+ by smt
+
+lemma "P ((2::int) < 3) = P True"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_07"]]
+ by smt
+
+lemma "x + 3 \<ge> 4 \<or> x < (1::int)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_08"]]
+ by smt
-lemma "(3::int) = 3" by smt
-lemma "(3::real) = 3" by smt
-lemma "(3 :: int) + 1 = 4" by smt
-lemma "max (3::int) 8 > 5" by smt
-lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt
-lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt
+lemma
+ assumes "x \<ge> (3::int)" and "y = x + 4"
+ shows "y - x > 0"
+ using assms
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_09"]]
+ by smt
+
+lemma "let x = (2 :: int) in x + x \<noteq> 5"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_10"]]
+ by smt
+
+lemma
+ fixes x :: real
+ assumes "3 * x + 7 * a < 4" and "3 < 2 * x"
+ shows "a < 0"
+ using assms
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_11"]]
+ by smt
+
+lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_12"]]
+ by smt
+
+lemma "distinct [x < (3::int), 3 \<le> x]"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_13"]]
+ by smt
+
+lemma
+ assumes "a > (0::int)"
+ shows "distinct [a, a * 2, a - a]"
+ using assms
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_14"]]
+ by smt
+
+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))"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_15"]]
+ by smt
text{*
The following example was taken from HOL/ex/PresburgerEx.thy, where it says:
@@ -47,107 +373,333 @@
Warning: it takes (in 2006) over 4.2 minutes!
There, it is proved by "arith". SMT is able to prove this within a fraction
-of one second.
+of one second. With proof reconstruction, it takes about 13 seconds on a Core2
+processor.
*}
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)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_linarith_16"]]
+ by smt
+
+
+subsection {* Linear arithmetic with quantifiers *}
+
+lemma "~ (\<exists>x::int. False)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_01"]]
+ by smt
+
+lemma "~ (\<exists>x::real. False)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_02"]]
+ by smt
+
+lemma "\<exists>x::int. 0 < x"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_03"]]
+ using [[z3_proofs=false]] (* no Z3 proof *)
+ by smt
+
+lemma "\<exists>x::real. 0 < x"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_04"]]
+ using [[z3_proofs=false]] (* no Z3 proof *)
+ by smt
+
+lemma "\<forall>x::int. \<exists>y. y > x"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_05"]]
+ using [[z3_proofs=false]] (* no Z3 proof *)
+ by smt
+
+lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_06"]]
+ by smt
+
+lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_07"]]
+ by smt
+
+lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_08"]]
+ by smt
+
+lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_09"]]
+ by smt
+
+lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_10"]]
by smt
-lemma "\<exists>x::int. 0 < x" by smt
-lemma "\<exists>x::real. 0 < x" 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 "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt
-lemma "~ (\<exists>x::int. False)" by smt
+lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_11"]]
+ by smt
+
+lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_12"]]
+ by smt
+
+lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_13"]]
+ by smt
+
+lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_14"]]
+ by smt
+
+lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_15"]]
+ by smt
+
+lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_16"]]
+ by smt
+
+lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_17"]]
+ by smt
+
+lemma "\<forall>x::int. trigger [pat x] (x < a \<longrightarrow> 2 * x < 2 * a)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_arith_quant_18"]]
+ by smt
-section {* Non-linear arithmetic *}
+subsection {* Non-linear arithmetic over integers and reals *}
+
+lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nlarith_01"]]
+ using [[z3_proofs=false]] -- {* Isabelle's arithmetic decision procedures
+ are too weak to automatically prove @{thm zero_less_mult_pos}. *}
+ by smt
-lemma "((x::int) * (1 + y) - x * (1 - y)) = (2 * x * y)" by smt
+lemma "(a::int) * (x + 1 + y) = a * x + a * (y + 1)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nlarith_02"]]
+ by smt
+
+lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nlarith_03"]]
+ by smt
+
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 [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nlarith_04"]]
by smt
-section {* Linear arithmetic for natural numbers *}
+subsection {* Linear arithmetic for natural numbers *}
+
+lemma "2 * (x::nat) ~= 1"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nat_arith_01"]]
+ by smt
-lemma "a < 3 \<Longrightarrow> (7::nat) > 2 * a" by smt
-lemma "let x = (1::nat) + y in x - y > 0 * x" by smt
+lemma "a < 3 \<Longrightarrow> (7::nat) > 2 * a"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nat_arith_02"]]
+ by smt
+
+lemma "let x = (1::nat) + y in x - y > 0 * x"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nat_arith_03"]]
+ by smt
+
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)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nat_arith_04"]]
by smt
+lemma "distinct [a + (1::nat), a * 2 + 3, a - a]"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nat_arith_05"]]
+ by smt
+
+lemma "int (nat \<bar>x::int\<bar>) = \<bar>x\<bar>"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nat_arith_06"]]
+ by smt
+
+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)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_nat_arith_07"]]
+ by (smt add: prime_nat_def)
+
section {* Bitvectors *}
locale bv
begin
-declare [[smt_solver=z3]]
+text {*
+The following examples only work for Z3, and only without proof reconstruction.
+*}
+
+declare [[smt_solver=z3, z3_proofs=false]]
+
+
+subsection {* Bitvector arithmetic *}
+
+lemma "(27 :: 4 word) = -5"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_01"]]
+ by smt
+
+lemma "(27 :: 4 word) = 11"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_02"]]
+ by smt
+
+lemma "23 < (27::8 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_03"]]
+ by smt
+
+lemma "27 + 11 = (6::5 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_04"]]
+ by smt
-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 "7 * 3 = (21::8 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_05"]]
+ by smt
+lemma "11 - 27 = (-16::8 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_06"]]
+ by smt
+
+lemma "- -11 = (11::5 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_07"]]
+ by smt
+
+lemma "-40 + 1 = (-39::7 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_08"]]
+ by smt
-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 "a + 2 * b + c - b = (b + c) + (a :: 32 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_09"]]
+ by smt
+
+lemma "x = (5 :: 4 word) \<Longrightarrow> 4 * x = 4"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_arith_10"]]
+ by smt
+
+
+subsection {* Bit-level logic *}
-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)"
+lemma "0b110 AND 0b101 = (0b100 :: 32 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_01"]]
+ by smt
+
+lemma "0b110 OR 0b011 = (0b111 :: 8 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_02"]]
+ by smt
+
+lemma "0xF0 XOR 0xFF = (0x0F :: 8 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_03"]]
by smt
-lemma "slice 1 (0b10110 :: 4 word) = (0b11 :: 2 word)" by smt
+lemma "NOT (0xF0 :: 16 word) = 0xFF0F"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_04"]]
+ by smt
+
+lemma "word_cat (27::4 word) (27::8 word) = (2843::12 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_05"]]
+ by smt
+
+lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_06"]]
+ by smt
-lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by smt
-lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt
+lemma "slice 1 (0b10110 :: 4 word) = (0b11 :: 2 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_07"]]
+ by smt
+
+lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_08"]]
+ by smt
+
+lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_09"]]
+ by smt
-lemma "bv_lshr 0b10011 2 = (0b100::8 word)" by smt
-lemma "bv_ashr 0b10011 2 = (0b100::8 word)" by smt
+lemma "bv_lshr 0b10011 2 = (0b100::8 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_10"]]
+ by smt
+
+lemma "bv_ashr 0b10011 2 = (0b100::8 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_11"]]
+ by smt
+
+lemma "word_rotr 2 0b0110 = (0b1001::4 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_12"]]
+ by smt
-lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt
-lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by smt
+lemma "word_rotl 1 0b1110 = (0b1101::4 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_13"]]
+ by smt
-lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" by smt
+lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_14"]]
+ by smt
-lemma "w < 256 \<Longrightarrow> (w :: 16 word) AND 0x00FF = w" by smt
+lemma "w < 256 \<Longrightarrow> (w :: 16 word) AND 0x00FF = w"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_bit_15"]]
+ by smt
end
+lemma
+ assumes "bv2int 0 = 0"
+ and "bv2int 1 = 1"
+ and "bv2int 2 = 2"
+ 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 [[smt_solver=z3]]
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_01"]]
+ by smt
+
+lemma "P (0 \<le> (a :: 4 word)) = P True"
+ using [[smt_solver=z3, z3_proofs=false]]
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_bv_02"]]
+ by smt
+
section {* Pairs *}
-lemma "fst (x, y) = a \<Longrightarrow> x = a" by smt
-lemma "p1 = (x, y) \<and> p2 = (y, x) \<Longrightarrow> fst p1 = snd p2" by smt
+lemma "fst (x, y) = a \<Longrightarrow> x = a"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_pair_01"]]
+ by smt
+
+lemma "p1 = (x, y) \<and> p2 = (y, x) \<Longrightarrow> fst p1 = snd p2"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_pair_02"]]
+ by smt
section {* Higher-order problems and recursion *}
-lemma "(f g x = (g x \<and> True)) \<or> (f g x = True) \<or> (g x = True)" by smt
-lemma "P ((2::int) < 3) = P True" by smt
-lemma "P ((2::int) < 3) = (P True :: bool)" by smt
-lemma "P (0 \<le> (a :: 4 word)) = P True" using [[smt_solver=z3]] by smt
-lemma "id 3 = 3 \<and> id True = True" by (smt add: id_def)
-lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> ((f (i1 := v1)) (i2 := v2)) i = f i" by smt
-lemma "map (\<lambda>i::nat. i + 1) [0, 1] = [1, 2]" by (smt add: map.simps)
-lemma "(ALL x. P x) | ~ All P" by smt
+lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> (f (i1 := v1, i2 := v2)) i = f i"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_hol_01"]]
+ by smt
+
+lemma "(f g x = (g x \<and> True)) \<or> (f g x = True) \<or> (g x = True)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_hol_02"]]
+ by smt
+
+lemma "id 3 = 3 \<and> id True = True"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_hol_03"]]
+ by (smt add: id_def)
+
+lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> ((f (i1 := v1)) (i2 := v2)) i = f i"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_hol_04"]]
+ by smt
+
+lemma "map (\<lambda>i::nat. i + 1) [0, 1] = [1, 2]"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_hol_05"]]
+ by (smt add: map.simps)
+
+lemma "(ALL x. P x) | ~ All P"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_hol_06"]]
+ by smt
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 add: dec_10.simps)
+lemma "dec_10 (4 * dec_10 4) = 6"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_hol_07"]]
+ by (smt add: dec_10.simps)
axiomatization
eval_dioph :: "int list \<Rightarrow> nat list \<Rightarrow> int"
@@ -163,7 +715,7 @@
(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_solver=z3]]
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_hol_08"]]
by (smt add: eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
@@ -171,13 +723,17 @@
definition P :: "'a \<Rightarrow> bool" where "P x = True"
lemma poly_P: "P x \<and> (P [x] \<or> \<not>P[x])" by (simp add: P_def)
-lemma "P (1::int)" by (smt add: poly_P)
+lemma "P (1::int)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_mono_01"]]
+ by (smt add: poly_P)
consts g :: "'a \<Rightarrow> nat"
axioms
g1: "g (Some x) = g [x]"
g2: "g None = g []"
g3: "g xs = length xs"
-lemma "g (Some (3::int)) = g (Some True)" by (smt add: g1 g2 g3 list.size)
+lemma "g (Some (3::int)) = g (Some True)"
+ using [[smt_cert="~/isabelle/SMT/Examples/cert/z3_mono_02"]]
+ by (smt add: g1 g2 g3 list.size)
end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (not (exists (?x1 Int) false)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,24 @@
+#2 := false
+#4 := (exists (vars (?x1 int)) false)
+#5 := (not #4)
+#6 := (not #5)
+#37 := (iff #6 false)
+#1 := true
+#32 := (not true)
+#35 := (iff #32 false)
+#36 := [rewrite]: #35
+#33 := (iff #6 #32)
+#30 := (iff #5 true)
+#25 := (not false)
+#28 := (iff #25 true)
+#29 := [rewrite]: #28
+#26 := (iff #5 #25)
+#23 := (iff #4 false)
+#24 := [elim-unused]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#22 := [asserted]: #6
+[mp #22 #38]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (not (exists (?x1 Real) false)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,24 @@
+#2 := false
+#4 := (exists (vars (?x1 real)) false)
+#5 := (not #4)
+#6 := (not #5)
+#37 := (iff #6 false)
+#1 := true
+#32 := (not true)
+#35 := (iff #32 false)
+#36 := [rewrite]: #35
+#33 := (iff #6 #32)
+#30 := (iff #5 true)
+#25 := (not false)
+#28 := (iff #25 true)
+#29 := [rewrite]: #28
+#26 := (iff #5 #25)
+#23 := (iff #4 false)
+#24 := [elim-unused]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#22 := [asserted]: #6
+[mp #22 #38]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (exists (?x1 Int) (< 0 ?x1)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (exists (?x1 Real) (< 0.0 ?x1)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_05 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (forall (?x1 Int) (exists (?x2 Int) (< ?x1 ?x2))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_05.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_06 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (forall (?x1 Int) (?x2 Int) (implies (and (= ?x1 0) (= ?x2 1)) (not (= ?x1 ?x2)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_06.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,73 @@
+#2 := false
+#5 := 0::int
+#8 := 1::int
+#143 := (= 1::int 0::int)
+#145 := (iff #143 false)
+#146 := [rewrite]: #145
+decl ?x1!1 :: int
+#47 := ?x1!1
+#51 := (= ?x1!1 0::int)
+decl ?x2!0 :: int
+#46 := ?x2!0
+#50 := (= ?x2!0 1::int)
+#63 := (and #50 #51)
+#69 := (= ?x2!0 ?x1!1)
+#72 := (not #69)
+#66 := (not #63)
+#75 := (or #66 #72)
+#78 := (not #75)
+#48 := (= ?x1!1 ?x2!0)
+#49 := (not #48)
+#52 := (and #51 #50)
+#53 := (not #52)
+#54 := (or #53 #49)
+#55 := (not #54)
+#79 := (iff #55 #78)
+#76 := (iff #54 #75)
+#73 := (iff #49 #72)
+#70 := (iff #48 #69)
+#71 := [rewrite]: #70
+#74 := [monotonicity #71]: #73
+#67 := (iff #53 #66)
+#64 := (iff #52 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#77 := [monotonicity #68 #74]: #76
+#80 := [monotonicity #77]: #79
+#7 := (:var 0 int)
+#4 := (:var 1 int)
+#11 := (= #4 #7)
+#12 := (not #11)
+#9 := (= #7 1::int)
+#6 := (= #4 0::int)
+#10 := (and #6 #9)
+#32 := (not #10)
+#33 := (or #32 #12)
+#36 := (forall (vars (?x1 int) (?x2 int)) #33)
+#39 := (not #36)
+#56 := (~ #39 #55)
+#57 := [sk]: #56
+#13 := (implies #10 #12)
+#14 := (forall (vars (?x1 int) (?x2 int)) #13)
+#15 := (not #14)
+#40 := (iff #15 #39)
+#37 := (iff #14 #36)
+#34 := (iff #13 #33)
+#35 := [rewrite]: #34
+#38 := [quant-intro #35]: #37
+#41 := [monotonicity #38]: #40
+#31 := [asserted]: #15
+#44 := [mp #31 #41]: #39
+#60 := [mp~ #44 #57]: #55
+#61 := [mp #60 #80]: #78
+#62 := [not-or-elim #61]: #63
+#82 := [and-elim #62]: #51
+#141 := (= 1::int ?x1!1)
+#83 := [not-or-elim #61]: #69
+#139 := (= 1::int ?x2!0)
+#81 := [and-elim #62]: #50
+#140 := [symm #81]: #139
+#142 := [trans #140 #83]: #141
+#144 := [trans #142 #82]: #143
+[mp #144 #146]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_07 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (exists (?x1 Int) (forall (?x2 Int) (implies (< ?x1 ?x2) (or (< ?x2 0) (<= 0 ?x2))))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_07.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,82 @@
+#2 := false
+#5 := (:var 0 int)
+#7 := 0::int
+#9 := (<= 0::int #5)
+#8 := (< #5 0::int)
+#10 := (or #8 #9)
+#4 := (:var 1 int)
+#6 := (< #4 #5)
+#11 := (implies #6 #10)
+#12 := (forall (vars (?x2 int)) #11)
+#13 := (exists (vars (?x1 int)) #12)
+#14 := (not #13)
+#95 := (iff #14 false)
+#31 := (not #6)
+#32 := (or #31 #10)
+#35 := (forall (vars (?x2 int)) #32)
+#38 := (exists (vars (?x1 int)) #35)
+#41 := (not #38)
+#93 := (iff #41 false)
+#1 := true
+#88 := (not true)
+#91 := (iff #88 false)
+#92 := [rewrite]: #91
+#89 := (iff #41 #88)
+#86 := (iff #38 true)
+#81 := (exists (vars (?x1 int)) true)
+#84 := (iff #81 true)
+#85 := [elim-unused]: #84
+#82 := (iff #38 #81)
+#79 := (iff #35 true)
+#74 := (forall (vars (?x2 int)) true)
+#77 := (iff #74 true)
+#78 := [elim-unused]: #77
+#75 := (iff #35 #74)
+#72 := (iff #32 true)
+#46 := (>= #5 0::int)
+#44 := (not #46)
+#64 := (or #44 #46)
+#50 := -1::int
+#53 := (* -1::int #5)
+#54 := (+ #4 #53)
+#52 := (>= #54 0::int)
+#67 := (or #52 #64)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #32 #67)
+#65 := (iff #10 #64)
+#48 := (iff #9 #46)
+#49 := [rewrite]: #48
+#45 := (iff #8 #44)
+#47 := [rewrite]: #45
+#66 := [monotonicity #47 #49]: #65
+#62 := (iff #31 #52)
+#51 := (not #52)
+#57 := (not #51)
+#60 := (iff #57 #52)
+#61 := [rewrite]: #60
+#58 := (iff #31 #57)
+#55 := (iff #6 #51)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#69 := [monotonicity #63 #66]: #68
+#73 := [trans #69 #71]: #72
+#76 := [quant-intro #73]: #75
+#80 := [trans #76 #78]: #79
+#83 := [quant-intro #80]: #82
+#87 := [trans #83 #85]: #86
+#90 := [monotonicity #87]: #89
+#94 := [trans #90 #92]: #93
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
+#36 := (iff #12 #35)
+#33 := (iff #11 #32)
+#34 := [rewrite]: #33
+#37 := [quant-intro #34]: #36
+#40 := [quant-intro #37]: #39
+#43 := [monotonicity #40]: #42
+#96 := [trans #43 #94]: #95
+#30 := [asserted]: #14
+[mp #30 #96]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_08 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (forall (?x1 Int) (?x2 Int) (implies (< ?x1 ?x2) (< (+ (* 2 ?x1) 1) (* 2 ?x2)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_08.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,128 @@
+#2 := false
+#9 := 1::int
+decl ?x1!1 :: int
+#91 := ?x1!1
+#68 := -2::int
+#129 := (* -2::int ?x1!1)
+decl ?x2!0 :: int
+#90 := ?x2!0
+#7 := 2::int
+#128 := (* 2::int ?x2!0)
+#130 := (+ #128 #129)
+#131 := (<= #130 1::int)
+#136 := (not #131)
+#55 := 0::int
+#53 := -1::int
+#115 := (* -1::int ?x1!1)
+#116 := (+ ?x2!0 #115)
+#117 := (<= #116 0::int)
+#139 := (or #117 #136)
+#142 := (not #139)
+#92 := (* -2::int ?x2!0)
+#93 := (* 2::int ?x1!1)
+#94 := (+ #93 #92)
+#95 := (>= #94 -1::int)
+#96 := (not #95)
+#97 := (* -1::int ?x2!0)
+#98 := (+ ?x1!1 #97)
+#99 := (>= #98 0::int)
+#100 := (or #99 #96)
+#101 := (not #100)
+#143 := (iff #101 #142)
+#140 := (iff #100 #139)
+#137 := (iff #96 #136)
+#134 := (iff #95 #131)
+#122 := (+ #92 #93)
+#125 := (>= #122 -1::int)
+#132 := (iff #125 #131)
+#133 := [rewrite]: #132
+#126 := (iff #95 #125)
+#123 := (= #94 #122)
+#124 := [rewrite]: #123
+#127 := [monotonicity #124]: #126
+#135 := [trans #127 #133]: #134
+#138 := [monotonicity #135]: #137
+#120 := (iff #99 #117)
+#109 := (+ #97 ?x1!1)
+#112 := (>= #109 0::int)
+#118 := (iff #112 #117)
+#119 := [rewrite]: #118
+#113 := (iff #99 #112)
+#110 := (= #98 #109)
+#111 := [rewrite]: #110
+#114 := [monotonicity #111]: #113
+#121 := [trans #114 #119]: #120
+#141 := [monotonicity #121 #138]: #140
+#144 := [monotonicity #141]: #143
+#5 := (:var 0 int)
+#71 := (* -2::int #5)
+#4 := (:var 1 int)
+#8 := (* 2::int #4)
+#72 := (+ #8 #71)
+#70 := (>= #72 -1::int)
+#69 := (not #70)
+#57 := (* -1::int #5)
+#58 := (+ #4 #57)
+#56 := (>= #58 0::int)
+#75 := (or #56 #69)
+#78 := (forall (vars (?x1 int) (?x2 int)) #75)
+#81 := (not #78)
+#102 := (~ #81 #101)
+#103 := [sk]: #102
+#11 := (* 2::int #5)
+#10 := (+ #8 1::int)
+#12 := (< #10 #11)
+#6 := (< #4 #5)
+#13 := (implies #6 #12)
+#14 := (forall (vars (?x1 int) (?x2 int)) #13)
+#15 := (not #14)
+#84 := (iff #15 #81)
+#32 := (+ 1::int #8)
+#35 := (< #32 #11)
+#41 := (not #6)
+#42 := (or #41 #35)
+#47 := (forall (vars (?x1 int) (?x2 int)) #42)
+#50 := (not #47)
+#82 := (iff #50 #81)
+#79 := (iff #47 #78)
+#76 := (iff #42 #75)
+#73 := (iff #35 #69)
+#74 := [rewrite]: #73
+#66 := (iff #41 #56)
+#54 := (not #56)
+#61 := (not #54)
+#64 := (iff #61 #56)
+#65 := [rewrite]: #64
+#62 := (iff #41 #61)
+#59 := (iff #6 #54)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#67 := [trans #63 #65]: #66
+#77 := [monotonicity #67 #74]: #76
+#80 := [quant-intro #77]: #79
+#83 := [monotonicity #80]: #82
+#51 := (iff #15 #50)
+#48 := (iff #14 #47)
+#45 := (iff #13 #42)
+#38 := (implies #6 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #13 #38)
+#36 := (iff #12 #35)
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [quant-intro #46]: #48
+#52 := [monotonicity #49]: #51
+#85 := [trans #52 #83]: #84
+#31 := [asserted]: #15
+#86 := [mp #31 #85]: #81
+#106 := [mp~ #86 #103]: #101
+#107 := [mp #106 #144]: #142
+#146 := [not-or-elim #107]: #131
+#108 := (not #117)
+#145 := [not-or-elim #107]: #108
+[th-lemma #145 #146]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_09 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (forall (?x1 Int) (?x2 Int) (not (= (+ (* 2 ?x1) 1) (* 2 ?x2)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_09.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,100 @@
+#2 := false
+#7 := 1::int
+decl ?x1!1 :: int
+#74 := ?x1!1
+#51 := -2::int
+#96 := (* -2::int ?x1!1)
+decl ?x2!0 :: int
+#73 := ?x2!0
+#4 := 2::int
+#95 := (* 2::int ?x2!0)
+#97 := (+ #95 #96)
+#166 := (<= #97 1::int)
+#94 := (= #97 1::int)
+#53 := -1::int
+#75 := (* -2::int ?x2!0)
+#76 := (* 2::int ?x1!1)
+#77 := (+ #76 #75)
+#78 := (= #77 -1::int)
+#79 := (not #78)
+#80 := (not #79)
+#110 := (iff #80 #94)
+#102 := (not #94)
+#105 := (not #102)
+#108 := (iff #105 #94)
+#109 := [rewrite]: #108
+#106 := (iff #80 #105)
+#103 := (iff #79 #102)
+#100 := (iff #78 #94)
+#88 := (+ #75 #76)
+#91 := (= #88 -1::int)
+#98 := (iff #91 #94)
+#99 := [rewrite]: #98
+#92 := (iff #78 #91)
+#89 := (= #77 #88)
+#90 := [rewrite]: #89
+#93 := [monotonicity #90]: #92
+#101 := [trans #93 #99]: #100
+#104 := [monotonicity #101]: #103
+#107 := [monotonicity #104]: #106
+#111 := [trans #107 #109]: #110
+#9 := (:var 0 int)
+#55 := (* -2::int #9)
+#5 := (:var 1 int)
+#6 := (* 2::int #5)
+#56 := (+ #6 #55)
+#54 := (= #56 -1::int)
+#58 := (not #54)
+#61 := (forall (vars (?x1 int) (?x2 int)) #58)
+#64 := (not #61)
+#81 := (~ #64 #80)
+#82 := [sk]: #81
+#10 := (* 2::int #9)
+#8 := (+ #6 1::int)
+#11 := (= #8 #10)
+#12 := (not #11)
+#13 := (forall (vars (?x1 int) (?x2 int)) #12)
+#14 := (not #13)
+#67 := (iff #14 #64)
+#31 := (+ 1::int #6)
+#37 := (= #10 #31)
+#42 := (not #37)
+#45 := (forall (vars (?x1 int) (?x2 int)) #42)
+#48 := (not #45)
+#65 := (iff #48 #64)
+#62 := (iff #45 #61)
+#59 := (iff #42 #58)
+#52 := (iff #37 #54)
+#57 := [rewrite]: #52
+#60 := [monotonicity #57]: #59
+#63 := [quant-intro #60]: #62
+#66 := [monotonicity #63]: #65
+#49 := (iff #14 #48)
+#46 := (iff #13 #45)
+#43 := (iff #12 #42)
+#40 := (iff #11 #37)
+#34 := (= #31 #10)
+#38 := (iff #34 #37)
+#39 := [rewrite]: #38
+#35 := (iff #11 #34)
+#32 := (= #8 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#41 := [trans #36 #39]: #40
+#44 := [monotonicity #41]: #43
+#47 := [quant-intro #44]: #46
+#50 := [monotonicity #47]: #49
+#68 := [trans #50 #66]: #67
+#30 := [asserted]: #14
+#69 := [mp #30 #68]: #64
+#85 := [mp~ #69 #82]: #80
+#86 := [mp #85 #111]: #94
+#168 := (or #102 #166)
+#169 := [th-lemma]: #168
+#170 := [unit-resolution #169 #86]: #166
+#167 := (>= #97 1::int)
+#171 := (or #102 #167)
+#172 := [th-lemma]: #171
+#173 := [unit-resolution #172 #86]: #167
+[th-lemma #173 #170]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_10 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (forall (?x1 Int) (?x2 Int) (or (< 2 (+ ?x1 ?x2)) (or (= (+ ?x1 ?x2) 2) (< (+ ?x1 ?x2) 2)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_10.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,111 @@
+#2 := false
+#4 := 2::int
+decl ?x1!1 :: int
+#85 := ?x1!1
+decl ?x2!0 :: int
+#84 := ?x2!0
+#101 := (+ ?x2!0 ?x1!1)
+#107 := (>= #101 2::int)
+#113 := (<= #101 2::int)
+#116 := (not #113)
+#110 := (not #107)
+#104 := (= #101 2::int)
+#119 := (or #104 #110 #116)
+#122 := (not #119)
+#86 := (+ ?x1!1 ?x2!0)
+#87 := (<= #86 2::int)
+#88 := (not #87)
+#89 := (>= #86 2::int)
+#90 := (not #89)
+#91 := (= #86 2::int)
+#92 := (or #91 #90 #88)
+#93 := (not #92)
+#123 := (iff #93 #122)
+#120 := (iff #92 #119)
+#117 := (iff #88 #116)
+#114 := (iff #87 #113)
+#102 := (= #86 #101)
+#103 := [rewrite]: #102
+#115 := [monotonicity #103]: #114
+#118 := [monotonicity #115]: #117
+#111 := (iff #90 #110)
+#108 := (iff #89 #107)
+#109 := [monotonicity #103]: #108
+#112 := [monotonicity #109]: #111
+#105 := (iff #91 #104)
+#106 := [monotonicity #103]: #105
+#121 := [monotonicity #106 #112 #118]: #120
+#124 := [monotonicity #121]: #123
+#6 := (:var 0 int)
+#5 := (:var 1 int)
+#7 := (+ #5 #6)
+#56 := (<= #7 2::int)
+#58 := (not #56)
+#54 := (>= #7 2::int)
+#51 := (not #54)
+#9 := (= #7 2::int)
+#67 := (or #9 #51 #58)
+#72 := (forall (vars (?x1 int) (?x2 int)) #67)
+#75 := (not #72)
+#94 := (~ #75 #93)
+#95 := [sk]: #94
+#10 := (< #7 2::int)
+#11 := (or #9 #10)
+#8 := (< 2::int #7)
+#12 := (or #8 #11)
+#13 := (forall (vars (?x1 int) (?x2 int)) #12)
+#14 := (not #13)
+#78 := (iff #14 #75)
+#31 := (= 2::int #7)
+#37 := (or #10 #31)
+#42 := (or #8 #37)
+#45 := (forall (vars (?x1 int) (?x2 int)) #42)
+#48 := (not #45)
+#76 := (iff #48 #75)
+#73 := (iff #45 #72)
+#70 := (iff #42 #67)
+#61 := (or #51 #9)
+#64 := (or #58 #61)
+#68 := (iff #64 #67)
+#69 := [rewrite]: #68
+#65 := (iff #42 #64)
+#62 := (iff #37 #61)
+#55 := (iff #31 #9)
+#57 := [rewrite]: #55
+#53 := (iff #10 #51)
+#52 := [rewrite]: #53
+#63 := [monotonicity #52 #57]: #62
+#59 := (iff #8 #58)
+#60 := [rewrite]: #59
+#66 := [monotonicity #60 #63]: #65
+#71 := [trans #66 #69]: #70
+#74 := [quant-intro #71]: #73
+#77 := [monotonicity #74]: #76
+#49 := (iff #14 #48)
+#46 := (iff #13 #45)
+#43 := (iff #12 #42)
+#40 := (iff #11 #37)
+#34 := (or #31 #10)
+#38 := (iff #34 #37)
+#39 := [rewrite]: #38
+#35 := (iff #11 #34)
+#32 := (iff #9 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#41 := [trans #36 #39]: #40
+#44 := [monotonicity #41]: #43
+#47 := [quant-intro #44]: #46
+#50 := [monotonicity #47]: #49
+#79 := [trans #50 #77]: #78
+#30 := [asserted]: #14
+#80 := [mp #30 #79]: #75
+#98 := [mp~ #80 #95]: #93
+#99 := [mp #98 #124]: #122
+#126 := [not-or-elim #99]: #107
+#100 := (not #104)
+#125 := [not-or-elim #99]: #100
+#127 := [not-or-elim #99]: #113
+#183 := (or #104 #116 #110)
+#184 := [th-lemma]: #183
+[unit-resolution #184 #127 #125 #126]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_11 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (forall (?x1 Int) (if_then_else (< 0 ?x1) (< 0 (+ ?x1 1)) (< ?x1 1))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_11.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,89 @@
+#2 := false
+#4 := 0::int
+decl ?x1!0 :: int
+#78 := ?x1!0
+#83 := (<= ?x1!0 0::int)
+#146 := (not #83)
+#155 := [hypothesis]: #83
+#7 := 1::int
+#81 := (>= ?x1!0 1::int)
+#82 := (not #81)
+#156 := (or #82 #146)
+#157 := [th-lemma]: #156
+#158 := [unit-resolution #157 #155]: #82
+#159 := (or #146 #81)
+#49 := -1::int
+#79 := (<= ?x1!0 -1::int)
+#80 := (not #79)
+#84 := (ite #83 #82 #80)
+#85 := (not #84)
+#5 := (:var 0 int)
+#50 := (<= #5 -1::int)
+#51 := (not #50)
+#55 := (>= #5 1::int)
+#54 := (not #55)
+#45 := (<= #5 0::int)
+#61 := (ite #45 #54 #51)
+#66 := (forall (vars (?x1 int)) #61)
+#69 := (not #66)
+#86 := (~ #69 #85)
+#87 := [sk]: #86
+#10 := (< #5 1::int)
+#8 := (+ #5 1::int)
+#9 := (< 0::int #8)
+#6 := (< 0::int #5)
+#11 := (ite #6 #9 #10)
+#12 := (forall (vars (?x1 int)) #11)
+#13 := (not #12)
+#72 := (iff #13 #69)
+#30 := (+ 1::int #5)
+#33 := (< 0::int #30)
+#36 := (ite #6 #33 #10)
+#39 := (forall (vars (?x1 int)) #36)
+#42 := (not #39)
+#70 := (iff #42 #69)
+#67 := (iff #39 #66)
+#64 := (iff #36 #61)
+#46 := (not #45)
+#58 := (ite #46 #51 #54)
+#62 := (iff #58 #61)
+#63 := [rewrite]: #62
+#59 := (iff #36 #58)
+#56 := (iff #10 #54)
+#57 := [rewrite]: #56
+#52 := (iff #33 #51)
+#53 := [rewrite]: #52
+#47 := (iff #6 #46)
+#48 := [rewrite]: #47
+#60 := [monotonicity #48 #53 #57]: #59
+#65 := [trans #60 #63]: #64
+#68 := [quant-intro #65]: #67
+#71 := [monotonicity #68]: #70
+#43 := (iff #13 #42)
+#40 := (iff #12 #39)
+#37 := (iff #11 #36)
+#34 := (iff #9 #33)
+#31 := (= #8 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35]: #37
+#41 := [quant-intro #38]: #40
+#44 := [monotonicity #41]: #43
+#73 := [trans #44 #71]: #72
+#29 := [asserted]: #13
+#74 := [mp #29 #73]: #69
+#90 := [mp~ #74 #87]: #85
+#151 := (or #84 #146 #81)
+#152 := [def-axiom]: #151
+#160 := [unit-resolution #152 #90]: #159
+#161 := [unit-resolution #160 #158 #155]: false
+#162 := [lemma #161]: #146
+#163 := (or #80 #83)
+#164 := [th-lemma]: #163
+#165 := [unit-resolution #164 #162]: #80
+#166 := (or #83 #79)
+#153 := (or #84 #83 #79)
+#154 := [def-axiom]: #153
+#167 := [unit-resolution #154 #90]: #166
+[unit-resolution #167 #165 #162]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_12 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (if_then_else (forall (?x1 Int) (or (< ?x1 0) (< 0 ?x1))) false true))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_12.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,83 @@
+#2 := false
+#5 := 0::int
+#4 := (:var 0 int)
+#42 := (<= #4 0::int)
+#43 := (not #42)
+#40 := (>= #4 0::int)
+#38 := (not #40)
+#46 := (or #38 #43)
+#49 := (forall (vars (?x1 int)) #46)
+#524 := (not #49)
+#118 := (<= 0::int 0::int)
+#205 := (not #118)
+#119 := (>= 0::int 0::int)
+#206 := (not #119)
+#120 := (or #206 #205)
+#183 := (or #524 #120)
+#172 := (iff #183 #524)
+#525 := (or #524 false)
+#168 := (iff #525 #524)
+#510 := [rewrite]: #168
+#184 := (iff #183 #525)
+#528 := (iff #120 false)
+#197 := (or false false)
+#532 := (iff #197 false)
+#533 := [rewrite]: #532
+#530 := (iff #120 #197)
+#523 := (iff #205 false)
+#1 := true
+#209 := (not true)
+#211 := (iff #209 false)
+#208 := [rewrite]: #211
+#185 := (iff #205 #209)
+#527 := (iff #118 true)
+#529 := [rewrite]: #527
+#316 := [monotonicity #529]: #185
+#196 := [trans #316 #208]: #523
+#212 := (iff #206 false)
+#210 := (iff #206 #209)
+#207 := (iff #119 true)
+#198 := [rewrite]: #207
+#138 := [monotonicity #198]: #210
+#191 := [trans #138 #208]: #212
+#531 := [monotonicity #191 #196]: #530
+#534 := [trans #531 #533]: #528
+#526 := [monotonicity #534]: #184
+#173 := [trans #526 #510]: #172
+#188 := [quant-inst]: #183
+#174 := [mp #188 #173]: #524
+#60 := (~ #49 #49)
+#58 := (~ #46 #46)
+#59 := [refl]: #58
+#61 := [nnf-pos #59]: #60
+#7 := (< 0::int #4)
+#6 := (< #4 0::int)
+#8 := (or #6 #7)
+#9 := (forall (vars (?x1 int)) #8)
+#10 := (ite #9 false true)
+#11 := (not #10)
+#52 := (iff #11 #49)
+#50 := (iff #9 #49)
+#47 := (iff #8 #46)
+#44 := (iff #7 #43)
+#45 := [rewrite]: #44
+#39 := (iff #6 #38)
+#41 := [rewrite]: #39
+#48 := [monotonicity #41 #45]: #47
+#51 := [quant-intro #48]: #50
+#36 := (iff #11 #9)
+#28 := (not #9)
+#31 := (not #28)
+#34 := (iff #31 #9)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#29 := (iff #10 #28)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#53 := [trans #37 #51]: #52
+#27 := [asserted]: #11
+#54 := [mp #27 #53]: #49
+#62 := [mp~ #54 #61]: #49
+[unit-resolution #62 #174]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_13 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (< 0 (ite (forall (?x1 Int) (or (< ?x1 0) (< 0 ?x1))) (~ 1) 3)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_13.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,180 @@
+#2 := false
+#4 := 0::int
+#5 := (:var 0 int)
+#48 := (<= #5 0::int)
+#49 := (not #48)
+#45 := (>= #5 0::int)
+#44 := (not #45)
+#52 := (or #44 #49)
+#55 := (forall (vars (?x1 int)) #52)
+#86 := (not #55)
+#604 := (<= 0::int 0::int)
+#264 := (not #604)
+#269 := (>= 0::int 0::int)
+#605 := (not #269)
+#265 := (or #605 #264)
+#588 := (or #86 #265)
+#584 := (iff #588 #86)
+#311 := (or #86 false)
+#314 := (iff #311 #86)
+#208 := [rewrite]: #314
+#312 := (iff #588 #311)
+#599 := (iff #265 false)
+#598 := (or false false)
+#241 := (iff #598 false)
+#601 := [rewrite]: #241
+#600 := (iff #265 #598)
+#597 := (iff #264 false)
+#1 := true
+#590 := (not true)
+#255 := (iff #590 false)
+#256 := [rewrite]: #255
+#596 := (iff #264 #590)
+#594 := (iff #604 true)
+#595 := [rewrite]: #594
+#591 := [monotonicity #595]: #596
+#235 := [trans #591 #256]: #597
+#592 := (iff #605 false)
+#253 := (iff #605 #590)
+#606 := (iff #269 true)
+#249 := [rewrite]: #606
+#254 := [monotonicity #249]: #253
+#593 := [trans #254 #256]: #592
+#240 := [monotonicity #593 #235]: #600
+#602 := [trans #240 #601]: #599
+#313 := [monotonicity #602]: #312
+#585 := [trans #313 #208]: #584
+#589 := [quant-inst]: #588
+#307 := [mp #589 #585]: #86
+decl z3name!0 :: bool
+#83 := z3name!0
+#12 := 3::int
+#32 := -1::int
+#92 := (ite z3name!0 -1::int 3::int)
+#290 := (= #92 3::int)
+#610 := (not #290)
+#607 := (>= #92 3::int)
+#609 := (not #607)
+#95 := (<= #92 0::int)
+#58 := (ite #55 -1::int 3::int)
+#64 := (<= #58 0::int)
+#96 := (~ #64 #95)
+#93 := (= #58 #92)
+#90 := (~ #55 z3name!0)
+#87 := (or z3name!0 #86)
+#84 := (not z3name!0)
+#85 := (or #84 #55)
+#88 := (and #85 #87)
+#89 := [intro-def]: #88
+#91 := [apply-def #89]: #90
+#94 := [monotonicity #91]: #93
+#97 := [monotonicity #94]: #96
+#10 := 1::int
+#11 := (- 1::int)
+#7 := (< 0::int #5)
+#6 := (< #5 0::int)
+#8 := (or #6 #7)
+#9 := (forall (vars (?x1 int)) #8)
+#13 := (ite #9 #11 3::int)
+#14 := (< 0::int #13)
+#15 := (not #14)
+#77 := (iff #15 #64)
+#35 := (ite #9 -1::int 3::int)
+#38 := (< 0::int #35)
+#41 := (not #38)
+#75 := (iff #41 #64)
+#65 := (not #64)
+#70 := (not #65)
+#73 := (iff #70 #64)
+#74 := [rewrite]: #73
+#71 := (iff #41 #70)
+#68 := (iff #38 #65)
+#61 := (< 0::int #58)
+#66 := (iff #61 #65)
+#67 := [rewrite]: #66
+#62 := (iff #38 #61)
+#59 := (= #35 #58)
+#56 := (iff #9 #55)
+#53 := (iff #8 #52)
+#50 := (iff #7 #49)
+#51 := [rewrite]: #50
+#46 := (iff #6 #44)
+#47 := [rewrite]: #46
+#54 := [monotonicity #47 #51]: #53
+#57 := [quant-intro #54]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#69 := [trans #63 #67]: #68
+#72 := [monotonicity #69]: #71
+#76 := [trans #72 #74]: #75
+#42 := (iff #15 #41)
+#39 := (iff #14 #38)
+#36 := (= #13 #35)
+#33 := (= #11 -1::int)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#78 := [trans #43 #76]: #77
+#31 := [asserted]: #15
+#79 := [mp #31 #78]: #64
+#126 := [mp~ #79 #97]: #95
+#266 := (not #95)
+#396 := (or #609 #266)
+#603 := [th-lemma]: #396
+#277 := [unit-resolution #603 #126]: #609
+#278 := [hypothesis]: #290
+#611 := (or #610 #607)
+#612 := [th-lemma]: #611
+#613 := [unit-resolution #612 #278 #277]: false
+#608 := [lemma #613]: #610
+#289 := (or z3name!0 #290)
+#293 := [def-axiom]: #289
+#308 := [unit-resolution #293 #608]: z3name!0
+#129 := (or #55 #84)
+decl ?x1!1 :: int
+#108 := ?x1!1
+#111 := (>= ?x1!1 0::int)
+#112 := (not #111)
+#109 := (<= ?x1!1 0::int)
+#110 := (not #109)
+#132 := (or #110 #112)
+#135 := (not #132)
+#138 := (or z3name!0 #135)
+#141 := (and #129 #138)
+#113 := (or #112 #110)
+#114 := (not #113)
+#119 := (or z3name!0 #114)
+#122 := (and #85 #119)
+#142 := (iff #122 #141)
+#139 := (iff #119 #138)
+#136 := (iff #114 #135)
+#133 := (iff #113 #132)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#130 := (iff #85 #129)
+#131 := [rewrite]: #130
+#143 := [monotonicity #131 #140]: #142
+#123 := (~ #88 #122)
+#120 := (~ #87 #119)
+#115 := (~ #86 #114)
+#116 := [sk]: #115
+#106 := (~ z3name!0 z3name!0)
+#107 := [refl]: #106
+#121 := [monotonicity #107 #116]: #120
+#104 := (~ #85 #85)
+#102 := (~ #55 #55)
+#100 := (~ #52 #52)
+#101 := [refl]: #100
+#103 := [nnf-pos #101]: #102
+#98 := (~ #84 #84)
+#99 := [refl]: #98
+#105 := [monotonicity #99 #103]: #104
+#124 := [monotonicity #105 #121]: #123
+#125 := [mp~ #89 #124]: #122
+#127 := [mp #125 #143]: #141
+#128 := [and-elim #127]: #129
+#582 := [unit-resolution #128 #308]: #55
+[unit-resolution #582 #307]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_14 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (not (exists (?x1 Int) (?x2 Int) (?x3 Int) (= (+ (* 4 ?x1) (* (~ 6) ?x2)) 1))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_14.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,103 @@
+#2 := false
+#104 := -1::int
+decl ?x1!1 :: int
+#86 := ?x1!1
+#106 := -4::int
+#107 := (* -4::int ?x1!1)
+decl ?x2!0 :: int
+#85 := ?x2!0
+#7 := 6::int
+#105 := (* 6::int ?x2!0)
+#108 := (+ #105 #107)
+#168 := (<= #108 -1::int)
+#109 := (= #108 -1::int)
+#12 := 1::int
+#33 := -6::int
+#87 := (* -6::int ?x2!0)
+#4 := 4::int
+#88 := (* 4::int ?x1!1)
+#89 := (+ #88 #87)
+#90 := (= #89 1::int)
+#112 := (iff #90 #109)
+#98 := (+ #87 #88)
+#101 := (= #98 1::int)
+#110 := (iff #101 #109)
+#111 := [rewrite]: #110
+#102 := (iff #90 #101)
+#99 := (= #89 #98)
+#100 := [rewrite]: #99
+#103 := [monotonicity #100]: #102
+#113 := [trans #103 #111]: #112
+#53 := (:var 0 int)
+#54 := (* -6::int #53)
+#9 := (:var 1 int)
+#55 := (* 4::int #9)
+#56 := (+ #55 #54)
+#76 := (= #56 1::int)
+#74 := (exists (vars (?x1 int) (?x2 int)) #76)
+#91 := (~ #74 #90)
+#92 := [sk]: #91
+#8 := (- 6::int)
+#10 := (* #8 #9)
+#5 := (:var 2 int)
+#6 := (* 4::int #5)
+#11 := (+ #6 #10)
+#13 := (= #11 1::int)
+#14 := (exists (vars (?x1 int) (?x2 int) (?x3 int)) #13)
+#15 := (not #14)
+#16 := (not #15)
+#79 := (iff #16 #74)
+#57 := (= 1::int #56)
+#58 := (exists (vars (?x1 int) (?x2 int)) #57)
+#77 := (iff #58 #74)
+#75 := (iff #57 #76)
+#73 := [rewrite]: #75
+#78 := [quant-intro #73]: #77
+#71 := (iff #16 #58)
+#63 := (not #58)
+#66 := (not #63)
+#69 := (iff #66 #58)
+#70 := [rewrite]: #69
+#67 := (iff #16 #66)
+#64 := (iff #15 #63)
+#61 := (iff #14 #58)
+#36 := (* -6::int #9)
+#39 := (+ #6 #36)
+#45 := (= 1::int #39)
+#50 := (exists (vars (?x1 int) (?x2 int) (?x3 int)) #45)
+#59 := (iff #50 #58)
+#60 := [elim-unused]: #59
+#51 := (iff #14 #50)
+#48 := (iff #13 #45)
+#42 := (= #39 1::int)
+#46 := (iff #42 #45)
+#47 := [rewrite]: #46
+#43 := (iff #13 #42)
+#40 := (= #11 #39)
+#37 := (= #10 #36)
+#34 := (= #8 -6::int)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#49 := [trans #44 #47]: #48
+#52 := [quant-intro #49]: #51
+#62 := [trans #52 #60]: #61
+#65 := [monotonicity #62]: #64
+#68 := [monotonicity #65]: #67
+#72 := [trans #68 #70]: #71
+#80 := [trans #72 #78]: #79
+#32 := [asserted]: #16
+#81 := [mp #32 #80]: #74
+#95 := [mp~ #81 #92]: #90
+#96 := [mp #95 #113]: #109
+#170 := (not #109)
+#171 := (or #170 #168)
+#172 := [th-lemma]: #171
+#173 := [unit-resolution #172 #96]: #168
+#169 := (>= #108 -1::int)
+#174 := (or #170 #169)
+#175 := [th-lemma]: #174
+#176 := [unit-resolution #175 #96]: #169
+[th-lemma #176 #173]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_15 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (exists (?x1 Int) (forall (?x2 Int) (?x3 Int) (implies (and (< 0 ?x2) (< 0 ?x3)) (< 0 (+ ?x2 ?x3))))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_15.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,107 @@
+#2 := false
+#4 := 0::int
+decl ?x2!1 :: int
+#83 := ?x2!1
+decl ?x3!0 :: int
+#82 := ?x3!0
+#108 := (+ ?x3!0 ?x2!1)
+#111 := (<= #108 0::int)
+#114 := (not #111)
+#89 := (<= ?x2!1 0::int)
+#90 := (not #89)
+#87 := (<= ?x3!0 0::int)
+#88 := (not #87)
+#102 := (and #88 #90)
+#105 := (not #102)
+#117 := (or #105 #114)
+#120 := (not #117)
+#84 := (+ ?x2!1 ?x3!0)
+#85 := (<= #84 0::int)
+#86 := (not #85)
+#91 := (and #90 #88)
+#92 := (not #91)
+#93 := (or #92 #86)
+#94 := (not #93)
+#121 := (iff #94 #120)
+#118 := (iff #93 #117)
+#115 := (iff #86 #114)
+#112 := (iff #85 #111)
+#109 := (= #84 #108)
+#110 := [rewrite]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#106 := (iff #92 #105)
+#103 := (iff #91 #102)
+#104 := [rewrite]: #103
+#107 := [monotonicity #104]: #106
+#119 := [monotonicity #107 #116]: #118
+#122 := [monotonicity #119]: #121
+#7 := (:var 0 int)
+#5 := (:var 1 int)
+#10 := (+ #5 #7)
+#63 := (<= #10 0::int)
+#64 := (not #63)
+#53 := (<= #7 0::int)
+#54 := (not #53)
+#49 := (<= #5 0::int)
+#50 := (not #49)
+#57 := (and #50 #54)
+#60 := (not #57)
+#67 := (or #60 #64)
+#70 := (forall (vars (?x2 int) (?x3 int)) #67)
+#73 := (not #70)
+#95 := (~ #73 #94)
+#96 := [sk]: #95
+#11 := (< 0::int #10)
+#8 := (< 0::int #7)
+#6 := (< 0::int #5)
+#9 := (and #6 #8)
+#12 := (implies #9 #11)
+#13 := (forall (vars (?x2 int) (?x3 int)) #12)
+#14 := (exists (vars (?x1 int)) #13)
+#15 := (not #14)
+#76 := (iff #15 #73)
+#32 := (not #9)
+#33 := (or #32 #11)
+#36 := (forall (vars (?x2 int) (?x3 int)) #33)
+#46 := (not #36)
+#74 := (iff #46 #73)
+#71 := (iff #36 #70)
+#68 := (iff #33 #67)
+#65 := (iff #11 #64)
+#66 := [rewrite]: #65
+#61 := (iff #32 #60)
+#58 := (iff #9 #57)
+#55 := (iff #8 #54)
+#56 := [rewrite]: #55
+#51 := (iff #6 #50)
+#52 := [rewrite]: #51
+#59 := [monotonicity #52 #56]: #58
+#62 := [monotonicity #59]: #61
+#69 := [monotonicity #62 #66]: #68
+#72 := [quant-intro #69]: #71
+#75 := [monotonicity #72]: #74
+#47 := (iff #15 #46)
+#44 := (iff #14 #36)
+#39 := (exists (vars (?x1 int)) #36)
+#42 := (iff #39 #36)
+#43 := [elim-unused]: #42
+#40 := (iff #14 #39)
+#37 := (iff #13 #36)
+#34 := (iff #12 #33)
+#35 := [rewrite]: #34
+#38 := [quant-intro #35]: #37
+#41 := [quant-intro #38]: #40
+#45 := [trans #41 #43]: #44
+#48 := [monotonicity #45]: #47
+#77 := [trans #48 #75]: #76
+#31 := [asserted]: #15
+#78 := [mp #31 #77]: #73
+#99 := [mp~ #78 #96]: #94
+#100 := [mp #99 #122]: #120
+#125 := [not-or-elim #100]: #111
+#101 := [not-or-elim #100]: #102
+#124 := [and-elim #101]: #90
+#123 := [and-elim #101]: #88
+[th-lemma #123 #124 #125]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_16 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (exists (?x1 Int) (forall (?x2 Int) (?x3 Real) (implies (and (< 0 ?x2) (< 0.0 ?x3)) (< (~ 1) ?x2)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_16.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,117 @@
+#2 := false
+#4 := 0::int
+decl ?x2!1 :: int
+#91 := ?x2!1
+#98 := (<= ?x2!1 0::int)
+#99 := (not #98)
+#7 := 0::real
+decl ?x3!0 :: real
+#93 := ?x3!0
+#96 := (<= ?x3!0 0::real)
+#97 := (not #96)
+#111 := (and #97 #99)
+#114 := (not #111)
+#33 := -1::int
+#94 := (<= ?x2!1 -1::int)
+#95 := (not #94)
+#120 := (or #95 #114)
+#125 := (not #120)
+#100 := (and #99 #97)
+#101 := (not #100)
+#102 := (or #101 #95)
+#103 := (not #102)
+#126 := (iff #103 #125)
+#123 := (iff #102 #120)
+#117 := (or #114 #95)
+#121 := (iff #117 #120)
+#122 := [rewrite]: #121
+#118 := (iff #102 #117)
+#115 := (iff #101 #114)
+#112 := (iff #100 #111)
+#113 := [rewrite]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#124 := [trans #119 #122]: #123
+#127 := [monotonicity #124]: #126
+#5 := (:var 1 int)
+#75 := (<= #5 -1::int)
+#76 := (not #75)
+#8 := (:var 0 real)
+#65 := (<= #8 0::real)
+#66 := (not #65)
+#61 := (<= #5 0::int)
+#62 := (not #61)
+#69 := (and #62 #66)
+#72 := (not #69)
+#79 := (or #72 #76)
+#82 := (forall (vars (?x2 int) (?x3 real)) #79)
+#85 := (not #82)
+#104 := (~ #85 #103)
+#105 := [sk]: #104
+#11 := 1::int
+#12 := (- 1::int)
+#13 := (< #12 #5)
+#9 := (< 0::real #8)
+#6 := (< 0::int #5)
+#10 := (and #6 #9)
+#14 := (implies #10 #13)
+#15 := (forall (vars (?x2 int) (?x3 real)) #14)
+#16 := (exists (vars (?x1 int)) #15)
+#17 := (not #16)
+#88 := (iff #17 #85)
+#36 := (< -1::int #5)
+#42 := (not #10)
+#43 := (or #42 #36)
+#48 := (forall (vars (?x2 int) (?x3 real)) #43)
+#58 := (not #48)
+#86 := (iff #58 #85)
+#83 := (iff #48 #82)
+#80 := (iff #43 #79)
+#77 := (iff #36 #76)
+#78 := [rewrite]: #77
+#73 := (iff #42 #72)
+#70 := (iff #10 #69)
+#67 := (iff #9 #66)
+#68 := [rewrite]: #67
+#63 := (iff #6 #62)
+#64 := [rewrite]: #63
+#71 := [monotonicity #64 #68]: #70
+#74 := [monotonicity #71]: #73
+#81 := [monotonicity #74 #78]: #80
+#84 := [quant-intro #81]: #83
+#87 := [monotonicity #84]: #86
+#59 := (iff #17 #58)
+#56 := (iff #16 #48)
+#51 := (exists (vars (?x1 int)) #48)
+#54 := (iff #51 #48)
+#55 := [elim-unused]: #54
+#52 := (iff #16 #51)
+#49 := (iff #15 #48)
+#46 := (iff #14 #43)
+#39 := (implies #10 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #14 #39)
+#37 := (iff #13 #36)
+#34 := (= #12 -1::int)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [quant-intro #47]: #49
+#53 := [quant-intro #50]: #52
+#57 := [trans #53 #55]: #56
+#60 := [monotonicity #57]: #59
+#89 := [trans #60 #87]: #88
+#32 := [asserted]: #17
+#90 := [mp #32 #89]: #85
+#108 := [mp~ #90 #105]: #103
+#109 := [mp #108 #127]: #125
+#128 := [not-or-elim #109]: #111
+#130 := [and-elim #128]: #99
+#110 := [not-or-elim #109]: #94
+#186 := (or #95 #98)
+#187 := [th-lemma]: #186
+#188 := [unit-resolution #187 #110]: #98
+[unit-resolution #188 #130]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_17 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (exists (?x1 Int) (implies (forall (?x2 Int) (implies (<= ?x1 ?x2) (< 0 ?x2))) (< 0 ?x1))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_17.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,148 @@
+#2 := false
+#144 := (not false)
+#7 := 0::int
+#5 := (:var 0 int)
+#52 := (<= #5 0::int)
+#53 := (not #52)
+#147 := (or #53 #144)
+#150 := (not #147)
+#153 := (forall (vars (?x1 int)) #150)
+#180 := (iff #153 false)
+#175 := (forall (vars (?x1 int)) false)
+#178 := (iff #175 false)
+#179 := [elim-unused]: #178
+#176 := (iff #153 #175)
+#173 := (iff #150 false)
+#1 := true
+#168 := (not true)
+#171 := (iff #168 false)
+#172 := [rewrite]: #171
+#169 := (iff #150 #168)
+#166 := (iff #147 true)
+#161 := (or #53 true)
+#164 := (iff #161 true)
+#165 := [rewrite]: #164
+#162 := (iff #147 #161)
+#159 := (iff #144 true)
+#160 := [rewrite]: #159
+#163 := [monotonicity #160]: #162
+#167 := [trans #163 #165]: #166
+#170 := [monotonicity #167]: #169
+#174 := [trans #170 #172]: #173
+#177 := [quant-intro #174]: #176
+#181 := [trans #177 #179]: #180
+#56 := -1::int
+#57 := (* -1::int #5)
+#4 := (:var 1 int)
+#58 := (+ #4 #57)
+#59 := (<= #58 0::int)
+#62 := (not #59)
+#68 := (or #53 #62)
+#73 := (forall (vars (?x2 int)) #68)
+#76 := (not #73)
+#79 := (or #53 #76)
+#105 := (not #79)
+#123 := (forall (vars (?x1 int)) #105)
+#156 := (iff #123 #153)
+#127 := (forall (vars (?x2 int)) #53)
+#130 := (not #127)
+#133 := (or #53 #130)
+#136 := (not #133)
+#139 := (forall (vars (?x1 int)) #136)
+#154 := (iff #139 #153)
+#155 := [rewrite]: #154
+#140 := (iff #123 #139)
+#141 := [rewrite]: #140
+#157 := [trans #141 #155]: #156
+#116 := (and #52 #73)
+#119 := (forall (vars (?x1 int)) #116)
+#124 := (iff #119 #123)
+#113 := (iff #116 #105)
+#122 := [rewrite]: #113
+#125 := [quant-intro #122]: #124
+#94 := (not #53)
+#104 := (and #94 #73)
+#108 := (forall (vars (?x1 int)) #104)
+#120 := (iff #108 #119)
+#117 := (iff #104 #116)
+#114 := (iff #94 #52)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#121 := [quant-intro #118]: #120
+#82 := (exists (vars (?x1 int)) #79)
+#85 := (not #82)
+#109 := (~ #85 #108)
+#106 := (~ #105 #104)
+#101 := (not #76)
+#102 := (~ #101 #73)
+#99 := (~ #73 #73)
+#97 := (~ #68 #68)
+#98 := [refl]: #97
+#100 := [nnf-pos #98]: #99
+#103 := [nnf-neg #100]: #102
+#95 := (~ #94 #94)
+#96 := [refl]: #95
+#107 := [nnf-neg #96 #103]: #106
+#110 := [nnf-neg #107]: #109
+#8 := (< 0::int #5)
+#6 := (<= #4 #5)
+#9 := (implies #6 #8)
+#10 := (forall (vars (?x2 int)) #9)
+#11 := (implies #10 #8)
+#12 := (exists (vars (?x1 int)) #11)
+#13 := (not #12)
+#88 := (iff #13 #85)
+#30 := (not #6)
+#31 := (or #30 #8)
+#34 := (forall (vars (?x2 int)) #31)
+#40 := (not #34)
+#41 := (or #8 #40)
+#46 := (exists (vars (?x1 int)) #41)
+#49 := (not #46)
+#86 := (iff #49 #85)
+#83 := (iff #46 #82)
+#80 := (iff #41 #79)
+#77 := (iff #40 #76)
+#74 := (iff #34 #73)
+#71 := (iff #31 #68)
+#65 := (or #62 #53)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #31 #65)
+#54 := (iff #8 #53)
+#55 := [rewrite]: #54
+#63 := (iff #30 #62)
+#60 := (iff #6 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64 #55]: #66
+#72 := [trans #67 #70]: #71
+#75 := [quant-intro #72]: #74
+#78 := [monotonicity #75]: #77
+#81 := [monotonicity #55 #78]: #80
+#84 := [quant-intro #81]: #83
+#87 := [monotonicity #84]: #86
+#50 := (iff #13 #49)
+#47 := (iff #12 #46)
+#44 := (iff #11 #41)
+#37 := (implies #34 #8)
+#42 := (iff #37 #41)
+#43 := [rewrite]: #42
+#38 := (iff #11 #37)
+#35 := (iff #10 #34)
+#32 := (iff #9 #31)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#39 := [monotonicity #36]: #38
+#45 := [trans #39 #43]: #44
+#48 := [quant-intro #45]: #47
+#51 := [monotonicity #48]: #50
+#89 := [trans #51 #87]: #88
+#29 := [asserted]: #13
+#90 := [mp #29 #89]: #85
+#111 := [mp~ #90 #110]: #108
+#112 := [mp #111 #121]: #119
+#126 := [mp #112 #125]: #123
+#158 := [mp #126 #157]: #153
+[mp #158 #181]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_18 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,7 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Int)
+ )
+:assumption (not (forall (?x1 Int) (implies (< ?x1 uf_1) (< (* 2 ?x1) (* 2 uf_1))) :pat{ ?x1 }))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_arith_quant_18.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,112 @@
+#2 := false
+#43 := 0::int
+decl ?x1!0 :: int
+#78 := ?x1!0
+#56 := -2::int
+#113 := (* -2::int ?x1!0)
+decl uf_1 :: int
+#6 := uf_1
+#8 := 2::int
+#10 := (* 2::int uf_1)
+#114 := (+ #10 #113)
+#115 := (<= #114 0::int)
+#120 := (not #115)
+#41 := -1::int
+#100 := (* -1::int ?x1!0)
+#101 := (+ uf_1 #100)
+#102 := (<= #101 0::int)
+#123 := (or #102 #120)
+#126 := (not #123)
+#59 := (* -2::int uf_1)
+#79 := (* 2::int ?x1!0)
+#80 := (+ #79 #59)
+#81 := (>= #80 0::int)
+#82 := (not #81)
+#45 := (* -1::int uf_1)
+#83 := (+ ?x1!0 #45)
+#84 := (>= #83 0::int)
+#85 := (or #84 #82)
+#86 := (not #85)
+#127 := (iff #86 #126)
+#124 := (iff #85 #123)
+#121 := (iff #82 #120)
+#118 := (iff #81 #115)
+#107 := (+ #59 #79)
+#110 := (>= #107 0::int)
+#116 := (iff #110 #115)
+#117 := [rewrite]: #116
+#111 := (iff #81 #110)
+#108 := (= #80 #107)
+#109 := [rewrite]: #108
+#112 := [monotonicity #109]: #111
+#119 := [trans #112 #117]: #118
+#122 := [monotonicity #119]: #121
+#105 := (iff #84 #102)
+#94 := (+ #45 ?x1!0)
+#97 := (>= #94 0::int)
+#103 := (iff #97 #102)
+#104 := [rewrite]: #103
+#98 := (iff #84 #97)
+#95 := (= #83 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#106 := [trans #99 #104]: #105
+#125 := [monotonicity #106 #122]: #124
+#128 := [monotonicity #125]: #127
+#4 := (:var 0 int)
+#5 := (pattern #4)
+#9 := (* 2::int #4)
+#60 := (+ #9 #59)
+#58 := (>= #60 0::int)
+#57 := (not #58)
+#46 := (+ #4 #45)
+#44 := (>= #46 0::int)
+#63 := (or #44 #57)
+#66 := (forall (vars (?x1 int)) (:pat #5) #63)
+#69 := (not #66)
+#87 := (~ #69 #86)
+#88 := [sk]: #87
+#11 := (< #9 #10)
+#7 := (< #4 uf_1)
+#12 := (implies #7 #11)
+#13 := (forall (vars (?x1 int)) (:pat #5) #12)
+#14 := (not #13)
+#72 := (iff #14 #69)
+#31 := (not #7)
+#32 := (or #31 #11)
+#35 := (forall (vars (?x1 int)) (:pat #5) #32)
+#38 := (not #35)
+#70 := (iff #38 #69)
+#67 := (iff #35 #66)
+#64 := (iff #32 #63)
+#61 := (iff #11 #57)
+#62 := [rewrite]: #61
+#54 := (iff #31 #44)
+#42 := (not #44)
+#49 := (not #42)
+#52 := (iff #49 #44)
+#53 := [rewrite]: #52
+#50 := (iff #31 #49)
+#47 := (iff #7 #42)
+#48 := [rewrite]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#65 := [monotonicity #55 #62]: #64
+#68 := [quant-intro #65]: #67
+#71 := [monotonicity #68]: #70
+#39 := (iff #14 #38)
+#36 := (iff #13 #35)
+#33 := (iff #12 #32)
+#34 := [rewrite]: #33
+#37 := [quant-intro #34]: #36
+#40 := [monotonicity #37]: #39
+#73 := [trans #40 #71]: #72
+#30 := [asserted]: #14
+#74 := [mp #30 #73]: #69
+#91 := [mp~ #74 #88]: #86
+#92 := [mp #91 #128]: #126
+#130 := [not-or-elim #92]: #115
+#93 := (not #102)
+#129 := [not-or-elim #92]: #93
+[th-lemma #129 #130]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,12 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 BitVec[2] Int)
+ )
+:assumption (= (uf_1 bv0[2]) 0)
+:assumption (= (uf_1 bv1[2]) 1)
+:assumption (= (uf_1 bv2[2]) 2)
+:assumption (= (uf_1 bv3[2]) 3)
+:assumption (forall (?x1 BitVec[2]) (< 0 (uf_1 ?x1)))
+:assumption (not (forall (?x2 Int) (implies (< ?x2 0) (forall (?x3 BitVec[2]) (< ?x2 (uf_1 ?x3))))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,43 @@
+#2 := false
+#6 := 0::int
+decl uf_1 :: (-> bv[2] int)
+#4 := bv[0:2]
+#5 := (uf_1 bv[0:2])
+#225 := (<= #5 0::int)
+#311 := (not #225)
+#20 := (:var 0 bv[2])
+#21 := (uf_1 #20)
+#640 := (pattern #21)
+#54 := (<= #21 0::int)
+#55 := (not #54)
+#641 := (forall (vars (?x1 bv[2])) (:pat #640) #55)
+#58 := (forall (vars (?x1 bv[2])) #55)
+#644 := (iff #58 #641)
+#642 := (iff #55 #55)
+#643 := [refl]: #642
+#645 := [quant-intro #643]: #644
+#113 := (~ #58 #58)
+#115 := (~ #55 #55)
+#116 := [refl]: #115
+#114 := [nnf-pos #116]: #113
+#22 := (< 0::int #21)
+#23 := (forall (vars (?x1 bv[2])) #22)
+#59 := (iff #23 #58)
+#56 := (iff #22 #55)
+#57 := [rewrite]: #56
+#60 := [quant-intro #57]: #59
+#51 := [asserted]: #23
+#61 := [mp #51 #60]: #58
+#111 := [mp~ #61 #114]: #58
+#646 := [mp #111 #645]: #641
+#227 := (not #641)
+#313 := (or #227 #311)
+#304 := [quant-inst]: #313
+#635 := [unit-resolution #304 #646]: #311
+#7 := (= #5 0::int)
+#47 := [asserted]: #7
+#638 := (not #7)
+#633 := (or #638 #225)
+#639 := [th-lemma]: #633
+[unit-resolution #639 #47 #635]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,12 @@
+(benchmark Isabelle
+:extrasorts ( T2 T1)
+:extrafuns (
+ (uf_2 T1)
+ (uf_1 BitVec[4] BitVec[4] T1)
+ (uf_3 T1 T2)
+ (uf_4 BitVec[4])
+ )
+:assumption (forall (?x1 BitVec[4]) (?x2 BitVec[4]) (iff (= (uf_1 ?x1 ?x2) uf_2) (bvule ?x1 ?x2)))
+:assumption (not (= (uf_3 (uf_1 bv0[4] uf_4)) (uf_3 uf_2)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= bv27[4] (bvneg bv5[4])))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= bv27[4] bv11[4]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (bvult bv23[8] bv27[8]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvadd bv27[5] bv11[5]) bv6[5]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_05 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvmul bv7[8] bv3[8]) bv21[8]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_05.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_06 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvsub bv11[8] bv27[8]) (bvneg bv16[8])))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_06.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_07 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvneg (bvneg bv11[5])) bv11[5]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_07.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_08 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvadd (bvneg bv40[7]) bv1[7]) (bvneg bv39[7])))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_08.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_09 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,9 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 BitVec[32])
+ (uf_2 BitVec[32])
+ (uf_3 BitVec[32])
+ )
+:assumption (not (= (bvsub (bvadd (bvadd uf_1 (bvmul bv2[32] uf_2)) uf_3) uf_2) (bvadd (bvadd uf_2 uf_3) uf_1)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_09.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_10 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 BitVec[4])
+ )
+:assumption (= uf_1 bv5[4])
+:assumption (not (= (bvmul bv4[4] uf_1) bv4[4]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_arith_10.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvand bv6[32] bv5[32]) bv4[32]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvor bv6[8] bv3[8]) bv7[8]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvxor bv240[8] bv255[8]) bv15[8]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvnot bv240[16]) bv65295[16]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_05 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (concat bv27[4] bv27[8]) bv2843[12]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_05.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_06 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (concat bv3[4] bv15[6]) bv207[10]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_06.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_07 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,12 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (not (= (extract[2:1] bv22[4]) bv3[2]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_07.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_08 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (zero_extend[6] bv10[4]) bv10[10]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_08.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_09 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (sign_extend[2] bv10[4]) bv58[6]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_09.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_10 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvlshr bv19[8] bv2[8]) bv4[8]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_10.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_11 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (bvashr bv19[8] bv2[8]) bv4[8]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_11.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_12 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,12 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (not (= (rotate_right[2] bv6[4]) bv9[4]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_12.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_13 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,12 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (not (= (rotate_left[1] bv14[4]) bv13[4]))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_13.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_14 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,7 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 BitVec[16])
+ )
+:assumption (not (= (bvor (bvand uf_1 bv65280[16]) (bvand uf_1 bv255[16])) uf_1))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_14.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_15 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 BitVec[16])
+ )
+:assumption (bvult uf_1 bv256[16])
+:assumption (not (= (bvand uf_1 bv255[16]) uf_1))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_bv_bit_15.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_fol_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1 Int)
+ )
+:assumption (not (forall (?x1 Int) (implies (up_1 ?x1) (forall (?x2 Int) (or (up_1 ?x1) (up_1 ?x2))))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_fol_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,78 @@
+#2 := false
+decl up_1 :: (-> int bool)
+decl ?x1!0 :: int
+#54 := ?x1!0
+#55 := (up_1 ?x1!0)
+#58 := (not #55)
+decl ?x2!1 :: int
+#66 := ?x2!1
+#67 := (up_1 ?x2!1)
+#85 := (or #55 #67)
+#88 := (not #85)
+#91 := (and #55 #88)
+#68 := (or #67 #55)
+#69 := (not #68)
+#63 := (not #58)
+#75 := (and #63 #69)
+#92 := (iff #75 #91)
+#89 := (iff #69 #88)
+#86 := (iff #68 #85)
+#87 := [rewrite]: #86
+#90 := [monotonicity #87]: #89
+#83 := (iff #63 #55)
+#84 := [rewrite]: #83
+#93 := [monotonicity #84 #90]: #92
+#6 := (:var 1 int)
+#7 := (up_1 #6)
+#4 := (:var 0 int)
+#5 := (up_1 #4)
+#29 := (or #5 #7)
+#32 := (forall (vars (?x2 int)) #29)
+#38 := (not #5)
+#39 := (or #38 #32)
+#44 := (forall (vars (?x1 int)) #39)
+#47 := (not #44)
+#78 := (~ #47 #75)
+#56 := (or #5 #55)
+#57 := (forall (vars (?x2 int)) #56)
+#59 := (or #58 #57)
+#60 := (not #59)
+#76 := (~ #60 #75)
+#70 := (not #57)
+#71 := (~ #70 #69)
+#72 := [sk]: #71
+#64 := (~ #63 #63)
+#65 := [refl]: #64
+#77 := [nnf-neg #65 #72]: #76
+#61 := (~ #47 #60)
+#62 := [sk]: #61
+#79 := [trans #62 #77]: #78
+#8 := (or #7 #5)
+#9 := (forall (vars (?x2 int)) #8)
+#10 := (implies #5 #9)
+#11 := (forall (vars (?x1 int)) #10)
+#12 := (not #11)
+#48 := (iff #12 #47)
+#45 := (iff #11 #44)
+#42 := (iff #10 #39)
+#35 := (implies #5 #32)
+#40 := (iff #35 #39)
+#41 := [rewrite]: #40
+#36 := (iff #10 #35)
+#33 := (iff #9 #32)
+#30 := (iff #8 #29)
+#31 := [rewrite]: #30
+#34 := [quant-intro #31]: #33
+#37 := [monotonicity #34]: #36
+#43 := [trans #37 #41]: #42
+#46 := [quant-intro #43]: #45
+#49 := [monotonicity #46]: #48
+#28 := [asserted]: #12
+#52 := [mp #28 #49]: #47
+#80 := [mp~ #52 #79]: #75
+#81 := [mp #80 #93]: #91
+#94 := [and-elim #81]: #88
+#95 := [not-or-elim #94]: #58
+#82 := [and-elim #81]: #55
+[unit-resolution #82 #95]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_fol_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,14 @@
+(benchmark Isabelle
+:extrasorts ( T2 T1)
+:extrafuns (
+ (uf_2 T1)
+ (uf_4 T2)
+ (uf_3 T1)
+ )
+:extrapreds (
+ (up_1 T1 T2)
+ )
+:assumption (forall (?x1 T1) (?x2 T2) (iff (up_1 ?x1 ?x2) (= ?x1 uf_2)))
+:assumption (not (iff (exists (?x3 T2) (up_1 uf_3 ?x3)) (up_1 uf_3 uf_4)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_fol_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,135 @@
+#2 := false
+decl up_1 :: (-> T1 T2 bool)
+#5 := (:var 0 T2)
+decl uf_3 :: T1
+#11 := uf_3
+#12 := (up_1 uf_3 #5)
+#560 := (pattern #12)
+#57 := (not #12)
+#561 := (forall (vars (?x3 T2)) (:pat #560) #57)
+decl uf_4 :: T2
+#14 := uf_4
+#15 := (up_1 uf_3 uf_4)
+decl uf_2 :: T1
+#7 := uf_2
+#136 := (= uf_2 uf_3)
+#543 := (iff #15 #136)
+#4 := (:var 1 T1)
+#6 := (up_1 #4 #5)
+#553 := (pattern #6)
+#8 := (= #4 uf_2)
+#9 := (iff #6 #8)
+#554 := (forall (vars (?x1 T1) (?x2 T2)) (:pat #553) #9)
+#10 := (forall (vars (?x1 T1) (?x2 T2)) #9)
+#557 := (iff #10 #554)
+#555 := (iff #9 #9)
+#556 := [refl]: #555
+#558 := [quant-intro #556]: #557
+#47 := (~ #10 #10)
+#45 := (~ #9 #9)
+#46 := [refl]: #45
+#48 := [nnf-pos #46]: #47
+#33 := [asserted]: #10
+#49 := [mp~ #33 #48]: #10
+#559 := [mp #49 #558]: #554
+#227 := (not #554)
+#185 := (or #227 #543)
+#135 := (= uf_3 uf_2)
+#205 := (iff #15 #135)
+#528 := (or #227 #205)
+#190 := (iff #528 #185)
+#192 := (iff #185 #185)
+#530 := [rewrite]: #192
+#201 := (iff #205 #543)
+#223 := (iff #135 #136)
+#137 := [rewrite]: #223
+#544 := [monotonicity #137]: #201
+#191 := [monotonicity #544]: #190
+#531 := [trans #191 #530]: #190
+#189 := [quant-inst]: #528
+#532 := [mp #189 #531]: #185
+#539 := [unit-resolution #532 #559]: #543
+decl ?x3!0 :: T2
+#50 := ?x3!0
+#51 := (up_1 uf_3 ?x3!0)
+#224 := (iff #51 #136)
+#155 := (or #227 #224)
+#222 := (iff #51 #135)
+#228 := (or #227 #222)
+#229 := (iff #228 #155)
+#545 := (iff #155 #155)
+#547 := [rewrite]: #545
+#215 := (iff #222 #224)
+#226 := [monotonicity #137]: #215
+#208 := [monotonicity #226]: #229
+#202 := [trans #208 #547]: #229
+#225 := [quant-inst]: #228
+#334 := [mp #225 #202]: #155
+#537 := [unit-resolution #334 #559]: #224
+#541 := (not #224)
+#527 := (or #541 #136)
+#63 := (not #15)
+#540 := [hypothesis]: #63
+#68 := (or #15 #51)
+#60 := (forall (vars (?x3 T2)) #57)
+#69 := (or #63 #60)
+#76 := (and #68 #69)
+#70 := (and #69 #68)
+#77 := (iff #70 #76)
+#78 := [rewrite]: #77
+#13 := (exists (vars (?x3 T2)) #12)
+#35 := (not #13)
+#36 := (iff #15 #35)
+#71 := (~ #36 #70)
+#61 := (~ #35 #60)
+#58 := (~ #57 #57)
+#59 := [refl]: #58
+#62 := [nnf-neg #59]: #61
+#54 := (not #35)
+#55 := (~ #54 #51)
+#42 := (~ #13 #51)
+#39 := [sk]: #42
+#56 := [nnf-neg #39]: #55
+#66 := (~ #15 #15)
+#67 := [refl]: #66
+#64 := (~ #63 #63)
+#65 := [refl]: #64
+#72 := [nnf-pos #65 #67 #56 #62]: #71
+#16 := (iff #13 #15)
+#17 := (not #16)
+#37 := (iff #17 #36)
+#38 := [rewrite]: #37
+#34 := [asserted]: #17
+#41 := [mp #34 #38]: #36
+#73 := [mp~ #41 #72]: #70
+#74 := [mp #73 #78]: #76
+#75 := [and-elim #74]: #68
+#526 := [unit-resolution #75 #540]: #51
+#549 := (not #51)
+#550 := (or #541 #549 #136)
+#551 := [def-axiom]: #550
+#233 := [unit-resolution #551 #526]: #527
+#249 := [unit-resolution #233 #537]: #136
+#213 := (not #136)
+#533 := (not #543)
+#250 := (or #533 #213)
+#534 := (or #533 #15 #213)
+#529 := [def-axiom]: #534
+#251 := [unit-resolution #529 #540]: #250
+#237 := [unit-resolution #251 #249 #539]: false
+#252 := [lemma #237]: #15
+#566 := (or #63 #561)
+#567 := (iff #69 #566)
+#564 := (iff #60 #561)
+#562 := (iff #57 #57)
+#563 := [refl]: #562
+#565 := [quant-intro #563]: #564
+#568 := [monotonicity #565]: #567
+#79 := [and-elim #74]: #69
+#569 := [mp #79 #568]: #566
+#535 := [unit-resolution #569 #252]: #561
+#536 := (not #561)
+#538 := (or #536 #63)
+#176 := [quant-inst]: #538
+[unit-resolution #176 #252 #535]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_fol_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,15 @@
+(benchmark Isabelle
+:extrasorts ( T2 T1)
+:extrafuns (
+ (uf_2 T1)
+ (uf_3 T2)
+ (uf_4 T1)
+ )
+:extrapreds (
+ (up_1 T1 T2)
+ )
+:assumption (forall (?x1 T1) (?x2 T2) (iff (up_1 ?x1 ?x2) (= ?x1 uf_2)))
+:assumption (iff (forall (?x3 T1) (exists (?x4 T2) (up_1 ?x3 ?x4))) (forall (?x5 T1) (up_1 ?x5 uf_3)))
+:assumption (not (iff (exists (?x6 T2) (up_1 uf_4 ?x6)) (up_1 uf_4 uf_3)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_fol_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,135 @@
+#2 := false
+decl up_1 :: (-> T1 T2 bool)
+#5 := (:var 0 T2)
+decl uf_4 :: T1
+#18 := uf_4
+#19 := (up_1 uf_4 #5)
+#635 := (pattern #19)
+#116 := (not #19)
+#636 := (forall (vars (?x6 T2)) (:pat #635) #116)
+decl uf_3 :: T2
+#14 := uf_3
+#21 := (up_1 uf_4 uf_3)
+decl uf_2 :: T1
+#7 := uf_2
+#195 := (= uf_2 uf_4)
+#602 := (iff #21 #195)
+#4 := (:var 1 T1)
+#6 := (up_1 #4 #5)
+#612 := (pattern #6)
+#8 := (= #4 uf_2)
+#9 := (iff #6 #8)
+#613 := (forall (vars (?x1 T1) (?x2 T2)) (:pat #612) #9)
+#10 := (forall (vars (?x1 T1) (?x2 T2)) #9)
+#616 := (iff #10 #613)
+#614 := (iff #9 #9)
+#615 := [refl]: #614
+#617 := [quant-intro #615]: #616
+#56 := (~ #10 #10)
+#54 := (~ #9 #9)
+#55 := [refl]: #54
+#57 := [nnf-pos #55]: #56
+#39 := [asserted]: #10
+#58 := [mp~ #39 #57]: #10
+#618 := [mp #58 #617]: #613
+#286 := (not #613)
+#244 := (or #286 #602)
+#194 := (= uf_4 uf_2)
+#264 := (iff #21 #194)
+#587 := (or #286 #264)
+#249 := (iff #587 #244)
+#251 := (iff #244 #244)
+#589 := [rewrite]: #251
+#260 := (iff #264 #602)
+#282 := (iff #194 #195)
+#196 := [rewrite]: #282
+#603 := [monotonicity #196]: #260
+#250 := [monotonicity #603]: #249
+#590 := [trans #250 #589]: #249
+#248 := [quant-inst]: #587
+#591 := [mp #248 #590]: #244
+#598 := [unit-resolution #591 #618]: #602
+decl ?x6!3 :: T2
+#63 := ?x6!3
+#64 := (up_1 uf_4 ?x6!3)
+#283 := (iff #64 #195)
+#214 := (or #286 #283)
+#281 := (iff #64 #194)
+#287 := (or #286 #281)
+#288 := (iff #287 #214)
+#604 := (iff #214 #214)
+#606 := [rewrite]: #604
+#274 := (iff #281 #283)
+#285 := [monotonicity #196]: #274
+#267 := [monotonicity #285]: #288
+#261 := [trans #267 #606]: #288
+#284 := [quant-inst]: #287
+#393 := [mp #284 #261]: #214
+#596 := [unit-resolution #393 #618]: #283
+#600 := (not #283)
+#586 := (or #600 #195)
+#122 := (not #21)
+#599 := [hypothesis]: #122
+#127 := (or #21 #64)
+#119 := (forall (vars (?x6 T2)) #116)
+#128 := (or #122 #119)
+#135 := (and #127 #128)
+#129 := (and #128 #127)
+#136 := (iff #129 #135)
+#137 := [rewrite]: #136
+#20 := (exists (vars (?x6 T2)) #19)
+#42 := (not #20)
+#43 := (iff #21 #42)
+#130 := (~ #43 #129)
+#120 := (~ #42 #119)
+#117 := (~ #116 #116)
+#118 := [refl]: #117
+#121 := [nnf-neg #118]: #120
+#113 := (not #42)
+#114 := (~ #113 #64)
+#88 := (~ #20 #64)
+#89 := [sk]: #88
+#115 := [nnf-neg #89]: #114
+#125 := (~ #21 #21)
+#126 := [refl]: #125
+#123 := (~ #122 #122)
+#124 := [refl]: #123
+#131 := [nnf-pos #124 #126 #115 #121]: #130
+#22 := (iff #20 #21)
+#23 := (not #22)
+#44 := (iff #23 #43)
+#45 := [rewrite]: #44
+#41 := [asserted]: #23
+#48 := [mp #41 #45]: #43
+#132 := [mp~ #48 #131]: #129
+#133 := [mp #132 #137]: #135
+#134 := [and-elim #133]: #127
+#585 := [unit-resolution #134 #599]: #64
+#608 := (not #64)
+#609 := (or #600 #608 #195)
+#610 := [def-axiom]: #609
+#292 := [unit-resolution #610 #585]: #586
+#308 := [unit-resolution #292 #596]: #195
+#272 := (not #195)
+#592 := (not #602)
+#309 := (or #592 #272)
+#593 := (or #592 #21 #272)
+#588 := [def-axiom]: #593
+#310 := [unit-resolution #588 #599]: #309
+#296 := [unit-resolution #310 #308 #598]: false
+#311 := [lemma #296]: #21
+#641 := (or #122 #636)
+#642 := (iff #128 #641)
+#639 := (iff #119 #636)
+#637 := (iff #116 #116)
+#638 := [refl]: #637
+#640 := [quant-intro #638]: #639
+#643 := [monotonicity #640]: #642
+#138 := [and-elim #133]: #128
+#644 := [mp #138 #643]: #641
+#594 := [unit-resolution #644 #311]: #636
+#595 := (not #636)
+#597 := (or #595 #122)
+#235 := [quant-inst]: #597
+[unit-resolution #235 #311 #594]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_fol_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T1 T2)
+:extrafuns (
+ (uf_2 T1)
+ (uf_3 T1)
+ )
+:extrapreds (
+ (up_1 T1)
+ )
+:assumption (if_then_else (up_1 uf_2) (not (exists (?x1 T1) (up_1 ?x1))) (forall (?x2 T1) (not (up_1 ?x2))))
+:assumption (not (implies (up_1 uf_2) (up_1 uf_3)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_fol_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,56 @@
+#2 := false
+decl up_1 :: (-> T1 bool)
+decl uf_2 :: T1
+#4 := uf_2
+#5 := (up_1 uf_2)
+decl uf_3 :: T1
+#13 := uf_3
+#14 := (up_1 uf_3)
+#34 := (not #5)
+#35 := (or #34 #14)
+#38 := (not #35)
+#15 := (implies #5 #14)
+#16 := (not #15)
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#33 := [asserted]: #16
+#43 := [mp #33 #40]: #38
+#41 := [not-or-elim #43]: #5
+#6 := (:var 0 T1)
+#7 := (up_1 #6)
+#536 := (pattern #7)
+#10 := (not #7)
+#537 := (forall (vars (?x2 T1)) (:pat #536) #10)
+#11 := (forall (vars (?x2 T1)) #10)
+#540 := (iff #11 #537)
+#538 := (iff #10 #10)
+#539 := [refl]: #538
+#541 := [quant-intro #539]: #540
+#8 := (exists (vars (?x1 T1)) #7)
+#9 := (not #8)
+#45 := (~ #9 #11)
+#50 := (~ #10 #10)
+#51 := [refl]: #50
+#59 := [nnf-neg #51]: #45
+#12 := (ite #5 #9 #11)
+#57 := (iff #12 #9)
+#1 := true
+#52 := (ite true #9 #11)
+#55 := (iff #52 #9)
+#56 := [rewrite]: #55
+#53 := (iff #12 #52)
+#48 := (iff #5 true)
+#49 := [iff-true #41]: #48
+#54 := [monotonicity #49]: #53
+#58 := [trans #54 #56]: #57
+#32 := [asserted]: #12
+#47 := [mp #32 #58]: #9
+#60 := [mp~ #47 #59]: #11
+#542 := [mp #60 #541]: #537
+#119 := (not #537)
+#206 := (or #119 #34)
+#120 := [quant-inst]: #206
+[unit-resolution #120 #542 #41]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,18 @@
+(benchmark Isabelle
+:extrasorts ( T2 T3 T1)
+:extrafuns (
+ (uf_2 T1 T2 T3 T1)
+ (uf_1 T1 T2 T3)
+ (uf_6 T1)
+ (uf_3 T2)
+ (uf_4 T2)
+ (uf_5 T2)
+ (uf_7 T3)
+ (uf_8 T3)
+ )
+:assumption (forall (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2) (= (uf_1 (uf_2 ?x1 ?x2 ?x3) ?x4) (ite (= ?x4 ?x2) ?x3 (uf_1 ?x1 ?x4))))
+:assumption (forall (?x5 T1) (?x6 T2) (?x7 T3) (= (uf_1 (uf_2 ?x5 ?x6 ?x7) ?x6) ?x7))
+:assumption (and (not (= uf_3 uf_4)) (not (= uf_3 uf_5)))
+:assumption (not (= (uf_1 (uf_2 (uf_2 uf_6 uf_4 uf_7) uf_5 uf_8) uf_3) (uf_1 uf_6 uf_3)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,181 @@
+#2 := false
+decl uf_1 :: (-> T1 T2 T3)
+decl uf_3 :: T2
+#22 := uf_3
+decl uf_6 :: T1
+#30 := uf_6
+#36 := (uf_1 uf_6 uf_3)
+decl uf_2 :: (-> T1 T2 T3 T1)
+decl uf_8 :: T3
+#33 := uf_8
+decl uf_5 :: T2
+#26 := uf_5
+decl uf_7 :: T3
+#31 := uf_7
+decl uf_4 :: T2
+#23 := uf_4
+#32 := (uf_2 uf_6 uf_4 uf_7)
+#34 := (uf_2 #32 uf_5 uf_8)
+#35 := (uf_1 #34 uf_3)
+#37 := (= #35 #36)
+#223 := (uf_1 #32 uf_4)
+#214 := (uf_2 uf_6 uf_4 #223)
+#552 := (uf_1 #214 uf_3)
+#555 := (= #552 #36)
+#560 := (= #36 #552)
+#556 := (= #223 #552)
+#24 := (= uf_3 uf_4)
+#561 := (ite #24 #556 #560)
+#8 := (:var 0 T2)
+#6 := (:var 1 T3)
+#5 := (:var 2 T2)
+#4 := (:var 3 T1)
+#7 := (uf_2 #4 #5 #6)
+#9 := (uf_1 #7 #8)
+#575 := (pattern #9)
+#11 := (uf_1 #4 #8)
+#100 := (= #9 #11)
+#99 := (= #6 #9)
+#55 := (= #5 #8)
+#83 := (ite #55 #99 #100)
+#576 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2)) (:pat #575) #83)
+#90 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2)) #83)
+#579 := (iff #90 #576)
+#577 := (iff #83 #83)
+#578 := [refl]: #577
+#580 := [quant-intro #578]: #579
+#58 := (ite #55 #6 #11)
+#61 := (= #9 #58)
+#64 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2)) #61)
+#87 := (iff #64 #90)
+#84 := (iff #61 #83)
+#89 := [rewrite]: #84
+#88 := [quant-intro #89]: #87
+#93 := (~ #64 #64)
+#91 := (~ #61 #61)
+#92 := [refl]: #91
+#94 := [nnf-pos #92]: #93
+#10 := (= #8 #5)
+#12 := (ite #10 #6 #11)
+#13 := (= #9 #12)
+#14 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2)) #13)
+#65 := (iff #14 #64)
+#62 := (iff #13 #61)
+#59 := (= #12 #58)
+#56 := (iff #10 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#66 := [quant-intro #63]: #65
+#54 := [asserted]: #14
+#69 := [mp #54 #66]: #64
+#95 := [mp~ #69 #94]: #64
+#85 := [mp #95 #88]: #90
+#581 := [mp #85 #580]: #576
+#250 := (not #576)
+#548 := (or #250 #561)
+#551 := (= uf_4 uf_3)
+#557 := (ite #551 #556 #555)
+#549 := (or #250 #557)
+#271 := (iff #549 #548)
+#273 := (iff #548 #548)
+#259 := [rewrite]: #273
+#559 := (iff #557 #561)
+#198 := (iff #555 #560)
+#199 := [rewrite]: #198
+#193 := (iff #551 #24)
+#558 := [rewrite]: #193
+#562 := [monotonicity #558 #199]: #559
+#272 := [monotonicity #562]: #271
+#274 := [trans #272 #259]: #271
+#255 := [quant-inst]: #549
+#165 := [mp #255 #274]: #548
+#510 := [unit-resolution #165 #581]: #561
+#544 := (not #561)
+#497 := (or #544 #560)
+#25 := (not #24)
+#27 := (= uf_3 uf_5)
+#28 := (not #27)
+#29 := (and #25 #28)
+#75 := [asserted]: #29
+#79 := [and-elim #75]: #25
+#268 := (or #544 #24 #560)
+#542 := [def-axiom]: #268
+#499 := [unit-resolution #542 #79]: #497
+#491 := [unit-resolution #499 #510]: #560
+#493 := [symm #491]: #555
+#494 := (= #35 #552)
+#157 := (uf_1 #32 uf_3)
+#503 := (= #157 #552)
+#502 := (= #552 #157)
+#509 := (= #214 #32)
+#415 := (= #223 uf_7)
+#566 := (= uf_7 #223)
+#17 := (:var 0 T3)
+#16 := (:var 1 T2)
+#15 := (:var 2 T1)
+#18 := (uf_2 #15 #16 #17)
+#582 := (pattern #18)
+#19 := (uf_1 #18 #16)
+#68 := (= #17 #19)
+#584 := (forall (vars (?x5 T1) (?x6 T2) (?x7 T3)) (:pat #582) #68)
+#72 := (forall (vars (?x5 T1) (?x6 T2) (?x7 T3)) #68)
+#583 := (iff #72 #584)
+#586 := (iff #584 #584)
+#587 := [rewrite]: #586
+#585 := [rewrite]: #583
+#588 := [trans #585 #587]: #583
+#82 := (~ #72 #72)
+#96 := (~ #68 #68)
+#97 := [refl]: #96
+#78 := [nnf-pos #97]: #82
+#20 := (= #19 #17)
+#21 := (forall (vars (?x5 T1) (?x6 T2) (?x7 T3)) #20)
+#73 := (iff #21 #72)
+#70 := (iff #20 #68)
+#71 := [rewrite]: #70
+#74 := [quant-intro #71]: #73
+#67 := [asserted]: #21
+#77 := [mp #67 #74]: #72
+#98 := [mp~ #77 #78]: #72
+#589 := [mp #98 #588]: #584
+#211 := (not #584)
+#212 := (or #211 #566)
+#213 := [quant-inst]: #212
+#414 := [unit-resolution #213 #589]: #566
+#416 := [symm #414]: #415
+#506 := [monotonicity #416]: #509
+#498 := [monotonicity #506]: #502
+#492 := [symm #498]: #503
+#244 := (= #35 #157)
+#158 := (= uf_8 #35)
+#248 := (ite #27 #158 #244)
+#247 := (or #250 #248)
+#245 := (= uf_5 uf_3)
+#159 := (ite #245 #158 #244)
+#251 := (or #250 #159)
+#567 := (iff #251 #247)
+#224 := (iff #247 #247)
+#356 := [rewrite]: #224
+#249 := (iff #159 #248)
+#246 := (iff #245 #27)
+#237 := [rewrite]: #246
+#177 := [monotonicity #237]: #249
+#569 := [monotonicity #177]: #567
+#563 := [trans #569 #356]: #567
+#230 := [quant-inst]: #251
+#235 := [mp #230 #563]: #247
+#488 := [unit-resolution #235 #581]: #248
+#236 := (not #248)
+#490 := (or #236 #244)
+#80 := [and-elim #75]: #28
+#572 := (or #236 #27 #244)
+#573 := [def-axiom]: #572
+#500 := [unit-resolution #573 #80]: #490
+#501 := [unit-resolution #500 #488]: #244
+#495 := [trans #501 #492]: #494
+#489 := [trans #495 #493]: #37
+#38 := (not #37)
+#76 := [asserted]: #38
+[unit-resolution #76 #489]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T2 T1 T3)
+:extrafuns (
+ (uf_2 T1)
+ (uf_3 T2)
+ )
+:extrapreds (
+ (up_4 T1 T2)
+ (up_1 T1 T2)
+ )
+:assumption (not (or (iff (up_1 uf_2 uf_3) (and (up_4 uf_2 uf_3) true)) (or (iff (up_1 uf_2 uf_3) true) (iff (up_4 uf_2 uf_3) true))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,62 @@
+#2 := false
+decl up_4 :: (-> T1 T2 bool)
+decl uf_3 :: T2
+#5 := uf_3
+decl uf_2 :: T1
+#4 := uf_2
+#7 := (up_4 uf_2 uf_3)
+#60 := (not #7)
+decl up_1 :: (-> T1 T2 bool)
+#6 := (up_1 uf_2 uf_3)
+#33 := (iff #6 #7)
+#49 := (or #6 #7 #33)
+#52 := (not #49)
+#1 := true
+#11 := (iff #7 true)
+#10 := (iff #6 true)
+#12 := (or #10 #11)
+#8 := (and #7 true)
+#9 := (iff #6 #8)
+#13 := (or #9 #12)
+#14 := (not #13)
+#55 := (iff #14 #52)
+#40 := (or #6 #7)
+#43 := (or #33 #40)
+#46 := (not #43)
+#53 := (iff #46 #52)
+#50 := (iff #43 #49)
+#51 := [rewrite]: #50
+#54 := [monotonicity #51]: #53
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#41 := (iff #12 #40)
+#38 := (iff #11 #7)
+#39 := [rewrite]: #38
+#36 := (iff #10 #6)
+#37 := [rewrite]: #36
+#42 := [monotonicity #37 #39]: #41
+#34 := (iff #9 #33)
+#31 := (iff #8 #7)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#45 := [monotonicity #35 #42]: #44
+#48 := [monotonicity #45]: #47
+#56 := [trans #48 #54]: #55
+#30 := [asserted]: #14
+#57 := [mp #30 #56]: #52
+#61 := [not-or-elim #57]: #60
+#58 := (not #6)
+#59 := [not-or-elim #57]: #58
+#72 := (or #7 #6)
+#66 := (iff #7 #58)
+#62 := (not #33)
+#64 := (iff #62 #66)
+#67 := [rewrite]: #64
+#63 := [not-or-elim #57]: #62
+#68 := [mp #63 #67]: #66
+#69 := (not #66)
+#70 := (or #7 #6 #69)
+#71 := [def-axiom]: #70
+#73 := [unit-resolution #71 #68]: #72
+[unit-resolution #73 #59 #61]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T1 T2)
+:extrafuns (
+ (uf_3 T2)
+ (uf_1 T1 T1)
+ (uf_2 T2 T2)
+ (uf_4 T1)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 ?x1) ?x1))
+:assumption (forall (?x2 T2) (iff (= (uf_2 ?x2) uf_3) (= ?x2 uf_3)))
+:assumption (not (and (= (uf_1 uf_4) uf_4) (iff (= (uf_2 uf_3) uf_3) true)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,120 @@
+#2 := false
+decl uf_1 :: (-> T1 T1)
+decl uf_4 :: T1
+#15 := uf_4
+#16 := (uf_1 uf_4)
+#48 := (= uf_4 #16)
+#83 := (not #48)
+decl uf_2 :: (-> T2 T2)
+decl uf_3 :: T2
+#10 := uf_3
+#18 := (uf_2 uf_3)
+#51 := (= uf_3 #18)
+#84 := (not #51)
+#556 := [hypothesis]: #84
+#8 := (:var 0 T2)
+#9 := (uf_2 #8)
+#575 := (pattern #9)
+#12 := (= #8 uf_3)
+#11 := (= #9 uf_3)
+#13 := (iff #11 #12)
+#576 := (forall (vars (?x2 T2)) (:pat #575) #13)
+#14 := (forall (vars (?x2 T2)) #13)
+#579 := (iff #14 #576)
+#577 := (iff #13 #13)
+#578 := [refl]: #577
+#580 := [quant-intro #578]: #579
+#70 := (~ #14 #14)
+#80 := (~ #13 #13)
+#81 := [refl]: #80
+#67 := [nnf-pos #81]: #70
+#45 := [asserted]: #14
+#82 := [mp~ #45 #67]: #14
+#581 := [mp #82 #580]: #576
+#242 := (not #576)
+#170 := (or #242 #51)
+#150 := (= uf_3 uf_3)
+#19 := (= #18 uf_3)
+#237 := (iff #19 #150)
+#243 := (or #242 #237)
+#244 := (iff #243 #170)
+#560 := (iff #170 #170)
+#562 := [rewrite]: #560
+#230 := (iff #237 #51)
+#1 := true
+#54 := (iff #51 true)
+#57 := (iff #54 #51)
+#58 := [rewrite]: #57
+#152 := (iff #237 #54)
+#151 := (iff #150 true)
+#238 := [rewrite]: #151
+#52 := (iff #19 #51)
+#53 := [rewrite]: #52
+#239 := [monotonicity #53 #238]: #152
+#241 := [trans #239 #58]: #230
+#223 := [monotonicity #241]: #244
+#217 := [trans #223 #562]: #244
+#240 := [quant-inst]: #243
+#349 := [mp #240 #217]: #170
+#228 := [unit-resolution #349 #581 #556]: false
+#229 := [lemma #228]: #51
+#71 := (or #83 #84)
+#61 := (and #48 #51)
+#64 := (not #61)
+#90 := (iff #64 #71)
+#72 := (not #71)
+#85 := (not #72)
+#88 := (iff #85 #71)
+#89 := [rewrite]: #88
+#86 := (iff #64 #85)
+#73 := (iff #61 #72)
+#74 := [rewrite]: #73
+#87 := [monotonicity #74]: #86
+#91 := [trans #87 #89]: #90
+#20 := (iff #19 true)
+#17 := (= #16 uf_4)
+#21 := (and #17 #20)
+#22 := (not #21)
+#65 := (iff #22 #64)
+#62 := (iff #21 #61)
+#59 := (iff #20 #51)
+#55 := (iff #20 #54)
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#49 := (iff #17 #48)
+#50 := [rewrite]: #49
+#63 := [monotonicity #50 #60]: #62
+#66 := [monotonicity #63]: #65
+#46 := [asserted]: #22
+#69 := [mp #46 #66]: #64
+#92 := [mp #69 #91]: #71
+#563 := [unit-resolution #92 #229]: #83
+#4 := (:var 0 T1)
+#5 := (uf_1 #4)
+#568 := (pattern #5)
+#39 := (= #4 #5)
+#569 := (forall (vars (?x1 T1)) (:pat #568) #39)
+#42 := (forall (vars (?x1 T1)) #39)
+#572 := (iff #42 #569)
+#570 := (iff #39 #39)
+#571 := [refl]: #570
+#573 := [quant-intro #571]: #572
+#77 := (~ #42 #42)
+#75 := (~ #39 #39)
+#76 := [refl]: #75
+#78 := [nnf-pos #76]: #77
+#6 := (= #5 #4)
+#7 := (forall (vars (?x1 T1)) #6)
+#43 := (iff #7 #42)
+#40 := (iff #6 #39)
+#41 := [rewrite]: #40
+#44 := [quant-intro #41]: #43
+#38 := [asserted]: #7
+#47 := [mp #38 #44]: #42
+#79 := [mp~ #47 #78]: #42
+#574 := [mp #79 #573]: #569
+#565 := (not #569)
+#566 := (or #565 #48)
+#561 := [quant-inst]: #566
+[unit-resolution #561 #574 #563]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,18 @@
+(benchmark Isabelle
+:extrasorts ( T2 T3 T1)
+:extrafuns (
+ (uf_2 T1 T2 T3 T1)
+ (uf_1 T1 T2 T3)
+ (uf_6 T1)
+ (uf_3 T2)
+ (uf_4 T2)
+ (uf_5 T2)
+ (uf_7 T3)
+ (uf_8 T3)
+ )
+:assumption (forall (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2) (= (uf_1 (uf_2 ?x1 ?x2 ?x3) ?x4) (ite (= ?x4 ?x2) ?x3 (uf_1 ?x1 ?x4))))
+:assumption (forall (?x5 T1) (?x6 T2) (?x7 T3) (= (uf_1 (uf_2 ?x5 ?x6 ?x7) ?x6) ?x7))
+:assumption (and (not (= uf_3 uf_4)) (not (= uf_3 uf_5)))
+:assumption (not (= (uf_1 (uf_2 (uf_2 uf_6 uf_4 uf_7) uf_5 uf_8) uf_3) (uf_1 uf_6 uf_3)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,181 @@
+#2 := false
+decl uf_1 :: (-> T1 T2 T3)
+decl uf_3 :: T2
+#22 := uf_3
+decl uf_6 :: T1
+#30 := uf_6
+#36 := (uf_1 uf_6 uf_3)
+decl uf_2 :: (-> T1 T2 T3 T1)
+decl uf_8 :: T3
+#33 := uf_8
+decl uf_5 :: T2
+#26 := uf_5
+decl uf_7 :: T3
+#31 := uf_7
+decl uf_4 :: T2
+#23 := uf_4
+#32 := (uf_2 uf_6 uf_4 uf_7)
+#34 := (uf_2 #32 uf_5 uf_8)
+#35 := (uf_1 #34 uf_3)
+#37 := (= #35 #36)
+#223 := (uf_1 #32 uf_4)
+#214 := (uf_2 uf_6 uf_4 #223)
+#552 := (uf_1 #214 uf_3)
+#555 := (= #552 #36)
+#560 := (= #36 #552)
+#556 := (= #223 #552)
+#24 := (= uf_3 uf_4)
+#561 := (ite #24 #556 #560)
+#8 := (:var 0 T2)
+#6 := (:var 1 T3)
+#5 := (:var 2 T2)
+#4 := (:var 3 T1)
+#7 := (uf_2 #4 #5 #6)
+#9 := (uf_1 #7 #8)
+#575 := (pattern #9)
+#11 := (uf_1 #4 #8)
+#100 := (= #9 #11)
+#99 := (= #6 #9)
+#55 := (= #5 #8)
+#83 := (ite #55 #99 #100)
+#576 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2)) (:pat #575) #83)
+#90 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2)) #83)
+#579 := (iff #90 #576)
+#577 := (iff #83 #83)
+#578 := [refl]: #577
+#580 := [quant-intro #578]: #579
+#58 := (ite #55 #6 #11)
+#61 := (= #9 #58)
+#64 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2)) #61)
+#87 := (iff #64 #90)
+#84 := (iff #61 #83)
+#89 := [rewrite]: #84
+#88 := [quant-intro #89]: #87
+#93 := (~ #64 #64)
+#91 := (~ #61 #61)
+#92 := [refl]: #91
+#94 := [nnf-pos #92]: #93
+#10 := (= #8 #5)
+#12 := (ite #10 #6 #11)
+#13 := (= #9 #12)
+#14 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3) (?x4 T2)) #13)
+#65 := (iff #14 #64)
+#62 := (iff #13 #61)
+#59 := (= #12 #58)
+#56 := (iff #10 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#66 := [quant-intro #63]: #65
+#54 := [asserted]: #14
+#69 := [mp #54 #66]: #64
+#95 := [mp~ #69 #94]: #64
+#85 := [mp #95 #88]: #90
+#581 := [mp #85 #580]: #576
+#250 := (not #576)
+#548 := (or #250 #561)
+#551 := (= uf_4 uf_3)
+#557 := (ite #551 #556 #555)
+#549 := (or #250 #557)
+#271 := (iff #549 #548)
+#273 := (iff #548 #548)
+#259 := [rewrite]: #273
+#559 := (iff #557 #561)
+#198 := (iff #555 #560)
+#199 := [rewrite]: #198
+#193 := (iff #551 #24)
+#558 := [rewrite]: #193
+#562 := [monotonicity #558 #199]: #559
+#272 := [monotonicity #562]: #271
+#274 := [trans #272 #259]: #271
+#255 := [quant-inst]: #549
+#165 := [mp #255 #274]: #548
+#510 := [unit-resolution #165 #581]: #561
+#544 := (not #561)
+#497 := (or #544 #560)
+#25 := (not #24)
+#27 := (= uf_3 uf_5)
+#28 := (not #27)
+#29 := (and #25 #28)
+#75 := [asserted]: #29
+#79 := [and-elim #75]: #25
+#268 := (or #544 #24 #560)
+#542 := [def-axiom]: #268
+#499 := [unit-resolution #542 #79]: #497
+#491 := [unit-resolution #499 #510]: #560
+#493 := [symm #491]: #555
+#494 := (= #35 #552)
+#157 := (uf_1 #32 uf_3)
+#503 := (= #157 #552)
+#502 := (= #552 #157)
+#509 := (= #214 #32)
+#415 := (= #223 uf_7)
+#566 := (= uf_7 #223)
+#17 := (:var 0 T3)
+#16 := (:var 1 T2)
+#15 := (:var 2 T1)
+#18 := (uf_2 #15 #16 #17)
+#582 := (pattern #18)
+#19 := (uf_1 #18 #16)
+#68 := (= #17 #19)
+#584 := (forall (vars (?x5 T1) (?x6 T2) (?x7 T3)) (:pat #582) #68)
+#72 := (forall (vars (?x5 T1) (?x6 T2) (?x7 T3)) #68)
+#583 := (iff #72 #584)
+#586 := (iff #584 #584)
+#587 := [rewrite]: #586
+#585 := [rewrite]: #583
+#588 := [trans #585 #587]: #583
+#82 := (~ #72 #72)
+#96 := (~ #68 #68)
+#97 := [refl]: #96
+#78 := [nnf-pos #97]: #82
+#20 := (= #19 #17)
+#21 := (forall (vars (?x5 T1) (?x6 T2) (?x7 T3)) #20)
+#73 := (iff #21 #72)
+#70 := (iff #20 #68)
+#71 := [rewrite]: #70
+#74 := [quant-intro #71]: #73
+#67 := [asserted]: #21
+#77 := [mp #67 #74]: #72
+#98 := [mp~ #77 #78]: #72
+#589 := [mp #98 #588]: #584
+#211 := (not #584)
+#212 := (or #211 #566)
+#213 := [quant-inst]: #212
+#414 := [unit-resolution #213 #589]: #566
+#416 := [symm #414]: #415
+#506 := [monotonicity #416]: #509
+#498 := [monotonicity #506]: #502
+#492 := [symm #498]: #503
+#244 := (= #35 #157)
+#158 := (= uf_8 #35)
+#248 := (ite #27 #158 #244)
+#247 := (or #250 #248)
+#245 := (= uf_5 uf_3)
+#159 := (ite #245 #158 #244)
+#251 := (or #250 #159)
+#567 := (iff #251 #247)
+#224 := (iff #247 #247)
+#356 := [rewrite]: #224
+#249 := (iff #159 #248)
+#246 := (iff #245 #27)
+#237 := [rewrite]: #246
+#177 := [monotonicity #237]: #249
+#569 := [monotonicity #177]: #567
+#563 := [trans #569 #356]: #567
+#230 := [quant-inst]: #251
+#235 := [mp #230 #563]: #247
+#488 := [unit-resolution #235 #581]: #248
+#236 := (not #248)
+#490 := (or #236 #244)
+#80 := [and-elim #75]: #28
+#572 := (or #236 #27 #244)
+#573 := [def-axiom]: #572
+#500 := [unit-resolution #573 #80]: #490
+#501 := [unit-resolution #500 #488]: #244
+#495 := [trans #501 #492]: #494
+#489 := [trans #495 #493]: #37
+#38 := (not #37)
+#76 := [asserted]: #38
+[unit-resolution #76 #489]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_05 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,20 @@
+(benchmark Isabelle
+:extrasorts ( T1 T2 T3)
+:extrafuns (
+ (uf_6 Int T2)
+ (uf_1 T1 T3 T3)
+ (uf_4 T3)
+ (uf_2 T2 T3 T3)
+ (uf_3 T1 T2 T2)
+ (uf_7 T2 Int)
+ (uf_5 T1)
+ )
+:assumption (forall (?x1 T1) (?x2 T2) (?x3 T3) (= (uf_1 ?x1 (uf_2 ?x2 ?x3)) (uf_2 (uf_3 ?x1 ?x2) (uf_1 ?x1 ?x3))))
+:assumption (forall (?x4 T1) (= (uf_1 ?x4 uf_4) uf_4))
+:assumption (forall (?x5 T2) (= (uf_3 uf_5 ?x5) (uf_6 (+ (uf_7 ?x5) 1))))
+:assumption (forall (?x6 T2) (= (uf_6 (uf_7 ?x6)) ?x6))
+:assumption (forall (?x7 Int) (implies (<= 0 ?x7) (= (uf_7 (uf_6 ?x7)) ?x7)))
+:assumption (forall (?x8 Int) (implies (< ?x8 0) (= (uf_7 (uf_6 ?x8)) 0)))
+:assumption (not (= (uf_1 uf_5 (uf_2 (uf_6 0) (uf_2 (uf_6 1) uf_4))) (uf_2 (uf_6 1) (uf_2 (uf_6 2) uf_4))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_05.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,464 @@
+#2 := false
+decl uf_2 :: (-> T2 T3 T3)
+decl uf_4 :: T3
+#15 := uf_4
+decl uf_6 :: (-> int T2)
+#48 := 2::int
+#49 := (uf_6 2::int)
+#50 := (uf_2 #49 uf_4)
+#23 := 1::int
+#44 := (uf_6 1::int)
+#51 := (uf_2 #44 #50)
+decl uf_1 :: (-> T1 T3 T3)
+#45 := (uf_2 #44 uf_4)
+#31 := 0::int
+#43 := (uf_6 0::int)
+#46 := (uf_2 #43 #45)
+decl uf_5 :: T1
+#19 := uf_5
+#47 := (uf_1 uf_5 #46)
+#52 := (= #47 #51)
+#266 := (uf_1 uf_5 #45)
+decl uf_3 :: (-> T1 T2 T2)
+#352 := (uf_3 uf_5 #43)
+#267 := (uf_2 #352 #266)
+#797 := (= #267 #51)
+#795 := (= #51 #267)
+#758 := (= #50 #266)
+#521 := (uf_1 uf_5 uf_4)
+#522 := (uf_3 uf_5 #44)
+#523 := (uf_2 #522 #521)
+#756 := (= #523 #266)
+#616 := (= #266 #523)
+#6 := (:var 0 T3)
+#4 := (:var 2 T1)
+#10 := (uf_1 #4 #6)
+#5 := (:var 1 T2)
+#9 := (uf_3 #4 #5)
+#11 := (uf_2 #9 #10)
+#683 := (pattern #11)
+#7 := (uf_2 #5 #6)
+#8 := (uf_1 #4 #7)
+#682 := (pattern #8)
+#12 := (= #8 #11)
+#684 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3)) (:pat #682 #683) #12)
+#13 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3)) #12)
+#687 := (iff #13 #684)
+#685 := (iff #12 #12)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#195 := (~ #13 #13)
+#193 := (~ #12 #12)
+#194 := [refl]: #193
+#196 := [nnf-pos #194]: #195
+#69 := [asserted]: #13
+#197 := [mp~ #69 #196]: #13
+#689 := [mp #197 #688]: #684
+#345 := (not #684)
+#604 := (or #345 #616)
+#606 := [quant-inst]: #604
+#277 := [unit-resolution #606 #689]: #616
+#757 := [symm #277]: #756
+#754 := (= #50 #523)
+#569 := (= uf_4 #521)
+#14 := (:var 0 T1)
+#16 := (uf_1 #14 uf_4)
+#690 := (pattern #16)
+#71 := (= uf_4 #16)
+#691 := (forall (vars (?x4 T1)) (:pat #690) #71)
+#74 := (forall (vars (?x4 T1)) #71)
+#694 := (iff #74 #691)
+#692 := (iff #71 #71)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#180 := (~ #74 #74)
+#198 := (~ #71 #71)
+#199 := [refl]: #198
+#178 := [nnf-pos #199]: #180
+#17 := (= #16 uf_4)
+#18 := (forall (vars (?x4 T1)) #17)
+#75 := (iff #18 #74)
+#72 := (iff #17 #71)
+#73 := [rewrite]: #72
+#76 := [quant-intro #73]: #75
+#70 := [asserted]: #18
+#79 := [mp #70 #76]: #74
+#200 := [mp~ #79 #178]: #74
+#696 := [mp #200 #695]: #691
+#572 := (not #691)
+#573 := (or #572 #569)
+#574 := [quant-inst]: #573
+#282 := [unit-resolution #574 #696]: #569
+#752 := (= #49 #522)
+decl uf_7 :: (-> T2 int)
+#666 := (uf_7 #44)
+#595 := (+ 1::int #666)
+#597 := (uf_6 #595)
+#748 := (= #597 #522)
+#605 := (= #522 #597)
+#20 := (:var 0 T2)
+#22 := (uf_7 #20)
+#698 := (pattern #22)
+#21 := (uf_3 uf_5 #20)
+#697 := (pattern #21)
+#78 := (+ 1::int #22)
+#82 := (uf_6 #78)
+#85 := (= #21 #82)
+#699 := (forall (vars (?x5 T2)) (:pat #697 #698) #85)
+#88 := (forall (vars (?x5 T2)) #85)
+#702 := (iff #88 #699)
+#700 := (iff #85 #85)
+#701 := [refl]: #700
+#703 := [quant-intro #701]: #702
+#181 := (~ #88 #88)
+#201 := (~ #85 #85)
+#202 := [refl]: #201
+#182 := [nnf-pos #202]: #181
+#24 := (+ #22 1::int)
+#25 := (uf_6 #24)
+#26 := (= #21 #25)
+#27 := (forall (vars (?x5 T2)) #26)
+#89 := (iff #27 #88)
+#86 := (iff #26 #85)
+#83 := (= #25 #82)
+#80 := (= #24 #78)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#87 := [monotonicity #84]: #86
+#90 := [quant-intro #87]: #89
+#77 := [asserted]: #27
+#93 := [mp #77 #90]: #88
+#203 := [mp~ #93 #182]: #88
+#704 := [mp #203 #703]: #699
+#607 := (not #699)
+#600 := (or #607 #605)
+#601 := [quant-inst]: #600
+#269 := [unit-resolution #601 #704]: #605
+#749 := [symm #269]: #748
+#750 := (= #49 #597)
+#499 := (uf_7 #597)
+#337 := (uf_6 #499)
+#318 := (= #337 #597)
+#28 := (uf_6 #22)
+#92 := (= #20 #28)
+#705 := (forall (vars (?x6 T2)) (:pat #698) #92)
+#96 := (forall (vars (?x6 T2)) #92)
+#706 := (iff #96 #705)
+#708 := (iff #705 #705)
+#709 := [rewrite]: #708
+#707 := [rewrite]: #706
+#710 := [trans #707 #709]: #706
+#183 := (~ #96 #96)
+#204 := (~ #92 #92)
+#205 := [refl]: #204
+#184 := [nnf-pos #205]: #183
+#29 := (= #28 #20)
+#30 := (forall (vars (?x6 T2)) #29)
+#97 := (iff #30 #96)
+#94 := (iff #29 #92)
+#95 := [rewrite]: #94
+#98 := [quant-intro #95]: #97
+#91 := [asserted]: #30
+#101 := [mp #91 #98]: #96
+#206 := [mp~ #101 #184]: #96
+#711 := [mp #206 #710]: #705
+#376 := (not #705)
+#325 := (or #376 #318)
+#316 := (= #597 #337)
+#326 := (or #376 #316)
+#328 := (iff #326 #325)
+#329 := (iff #325 #325)
+#310 := [rewrite]: #329
+#323 := (iff #316 #318)
+#324 := [rewrite]: #323
+#317 := [monotonicity #324]: #328
+#312 := [trans #317 #310]: #328
+#327 := [quant-inst]: #326
+#313 := [mp #327 #312]: #325
+#271 := [unit-resolution #313 #711]: #318
+#746 := (= #49 #337)
+#744 := (= 2::int #499)
+#742 := (= #499 2::int)
+#578 := -1::int
+#513 := (* -1::int #666)
+#514 := (+ #499 #513)
+#474 := (<= #514 1::int)
+#512 := (= #514 1::int)
+#504 := (>= #666 -1::int)
+#586 := (>= #666 1::int)
+#378 := (= #666 1::int)
+#32 := (:var 0 int)
+#34 := (uf_6 #32)
+#712 := (pattern #34)
+#118 := (>= #32 0::int)
+#119 := (not #118)
+#35 := (uf_7 #34)
+#100 := (= #32 #35)
+#125 := (or #100 #119)
+#713 := (forall (vars (?x7 int)) (:pat #712) #125)
+#130 := (forall (vars (?x7 int)) #125)
+#716 := (iff #130 #713)
+#714 := (iff #125 #125)
+#715 := [refl]: #714
+#717 := [quant-intro #715]: #716
+#185 := (~ #130 #130)
+#207 := (~ #125 #125)
+#208 := [refl]: #207
+#186 := [nnf-pos #208]: #185
+#36 := (= #35 #32)
+#33 := (<= 0::int #32)
+#37 := (implies #33 #36)
+#38 := (forall (vars (?x7 int)) #37)
+#133 := (iff #38 #130)
+#107 := (not #33)
+#108 := (or #107 #100)
+#113 := (forall (vars (?x7 int)) #108)
+#131 := (iff #113 #130)
+#128 := (iff #108 #125)
+#122 := (or #119 #100)
+#126 := (iff #122 #125)
+#127 := [rewrite]: #126
+#123 := (iff #108 #122)
+#120 := (iff #107 #119)
+#116 := (iff #33 #118)
+#117 := [rewrite]: #116
+#121 := [monotonicity #117]: #120
+#124 := [monotonicity #121]: #123
+#129 := [trans #124 #127]: #128
+#132 := [quant-intro #129]: #131
+#114 := (iff #38 #113)
+#111 := (iff #37 #108)
+#104 := (implies #33 #100)
+#109 := (iff #104 #108)
+#110 := [rewrite]: #109
+#105 := (iff #37 #104)
+#102 := (iff #36 #100)
+#103 := [rewrite]: #102
+#106 := [monotonicity #103]: #105
+#112 := [trans #106 #110]: #111
+#115 := [quant-intro #112]: #114
+#134 := [trans #115 #132]: #133
+#99 := [asserted]: #38
+#135 := [mp #99 #134]: #130
+#209 := [mp~ #135 #186]: #130
+#718 := [mp #209 #717]: #713
+#673 := (not #713)
+#365 := (or #673 #378)
+#307 := (>= 1::int 0::int)
+#668 := (not #307)
+#669 := (= 1::int #666)
+#655 := (or #669 #668)
+#366 := (or #673 #655)
+#645 := (iff #366 #365)
+#360 := (iff #365 #365)
+#643 := [rewrite]: #360
+#654 := (iff #655 #378)
+#374 := (or #378 false)
+#653 := (iff #374 #378)
+#650 := [rewrite]: #653
+#375 := (iff #655 #374)
+#651 := (iff #668 false)
+#1 := true
+#670 := (not true)
+#677 := (iff #670 false)
+#678 := [rewrite]: #677
+#381 := (iff #668 #670)
+#379 := (iff #307 true)
+#380 := [rewrite]: #379
+#274 := [monotonicity #380]: #381
+#652 := [trans #274 #678]: #651
+#656 := (iff #669 #378)
+#363 := [rewrite]: #656
+#649 := [monotonicity #363 #652]: #375
+#364 := [trans #649 #650]: #654
+#646 := [monotonicity #364]: #645
+#647 := [trans #646 #643]: #645
+#367 := [quant-inst]: #366
+#644 := [mp #367 #647]: #365
+#272 := [unit-resolution #644 #718]: #378
+#270 := (not #378)
+#273 := (or #270 #586)
+#725 := [th-lemma]: #273
+#726 := [unit-resolution #725 #272]: #586
+#727 := (not #586)
+#728 := (or #727 #504)
+#729 := [th-lemma]: #728
+#730 := [unit-resolution #729 #726]: #504
+#481 := (not #504)
+#496 := (or #673 #481 #512)
+#509 := (>= #595 0::int)
+#468 := (not #509)
+#501 := (= #595 #499)
+#503 := (or #501 #468)
+#497 := (or #673 #503)
+#470 := (iff #497 #496)
+#491 := (or #481 #512)
+#498 := (or #673 #491)
+#467 := (iff #498 #496)
+#469 := [rewrite]: #467
+#459 := (iff #497 #498)
+#494 := (iff #503 #491)
+#488 := (or #512 #481)
+#492 := (iff #488 #491)
+#493 := [rewrite]: #492
+#489 := (iff #503 #488)
+#486 := (iff #468 #481)
+#525 := (iff #509 #504)
+#480 := [rewrite]: #525
+#487 := [monotonicity #480]: #486
+#510 := (iff #501 #512)
+#524 := [rewrite]: #510
+#490 := [monotonicity #524 #487]: #489
+#495 := [trans #490 #493]: #494
+#460 := [monotonicity #495]: #459
+#471 := [trans #460 #469]: #470
+#482 := [quant-inst]: #497
+#473 := [mp #482 #471]: #496
+#731 := [unit-resolution #473 #718 #730]: #512
+#732 := (not #512)
+#733 := (or #732 #474)
+#734 := [th-lemma]: #733
+#735 := [unit-resolution #734 #731]: #474
+#475 := (>= #514 1::int)
+#736 := (or #732 #475)
+#737 := [th-lemma]: #736
+#738 := [unit-resolution #737 #731]: #475
+#582 := (<= #666 1::int)
+#739 := (or #270 #582)
+#740 := [th-lemma]: #739
+#741 := [unit-resolution #740 #272]: #582
+#743 := [th-lemma #726 #741 #738 #735]: #742
+#745 := [symm #743]: #744
+#747 := [monotonicity #745]: #746
+#751 := [trans #747 #271]: #750
+#753 := [trans #751 #749]: #752
+#755 := [monotonicity #753 #282]: #754
+#759 := [trans #755 #757]: #758
+#792 := (= #44 #352)
+#358 := (uf_7 #43)
+#613 := (+ 1::int #358)
+#617 := (uf_6 #613)
+#788 := (= #617 #352)
+#598 := (= #352 #617)
+#608 := (or #607 #598)
+#609 := [quant-inst]: #608
+#760 := [unit-resolution #609 #704]: #598
+#789 := [symm #760]: #788
+#790 := (= #44 #617)
+#575 := (uf_7 #617)
+#390 := (uf_6 #575)
+#382 := (= #390 #617)
+#385 := (or #376 #382)
+#392 := (= #617 #390)
+#386 := (or #376 #392)
+#387 := (iff #386 #385)
+#369 := (iff #385 #385)
+#370 := [rewrite]: #369
+#383 := (iff #392 #382)
+#384 := [rewrite]: #383
+#368 := [monotonicity #384]: #387
+#361 := [trans #368 #370]: #387
+#377 := [quant-inst]: #386
+#371 := [mp #377 #361]: #385
+#761 := [unit-resolution #371 #711]: #382
+#786 := (= #44 #390)
+#784 := (= 1::int #575)
+#782 := (= #575 1::int)
+#568 := (* -1::int #575)
+#579 := (+ #358 #568)
+#535 := (<= #579 -1::int)
+#557 := (= #579 -1::int)
+#561 := (>= #358 -1::int)
+#585 := (>= #358 0::int)
+#676 := (= #358 0::int)
+#315 := (or #673 #676)
+#268 := (>= 0::int 0::int)
+#354 := (not #268)
+#355 := (= 0::int #358)
+#359 := (or #355 #354)
+#657 := (or #673 #359)
+#320 := (iff #657 #315)
+#322 := (iff #315 #315)
+#659 := [rewrite]: #322
+#672 := (iff #359 #676)
+#675 := (or #676 false)
+#330 := (iff #675 #676)
+#335 := [rewrite]: #330
+#681 := (iff #359 #675)
+#679 := (iff #354 false)
+#343 := (iff #354 #670)
+#332 := (iff #268 true)
+#463 := [rewrite]: #332
+#344 := [monotonicity #463]: #343
+#680 := [trans #344 #678]: #679
+#338 := (iff #355 #676)
+#674 := [rewrite]: #338
+#671 := [monotonicity #674 #680]: #681
+#331 := [trans #671 #335]: #672
+#321 := [monotonicity #331]: #320
+#660 := [trans #321 #659]: #320
+#319 := [quant-inst]: #657
+#661 := [mp #319 #660]: #315
+#762 := [unit-resolution #661 #718]: #676
+#763 := (not #676)
+#764 := (or #763 #585)
+#765 := [th-lemma]: #764
+#766 := [unit-resolution #765 #762]: #585
+#767 := (not #585)
+#768 := (or #767 #561)
+#769 := [th-lemma]: #768
+#770 := [unit-resolution #769 #766]: #561
+#564 := (not #561)
+#549 := (or #673 #557 #564)
+#570 := (>= #613 0::int)
+#571 := (not #570)
+#576 := (= #613 #575)
+#577 := (or #576 #571)
+#552 := (or #673 #577)
+#530 := (iff #552 #549)
+#551 := (or #557 #564)
+#554 := (or #673 #551)
+#556 := (iff #554 #549)
+#529 := [rewrite]: #556
+#555 := (iff #552 #554)
+#547 := (iff #577 #551)
+#559 := (iff #571 #564)
+#562 := (iff #570 #561)
+#563 := [rewrite]: #562
+#565 := [monotonicity #563]: #559
+#558 := (iff #576 #557)
+#560 := [rewrite]: #558
+#548 := [monotonicity #560 #565]: #547
+#550 := [monotonicity #548]: #555
+#531 := [trans #550 #529]: #530
+#553 := [quant-inst]: #552
+#424 := [mp #553 #531]: #549
+#771 := [unit-resolution #424 #718 #770]: #557
+#772 := (not #557)
+#773 := (or #772 #535)
+#774 := [th-lemma]: #773
+#775 := [unit-resolution #774 #771]: #535
+#536 := (>= #579 -1::int)
+#776 := (or #772 #536)
+#777 := [th-lemma]: #776
+#778 := [unit-resolution #777 #771]: #536
+#584 := (<= #358 0::int)
+#779 := (or #763 #584)
+#780 := [th-lemma]: #779
+#781 := [unit-resolution #780 #762]: #584
+#783 := [th-lemma #766 #781 #778 #775]: #782
+#785 := [symm #783]: #784
+#787 := [monotonicity #785]: #786
+#791 := [trans #787 #761]: #790
+#793 := [trans #791 #789]: #792
+#796 := [monotonicity #793 #759]: #795
+#798 := [symm #796]: #797
+#353 := (= #47 #267)
+#356 := (or #345 #353)
+#357 := [quant-inst]: #356
+#794 := [unit-resolution #357 #689]: #353
+#799 := [trans #794 #798]: #52
+#53 := (not #52)
+#177 := [asserted]: #53
+[unit-resolution #177 #799]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_06 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrasorts ( T1 T2)
+:extrapreds (
+ (up_1 T1)
+ )
+:assumption (not (or (forall (?x1 T1) (up_1 ?x1)) (not (forall (?x2 T1) (up_1 ?x2)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_06.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,21 @@
+#2 := false
+decl up_1 :: (-> T1 bool)
+#4 := (:var 0 T1)
+#5 := (up_1 #4)
+#6 := (forall (vars (?x1 T1)) #5)
+#7 := (not #6)
+#8 := (or #6 #7)
+#9 := (not #8)
+#33 := (iff #9 false)
+#1 := true
+#28 := (not true)
+#31 := (iff #28 false)
+#32 := [rewrite]: #31
+#29 := (iff #9 #28)
+#26 := (iff #8 true)
+#27 := [rewrite]: #26
+#30 := [monotonicity #27]: #29
+#34 := [trans #30 #32]: #33
+#25 := [asserted]: #9
+[mp #25 #34]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_07 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,14 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_3 T1 T1)
+ (uf_2 T1 Int)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (forall (?x4 T1) (= (uf_3 ?x4) (ite (< (uf_2 ?x4) 10) ?x4 (uf_3 (uf_1 (- (uf_2 ?x4) 10))))))
+:assumption (not (= (uf_3 (uf_1 (* 4 (uf_2 (uf_3 (uf_1 4)))))) (uf_1 6)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_07.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,373 @@
+#2 := false
+decl uf_1 :: (-> int T1)
+#37 := 6::int
+#38 := (uf_1 6::int)
+decl uf_3 :: (-> T1 T1)
+decl uf_2 :: (-> T1 int)
+#30 := 4::int
+#31 := (uf_1 4::int)
+#32 := (uf_3 #31)
+#33 := (uf_2 #32)
+#34 := (* 4::int #33)
+#35 := (uf_1 #34)
+#36 := (uf_3 #35)
+#39 := (= #36 #38)
+#548 := (uf_3 #38)
+#394 := (= #548 #38)
+#549 := (= #38 #548)
+#523 := (uf_2 #38)
+#142 := -10::int
+#513 := (+ -10::int #523)
+#537 := (uf_1 #513)
+#538 := (uf_3 #537)
+#514 := (= #538 #548)
+#22 := 10::int
+#539 := (>= #523 10::int)
+#506 := (ite #539 #514 #549)
+#4 := (:var 0 T1)
+#21 := (uf_3 #4)
+#708 := (pattern #21)
+#5 := (uf_2 #4)
+#687 := (pattern #5)
+#209 := (= #4 #21)
+#143 := (+ -10::int #5)
+#146 := (uf_1 #143)
+#149 := (uf_3 #146)
+#208 := (= #21 #149)
+#163 := (>= #5 10::int)
+#190 := (ite #163 #208 #209)
+#709 := (forall (vars (?x4 T1)) (:pat #687 #708) #190)
+#193 := (forall (vars (?x4 T1)) #190)
+#712 := (iff #193 #709)
+#710 := (iff #190 #190)
+#711 := [refl]: #710
+#713 := [quant-intro #711]: #712
+#168 := (ite #163 #149 #4)
+#173 := (= #21 #168)
+#176 := (forall (vars (?x4 T1)) #173)
+#210 := (iff #176 #193)
+#191 := (iff #173 #190)
+#192 := [rewrite]: #191
+#211 := [quant-intro #192]: #210
+#188 := (~ #176 #176)
+#205 := (~ #173 #173)
+#206 := [refl]: #205
+#189 := [nnf-pos #206]: #188
+#24 := (- #5 10::int)
+#25 := (uf_1 #24)
+#26 := (uf_3 #25)
+#23 := (< #5 10::int)
+#27 := (ite #23 #4 #26)
+#28 := (= #21 #27)
+#29 := (forall (vars (?x4 T1)) #28)
+#179 := (iff #29 #176)
+#152 := (ite #23 #4 #149)
+#155 := (= #21 #152)
+#158 := (forall (vars (?x4 T1)) #155)
+#177 := (iff #158 #176)
+#174 := (iff #155 #173)
+#171 := (= #152 #168)
+#161 := (not #163)
+#165 := (ite #161 #4 #149)
+#169 := (= #165 #168)
+#170 := [rewrite]: #169
+#166 := (= #152 #165)
+#162 := (iff #23 #161)
+#164 := [rewrite]: #162
+#167 := [monotonicity #164]: #166
+#172 := [trans #167 #170]: #171
+#175 := [monotonicity #172]: #174
+#178 := [quant-intro #175]: #177
+#159 := (iff #29 #158)
+#156 := (iff #28 #155)
+#153 := (= #27 #152)
+#150 := (= #26 #149)
+#147 := (= #25 #146)
+#144 := (= #24 #143)
+#145 := [rewrite]: #144
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [quant-intro #157]: #159
+#180 := [trans #160 #178]: #179
+#141 := [asserted]: #29
+#181 := [mp #141 #180]: #176
+#207 := [mp~ #181 #189]: #176
+#212 := [mp #207 #211]: #193
+#714 := [mp #212 #713]: #709
+#681 := (not #709)
+#517 := (or #681 #506)
+#533 := (= #548 #538)
+#507 := (ite #539 #533 #549)
+#518 := (or #681 #507)
+#529 := (iff #518 #517)
+#530 := (iff #517 #517)
+#485 := [rewrite]: #530
+#508 := (iff #507 #506)
+#473 := (iff #533 #514)
+#504 := [rewrite]: #473
+#515 := [monotonicity #504]: #508
+#509 := [monotonicity #515]: #529
+#486 := [trans #509 #485]: #529
+#519 := [quant-inst]: #518
+#491 := [mp #519 #486]: #517
+#484 := [unit-resolution #491 #714]: #506
+#493 := (not #539)
+#465 := (<= #523 6::int)
+#526 := (= #523 6::int)
+#10 := (:var 0 int)
+#12 := (uf_1 #10)
+#695 := (pattern #12)
+#9 := 0::int
+#82 := (>= #10 0::int)
+#83 := (not #82)
+#13 := (uf_2 #12)
+#64 := (= #10 #13)
+#89 := (or #64 #83)
+#696 := (forall (vars (?x2 int)) (:pat #695) #89)
+#94 := (forall (vars (?x2 int)) #89)
+#699 := (iff #94 #696)
+#697 := (iff #89 #89)
+#698 := [refl]: #697
+#700 := [quant-intro #698]: #699
+#185 := (~ #94 #94)
+#199 := (~ #89 #89)
+#200 := [refl]: #199
+#183 := [nnf-pos #200]: #185
+#14 := (= #13 #10)
+#11 := (<= 0::int #10)
+#15 := (implies #11 #14)
+#16 := (forall (vars (?x2 int)) #15)
+#97 := (iff #16 #94)
+#71 := (not #11)
+#72 := (or #71 #64)
+#77 := (forall (vars (?x2 int)) #72)
+#95 := (iff #77 #94)
+#92 := (iff #72 #89)
+#86 := (or #83 #64)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #72 #86)
+#84 := (iff #71 #83)
+#80 := (iff #11 #82)
+#81 := [rewrite]: #80
+#85 := [monotonicity #81]: #84
+#88 := [monotonicity #85]: #87
+#93 := [trans #88 #91]: #92
+#96 := [quant-intro #93]: #95
+#78 := (iff #16 #77)
+#75 := (iff #15 #72)
+#68 := (implies #11 #64)
+#73 := (iff #68 #72)
+#74 := [rewrite]: #73
+#69 := (iff #15 #68)
+#66 := (iff #14 #64)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#76 := [trans #70 #74]: #75
+#79 := [quant-intro #76]: #78
+#98 := [trans #79 #96]: #97
+#63 := [asserted]: #16
+#99 := [mp #63 #98]: #94
+#201 := [mp~ #99 #183]: #94
+#701 := [mp #201 #700]: #696
+#671 := (not #696)
+#615 := (or #671 #526)
+#520 := (>= 6::int 0::int)
+#522 := (not #520)
+#516 := (= 6::int #523)
+#524 := (or #516 #522)
+#604 := (or #671 #524)
+#606 := (iff #604 #615)
+#601 := (iff #615 #615)
+#608 := [rewrite]: #601
+#614 := (iff #524 #526)
+#603 := (or #526 false)
+#612 := (iff #603 #526)
+#613 := [rewrite]: #612
+#600 := (iff #524 #603)
+#609 := (iff #522 false)
+#1 := true
+#327 := (not true)
+#666 := (iff #327 false)
+#667 := [rewrite]: #666
+#618 := (iff #522 #327)
+#528 := (iff #520 true)
+#621 := [rewrite]: #528
+#622 := [monotonicity #621]: #618
+#611 := [trans #622 #667]: #609
+#525 := (iff #516 #526)
+#527 := [rewrite]: #525
+#602 := [monotonicity #527 #611]: #600
+#610 := [trans #602 #613]: #614
+#607 := [monotonicity #610]: #606
+#592 := [trans #607 #608]: #606
+#605 := [quant-inst]: #604
+#593 := [mp #605 #592]: #615
+#454 := [unit-resolution #593 #701]: #526
+#303 := (not #526)
+#462 := (or #303 #465)
+#458 := [th-lemma]: #462
+#463 := [unit-resolution #458 #454]: #465
+#442 := (not #465)
+#445 := (or #442 #493)
+#449 := [th-lemma]: #445
+#451 := [unit-resolution #449 #463]: #493
+#492 := (not #506)
+#496 := (or #492 #539 #549)
+#497 := [def-axiom]: #496
+#452 := [unit-resolution #497 #451 #484]: #549
+#395 := [symm #452]: #394
+#397 := (= #36 #548)
+#372 := (uf_2 #35)
+#576 := (+ -10::int #372)
+#568 := (uf_1 #576)
+#569 := (uf_3 #568)
+#408 := (= #569 #548)
+#401 := (= #568 #38)
+#422 := (= #576 6::int)
+#677 := (uf_2 #31)
+#365 := -1::int
+#478 := (* -1::int #677)
+#479 := (+ #33 #478)
+#480 := (<= #479 0::int)
+#476 := (= #33 #677)
+#431 := (= #32 #31)
+#589 := (= #31 #32)
+#590 := (+ -10::int #677)
+#587 := (uf_1 #590)
+#591 := (uf_3 #587)
+#571 := (= #32 #591)
+#572 := (>= #677 10::int)
+#574 := (ite #572 #571 #589)
+#577 := (or #681 #574)
+#578 := [quant-inst]: #577
+#450 := [unit-resolution #578 #714]: #574
+#580 := (not #572)
+#552 := (<= #677 4::int)
+#324 := (= #677 4::int)
+#674 := (or #671 #324)
+#343 := (>= 4::int 0::int)
+#679 := (not #343)
+#336 := (= 4::int #677)
+#678 := (or #336 #679)
+#660 := (or #671 #678)
+#368 := (iff #660 #674)
+#384 := (iff #674 #674)
+#385 := [rewrite]: #384
+#312 := (iff #678 #324)
+#669 := (or #324 false)
+#672 := (iff #669 #324)
+#311 := [rewrite]: #672
+#306 := (iff #678 #669)
+#668 := (iff #679 false)
+#664 := (iff #679 #327)
+#325 := (iff #343 true)
+#326 := [rewrite]: #325
+#665 := [monotonicity #326]: #664
+#663 := [trans #665 #667]: #668
+#320 := (iff #336 #324)
+#662 := [rewrite]: #320
+#670 := [monotonicity #662 #663]: #306
+#673 := [trans #670 #311]: #312
+#383 := [monotonicity #673]: #368
+#386 := [trans #383 #385]: #368
+#661 := [quant-inst]: #660
+#278 := [mp #661 #386]: #674
+#453 := [unit-resolution #278 #701]: #324
+#441 := (not #324)
+#444 := (or #441 #552)
+#446 := [th-lemma]: #444
+#447 := [unit-resolution #446 #453]: #552
+#443 := (not #552)
+#448 := (or #443 #580)
+#438 := [th-lemma]: #448
+#428 := [unit-resolution #438 #447]: #580
+#579 := (not #574)
+#583 := (or #579 #572 #589)
+#573 := [def-axiom]: #583
+#430 := [unit-resolution #573 #428 #450]: #589
+#434 := [symm #430]: #431
+#435 := [monotonicity #434]: #476
+#439 := (not #476)
+#432 := (or #439 #480)
+#440 := [th-lemma]: #432
+#433 := [unit-resolution #440 #435]: #480
+#481 := (>= #479 0::int)
+#436 := (or #439 #481)
+#437 := [th-lemma]: #436
+#423 := [unit-resolution #437 #435]: #481
+#553 := (>= #677 4::int)
+#425 := (or #441 #553)
+#426 := [th-lemma]: #425
+#424 := [unit-resolution #426 #453]: #553
+#648 := (* -1::int #372)
+#652 := (+ #34 #648)
+#631 := (<= #652 0::int)
+#649 := (= #652 0::int)
+#370 := (>= #34 0::int)
+#409 := (not #481)
+#427 := (not #553)
+#411 := (or #370 #427 #409)
+#412 := [th-lemma]: #411
+#413 := [unit-resolution #412 #424 #423]: #370
+#371 := (not #370)
+#640 := (or #371 #649)
+#488 := (or #671 #371 #649)
+#650 := (= #34 #372)
+#651 := (or #650 #371)
+#489 := (or #671 #651)
+#630 := (iff #489 #488)
+#632 := (or #671 #640)
+#635 := (iff #632 #488)
+#629 := [rewrite]: #635
+#633 := (iff #489 #632)
+#641 := (iff #651 #640)
+#643 := (or #649 #371)
+#645 := (iff #643 #640)
+#646 := [rewrite]: #645
+#644 := (iff #651 #643)
+#653 := (iff #650 #649)
+#642 := [rewrite]: #653
+#639 := [monotonicity #642]: #644
+#647 := [trans #639 #646]: #641
+#634 := [monotonicity #647]: #633
+#636 := [trans #634 #629]: #630
+#490 := [quant-inst]: #489
+#637 := [mp #490 #636]: #488
+#414 := [unit-resolution #637 #701]: #640
+#415 := [unit-resolution #414 #413]: #649
+#416 := (not #649)
+#417 := (or #416 #631)
+#418 := [th-lemma]: #417
+#419 := [unit-resolution #418 #415]: #631
+#638 := (>= #652 0::int)
+#420 := (or #416 #638)
+#421 := [th-lemma]: #420
+#410 := [unit-resolution #421 #415]: #638
+#399 := [th-lemma #410 #419 #424 #447 #423 #433]: #422
+#402 := [monotonicity #399]: #401
+#393 := [monotonicity #402]: #408
+#564 := (= #36 #569)
+#575 := (= #35 #36)
+#570 := (>= #372 10::int)
+#556 := (ite #570 #564 #575)
+#554 := (or #681 #556)
+#557 := [quant-inst]: #554
+#403 := [unit-resolution #557 #714]: #556
+#404 := (not #631)
+#405 := (or #570 #404 #427 #409)
+#406 := [th-lemma]: #405
+#407 := [unit-resolution #406 #419 #424 #423]: #570
+#559 := (not #570)
+#558 := (not #556)
+#560 := (or #558 #559 #564)
+#555 := [def-axiom]: #560
+#400 := [unit-resolution #555 #407 #403]: #564
+#396 := [trans #400 #393]: #397
+#398 := [trans #396 #395]: #39
+#40 := (not #39)
+#182 := [asserted]: #40
+[unit-resolution #182 #398]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_08 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,24 @@
+(benchmark Isabelle
+:extrasorts ( T2 T1 T4 T3)
+:extrafuns (
+ (uf_3 Int T1)
+ (uf_7 T2 T4 T4)
+ (uf_1 T2 T1 T1)
+ (uf_6 T3 T4 Int)
+ (uf_4 T1 Int)
+ (uf_5 T2)
+ (uf_2 T2)
+ (uf_10 Int)
+ (uf_8 T3)
+ (uf_9 T4)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 uf_2 ?x1) (uf_3 (div (uf_4 ?x1) 2))))
+:assumption (forall (?x2 T1) (= (uf_1 uf_5 ?x2) (uf_3 (mod (uf_4 ?x2) 2))))
+:assumption (forall (?x3 T1) (= (uf_3 (uf_4 ?x3)) ?x3))
+:assumption (forall (?x4 Int) (implies (<= 0 ?x4) (= (uf_4 (uf_3 ?x4)) ?x4)))
+:assumption (forall (?x5 Int) (implies (< ?x5 0) (= (uf_4 (uf_3 ?x5)) 0)))
+:assumption (forall (?x6 T3) (?x7 T4) (= (mod (uf_6 ?x6 ?x7) 2) (mod (uf_6 ?x6 (uf_7 uf_5 ?x7)) 2)))
+:assumption (forall (?x8 T3) (?x9 T4) (= (+ (* (uf_6 ?x8 (uf_7 uf_2 ?x9)) 2) (uf_6 ?x8 (uf_7 uf_5 ?x9))) (uf_6 ?x8 ?x9)))
+:assumption (iff (= (uf_6 uf_8 uf_9) uf_10) (implies (= (mod (uf_6 uf_8 (uf_7 uf_5 uf_9)) 2) (mod uf_10 2)) (not (= (uf_6 uf_8 (uf_7 uf_2 uf_9)) (div (- uf_10 (uf_6 uf_8 (uf_7 uf_5 uf_9))) 2)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_hol_08.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,410 @@
+#2 := false
+#22 := 0::int
+decl uf_6 :: (-> T3 T4 int)
+decl uf_7 :: (-> T2 T4 T4)
+decl uf_9 :: T4
+#50 := uf_9
+decl uf_2 :: T2
+#4 := uf_2
+#59 := (uf_7 uf_2 uf_9)
+decl uf_8 :: T3
+#49 := uf_8
+#60 := (uf_6 uf_8 #59)
+#204 := -2::int
+#683 := (* -2::int #60)
+decl uf_5 :: T2
+#13 := uf_5
+#54 := (uf_7 uf_5 uf_9)
+#55 := (uf_6 uf_8 #54)
+#172 := -1::int
+#218 := (* -1::int #55)
+#685 := (+ #218 #683)
+#51 := (uf_6 uf_8 uf_9)
+#686 := (+ #51 #685)
+#679 := (>= #686 0::int)
+#687 := (= #686 0::int)
+#35 := (:var 0 T4)
+#43 := (uf_7 uf_2 #35)
+#34 := (:var 1 T3)
+#44 := (uf_6 #34 #43)
+#819 := (pattern #44)
+#38 := (uf_7 uf_5 #35)
+#39 := (uf_6 #34 #38)
+#812 := (pattern #39)
+#205 := (* -2::int #44)
+#203 := (* -1::int #39)
+#206 := (+ #203 #205)
+#36 := (uf_6 #34 #35)
+#207 := (+ #36 #206)
+#208 := (= #207 0::int)
+#820 := (forall (vars (?x8 T3) (?x9 T4)) (:pat #812 #819) #208)
+#211 := (forall (vars (?x8 T3) (?x9 T4)) #208)
+#823 := (iff #211 #820)
+#821 := (iff #208 #208)
+#822 := [refl]: #821
+#824 := [quant-intro #822]: #823
+#279 := (~ #211 #211)
+#305 := (~ #208 #208)
+#306 := [refl]: #305
+#280 := [nnf-pos #306]: #279
+#8 := 2::int
+#45 := (* #44 2::int)
+#46 := (+ #45 #39)
+#47 := (= #46 #36)
+#48 := (forall (vars (?x8 T3) (?x9 T4)) #47)
+#214 := (iff #48 #211)
+#171 := (* 2::int #44)
+#187 := (+ #39 #171)
+#195 := (= #36 #187)
+#200 := (forall (vars (?x8 T3) (?x9 T4)) #195)
+#212 := (iff #200 #211)
+#209 := (iff #195 #208)
+#210 := [rewrite]: #209
+#213 := [quant-intro #210]: #212
+#201 := (iff #48 #200)
+#198 := (iff #47 #195)
+#192 := (= #187 #36)
+#196 := (iff #192 #195)
+#197 := [rewrite]: #196
+#193 := (iff #47 #192)
+#190 := (= #46 #187)
+#184 := (+ #171 #39)
+#188 := (= #184 #187)
+#189 := [rewrite]: #188
+#185 := (= #46 #184)
+#182 := (= #45 #171)
+#183 := [rewrite]: #182
+#186 := [monotonicity #183]: #185
+#191 := [trans #186 #189]: #190
+#194 := [monotonicity #191]: #193
+#199 := [trans #194 #197]: #198
+#202 := [quant-intro #199]: #201
+#215 := [trans #202 #213]: #214
+#170 := [asserted]: #48
+#216 := [mp #170 #215]: #211
+#307 := [mp~ #216 #280]: #211
+#825 := [mp #307 #824]: #820
+#689 := (not #820)
+#675 := (or #689 #687)
+#676 := [quant-inst]: #675
+#536 := [unit-resolution #676 #825]: #687
+#537 := (not #687)
+#533 := (or #537 #679)
+#538 := [th-lemma]: #533
+#528 := [unit-resolution #538 #536]: #679
+decl uf_10 :: int
+#52 := uf_10
+#219 := (+ uf_10 #218)
+#222 := (div #219 2::int)
+#251 := (* -1::int #222)
+#252 := (+ #60 #251)
+#449 := (<= #252 0::int)
+#399 := (not #449)
+#253 := (= #252 0::int)
+#256 := (not #253)
+#57 := (mod uf_10 2::int)
+#243 := (* -1::int #57)
+#56 := (mod #55 2::int)
+#244 := (+ #56 #243)
+#245 := (= #244 0::int)
+#448 := (>= #244 0::int)
+#688 := (mod #51 2::int)
+#666 := (* -1::int #688)
+#667 := (+ #56 #666)
+#660 := (>= #667 0::int)
+#668 := (= #667 0::int)
+#40 := (mod #39 2::int)
+#173 := (* -1::int #40)
+#37 := (mod #36 2::int)
+#174 := (+ #37 #173)
+#175 := (= #174 0::int)
+#813 := (forall (vars (?x6 T3) (?x7 T4)) (:pat #812) #175)
+#178 := (forall (vars (?x6 T3) (?x7 T4)) #175)
+#816 := (iff #178 #813)
+#814 := (iff #175 #175)
+#815 := [refl]: #814
+#817 := [quant-intro #815]: #816
+#277 := (~ #178 #178)
+#302 := (~ #175 #175)
+#303 := [refl]: #302
+#278 := [nnf-pos #303]: #277
+#41 := (= #37 #40)
+#42 := (forall (vars (?x6 T3) (?x7 T4)) #41)
+#179 := (iff #42 #178)
+#176 := (iff #41 #175)
+#177 := [rewrite]: #176
+#180 := [quant-intro #177]: #179
+#169 := [asserted]: #42
+#181 := [mp #169 #180]: #178
+#304 := [mp~ #181 #278]: #178
+#818 := [mp #304 #817]: #813
+#673 := (not #813)
+#663 := (or #673 #668)
+#756 := (* -1::int #56)
+#684 := (+ #688 #756)
+#680 := (= #684 0::int)
+#674 := (or #673 #680)
+#653 := (iff #674 #663)
+#656 := (iff #663 #663)
+#657 := [rewrite]: #656
+#671 := (iff #680 #668)
+#677 := (+ #756 #688)
+#662 := (= #677 0::int)
+#669 := (iff #662 #668)
+#670 := [rewrite]: #669
+#664 := (iff #680 #662)
+#681 := (= #684 #677)
+#661 := [rewrite]: #681
+#665 := [monotonicity #661]: #664
+#672 := [trans #665 #670]: #671
+#655 := [monotonicity #672]: #653
+#658 := [trans #655 #657]: #653
+#652 := [quant-inst]: #674
+#659 := [mp #652 #658]: #663
+#394 := [unit-resolution #659 #818]: #668
+#552 := (not #668)
+#514 := (or #552 #660)
+#517 := [th-lemma]: #514
+#499 := [unit-resolution #517 #394]: #660
+#503 := (not #448)
+#414 := [hypothesis]: #503
+#561 := (+ #57 #666)
+#709 := (<= #561 0::int)
+#602 := (= #57 #688)
+#468 := (= #688 #57)
+#53 := (= #51 uf_10)
+#248 := (not #245)
+#259 := (or #248 #256)
+#362 := (mod #219 2::int)
+#699 := (>= #362 0::int)
+#1 := true
+#81 := [true-axiom]: true
+#604 := (or false #699)
+#506 := [th-lemma]: #604
+#507 := [unit-resolution #506 #81]: #699
+#628 := (* -1::int uf_10)
+#623 := (+ #51 #628)
+#629 := (<= #623 0::int)
+#498 := (not #629)
+#597 := (>= #623 0::int)
+#381 := (not #259)
+#508 := [hypothesis]: #381
+#450 := (or #259 #245)
+#441 := [def-axiom]: #450
+#509 := [unit-resolution #441 #508]: #245
+#510 := (or #248 #448)
+#511 := [th-lemma]: #510
+#500 := [unit-resolution #511 #509]: #448
+#743 := (div uf_10 2::int)
+#723 := (* -2::int #743)
+#545 := (* -2::int #688)
+#546 := (+ #545 #723)
+#646 := (div #51 2::int)
+#645 := (* -2::int #646)
+#547 := (+ #645 #546)
+#605 := (* -2::int #57)
+#549 := (+ #605 #547)
+#594 := (* 2::int #56)
+#550 := (+ #594 #549)
+#598 := (* 2::int uf_10)
+#551 := (+ #598 #550)
+#563 := (>= #551 2::int)
+#520 := (not #563)
+#361 := (<= #244 0::int)
+#512 := (or #248 #361)
+#489 := [th-lemma]: #512
+#491 := [unit-resolution #489 #509]: #361
+#363 := (>= #252 0::int)
+#452 := (or #259 #253)
+#453 := [def-axiom]: #452
+#492 := [unit-resolution #453 #508]: #253
+#493 := (or #256 #363)
+#494 := [th-lemma]: #493
+#495 := [unit-resolution #494 #492]: #363
+#556 := (not #361)
+#573 := (not #363)
+#521 := (or #520 #573 #556)
+#703 := (>= #362 2::int)
+#704 := (not #703)
+#599 := (or false #704)
+#620 := [th-lemma]: #599
+#575 := [unit-resolution #620 #81]: #704
+#654 := (<= #667 0::int)
+#548 := (or #552 #654)
+#553 := [th-lemma]: #548
+#532 := [unit-resolution #553 #394]: #654
+#651 := (+ #645 #666)
+#624 := (+ #51 #651)
+#626 := (<= #624 0::int)
+#650 := (= #624 0::int)
+#535 := (or false #650)
+#539 := [th-lemma]: #535
+#541 := [unit-resolution #539 #81]: #650
+#542 := (not #650)
+#540 := (or #542 #626)
+#543 := [th-lemma]: #540
+#531 := [unit-resolution #543 #541]: #626
+#587 := [hypothesis]: #361
+#724 := (+ #243 #723)
+#725 := (+ uf_10 #724)
+#727 := (<= #725 0::int)
+#722 := (= #725 0::int)
+#576 := (or false #722)
+#581 := [th-lemma]: #576
+#582 := [unit-resolution #581 #81]: #722
+#583 := (not #722)
+#584 := (or #583 #727)
+#585 := [th-lemma]: #584
+#586 := [unit-resolution #585 #582]: #727
+#534 := [hypothesis]: #563
+#555 := [hypothesis]: #363
+#616 := (* -1::int #362)
+#615 := (* -2::int #222)
+#617 := (+ #615 #616)
+#618 := (+ #218 #617)
+#711 := (+ uf_10 #618)
+#708 := (<= #711 0::int)
+#606 := (= #711 0::int)
+#562 := (or false #606)
+#564 := [th-lemma]: #562
+#565 := [unit-resolution #564 #81]: #606
+#566 := (not #606)
+#568 := (or #566 #708)
+#569 := [th-lemma]: #568
+#570 := [unit-resolution #569 #565]: #708
+#518 := [th-lemma #570 #555 #528 #534 #586 #587 #531 #532 #575]: false
+#524 := [lemma #518]: #521
+#496 := [unit-resolution #524 #495 #491]: #520
+#504 := (or #597 #563 #503)
+#529 := (not #597)
+#522 := [hypothesis]: #529
+#519 := (>= #624 0::int)
+#530 := (or #542 #519)
+#523 := [th-lemma]: #530
+#526 := [unit-resolution #523 #541]: #519
+#527 := [hypothesis]: #448
+#721 := (>= #725 0::int)
+#513 := (or #583 #721)
+#515 := [th-lemma]: #513
+#516 := [unit-resolution #515 #582]: #721
+#501 := [th-lemma #499 #516 #527 #526 #522]: #563
+#525 := [hypothesis]: #520
+#502 := [unit-resolution #525 #501]: false
+#505 := [lemma #502]: #504
+#497 := [unit-resolution #505 #496 #500]: #597
+#485 := (or #498 #529)
+#558 := (not #53)
+#440 := (or #558 #259)
+#262 := (iff #53 #259)
+#61 := (- uf_10 #55)
+#62 := (div #61 2::int)
+#63 := (= #60 #62)
+#64 := (not #63)
+#58 := (= #56 #57)
+#65 := (implies #58 #64)
+#66 := (iff #53 #65)
+#265 := (iff #66 #262)
+#225 := (= #60 #222)
+#228 := (not #225)
+#234 := (not #58)
+#235 := (or #234 #228)
+#240 := (iff #53 #235)
+#263 := (iff #240 #262)
+#260 := (iff #235 #259)
+#257 := (iff #228 #256)
+#254 := (iff #225 #253)
+#255 := [rewrite]: #254
+#258 := [monotonicity #255]: #257
+#249 := (iff #234 #248)
+#246 := (iff #58 #245)
+#247 := [rewrite]: #246
+#250 := [monotonicity #247]: #249
+#261 := [monotonicity #250 #258]: #260
+#264 := [monotonicity #261]: #263
+#241 := (iff #66 #240)
+#238 := (iff #65 #235)
+#231 := (implies #58 #228)
+#236 := (iff #231 #235)
+#237 := [rewrite]: #236
+#232 := (iff #65 #231)
+#229 := (iff #64 #228)
+#226 := (iff #63 #225)
+#223 := (= #62 #222)
+#220 := (= #61 #219)
+#221 := [rewrite]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#239 := [trans #233 #237]: #238
+#242 := [monotonicity #239]: #241
+#266 := [trans #242 #264]: #265
+#217 := [asserted]: #66
+#267 := [mp #217 #266]: #262
+#455 := (not #262)
+#765 := (or #558 #259 #455)
+#439 := [def-axiom]: #765
+#772 := [unit-resolution #439 #267]: #440
+#490 := [unit-resolution #772 #508]: #558
+#483 := (or #53 #498 #529)
+#484 := [th-lemma]: #483
+#487 := [unit-resolution #484 #490]: #485
+#486 := [unit-resolution #487 #497]: #498
+#678 := (<= #686 0::int)
+#488 := (or #537 #678)
+#477 := [th-lemma]: #488
+#478 := [unit-resolution #477 #536]: #678
+#479 := (or #256 #449)
+#471 := [th-lemma]: #479
+#480 := [unit-resolution #471 #492]: #449
+#712 := (>= #711 0::int)
+#481 := (or #566 #712)
+#472 := [th-lemma]: #481
+#482 := [unit-resolution #472 #565]: #712
+#463 := [th-lemma #482 #480 #478 #486 #507]: false
+#464 := [lemma #463]: #259
+#771 := (or #53 #381)
+#434 := (or #53 #381 #455)
+#769 := [def-axiom]: #434
+#428 := [unit-resolution #769 #267]: #771
+#442 := [unit-resolution #428 #464]: #53
+#435 := [monotonicity #442]: #468
+#437 := [symm #435]: #602
+#438 := (not #602)
+#419 := (or #438 #709)
+#420 := [th-lemma]: #419
+#421 := [unit-resolution #420 #437]: #709
+#422 := [th-lemma #421 #414 #499]: false
+#423 := [lemma #422]: #448
+#410 := (or #245 #503)
+#611 := (>= #561 0::int)
+#682 := (or #438 #611)
+#447 := [th-lemma]: #682
+#430 := [unit-resolution #447 #437]: #611
+#432 := [hypothesis]: #556
+#433 := [th-lemma #532 #432 #430]: false
+#412 := [lemma #433]: #361
+#409 := (or #245 #556 #503)
+#407 := [th-lemma]: #409
+#398 := [unit-resolution #407 #412]: #410
+#400 := [unit-resolution #398 #423]: #245
+#454 := (or #381 #248 #256)
+#451 := [def-axiom]: #454
+#401 := [unit-resolution #451 #464]: #259
+#404 := [unit-resolution #401 #400]: #256
+#384 := (or #253 #399)
+#429 := [hypothesis]: #573
+#443 := (or #558 #597)
+#444 := [th-lemma]: #443
+#445 := [unit-resolution #444 #442]: #597
+#446 := [th-lemma #445 #507 #482 #429 #478]: false
+#436 := [lemma #446]: #363
+#405 := (or #253 #399 #573)
+#379 := [th-lemma]: #405
+#385 := [unit-resolution #379 #436]: #384
+#390 := [unit-resolution #385 #404]: #399
+#392 := (or #558 #629)
+#393 := [th-lemma]: #392
+#395 := [unit-resolution #393 #442]: #629
+[th-lemma #395 #575 #570 #390 #528]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= 3 3))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,17 @@
+#2 := false
+#4 := 3::int
+#5 := (= 3::int 3::int)
+#6 := (not #5)
+#30 := (iff #6 false)
+#1 := true
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #6 #25)
+#23 := (iff #5 true)
+#24 := [rewrite]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#22 := [asserted]: #6
+[mp #22 #31]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= 3.0 3.0))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,17 @@
+#2 := false
+#4 := 3::real
+#5 := (= 3::real 3::real)
+#6 := (not #5)
+#30 := (iff #6 false)
+#1 := true
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #6 #25)
+#23 := (iff #5 true)
+#24 := [rewrite]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#22 := [asserted]: #6
+[mp #22 #31]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (= (+ 3 1) 4))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,26 @@
+#2 := false
+#7 := 4::int
+#5 := 1::int
+#4 := 3::int
+#6 := (+ 3::int 1::int)
+#8 := (= #6 4::int)
+#9 := (not #8)
+#39 := (iff #9 false)
+#1 := true
+#34 := (not true)
+#37 := (iff #34 false)
+#38 := [rewrite]: #37
+#35 := (iff #9 #34)
+#32 := (iff #8 true)
+#27 := (= 4::int 4::int)
+#30 := (iff #27 true)
+#31 := [rewrite]: #30
+#28 := (iff #8 #27)
+#26 := [rewrite]: #8
+#29 := [monotonicity #26]: #28
+#33 := [trans #29 #31]: #32
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#25 := [asserted]: #9
+[mp #25 #40]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,9 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Int)
+ (uf_2 Int)
+ (uf_3 Int)
+ )
+:assumption (not (= (+ uf_1 (+ uf_2 uf_3)) (+ uf_2 (+ uf_3 uf_1))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,41 @@
+#2 := false
+decl uf_1 :: int
+#4 := uf_1
+decl uf_3 :: int
+#6 := uf_3
+#9 := (+ uf_3 uf_1)
+decl uf_2 :: int
+#5 := uf_2
+#10 := (+ uf_2 #9)
+#7 := (+ uf_2 uf_3)
+#8 := (+ uf_1 #7)
+#11 := (= #8 #10)
+#12 := (not #11)
+#51 := (iff #12 false)
+#1 := true
+#46 := (not true)
+#49 := (iff #46 false)
+#50 := [rewrite]: #49
+#47 := (iff #12 #46)
+#44 := (iff #11 true)
+#39 := (= #8 #8)
+#42 := (iff #39 true)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (= #10 #8)
+#29 := (+ uf_1 uf_3)
+#32 := (+ uf_2 #29)
+#35 := (= #32 #8)
+#36 := [rewrite]: #35
+#33 := (= #10 #32)
+#30 := (= #9 #29)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#48 := [monotonicity #45]: #47
+#52 := [trans #48 #50]: #51
+#28 := [asserted]: #12
+[mp #28 #52]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_05 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (< 5 (ite (<= 3 8) 8 3)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_05.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,35 @@
+#2 := false
+#5 := 3::int
+#6 := 8::int
+#7 := (<= 3::int 8::int)
+#8 := (ite #7 8::int 3::int)
+#4 := 5::int
+#9 := (< 5::int #8)
+#10 := (not #9)
+#50 := (iff #10 false)
+#1 := true
+#45 := (not true)
+#48 := (iff #45 false)
+#49 := [rewrite]: #48
+#46 := (iff #10 #45)
+#43 := (iff #9 true)
+#38 := (< 5::int 8::int)
+#41 := (iff #38 true)
+#42 := [rewrite]: #41
+#39 := (iff #9 #38)
+#36 := (= #8 8::int)
+#31 := (ite true 8::int 3::int)
+#34 := (= #31 8::int)
+#35 := [rewrite]: #34
+#32 := (= #8 #31)
+#29 := (iff #7 true)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#47 := [monotonicity #44]: #46
+#51 := [trans #47 #49]: #50
+#26 := [asserted]: #10
+[mp #26 #51]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_06 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Real)
+ (uf_2 Real)
+ )
+:assumption (not (<= (ite (< (+ uf_1 uf_2) 0.0) (~ (+ uf_1 uf_2)) (+ uf_1 uf_2)) (+ (ite (< uf_1 0.0) (~ uf_1) uf_1) (ite (< uf_2 0.0) (~ uf_2) uf_2))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_06.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,250 @@
+#2 := false
+#7 := 0::real
+decl uf_2 :: real
+#5 := uf_2
+#143 := 2::real
+#144 := (* 2::real uf_2)
+#165 := (<= #144 0::real)
+#188 := (not #165)
+#88 := (>= uf_2 0::real)
+#166 := (or #88 #165)
+#191 := (not #166)
+decl uf_1 :: real
+#4 := uf_1
+#76 := (>= uf_1 0::real)
+#89 := (not #88)
+#146 := (* 2::real uf_1)
+#167 := (<= #146 0::real)
+#199 := (not #167)
+#263 := [hypothesis]: #88
+#147 := (+ #146 #144)
+#168 := (<= #147 0::real)
+#169 := (ite #88 #167 #168)
+#194 := (not #169)
+#186 := (or #166 #89)
+#187 := [def-axiom]: #186
+#271 := [unit-resolution #187 #263]: #166
+#170 := (ite #76 #166 #169)
+#205 := (not #170)
+#6 := (+ uf_1 uf_2)
+#64 := (>= #6 0::real)
+#269 := (or #64 #89)
+#65 := (not #64)
+#262 := [hypothesis]: #65
+#174 := (>= #144 0::real)
+#175 := (or #89 #174)
+#230 := (not #175)
+#257 := [hypothesis]: #230
+#225 := (or #175 #88)
+#226 := [def-axiom]: #225
+#258 := [unit-resolution #226 #257]: #88
+#227 := (not #174)
+#228 := (or #175 #227)
+#229 := [def-axiom]: #228
+#259 := [unit-resolution #229 #257]: #227
+#260 := [th-lemma #259 #258]: false
+#261 := [lemma #260]: #175
+#172 := (>= #146 0::real)
+#171 := (>= #147 0::real)
+#173 := (ite #88 #171 #172)
+#176 := (ite #76 #173 #175)
+#233 := (not #176)
+#264 := (or #64 #233)
+#177 := (ite #64 #170 #176)
+#182 := (not #177)
+#36 := -1::real
+#38 := (* -1::real uf_2)
+#95 := (ite #88 uf_2 #38)
+#107 := (* -1::real #95)
+#37 := (* -1::real uf_1)
+#83 := (ite #76 uf_1 #37)
+#106 := (* -1::real #83)
+#108 := (+ #106 #107)
+#39 := (+ #37 #38)
+#71 := (ite #64 #6 #39)
+#109 := (+ #71 #108)
+#110 := (<= #109 0::real)
+#115 := (not #110)
+#183 := (iff #115 #182)
+#180 := (iff #110 #177)
+#150 := -2::real
+#152 := (* -2::real uf_2)
+#155 := (ite #88 #152 0::real)
+#151 := (* -2::real uf_1)
+#153 := (+ #151 #152)
+#154 := (ite #88 #153 #151)
+#156 := (ite #76 #154 #155)
+#148 := (ite #88 #146 #147)
+#145 := (ite #88 0::real #144)
+#149 := (ite #76 #145 #148)
+#157 := (ite #64 #149 #156)
+#162 := (<= #157 0::real)
+#178 := (iff #162 #177)
+#179 := [rewrite]: #178
+#163 := (iff #110 #162)
+#160 := (= #109 #157)
+#133 := (+ uf_1 #38)
+#134 := (ite #88 #133 #6)
+#131 := (+ #37 uf_2)
+#132 := (ite #88 #39 #131)
+#135 := (ite #76 #132 #134)
+#140 := (+ #71 #135)
+#158 := (= #140 #157)
+#159 := [rewrite]: #158
+#141 := (= #109 #140)
+#138 := (= #108 #135)
+#125 := (ite #88 #38 uf_2)
+#123 := (ite #76 #37 uf_1)
+#128 := (+ #123 #125)
+#136 := (= #128 #135)
+#137 := [rewrite]: #136
+#129 := (= #108 #128)
+#126 := (= #107 #125)
+#127 := [rewrite]: #126
+#121 := (= #106 #123)
+#124 := [rewrite]: #121
+#130 := [monotonicity #124 #127]: #129
+#139 := [trans #130 #137]: #138
+#142 := [monotonicity #139]: #141
+#161 := [trans #142 #159]: #160
+#164 := [monotonicity #161]: #163
+#181 := [trans #164 #179]: #180
+#184 := [monotonicity #181]: #183
+#15 := (- uf_2)
+#14 := (< uf_2 0::real)
+#16 := (ite #14 #15 uf_2)
+#12 := (- uf_1)
+#11 := (< uf_1 0::real)
+#13 := (ite #11 #12 uf_1)
+#17 := (+ #13 #16)
+#9 := (- #6)
+#8 := (< #6 0::real)
+#10 := (ite #8 #9 #6)
+#18 := (<= #10 #17)
+#19 := (not #18)
+#118 := (iff #19 #115)
+#52 := (ite #14 #38 uf_2)
+#47 := (ite #11 #37 uf_1)
+#55 := (+ #47 #52)
+#42 := (ite #8 #39 #6)
+#58 := (<= #42 #55)
+#61 := (not #58)
+#116 := (iff #61 #115)
+#113 := (iff #58 #110)
+#100 := (+ #83 #95)
+#103 := (<= #71 #100)
+#111 := (iff #103 #110)
+#112 := [rewrite]: #111
+#104 := (iff #58 #103)
+#101 := (= #55 #100)
+#98 := (= #52 #95)
+#92 := (ite #89 #38 uf_2)
+#96 := (= #92 #95)
+#97 := [rewrite]: #96
+#93 := (= #52 #92)
+#90 := (iff #14 #89)
+#91 := [rewrite]: #90
+#94 := [monotonicity #91]: #93
+#99 := [trans #94 #97]: #98
+#86 := (= #47 #83)
+#77 := (not #76)
+#80 := (ite #77 #37 uf_1)
+#84 := (= #80 #83)
+#85 := [rewrite]: #84
+#81 := (= #47 #80)
+#78 := (iff #11 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#87 := [trans #82 #85]: #86
+#102 := [monotonicity #87 #99]: #101
+#74 := (= #42 #71)
+#68 := (ite #65 #39 #6)
+#72 := (= #68 #71)
+#73 := [rewrite]: #72
+#69 := (= #42 #68)
+#66 := (iff #8 #65)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#75 := [trans #70 #73]: #74
+#105 := [monotonicity #75 #102]: #104
+#114 := [trans #105 #112]: #113
+#117 := [monotonicity #114]: #116
+#62 := (iff #19 #61)
+#59 := (iff #18 #58)
+#56 := (= #17 #55)
+#53 := (= #16 #52)
+#50 := (= #15 #38)
+#51 := [rewrite]: #50
+#54 := [monotonicity #51]: #53
+#48 := (= #13 #47)
+#45 := (= #12 #37)
+#46 := [rewrite]: #45
+#49 := [monotonicity #46]: #48
+#57 := [monotonicity #49 #54]: #56
+#43 := (= #10 #42)
+#40 := (= #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#60 := [monotonicity #44 #57]: #59
+#63 := [monotonicity #60]: #62
+#119 := [trans #63 #117]: #118
+#35 := [asserted]: #19
+#120 := [mp #35 #119]: #115
+#185 := [mp #120 #184]: #182
+#248 := (or #177 #64 #233)
+#249 := [def-axiom]: #248
+#265 := [unit-resolution #249 #185]: #264
+#266 := [unit-resolution #265 #262]: #233
+#240 := (or #176 #76 #230)
+#241 := [def-axiom]: #240
+#267 := [unit-resolution #241 #266 #261]: #76
+#268 := [th-lemma #267 #263 #262]: false
+#270 := [lemma #268]: #269
+#272 := [unit-resolution #270 #263]: #64
+#273 := (or #65 #205)
+#246 := (or #177 #65 #205)
+#247 := [def-axiom]: #246
+#274 := [unit-resolution #247 #185]: #273
+#275 := [unit-resolution #274 #272]: #205
+#255 := (or #170 #194 #191)
+#250 := [hypothesis]: #169
+#251 := [hypothesis]: #205
+#252 := [hypothesis]: #166
+#210 := (or #170 #77 #191)
+#211 := [def-axiom]: #210
+#253 := [unit-resolution #211 #251 #252]: #77
+#212 := (or #170 #76 #194)
+#213 := [def-axiom]: #212
+#254 := [unit-resolution #213 #253 #251 #250]: false
+#256 := [lemma #254]: #255
+#276 := [unit-resolution #256 #275 #271]: #194
+#200 := (or #169 #89 #199)
+#201 := [def-axiom]: #200
+#277 := [unit-resolution #201 #276 #263]: #199
+#278 := [unit-resolution #211 #275 #271]: #77
+#279 := [th-lemma #278 #277]: false
+#280 := [lemma #279]: #89
+#281 := [hypothesis]: #77
+#282 := [unit-resolution #241 #281 #261]: #176
+#283 := [unit-resolution #265 #282]: #64
+#284 := [th-lemma #281 #283 #280]: false
+#285 := [lemma #284]: #76
+#222 := (not #172)
+#286 := [hypothesis]: #222
+#287 := [th-lemma #285 #286]: false
+#288 := [lemma #287]: #172
+#223 := (or #173 #88 #222)
+#224 := [def-axiom]: #223
+#289 := [unit-resolution #224 #288 #280]: #173
+#214 := (not #173)
+#238 := (or #176 #77 #214)
+#239 := [def-axiom]: #238
+#290 := [unit-resolution #239 #289 #285]: #176
+#291 := [unit-resolution #265 #290]: #64
+#292 := [unit-resolution #274 #291]: #205
+#293 := [unit-resolution #211 #292 #285]: #191
+#189 := (or #166 #188)
+#190 := [def-axiom]: #189
+#294 := [unit-resolution #190 #293]: #188
+[th-lemma #280 #294]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_07 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,11 @@
+(benchmark Isabelle
+:extrasorts ( T2 T1)
+:extrafuns (
+ (uf_2 T1)
+ (uf_1 Int Int T1)
+ (uf_3 T1 T2)
+ )
+:assumption (forall (?x1 Int) (?x2 Int) (iff (= (uf_1 ?x1 ?x2) uf_2) (< ?x1 ?x2)))
+:assumption (not (= (uf_3 (uf_1 2 3)) (uf_3 uf_2)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_07.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,105 @@
+#2 := false
+decl uf_3 :: (-> T1 T2)
+decl uf_2 :: T1
+#7 := uf_2
+#16 := (uf_3 uf_2)
+decl uf_1 :: (-> int int T1)
+#13 := 3::int
+#12 := 2::int
+#14 := (uf_1 2::int 3::int)
+#15 := (uf_3 #14)
+#17 := (= #15 #16)
+#516 := (= #16 #15)
+#194 := (= uf_2 #14)
+#5 := (:var 0 int)
+#4 := (:var 1 int)
+#6 := (uf_1 #4 #5)
+#530 := (pattern #6)
+#39 := 0::int
+#37 := -1::int
+#41 := (* -1::int #5)
+#42 := (+ #4 #41)
+#40 := (>= #42 0::int)
+#38 := (not #40)
+#8 := (= #6 uf_2)
+#45 := (iff #8 #38)
+#531 := (forall (vars (?x1 int) (?x2 int)) (:pat #530) #45)
+#48 := (forall (vars (?x1 int) (?x2 int)) #45)
+#534 := (iff #48 #531)
+#532 := (iff #45 #45)
+#533 := [refl]: #532
+#535 := [quant-intro #533]: #534
+#58 := (~ #48 #48)
+#56 := (~ #45 #45)
+#57 := [refl]: #56
+#59 := [nnf-pos #57]: #58
+#9 := (< #4 #5)
+#10 := (iff #8 #9)
+#11 := (forall (vars (?x1 int) (?x2 int)) #10)
+#49 := (iff #11 #48)
+#46 := (iff #10 #45)
+#43 := (iff #9 #38)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#50 := [quant-intro #47]: #49
+#34 := [asserted]: #11
+#51 := [mp #34 #50]: #48
+#60 := [mp~ #51 #59]: #48
+#536 := [mp #60 #535]: #531
+#508 := (not #531)
+#509 := (or #508 #194)
+#201 := (* -1::int 3::int)
+#115 := (+ 2::int #201)
+#202 := (>= #115 0::int)
+#116 := (not #202)
+#114 := (= #14 uf_2)
+#203 := (iff #114 #116)
+#510 := (or #508 #203)
+#506 := (iff #510 #509)
+#150 := (iff #509 #509)
+#513 := [rewrite]: #150
+#171 := (iff #203 #194)
+#1 := true
+#164 := (iff #194 true)
+#169 := (iff #164 #194)
+#170 := [rewrite]: #169
+#505 := (iff #203 #164)
+#180 := (iff #116 true)
+#529 := (not false)
+#184 := (iff #529 true)
+#520 := [rewrite]: #184
+#519 := (iff #116 #529)
+#528 := (iff #202 false)
+#192 := (>= -1::int 0::int)
+#526 := (iff #192 false)
+#527 := [rewrite]: #526
+#193 := (iff #202 #192)
+#311 := (= #115 -1::int)
+#134 := -3::int
+#208 := (+ 2::int -3::int)
+#524 := (= #208 -1::int)
+#181 := [rewrite]: #524
+#187 := (= #115 #208)
+#207 := (= #201 -3::int)
+#204 := [rewrite]: #207
+#522 := [monotonicity #204]: #187
+#518 := [trans #522 #181]: #311
+#525 := [monotonicity #518]: #193
+#523 := [trans #525 #527]: #528
+#179 := [monotonicity #523]: #519
+#521 := [trans #179 #520]: #180
+#205 := (iff #114 #194)
+#206 := [rewrite]: #205
+#168 := [monotonicity #206 #521]: #505
+#507 := [trans #168 #170]: #171
+#512 := [monotonicity #507]: #506
+#515 := [trans #512 #513]: #506
+#511 := [quant-inst]: #510
+#155 := [mp #511 #515]: #509
+#156 := [unit-resolution #155 #536]: #194
+#514 := [monotonicity #156]: #516
+#517 := [symm #514]: #17
+#18 := (not #17)
+#35 := [asserted]: #18
+[unit-resolution #35 #517]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_08 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,7 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Int)
+ )
+:assumption (not (or (<= 4 (+ uf_1 3)) (< uf_1 1)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_08.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,54 @@
+#2 := false
+#9 := 1::int
+decl uf_1 :: int
+#5 := uf_1
+#10 := (< uf_1 1::int)
+#6 := 3::int
+#7 := (+ uf_1 3::int)
+#4 := 4::int
+#8 := (<= 4::int #7)
+#11 := (or #8 #10)
+#12 := (not #11)
+#66 := (iff #12 false)
+#29 := (+ 3::int uf_1)
+#32 := (<= 4::int #29)
+#38 := (or #10 #32)
+#43 := (not #38)
+#64 := (iff #43 false)
+#1 := true
+#59 := (not true)
+#62 := (iff #59 false)
+#63 := [rewrite]: #62
+#60 := (iff #43 #59)
+#57 := (iff #38 true)
+#48 := (>= uf_1 1::int)
+#46 := (not #48)
+#52 := (or #46 #48)
+#55 := (iff #52 true)
+#56 := [rewrite]: #55
+#53 := (iff #38 #52)
+#50 := (iff #32 #48)
+#51 := [rewrite]: #50
+#47 := (iff #10 #46)
+#49 := [rewrite]: #47
+#54 := [monotonicity #49 #51]: #53
+#58 := [trans #54 #56]: #57
+#61 := [monotonicity #58]: #60
+#65 := [trans #61 #63]: #64
+#44 := (iff #12 #43)
+#41 := (iff #11 #38)
+#35 := (or #32 #10)
+#39 := (iff #35 #38)
+#40 := [rewrite]: #39
+#36 := (iff #11 #35)
+#33 := (iff #8 #32)
+#30 := (= #7 #29)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#37 := [monotonicity #34]: #36
+#42 := [trans #37 #40]: #41
+#45 := [monotonicity #42]: #44
+#67 := [trans #45 #65]: #66
+#28 := [asserted]: #12
+[mp #28 #67]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_09 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,10 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Int)
+ (uf_2 Int)
+ )
+:assumption (<= 3 uf_1)
+:assumption (= uf_2 (+ uf_1 4))
+:assumption (not (< 0 (- uf_2 uf_1)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_09.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,63 @@
+#2 := false
+#11 := 0::int
+decl uf_2 :: int
+#7 := uf_2
+#42 := -1::int
+#45 := (* -1::int uf_2)
+decl uf_1 :: int
+#5 := uf_1
+#46 := (+ uf_1 #45)
+#63 := (>= #46 0::int)
+#83 := (iff #63 false)
+#44 := -4::int
+#79 := (>= -4::int 0::int)
+#81 := (iff #79 false)
+#82 := [rewrite]: #81
+#77 := (iff #63 #79)
+#47 := (= #46 -4::int)
+#8 := 4::int
+#9 := (+ uf_1 4::int)
+#10 := (= uf_2 #9)
+#49 := (iff #10 #47)
+#32 := (+ 4::int uf_1)
+#39 := (= uf_2 #32)
+#43 := (iff #39 #47)
+#48 := [rewrite]: #43
+#40 := (iff #10 #39)
+#37 := (= #9 #32)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#50 := [trans #41 #48]: #49
+#31 := [asserted]: #10
+#51 := [mp #31 #50]: #47
+#80 := [monotonicity #51]: #77
+#84 := [trans #80 #82]: #83
+#12 := (- uf_2 uf_1)
+#13 := (< 0::int #12)
+#14 := (not #13)
+#74 := (iff #14 #63)
+#53 := (* -1::int uf_1)
+#54 := (+ #53 uf_2)
+#57 := (< 0::int #54)
+#60 := (not #57)
+#72 := (iff #60 #63)
+#64 := (not #63)
+#67 := (not #64)
+#70 := (iff #67 #63)
+#71 := [rewrite]: #70
+#68 := (iff #60 #67)
+#65 := (iff #57 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#61 := (iff #14 #60)
+#58 := (iff #13 #57)
+#55 := (= #12 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59]: #61
+#75 := [trans #62 #73]: #74
+#52 := [asserted]: #14
+#76 := [mp #52 #75]: #63
+[mp #76 #84]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_10 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not (let (?x1 2) (not (= (+ ?x1 ?x1) 5))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_10.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,35 @@
+#2 := false
+#6 := 5::int
+#4 := 2::int
+#5 := (+ 2::int 2::int)
+#7 := (= #5 5::int)
+#8 := (not #7)
+#9 := (not #8)
+#48 := (iff #9 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #9 #43)
+#41 := (iff #8 true)
+#36 := (not false)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #8 #36)
+#34 := (iff #7 false)
+#26 := 4::int
+#29 := (= 4::int 5::int)
+#32 := (iff #29 false)
+#33 := [rewrite]: #32
+#30 := (iff #7 #29)
+#27 := (= #5 4::int)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#25 := [asserted]: #9
+[mp #25 #49]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_11 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,10 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_2 Real)
+ (uf_1 Real)
+ )
+:assumption (< (+ (* 3.0 uf_1) (* 7.0 uf_2)) 4.0)
+:assumption (< 3.0 (* 2.0 uf_1))
+:assumption (not (< uf_2 0.0))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_11.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,45 @@
+#2 := false
+#11 := 4::real
+decl uf_2 :: real
+#8 := uf_2
+#7 := 7::real
+#9 := (* 7::real uf_2)
+decl uf_1 :: real
+#5 := uf_1
+#4 := 3::real
+#6 := (* 3::real uf_1)
+#10 := (+ #6 #9)
+#41 := (>= #10 4::real)
+#39 := (not #41)
+#12 := (< #10 4::real)
+#40 := (iff #12 #39)
+#37 := [rewrite]: #40
+#34 := [asserted]: #12
+#38 := [mp #34 #37]: #39
+#13 := 2::real
+#14 := (* 2::real uf_1)
+#43 := (<= #14 3::real)
+#44 := (not #43)
+#15 := (< 3::real #14)
+#45 := (iff #15 #44)
+#46 := [rewrite]: #45
+#35 := [asserted]: #15
+#47 := [mp #35 #46]: #44
+#16 := 0::real
+#51 := (>= uf_2 0::real)
+#17 := (< uf_2 0::real)
+#18 := (not #17)
+#58 := (iff #18 #51)
+#49 := (not #51)
+#53 := (not #49)
+#56 := (iff #53 #51)
+#57 := [rewrite]: #56
+#54 := (iff #18 #53)
+#50 := (iff #17 #49)
+#52 := [rewrite]: #50
+#55 := [monotonicity #52]: #54
+#59 := [trans #55 #57]: #58
+#36 := [asserted]: #18
+#60 := [mp #36 #59]: #51
+[th-lemma #60 #47 #38]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_12 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_2 Int)
+ (uf_1 Int)
+ )
+:assumption (not (iff (or (<= 0 (+ uf_1 (* (~ 1) uf_2))) (or (not (<= 0 uf_2)) (<= 0 uf_2))) (not false)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_12.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,59 @@
+#2 := false
+#16 := (not false)
+decl uf_2 :: int
+#8 := uf_2
+#4 := 0::int
+#12 := (<= 0::int uf_2)
+#13 := (not #12)
+#14 := (or #13 #12)
+#6 := 1::int
+#7 := (- 1::int)
+#9 := (* #7 uf_2)
+decl uf_1 :: int
+#5 := uf_1
+#10 := (+ uf_1 #9)
+#11 := (<= 0::int #10)
+#15 := (or #11 #14)
+#17 := (iff #15 #16)
+#18 := (not #17)
+#70 := (iff #18 false)
+#1 := true
+#65 := (not true)
+#68 := (iff #65 false)
+#69 := [rewrite]: #68
+#66 := (iff #18 #65)
+#63 := (iff #17 true)
+#58 := (iff true true)
+#61 := (iff #58 true)
+#62 := [rewrite]: #61
+#59 := (iff #17 #58)
+#56 := (iff #16 true)
+#57 := [rewrite]: #56
+#54 := (iff #15 true)
+#35 := -1::int
+#38 := (* -1::int uf_2)
+#41 := (+ uf_1 #38)
+#44 := (<= 0::int #41)
+#49 := (or #44 true)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #15 #49)
+#47 := (iff #14 true)
+#48 := [rewrite]: #47
+#45 := (iff #11 #44)
+#42 := (= #10 #41)
+#39 := (= #9 #38)
+#36 := (= #7 -1::int)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#51 := [monotonicity #46 #48]: #50
+#55 := [trans #51 #53]: #54
+#60 := [monotonicity #55 #57]: #59
+#64 := [trans #60 #62]: #63
+#67 := [monotonicity #64]: #66
+#71 := [trans #67 #69]: #70
+#34 := [asserted]: #18
+[mp #34 #71]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_13 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_2 T1)
+ (uf_3 Int Int T1)
+ (uf_1 Int Int T1)
+ (uf_4 Int)
+ )
+:assumption (forall (?x1 Int) (?x2 Int) (iff (= (uf_1 ?x1 ?x2) uf_2) (<= ?x1 ?x2)))
+:assumption (forall (?x3 Int) (?x4 Int) (iff (= (uf_3 ?x3 ?x4) uf_2) (< ?x3 ?x4)))
+:assumption (not (distinct (uf_3 uf_4 3) (uf_1 3 uf_4)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_13.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,212 @@
+#2 := false
+decl uf_3 :: (-> int int T1)
+#18 := 3::int
+decl uf_4 :: int
+#17 := uf_4
+#19 := (uf_3 uf_4 3::int)
+decl uf_2 :: T1
+#7 := uf_2
+#221 := (= uf_2 #19)
+decl uf_1 :: (-> int int T1)
+#20 := (uf_1 3::int uf_4)
+#256 := (= uf_2 #20)
+#531 := (iff #256 #221)
+#529 := (iff #221 #256)
+#87 := (= #19 #20)
+#21 := (distinct #19 #20)
+#22 := (not #21)
+#96 := (iff #22 #87)
+#88 := (not #87)
+#91 := (not #88)
+#94 := (iff #91 #87)
+#95 := [rewrite]: #94
+#92 := (iff #22 #91)
+#89 := (iff #21 #88)
+#90 := [rewrite]: #89
+#93 := [monotonicity #90]: #92
+#97 := [trans #93 #95]: #96
+#86 := [asserted]: #22
+#100 := [mp #86 #97]: #87
+#530 := [monotonicity #100]: #529
+#525 := [symm #530]: #531
+#548 := (not #221)
+#232 := (not #256)
+#526 := (iff #232 #548)
+#532 := [monotonicity #525]: #526
+#536 := [hypothesis]: #232
+#533 := [mp #536 #532]: #548
+#259 := (>= uf_4 3::int)
+#576 := (not #259)
+#542 := (or #256 #576)
+#257 := (iff #256 #259)
+#5 := (:var 0 int)
+#4 := (:var 1 int)
+#6 := (uf_1 #4 #5)
+#583 := (pattern #6)
+#44 := 0::int
+#41 := -1::int
+#42 := (* -1::int #5)
+#43 := (+ #4 #42)
+#45 := (<= #43 0::int)
+#8 := (= #6 uf_2)
+#48 := (iff #8 #45)
+#584 := (forall (vars (?x1 int) (?x2 int)) (:pat #583) #48)
+#51 := (forall (vars (?x1 int) (?x2 int)) #48)
+#587 := (iff #51 #584)
+#585 := (iff #48 #48)
+#586 := [refl]: #585
+#588 := [quant-intro #586]: #587
+#108 := (~ #51 #51)
+#106 := (~ #48 #48)
+#107 := [refl]: #106
+#109 := [nnf-pos #107]: #108
+#9 := (<= #4 #5)
+#10 := (iff #8 #9)
+#11 := (forall (vars (?x1 int) (?x2 int)) #10)
+#52 := (iff #11 #51)
+#49 := (iff #10 #48)
+#46 := (iff #9 #45)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#53 := [quant-intro #50]: #52
+#38 := [asserted]: #11
+#54 := [mp #38 #53]: #51
+#110 := [mp~ #54 #109]: #51
+#589 := [mp #110 #588]: #584
+#575 := (not #584)
+#577 := (or #575 #257)
+#167 := (* -1::int uf_4)
+#254 := (+ 3::int #167)
+#168 := (<= #254 0::int)
+#255 := (= #20 uf_2)
+#169 := (iff #255 #168)
+#234 := (or #575 #169)
+#571 := (iff #234 #577)
+#246 := (iff #577 #577)
+#578 := [rewrite]: #246
+#261 := (iff #169 #257)
+#187 := (iff #168 #259)
+#260 := [rewrite]: #187
+#247 := (iff #255 #256)
+#258 := [rewrite]: #247
+#240 := [monotonicity #258 #260]: #261
+#245 := [monotonicity #240]: #571
+#579 := [trans #245 #578]: #571
+#364 := [quant-inst]: #234
+#580 := [mp #364 #579]: #577
+#541 := [unit-resolution #580 #589]: #257
+#581 := (not #257)
+#582 := (or #581 #256 #576)
+#572 := [def-axiom]: #582
+#537 := [unit-resolution #572 #541]: #542
+#543 := [unit-resolution #537 #536]: #576
+#385 := (or #221 #259)
+#552 := (iff #221 #576)
+#12 := (uf_3 #4 #5)
+#590 := (pattern #12)
+#69 := (>= #43 0::int)
+#68 := (not #69)
+#40 := (= uf_2 #12)
+#75 := (iff #40 #68)
+#591 := (forall (vars (?x3 int) (?x4 int)) (:pat #590) #75)
+#80 := (forall (vars (?x3 int) (?x4 int)) #75)
+#594 := (iff #80 #591)
+#592 := (iff #75 #75)
+#593 := [refl]: #592
+#595 := [quant-intro #593]: #594
+#101 := (~ #80 #80)
+#111 := (~ #75 #75)
+#112 := [refl]: #111
+#98 := [nnf-pos #112]: #101
+#14 := (< #4 #5)
+#13 := (= #12 uf_2)
+#15 := (iff #13 #14)
+#16 := (forall (vars (?x3 int) (?x4 int)) #15)
+#83 := (iff #16 #80)
+#60 := (iff #14 #40)
+#65 := (forall (vars (?x3 int) (?x4 int)) #60)
+#81 := (iff #65 #80)
+#78 := (iff #60 #75)
+#72 := (iff #68 #40)
+#76 := (iff #72 #75)
+#77 := [rewrite]: #76
+#73 := (iff #60 #72)
+#70 := (iff #14 #68)
+#71 := [rewrite]: #70
+#74 := [monotonicity #71]: #73
+#79 := [trans #74 #77]: #78
+#82 := [quant-intro #79]: #81
+#66 := (iff #16 #65)
+#63 := (iff #15 #60)
+#57 := (iff #40 #14)
+#61 := (iff #57 #60)
+#62 := [rewrite]: #61
+#58 := (iff #15 #57)
+#55 := (iff #13 #40)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#64 := [trans #59 #62]: #63
+#67 := [quant-intro #64]: #66
+#84 := [trans #67 #82]: #83
+#39 := [asserted]: #16
+#85 := [mp #39 #84]: #80
+#113 := [mp~ #85 #98]: #80
+#596 := [mp #113 #595]: #591
+#276 := (not #591)
+#550 := (or #276 #552)
+#222 := (* -1::int 3::int)
+#223 := (+ uf_4 #222)
+#224 := (>= #223 0::int)
+#560 := (not #224)
+#561 := (iff #221 #560)
+#554 := (or #276 #561)
+#555 := (iff #554 #550)
+#266 := (iff #550 #550)
+#267 := [rewrite]: #266
+#553 := (iff #561 #552)
+#282 := (iff #560 #576)
+#280 := (iff #224 #259)
+#562 := -3::int
+#566 := (+ -3::int uf_4)
+#567 := (>= #566 0::int)
+#557 := (iff #567 #259)
+#279 := [rewrite]: #557
+#570 := (iff #224 #567)
+#209 := (= #223 #566)
+#559 := (+ uf_4 -3::int)
+#568 := (= #559 #566)
+#208 := [rewrite]: #568
+#565 := (= #223 #559)
+#563 := (= #222 -3::int)
+#564 := [rewrite]: #563
+#203 := [monotonicity #564]: #565
+#569 := [trans #203 #208]: #209
+#556 := [monotonicity #569]: #570
+#281 := [trans #556 #279]: #280
+#175 := [monotonicity #281]: #282
+#275 := [monotonicity #175]: #553
+#265 := [monotonicity #275]: #555
+#268 := [trans #265 #267]: #555
+#551 := [quant-inst]: #554
+#546 := [mp #551 #268]: #550
+#384 := [unit-resolution #546 #596]: #552
+#547 := (not #552)
+#262 := (or #547 #221 #259)
+#544 := [def-axiom]: #262
+#386 := [unit-resolution #544 #384]: #385
+#528 := [unit-resolution #386 #543]: #221
+#527 := [unit-resolution #528 #533]: false
+#534 := [lemma #527]: #256
+#523 := [mp #534 #525]: #221
+#363 := (or #232 #259)
+#237 := (or #581 #232 #259)
+#573 := [def-axiom]: #237
+#365 := [unit-resolution #573 #541]: #363
+#366 := [unit-resolution #365 #534]: #259
+#519 := (or #548 #576)
+#545 := (or #547 #548 #576)
+#549 := [def-axiom]: #545
+#520 := [unit-resolution #549 #384]: #519
+#522 := [unit-resolution #520 #366]: #548
+[unit-resolution #522 #523]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_14 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Int)
+ )
+:assumption (< 0 uf_1)
+:assumption (not (distinct uf_1 (* uf_1 2) (- uf_1 uf_1)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_14.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,86 @@
+#2 := false
+decl uf_1 :: int
+#5 := uf_1
+#7 := 2::int
+#29 := (* 2::int uf_1)
+#4 := 0::int
+#54 := (= 0::int #29)
+#55 := (not #54)
+#61 := (= #29 0::int)
+#104 := (not #61)
+#110 := (iff #104 #55)
+#108 := (iff #61 #54)
+#109 := [commutativity]: #108
+#111 := [monotonicity #109]: #110
+#62 := (<= #29 0::int)
+#100 := (not #62)
+#30 := (<= uf_1 0::int)
+#31 := (not #30)
+#6 := (< 0::int uf_1)
+#32 := (iff #6 #31)
+#33 := [rewrite]: #32
+#27 := [asserted]: #6
+#34 := [mp #27 #33]: #31
+#101 := (or #100 #30)
+#102 := [th-lemma]: #101
+#103 := [unit-resolution #102 #34]: #100
+#105 := (or #104 #62)
+#106 := [th-lemma]: #105
+#107 := [unit-resolution #106 #103]: #104
+#112 := [mp #107 #111]: #55
+#56 := (= uf_1 #29)
+#57 := (not #56)
+#53 := (= 0::int uf_1)
+#50 := (not #53)
+#58 := (and #50 #55 #57)
+#69 := (not #58)
+#42 := (distinct 0::int uf_1 #29)
+#47 := (not #42)
+#9 := (- uf_1 uf_1)
+#8 := (* uf_1 2::int)
+#10 := (distinct uf_1 #8 #9)
+#11 := (not #10)
+#48 := (iff #11 #47)
+#45 := (iff #10 #42)
+#39 := (distinct uf_1 #29 0::int)
+#43 := (iff #39 #42)
+#44 := [rewrite]: #43
+#40 := (iff #10 #39)
+#37 := (= #9 0::int)
+#38 := [rewrite]: #37
+#35 := (= #8 #29)
+#36 := [rewrite]: #35
+#41 := [monotonicity #36 #38]: #40
+#46 := [trans #41 #44]: #45
+#49 := [monotonicity #46]: #48
+#28 := [asserted]: #11
+#52 := [mp #28 #49]: #47
+#80 := (or #42 #69)
+#81 := [def-axiom]: #80
+#82 := [unit-resolution #81 #52]: #69
+#59 := (= uf_1 0::int)
+#83 := (not #59)
+#89 := (iff #83 #50)
+#87 := (iff #59 #53)
+#88 := [commutativity]: #87
+#90 := [monotonicity #88]: #89
+#84 := (or #83 #30)
+#85 := [th-lemma]: #84
+#86 := [unit-resolution #85 #34]: #83
+#91 := [mp #86 #90]: #50
+#64 := -1::int
+#65 := (* -1::int #29)
+#66 := (+ uf_1 #65)
+#68 := (>= #66 0::int)
+#92 := (not #68)
+#93 := (or #92 #30)
+#94 := [th-lemma]: #93
+#95 := [unit-resolution #94 #34]: #92
+#96 := (or #57 #68)
+#97 := [th-lemma]: #96
+#98 := [unit-resolution #97 #95]: #57
+#76 := (or #58 #53 #54 #56)
+#77 := [def-axiom]: #76
+#99 := [unit-resolution #77 #98 #91 #82]: #54
+[unit-resolution #99 #112]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_15 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,9 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_2 Int)
+ (uf_1 Int)
+ (uf_3 Int)
+ )
+:assumption (not (or (and (< uf_1 uf_2) (< uf_2 uf_3)) (or (and (< uf_1 uf_2) (= uf_2 uf_3)) (or (and (< uf_1 uf_3) (< uf_3 uf_2)) (or (and (= uf_1 uf_3) (< uf_3 uf_2)) (or (and (= uf_1 uf_2) (< uf_2 uf_3)) (or (and (< uf_3 uf_2) (< uf_2 uf_1)) (or (and (< uf_3 uf_2) (= uf_2 uf_1)) (or (and (< uf_3 uf_1) (< uf_1 uf_2)) (or (and (= uf_3 uf_1) (< uf_1 uf_2)) (or (and (= uf_3 uf_2) (< uf_2 uf_1)) (or (and (< uf_2 uf_1) (< uf_1 uf_3)) (or (and (< uf_2 uf_1) (= uf_3 uf_1)) (or (and (< uf_2 uf_3) (< uf_3 uf_1)) (or (and (= uf_2 uf_1) (< uf_1 uf_3)) (or (and (= uf_2 uf_3) (< uf_3 uf_1)) (and (= uf_3 uf_2) (= uf_2 uf_1))))))))))))))))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_15.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,673 @@
+#2 := false
+#169 := 0::int
+decl uf_2 :: int
+#5 := uf_2
+#166 := -1::int
+#202 := (* -1::int uf_2)
+decl uf_1 :: int
+#4 := uf_1
+#203 := (+ uf_1 #202)
+#218 := (>= #203 0::int)
+decl uf_3 :: int
+#7 := uf_3
+#167 := (* -1::int uf_3)
+#168 := (+ uf_1 #167)
+#178 := (>= #168 0::int)
+#217 := (not #218)
+#204 := (<= #203 0::int)
+#205 := (not #204)
+#692 := [hypothesis]: #205
+#177 := (not #178)
+#693 := (or #177 #204)
+#170 := (<= #168 0::int)
+#191 := (+ uf_2 #167)
+#237 := (<= #191 0::int)
+#238 := (not #237)
+#171 := (not #170)
+#685 := [hypothesis]: #171
+#190 := (>= #191 0::int)
+#455 := (or #170 #190)
+#189 := (not #190)
+#197 := (and #171 #189)
+#354 := (not #197)
+#464 := (iff #354 #455)
+#456 := (not #455)
+#459 := (not #456)
+#462 := (iff #459 #455)
+#463 := [rewrite]: #462
+#460 := (iff #354 #459)
+#457 := (iff #197 #456)
+#458 := [rewrite]: #457
+#461 := [monotonicity #458]: #460
+#465 := [trans #461 #463]: #464
+#287 := (and #189 #217)
+#10 := (= uf_2 uf_3)
+#279 := (and #10 #217)
+#273 := (and #177 #238)
+#15 := (= uf_1 uf_3)
+#268 := (and #15 #238)
+#17 := (= uf_1 uf_2)
+#260 := (and #17 #189)
+#252 := (and #205 #238)
+#244 := (and #17 #238)
+#232 := (and #171 #217)
+#224 := (and #15 #217)
+#214 := (and #10 #205)
+#211 := (and #177 #205)
+#208 := (and #15 #205)
+#184 := (and #17 #177)
+#174 := (and #10 #171)
+#115 := (and #10 #17)
+#337 := (or #115 #174 #184 #197 #208 #211 #214 #224 #232 #244 #252 #260 #268 #273 #279 #287)
+#342 := (not #337)
+#21 := (= uf_2 uf_1)
+#27 := (= uf_3 uf_2)
+#34 := (and #27 #21)
+#23 := (< uf_3 uf_1)
+#33 := (and #10 #23)
+#35 := (or #33 #34)
+#12 := (< uf_1 uf_3)
+#32 := (and #21 #12)
+#36 := (or #32 #35)
+#8 := (< uf_2 uf_3)
+#31 := (and #8 #23)
+#37 := (or #31 #36)
+#25 := (= uf_3 uf_1)
+#19 := (< uf_2 uf_1)
+#30 := (and #19 #25)
+#38 := (or #30 #37)
+#29 := (and #19 #12)
+#39 := (or #29 #38)
+#28 := (and #27 #19)
+#40 := (or #28 #39)
+#6 := (< uf_1 uf_2)
+#26 := (and #25 #6)
+#41 := (or #26 #40)
+#24 := (and #23 #6)
+#42 := (or #24 #41)
+#13 := (< uf_3 uf_2)
+#22 := (and #13 #21)
+#43 := (or #22 #42)
+#20 := (and #13 #19)
+#44 := (or #20 #43)
+#18 := (and #17 #8)
+#45 := (or #18 #44)
+#16 := (and #15 #13)
+#46 := (or #16 #45)
+#14 := (and #12 #13)
+#47 := (or #14 #46)
+#11 := (and #6 #10)
+#48 := (or #11 #47)
+#9 := (and #6 #8)
+#49 := (or #9 #48)
+#50 := (not #49)
+#345 := (iff #50 #342)
+#118 := (or #33 #115)
+#110 := (and #12 #17)
+#121 := (or #110 #118)
+#124 := (or #31 #121)
+#102 := (and #15 #19)
+#127 := (or #102 #124)
+#96 := (and #12 #19)
+#130 := (or #96 #127)
+#93 := (and #10 #19)
+#133 := (or #93 #130)
+#86 := (and #6 #15)
+#136 := (or #86 #133)
+#78 := (and #6 #23)
+#139 := (or #78 #136)
+#75 := (and #13 #17)
+#142 := (or #75 #139)
+#145 := (or #20 #142)
+#70 := (and #8 #17)
+#148 := (or #70 #145)
+#67 := (and #13 #15)
+#151 := (or #67 #148)
+#154 := (or #14 #151)
+#157 := (or #11 #154)
+#160 := (or #9 #157)
+#163 := (not #160)
+#343 := (iff #163 #342)
+#340 := (iff #160 #337)
+#292 := (or #174 #115)
+#295 := (or #184 #292)
+#298 := (or #197 #295)
+#301 := (or #208 #298)
+#304 := (or #211 #301)
+#307 := (or #214 #304)
+#310 := (or #224 #307)
+#313 := (or #232 #310)
+#316 := (or #244 #313)
+#319 := (or #252 #316)
+#322 := (or #260 #319)
+#325 := (or #268 #322)
+#328 := (or #273 #325)
+#331 := (or #279 #328)
+#334 := (or #287 #331)
+#338 := (iff #334 #337)
+#339 := [rewrite]: #338
+#335 := (iff #160 #334)
+#332 := (iff #157 #331)
+#329 := (iff #154 #328)
+#326 := (iff #151 #325)
+#323 := (iff #148 #322)
+#320 := (iff #145 #319)
+#317 := (iff #142 #316)
+#314 := (iff #139 #313)
+#311 := (iff #136 #310)
+#308 := (iff #133 #307)
+#305 := (iff #130 #304)
+#302 := (iff #127 #301)
+#299 := (iff #124 #298)
+#296 := (iff #121 #295)
+#293 := (iff #118 #292)
+#175 := (iff #33 #174)
+#172 := (iff #23 #171)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173]: #175
+#294 := [monotonicity #176]: #293
+#187 := (iff #110 #184)
+#181 := (and #177 #17)
+#185 := (iff #181 #184)
+#186 := [rewrite]: #185
+#182 := (iff #110 #181)
+#179 := (iff #12 #177)
+#180 := [rewrite]: #179
+#183 := [monotonicity #180]: #182
+#188 := [trans #183 #186]: #187
+#297 := [monotonicity #188 #294]: #296
+#200 := (iff #31 #197)
+#194 := (and #189 #171)
+#198 := (iff #194 #197)
+#199 := [rewrite]: #198
+#195 := (iff #31 #194)
+#192 := (iff #8 #189)
+#193 := [rewrite]: #192
+#196 := [monotonicity #193 #173]: #195
+#201 := [trans #196 #199]: #200
+#300 := [monotonicity #201 #297]: #299
+#209 := (iff #102 #208)
+#206 := (iff #19 #205)
+#207 := [rewrite]: #206
+#210 := [monotonicity #207]: #209
+#303 := [monotonicity #210 #300]: #302
+#212 := (iff #96 #211)
+#213 := [monotonicity #180 #207]: #212
+#306 := [monotonicity #213 #303]: #305
+#215 := (iff #93 #214)
+#216 := [monotonicity #207]: #215
+#309 := [monotonicity #216 #306]: #308
+#227 := (iff #86 #224)
+#221 := (and #217 #15)
+#225 := (iff #221 #224)
+#226 := [rewrite]: #225
+#222 := (iff #86 #221)
+#219 := (iff #6 #217)
+#220 := [rewrite]: #219
+#223 := [monotonicity #220]: #222
+#228 := [trans #223 #226]: #227
+#312 := [monotonicity #228 #309]: #311
+#235 := (iff #78 #232)
+#229 := (and #217 #171)
+#233 := (iff #229 #232)
+#234 := [rewrite]: #233
+#230 := (iff #78 #229)
+#231 := [monotonicity #220 #173]: #230
+#236 := [trans #231 #234]: #235
+#315 := [monotonicity #236 #312]: #314
+#247 := (iff #75 #244)
+#241 := (and #238 #17)
+#245 := (iff #241 #244)
+#246 := [rewrite]: #245
+#242 := (iff #75 #241)
+#239 := (iff #13 #238)
+#240 := [rewrite]: #239
+#243 := [monotonicity #240]: #242
+#248 := [trans #243 #246]: #247
+#318 := [monotonicity #248 #315]: #317
+#255 := (iff #20 #252)
+#249 := (and #238 #205)
+#253 := (iff #249 #252)
+#254 := [rewrite]: #253
+#250 := (iff #20 #249)
+#251 := [monotonicity #240 #207]: #250
+#256 := [trans #251 #254]: #255
+#321 := [monotonicity #256 #318]: #320
+#263 := (iff #70 #260)
+#257 := (and #189 #17)
+#261 := (iff #257 #260)
+#262 := [rewrite]: #261
+#258 := (iff #70 #257)
+#259 := [monotonicity #193]: #258
+#264 := [trans #259 #262]: #263
+#324 := [monotonicity #264 #321]: #323
+#271 := (iff #67 #268)
+#265 := (and #238 #15)
+#269 := (iff #265 #268)
+#270 := [rewrite]: #269
+#266 := (iff #67 #265)
+#267 := [monotonicity #240]: #266
+#272 := [trans #267 #270]: #271
+#327 := [monotonicity #272 #324]: #326
+#274 := (iff #14 #273)
+#275 := [monotonicity #180 #240]: #274
+#330 := [monotonicity #275 #327]: #329
+#282 := (iff #11 #279)
+#276 := (and #217 #10)
+#280 := (iff #276 #279)
+#281 := [rewrite]: #280
+#277 := (iff #11 #276)
+#278 := [monotonicity #220]: #277
+#283 := [trans #278 #281]: #282
+#333 := [monotonicity #283 #330]: #332
+#290 := (iff #9 #287)
+#284 := (and #217 #189)
+#288 := (iff #284 #287)
+#289 := [rewrite]: #288
+#285 := (iff #9 #284)
+#286 := [monotonicity #220 #193]: #285
+#291 := [trans #286 #289]: #290
+#336 := [monotonicity #291 #333]: #335
+#341 := [trans #336 #339]: #340
+#344 := [monotonicity #341]: #343
+#164 := (iff #50 #163)
+#161 := (iff #49 #160)
+#158 := (iff #48 #157)
+#155 := (iff #47 #154)
+#152 := (iff #46 #151)
+#149 := (iff #45 #148)
+#146 := (iff #44 #145)
+#143 := (iff #43 #142)
+#140 := (iff #42 #139)
+#137 := (iff #41 #136)
+#134 := (iff #40 #133)
+#131 := (iff #39 #130)
+#128 := (iff #38 #127)
+#125 := (iff #37 #124)
+#122 := (iff #36 #121)
+#119 := (iff #35 #118)
+#116 := (iff #34 #115)
+#73 := (iff #21 #17)
+#74 := [rewrite]: #73
+#91 := (iff #27 #10)
+#92 := [rewrite]: #91
+#117 := [monotonicity #92 #74]: #116
+#120 := [monotonicity #117]: #119
+#113 := (iff #32 #110)
+#107 := (and #17 #12)
+#111 := (iff #107 #110)
+#112 := [rewrite]: #111
+#108 := (iff #32 #107)
+#109 := [monotonicity #74]: #108
+#114 := [trans #109 #112]: #113
+#123 := [monotonicity #114 #120]: #122
+#126 := [monotonicity #123]: #125
+#105 := (iff #30 #102)
+#99 := (and #19 #15)
+#103 := (iff #99 #102)
+#104 := [rewrite]: #103
+#100 := (iff #30 #99)
+#81 := (iff #25 #15)
+#82 := [rewrite]: #81
+#101 := [monotonicity #82]: #100
+#106 := [trans #101 #104]: #105
+#129 := [monotonicity #106 #126]: #128
+#97 := (iff #29 #96)
+#98 := [rewrite]: #97
+#132 := [monotonicity #98 #129]: #131
+#94 := (iff #28 #93)
+#95 := [monotonicity #92]: #94
+#135 := [monotonicity #95 #132]: #134
+#89 := (iff #26 #86)
+#83 := (and #15 #6)
+#87 := (iff #83 #86)
+#88 := [rewrite]: #87
+#84 := (iff #26 #83)
+#85 := [monotonicity #82]: #84
+#90 := [trans #85 #88]: #89
+#138 := [monotonicity #90 #135]: #137
+#79 := (iff #24 #78)
+#80 := [rewrite]: #79
+#141 := [monotonicity #80 #138]: #140
+#76 := (iff #22 #75)
+#77 := [monotonicity #74]: #76
+#144 := [monotonicity #77 #141]: #143
+#147 := [monotonicity #144]: #146
+#71 := (iff #18 #70)
+#72 := [rewrite]: #71
+#150 := [monotonicity #72 #147]: #149
+#68 := (iff #16 #67)
+#69 := [rewrite]: #68
+#153 := [monotonicity #69 #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [monotonicity #162]: #164
+#346 := [trans #165 #344]: #345
+#66 := [asserted]: #50
+#347 := [mp #66 #346]: #342
+#355 := [not-or-elim #347]: #354
+#466 := [mp #355 #465]: #455
+#686 := [unit-resolution #466 #685]: #190
+#427 := (or #170 #189 #238)
+#350 := (not #174)
+#430 := (iff #350 #427)
+#382 := (or #189 #238)
+#414 := (or #170 #382)
+#428 := (iff #414 #427)
+#429 := [rewrite]: #428
+#425 := (iff #350 #414)
+#415 := (not #414)
+#420 := (not #415)
+#423 := (iff #420 #414)
+#424 := [rewrite]: #423
+#421 := (iff #350 #420)
+#418 := (iff #174 #415)
+#380 := (not #382)
+#411 := (and #380 #171)
+#416 := (iff #411 #415)
+#417 := [rewrite]: #416
+#412 := (iff #174 #411)
+#383 := (iff #10 #380)
+#384 := [rewrite]: #383
+#413 := [monotonicity #384]: #412
+#419 := [trans #413 #417]: #418
+#422 := [monotonicity #419]: #421
+#426 := [trans #422 #424]: #425
+#431 := [trans #426 #429]: #430
+#351 := [not-or-elim #347]: #350
+#432 := [mp #351 #431]: #427
+#687 := [unit-resolution #432 #686 #685]: #238
+#549 := (or #170 #218)
+#364 := (not #232)
+#558 := (iff #364 #549)
+#550 := (not #549)
+#553 := (not #550)
+#556 := (iff #553 #549)
+#557 := [rewrite]: #556
+#554 := (iff #364 #553)
+#551 := (iff #232 #550)
+#552 := [rewrite]: #551
+#555 := [monotonicity #552]: #554
+#559 := [trans #555 #557]: #558
+#365 := [not-or-elim #347]: #364
+#560 := [mp #365 #559]: #549
+#688 := [unit-resolution #560 #685]: #218
+#577 := (or #205 #217 #237)
+#366 := (not #244)
+#580 := (iff #366 #577)
+#385 := (or #205 #217)
+#564 := (or #237 #385)
+#578 := (iff #564 #577)
+#579 := [rewrite]: #578
+#575 := (iff #366 #564)
+#565 := (not #564)
+#570 := (not #565)
+#573 := (iff #570 #564)
+#574 := [rewrite]: #573
+#571 := (iff #366 #570)
+#568 := (iff #244 #565)
+#386 := (not #385)
+#561 := (and #386 #238)
+#566 := (iff #561 #565)
+#567 := [rewrite]: #566
+#562 := (iff #244 #561)
+#387 := (iff #17 #386)
+#388 := [rewrite]: #387
+#563 := [monotonicity #388]: #562
+#569 := [trans #563 #567]: #568
+#572 := [monotonicity #569]: #571
+#576 := [trans #572 #574]: #575
+#581 := [trans #576 #579]: #580
+#367 := [not-or-elim #347]: #366
+#582 := [mp #367 #581]: #577
+#689 := [unit-resolution #582 #688 #687]: #205
+#583 := (or #204 #237)
+#368 := (not #252)
+#592 := (iff #368 #583)
+#584 := (not #583)
+#587 := (not #584)
+#590 := (iff #587 #583)
+#591 := [rewrite]: #590
+#588 := (iff #368 #587)
+#585 := (iff #252 #584)
+#586 := [rewrite]: #585
+#589 := [monotonicity #586]: #588
+#593 := [trans #589 #591]: #592
+#369 := [not-or-elim #347]: #368
+#594 := [mp #369 #593]: #583
+#690 := [unit-resolution #594 #689 #687]: false
+#691 := [lemma #690]: #170
+#487 := (or #171 #177 #204)
+#356 := (not #208)
+#490 := (iff #356 #487)
+#467 := (or #171 #177)
+#474 := (or #204 #467)
+#488 := (iff #474 #487)
+#489 := [rewrite]: #488
+#485 := (iff #356 #474)
+#475 := (not #474)
+#480 := (not #475)
+#483 := (iff #480 #474)
+#484 := [rewrite]: #483
+#481 := (iff #356 #480)
+#478 := (iff #208 #475)
+#468 := (not #467)
+#471 := (and #468 #205)
+#476 := (iff #471 #475)
+#477 := [rewrite]: #476
+#472 := (iff #208 #471)
+#469 := (iff #15 #468)
+#470 := [rewrite]: #469
+#473 := [monotonicity #470]: #472
+#479 := [trans #473 #477]: #478
+#482 := [monotonicity #479]: #481
+#486 := [trans #482 #484]: #485
+#491 := [trans #486 #489]: #490
+#357 := [not-or-elim #347]: #356
+#492 := [mp #357 #491]: #487
+#694 := [unit-resolution #492 #691]: #693
+#695 := [unit-resolution #694 #692]: #177
+#493 := (or #178 #204)
+#358 := (not #211)
+#502 := (iff #358 #493)
+#494 := (not #493)
+#497 := (not #494)
+#500 := (iff #497 #493)
+#501 := [rewrite]: #500
+#498 := (iff #358 #497)
+#495 := (iff #211 #494)
+#496 := [rewrite]: #495
+#499 := [monotonicity #496]: #498
+#503 := [trans #499 #501]: #502
+#359 := [not-or-elim #347]: #358
+#504 := [mp #359 #503]: #493
+#696 := [unit-resolution #504 #695 #692]: false
+#697 := [lemma #696]: #204
+#698 := [hypothesis]: #177
+#449 := (or #178 #205 #217)
+#352 := (not #184)
+#452 := (iff #352 #449)
+#436 := (or #178 #385)
+#450 := (iff #436 #449)
+#451 := [rewrite]: #450
+#447 := (iff #352 #436)
+#437 := (not #436)
+#442 := (not #437)
+#445 := (iff #442 #436)
+#446 := [rewrite]: #445
+#443 := (iff #352 #442)
+#440 := (iff #184 #437)
+#433 := (and #386 #177)
+#438 := (iff #433 #437)
+#439 := [rewrite]: #438
+#434 := (iff #184 #433)
+#435 := [monotonicity #388]: #434
+#441 := [trans #435 #439]: #440
+#444 := [monotonicity #441]: #443
+#448 := [trans #444 #446]: #447
+#453 := [trans #448 #451]: #452
+#353 := [not-or-elim #347]: #352
+#454 := [mp #353 #453]: #449
+#699 := [unit-resolution #454 #698 #697]: #217
+#639 := (or #178 #237)
+#374 := (not #273)
+#648 := (iff #374 #639)
+#640 := (not #639)
+#643 := (not #640)
+#646 := (iff #643 #639)
+#647 := [rewrite]: #646
+#644 := (iff #374 #643)
+#641 := (iff #273 #640)
+#642 := [rewrite]: #641
+#645 := [monotonicity #642]: #644
+#649 := [trans #645 #647]: #648
+#375 := [not-or-elim #347]: #374
+#650 := [mp #375 #649]: #639
+#700 := [unit-resolution #650 #698]: #237
+#667 := (or #189 #218 #238)
+#376 := (not #279)
+#670 := (iff #376 #667)
+#654 := (or #218 #382)
+#668 := (iff #654 #667)
+#669 := [rewrite]: #668
+#665 := (iff #376 #654)
+#655 := (not #654)
+#660 := (not #655)
+#663 := (iff #660 #654)
+#664 := [rewrite]: #663
+#661 := (iff #376 #660)
+#658 := (iff #279 #655)
+#651 := (and #380 #217)
+#656 := (iff #651 #655)
+#657 := [rewrite]: #656
+#652 := (iff #279 #651)
+#653 := [monotonicity #384]: #652
+#659 := [trans #653 #657]: #658
+#662 := [monotonicity #659]: #661
+#666 := [trans #662 #664]: #665
+#671 := [trans #666 #669]: #670
+#377 := [not-or-elim #347]: #376
+#672 := [mp #377 #671]: #667
+#701 := [unit-resolution #672 #699 #700]: #189
+#673 := (or #190 #218)
+#378 := (not #287)
+#682 := (iff #378 #673)
+#674 := (not #673)
+#677 := (not #674)
+#680 := (iff #677 #673)
+#681 := [rewrite]: #680
+#678 := (iff #378 #677)
+#675 := (iff #287 #674)
+#676 := [rewrite]: #675
+#679 := [monotonicity #676]: #678
+#683 := [trans #679 #681]: #682
+#379 := [not-or-elim #347]: #378
+#684 := [mp #379 #683]: #673
+#702 := [unit-resolution #684 #701 #699]: false
+#703 := [lemma #702]: #178
+#704 := (or #177 #218)
+#543 := (or #171 #177 #218)
+#362 := (not #224)
+#546 := (iff #362 #543)
+#530 := (or #218 #467)
+#544 := (iff #530 #543)
+#545 := [rewrite]: #544
+#541 := (iff #362 #530)
+#531 := (not #530)
+#536 := (not #531)
+#539 := (iff #536 #530)
+#540 := [rewrite]: #539
+#537 := (iff #362 #536)
+#534 := (iff #224 #531)
+#527 := (and #468 #217)
+#532 := (iff #527 #531)
+#533 := [rewrite]: #532
+#528 := (iff #224 #527)
+#529 := [monotonicity #470]: #528
+#535 := [trans #529 #533]: #534
+#538 := [monotonicity #535]: #537
+#542 := [trans #538 #540]: #541
+#547 := [trans #542 #545]: #546
+#363 := [not-or-elim #347]: #362
+#548 := [mp #363 #547]: #543
+#705 := [unit-resolution #548 #691]: #704
+#706 := [unit-resolution #705 #703]: #218
+#707 := (or #177 #237)
+#633 := (or #171 #177 #237)
+#372 := (not #268)
+#636 := (iff #372 #633)
+#620 := (or #237 #467)
+#634 := (iff #620 #633)
+#635 := [rewrite]: #634
+#631 := (iff #372 #620)
+#621 := (not #620)
+#626 := (not #621)
+#629 := (iff #626 #620)
+#630 := [rewrite]: #629
+#627 := (iff #372 #626)
+#624 := (iff #268 #621)
+#617 := (and #468 #238)
+#622 := (iff #617 #621)
+#623 := [rewrite]: #622
+#618 := (iff #268 #617)
+#619 := [monotonicity #470]: #618
+#625 := [trans #619 #623]: #624
+#628 := [monotonicity #625]: #627
+#632 := [trans #628 #630]: #631
+#637 := [trans #632 #635]: #636
+#373 := [not-or-elim #347]: #372
+#638 := [mp #373 #637]: #633
+#708 := [unit-resolution #638 #691]: #707
+#709 := [unit-resolution #708 #703]: #237
+#611 := (or #190 #205 #217)
+#370 := (not #260)
+#614 := (iff #370 #611)
+#598 := (or #190 #385)
+#612 := (iff #598 #611)
+#613 := [rewrite]: #612
+#609 := (iff #370 #598)
+#599 := (not #598)
+#604 := (not #599)
+#607 := (iff #604 #598)
+#608 := [rewrite]: #607
+#605 := (iff #370 #604)
+#602 := (iff #260 #599)
+#595 := (and #386 #189)
+#600 := (iff #595 #599)
+#601 := [rewrite]: #600
+#596 := (iff #260 #595)
+#597 := [monotonicity #388]: #596
+#603 := [trans #597 #601]: #602
+#606 := [monotonicity #603]: #605
+#610 := [trans #606 #608]: #609
+#615 := [trans #610 #613]: #614
+#371 := [not-or-elim #347]: #370
+#616 := [mp #371 #615]: #611
+#710 := [unit-resolution #616 #706 #697]: #190
+#405 := (or #189 #205 #217 #238)
+#348 := (not #115)
+#408 := (iff #348 #405)
+#392 := (or #382 #385)
+#406 := (iff #392 #405)
+#407 := [rewrite]: #406
+#403 := (iff #348 #392)
+#393 := (not #392)
+#398 := (not #393)
+#401 := (iff #398 #392)
+#402 := [rewrite]: #401
+#399 := (iff #348 #398)
+#396 := (iff #115 #393)
+#389 := (and #380 #386)
+#394 := (iff #389 #393)
+#395 := [rewrite]: #394
+#390 := (iff #115 #389)
+#391 := [monotonicity #384 #388]: #390
+#397 := [trans #391 #395]: #396
+#400 := [monotonicity #397]: #399
+#404 := [trans #400 #402]: #403
+#409 := [trans #404 #407]: #408
+#349 := [not-or-elim #347]: #348
+#410 := [mp #349 #409]: #405
+[unit-resolution #410 #710 #709 #697 #706]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_16 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,26 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_3 Int)
+ (uf_2 Int)
+ (uf_1 Int)
+ (uf_4 Int)
+ (uf_5 Int)
+ (uf_6 Int)
+ (uf_7 Int)
+ (uf_8 Int)
+ (uf_9 Int)
+ (uf_10 Int)
+ (uf_11 Int)
+ )
+:assumption (= uf_1 (- (ite (< uf_2 0) (~ uf_2) uf_2) uf_3))
+:assumption (= uf_4 (- (ite (< uf_1 0) (~ uf_1) uf_1) uf_2))
+:assumption (= uf_5 (- (ite (< uf_4 0) (~ uf_4) uf_4) uf_1))
+:assumption (= uf_6 (- (ite (< uf_5 0) (~ uf_5) uf_5) uf_4))
+:assumption (= uf_7 (- (ite (< uf_6 0) (~ uf_6) uf_6) uf_5))
+:assumption (= uf_8 (- (ite (< uf_7 0) (~ uf_7) uf_7) uf_6))
+:assumption (= uf_9 (- (ite (< uf_8 0) (~ uf_8) uf_8) uf_7))
+:assumption (= uf_10 (- (ite (< uf_9 0) (~ uf_9) uf_9) uf_8))
+:assumption (= uf_11 (- (ite (< uf_10 0) (~ uf_10) uf_10) uf_9))
+:assumption (not (and (= uf_3 uf_10) (= uf_2 uf_11)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_linarith_16.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,2291 @@
+#2 := false
+#6 := 0::int
+decl z3name!0 :: int
+#647 := z3name!0
+#81 := -1::int
+#656 := (* -1::int z3name!0)
+decl uf_2 :: int
+#5 := uf_2
+#882 := (+ uf_2 #656)
+#883 := (<= #882 0::int)
+#885 := (not #883)
+#881 := (>= #882 0::int)
+#884 := (not #881)
+#886 := (or #884 #885)
+decl uf_11 :: int
+#55 := uf_11
+#513 := (* -1::int uf_11)
+#514 := (+ uf_2 #513)
+#515 := (<= #514 0::int)
+decl z3name!5 :: int
+#777 := z3name!5
+decl uf_7 :: int
+#31 := uf_7
+#1083 := (+ uf_7 z3name!5)
+#1084 := (<= #1083 0::int)
+#335 := (>= uf_7 0::int)
+#1085 := (>= #1083 0::int)
+#1087 := (not #1085)
+#1086 := (not #1084)
+#1088 := (or #1086 #1087)
+#2302 := [hypothesis]: #1086
+#1289 := (or #1088 #1084)
+#1290 := [def-axiom]: #1289
+#2303 := [unit-resolution #1290 #2302]: #1088
+#1089 := (not #1088)
+#1092 := (or #335 #1089)
+#1099 := (not #1092)
+#786 := (* -1::int z3name!5)
+#1072 := (+ uf_7 #786)
+#1073 := (<= #1072 0::int)
+#1075 := (not #1073)
+#1071 := (>= #1072 0::int)
+#1074 := (not #1071)
+#1076 := (or #1074 #1075)
+#1077 := (not #1076)
+#336 := (not #335)
+#1080 := (or #336 #1077)
+#1098 := (not #1080)
+#1100 := (or #1098 #1099)
+#1101 := (not #1100)
+#318 := (* -1::int uf_7)
+#780 := (= z3name!5 #318)
+#781 := (or #335 #780)
+#778 := (= z3name!5 uf_7)
+#779 := (or #336 #778)
+#782 := (and #779 #781)
+#1104 := (iff #782 #1101)
+#1095 := (and #1080 #1092)
+#1102 := (iff #1095 #1101)
+#1103 := [rewrite]: #1102
+#1096 := (iff #782 #1095)
+#1093 := (iff #781 #1092)
+#1090 := (iff #780 #1089)
+#1091 := [rewrite]: #1090
+#1094 := [monotonicity #1091]: #1093
+#1081 := (iff #779 #1080)
+#1078 := (iff #778 #1077)
+#1079 := [rewrite]: #1078
+#1082 := [monotonicity #1079]: #1081
+#1097 := [monotonicity #1082 #1094]: #1096
+#1105 := [trans #1097 #1103]: #1104
+#783 := [intro-def]: #782
+#1106 := [mp #783 #1105]: #1101
+#1108 := [not-or-elim #1106]: #1092
+#2304 := [unit-resolution #1108 #2303]: #335
+decl uf_4 :: int
+#13 := uf_4
+#194 := (>= uf_4 0::int)
+decl uf_10 :: int
+#49 := uf_10
+#459 := (* -1::int uf_10)
+decl uf_3 :: int
+#10 := uf_3
+#508 := (+ uf_3 #459)
+#509 := (>= #508 0::int)
+decl z3name!1 :: int
+#673 := z3name!1
+#682 := (* -1::int z3name!1)
+decl uf_1 :: int
+#4 := uf_1
+#920 := (+ uf_1 #682)
+#921 := (<= #920 0::int)
+#931 := (+ uf_1 z3name!1)
+#933 := (>= #931 0::int)
+#935 := (not #933)
+#932 := (<= #931 0::int)
+#934 := (not #932)
+#936 := (or #934 #935)
+#937 := (not #936)
+#147 := (>= uf_1 0::int)
+#148 := (not #147)
+#923 := (not #921)
+#919 := (>= #920 0::int)
+#922 := (not #919)
+#924 := (or #922 #923)
+#2022 := [hypothesis]: #923
+#1237 := (or #924 #921)
+#1238 := [def-axiom]: #1237
+#2023 := [unit-resolution #1238 #2022]: #924
+#925 := (not #924)
+#928 := (or #148 #925)
+#940 := (or #147 #937)
+#947 := (not #940)
+#946 := (not #928)
+#948 := (or #946 #947)
+#949 := (not #948)
+#130 := (* -1::int uf_1)
+#676 := (= z3name!1 #130)
+#677 := (or #147 #676)
+#674 := (= z3name!1 uf_1)
+#675 := (or #148 #674)
+#678 := (and #675 #677)
+#952 := (iff #678 #949)
+#943 := (and #928 #940)
+#950 := (iff #943 #949)
+#951 := [rewrite]: #950
+#944 := (iff #678 #943)
+#941 := (iff #677 #940)
+#938 := (iff #676 #937)
+#939 := [rewrite]: #938
+#942 := [monotonicity #939]: #941
+#929 := (iff #675 #928)
+#926 := (iff #674 #925)
+#927 := [rewrite]: #926
+#930 := [monotonicity #927]: #929
+#945 := [monotonicity #930 #942]: #944
+#953 := [trans #945 #951]: #952
+#679 := [intro-def]: #678
+#954 := [mp #679 #953]: #949
+#955 := [not-or-elim #954]: #928
+#2024 := [unit-resolution #955 #2023]: #148
+#956 := [not-or-elim #954]: #940
+#2025 := [unit-resolution #956 #2024]: #937
+#2026 := (or #921 #919)
+#2027 := [th-lemma]: #2026
+#2028 := [unit-resolution #2027 #2022]: #919
+#2029 := (or #922 #147 #935)
+#2030 := [th-lemma]: #2029
+#2031 := [unit-resolution #2030 #2024 #2028]: #935
+#1243 := (or #936 #933)
+#1244 := [def-axiom]: #1243
+#2032 := [unit-resolution #1244 #2031 #2025]: false
+#2033 := [lemma #2032]: #921
+decl z3name!7 :: int
+#829 := z3name!7
+decl uf_9 :: int
+#43 := uf_9
+#1159 := (+ uf_9 z3name!7)
+#1160 := (<= #1159 0::int)
+#838 := (* -1::int z3name!7)
+#1148 := (+ uf_9 #838)
+#1147 := (>= #1148 0::int)
+decl z3name!4 :: int
+#751 := z3name!4
+#760 := (* -1::int z3name!4)
+decl uf_6 :: int
+#25 := uf_6
+#1034 := (+ uf_6 #760)
+#1033 := (>= #1034 0::int)
+#1035 := (<= #1034 0::int)
+#1037 := (not #1035)
+#1036 := (not #1033)
+#1038 := (or #1036 #1037)
+#1039 := (not #1038)
+#288 := (>= uf_6 0::int)
+#893 := (+ uf_2 z3name!0)
+#895 := (>= #893 0::int)
+#897 := (not #895)
+#894 := (<= #893 0::int)
+#896 := (not #894)
+#898 := (or #896 #897)
+#899 := (not #898)
+#100 := (>= uf_2 0::int)
+#101 := (not #100)
+#1736 := [hypothesis]: #885
+#1225 := (or #886 #883)
+#1226 := [def-axiom]: #1225
+#1737 := [unit-resolution #1226 #1736]: #886
+#887 := (not #886)
+#890 := (or #101 #887)
+#902 := (or #100 #899)
+#909 := (not #902)
+#908 := (not #890)
+#910 := (or #908 #909)
+#911 := (not #910)
+#82 := (* -1::int uf_2)
+#650 := (= z3name!0 #82)
+#651 := (or #100 #650)
+#648 := (= z3name!0 uf_2)
+#649 := (or #101 #648)
+#652 := (and #649 #651)
+#914 := (iff #652 #911)
+#905 := (and #890 #902)
+#912 := (iff #905 #911)
+#913 := [rewrite]: #912
+#906 := (iff #652 #905)
+#903 := (iff #651 #902)
+#900 := (iff #650 #899)
+#901 := [rewrite]: #900
+#904 := [monotonicity #901]: #903
+#891 := (iff #649 #890)
+#888 := (iff #648 #887)
+#889 := [rewrite]: #888
+#892 := [monotonicity #889]: #891
+#907 := [monotonicity #892 #904]: #906
+#915 := [trans #907 #913]: #914
+#653 := [intro-def]: #652
+#916 := [mp #653 #915]: #911
+#917 := [not-or-elim #916]: #890
+#1738 := [unit-resolution #917 #1737]: #101
+#918 := [not-or-elim #916]: #902
+#1739 := [unit-resolution #918 #1738]: #899
+#1231 := (or #898 #895)
+#1232 := [def-axiom]: #1231
+#1740 := [unit-resolution #1232 #1739]: #895
+#1741 := [th-lemma #1736 #1738 #1740]: false
+#1742 := [lemma #1741]: #883
+#1149 := (<= #1148 0::int)
+#1151 := (not #1149)
+#1150 := (not #1147)
+#1152 := (or #1150 #1151)
+#1153 := (not #1152)
+#429 := (>= uf_9 0::int)
+decl z3name!6 :: int
+#803 := z3name!6
+#812 := (* -1::int z3name!6)
+decl uf_8 :: int
+#37 := uf_8
+#1110 := (+ uf_8 #812)
+#1111 := (<= #1110 0::int)
+#1113 := (not #1111)
+#1109 := (>= #1110 0::int)
+#1112 := (not #1109)
+#1114 := (or #1112 #1113)
+#1865 := [hypothesis]: #1113
+#1297 := (or #1114 #1111)
+#1298 := [def-axiom]: #1297
+#1866 := [unit-resolution #1298 #1865]: #1114
+#382 := (>= uf_8 0::int)
+#1685 := (or #1111 #1109)
+#1686 := [th-lemma]: #1685
+#1867 := [unit-resolution #1686 #1865]: #1109
+#1734 := (or #382 #1112)
+#1121 := (+ uf_8 z3name!6)
+#1123 := (>= #1121 0::int)
+#1125 := (not #1123)
+#1122 := (<= #1121 0::int)
+#1124 := (not #1122)
+#1126 := (or #1124 #1125)
+#1127 := (not #1126)
+#383 := (not #382)
+#1428 := [hypothesis]: #383
+#1130 := (or #382 #1127)
+#1137 := (not #1130)
+#1115 := (not #1114)
+#1118 := (or #383 #1115)
+#1136 := (not #1118)
+#1138 := (or #1136 #1137)
+#1139 := (not #1138)
+#365 := (* -1::int uf_8)
+#806 := (= z3name!6 #365)
+#807 := (or #382 #806)
+#804 := (= z3name!6 uf_8)
+#805 := (or #383 #804)
+#808 := (and #805 #807)
+#1142 := (iff #808 #1139)
+#1133 := (and #1118 #1130)
+#1140 := (iff #1133 #1139)
+#1141 := [rewrite]: #1140
+#1134 := (iff #808 #1133)
+#1131 := (iff #807 #1130)
+#1128 := (iff #806 #1127)
+#1129 := [rewrite]: #1128
+#1132 := [monotonicity #1129]: #1131
+#1119 := (iff #805 #1118)
+#1116 := (iff #804 #1115)
+#1117 := [rewrite]: #1116
+#1120 := [monotonicity #1117]: #1119
+#1135 := [monotonicity #1120 #1132]: #1134
+#1143 := [trans #1135 #1141]: #1142
+#809 := [intro-def]: #808
+#1144 := [mp #809 #1143]: #1139
+#1146 := [not-or-elim #1144]: #1130
+#1729 := [unit-resolution #1146 #1428]: #1127
+#1637 := [hypothesis]: #1109
+#1730 := (or #1112 #1125 #382)
+#1731 := [th-lemma]: #1730
+#1732 := [unit-resolution #1731 #1428 #1637]: #1125
+#1303 := (or #1126 #1123)
+#1304 := [def-axiom]: #1303
+#1733 := [unit-resolution #1304 #1732 #1729]: false
+#1735 := [lemma #1733]: #1734
+#1868 := [unit-resolution #1735 #1867]: #382
+#1145 := [not-or-elim #1144]: #1118
+#1869 := [unit-resolution #1145 #1868 #1866]: false
+#1870 := [lemma #1869]: #1111
+#289 := (not #288)
+#1405 := [hypothesis]: #289
+#1688 := (or #288 #429 #1113)
+#815 := (+ uf_9 #812)
+#818 := (+ uf_7 #815)
+#825 := (>= #818 0::int)
+#389 := (ite #382 uf_8 #365)
+#400 := (* -1::int #389)
+#401 := (+ uf_9 #400)
+#402 := (+ uf_7 #401)
+#599 := (>= #402 0::int)
+#826 := (= #599 #825)
+#819 := (~ #402 #818)
+#816 := (~ #401 #815)
+#813 := (~ #400 #812)
+#810 := (~ #389 z3name!6)
+#811 := [apply-def #809]: #810
+#814 := [monotonicity #811]: #813
+#817 := [monotonicity #814]: #816
+#820 := [monotonicity #817]: #819
+#827 := [monotonicity #820]: #826
+#601 := (not #599)
+#598 := (<= #402 0::int)
+#600 := (not #598)
+#602 := (or #600 #601)
+#603 := (not #602)
+#403 := (= #402 0::int)
+#604 := (iff #403 #603)
+#605 := [rewrite]: #604
+#45 := (- uf_8)
+#44 := (< uf_8 0::int)
+#46 := (ite #44 #45 uf_8)
+#47 := (- #46 uf_7)
+#48 := (= uf_9 #47)
+#408 := (iff #48 #403)
+#368 := (ite #44 #365 uf_8)
+#374 := (+ #318 #368)
+#379 := (= uf_9 #374)
+#406 := (iff #379 #403)
+#394 := (+ #318 #389)
+#397 := (= uf_9 #394)
+#404 := (iff #397 #403)
+#405 := [rewrite]: #404
+#398 := (iff #379 #397)
+#395 := (= #374 #394)
+#392 := (= #368 #389)
+#386 := (ite #383 #365 uf_8)
+#390 := (= #386 #389)
+#391 := [rewrite]: #390
+#387 := (= #368 #386)
+#384 := (iff #44 #383)
+#385 := [rewrite]: #384
+#388 := [monotonicity #385]: #387
+#393 := [trans #388 #391]: #392
+#396 := [monotonicity #393]: #395
+#399 := [monotonicity #396]: #398
+#407 := [trans #399 #405]: #406
+#380 := (iff #48 #379)
+#377 := (= #47 #374)
+#371 := (- #368 uf_7)
+#375 := (= #371 #374)
+#376 := [rewrite]: #375
+#372 := (= #47 #371)
+#369 := (= #46 #368)
+#366 := (= #45 #365)
+#367 := [rewrite]: #366
+#370 := [monotonicity #367]: #369
+#373 := [monotonicity #370]: #372
+#378 := [trans #373 #376]: #377
+#381 := [monotonicity #378]: #380
+#409 := [trans #381 #407]: #408
+#364 := [asserted]: #48
+#410 := [mp #364 #409]: #403
+#606 := [mp #410 #605]: #603
+#608 := [not-or-elim #606]: #599
+#828 := [mp~ #608 #827]: #825
+#1441 := [hypothesis]: #1075
+#1285 := (or #1076 #1073)
+#1286 := [def-axiom]: #1285
+#1442 := [unit-resolution #1286 #1441]: #1076
+#1107 := [not-or-elim #1106]: #1080
+#1443 := [unit-resolution #1107 #1442]: #336
+#1444 := [unit-resolution #1108 #1443]: #1089
+#1291 := (or #1088 #1085)
+#1292 := [def-axiom]: #1291
+#1445 := [unit-resolution #1292 #1444]: #1085
+#1446 := [th-lemma #1441 #1445 #1443]: false
+#1447 := [lemma #1446]: #1073
+#789 := (+ uf_8 #786)
+#792 := (+ uf_6 #789)
+#799 := (>= #792 0::int)
+#342 := (ite #335 uf_7 #318)
+#353 := (* -1::int #342)
+#354 := (+ uf_8 #353)
+#355 := (+ uf_6 #354)
+#588 := (>= #355 0::int)
+#800 := (= #588 #799)
+#793 := (~ #355 #792)
+#790 := (~ #354 #789)
+#787 := (~ #353 #786)
+#784 := (~ #342 z3name!5)
+#785 := [apply-def #783]: #784
+#788 := [monotonicity #785]: #787
+#791 := [monotonicity #788]: #790
+#794 := [monotonicity #791]: #793
+#801 := [monotonicity #794]: #800
+#590 := (not #588)
+#587 := (<= #355 0::int)
+#589 := (not #587)
+#591 := (or #589 #590)
+#592 := (not #591)
+#356 := (= #355 0::int)
+#593 := (iff #356 #592)
+#594 := [rewrite]: #593
+#39 := (- uf_7)
+#38 := (< uf_7 0::int)
+#40 := (ite #38 #39 uf_7)
+#41 := (- #40 uf_6)
+#42 := (= uf_8 #41)
+#361 := (iff #42 #356)
+#321 := (ite #38 #318 uf_7)
+#271 := (* -1::int uf_6)
+#327 := (+ #271 #321)
+#332 := (= uf_8 #327)
+#359 := (iff #332 #356)
+#347 := (+ #271 #342)
+#350 := (= uf_8 #347)
+#357 := (iff #350 #356)
+#358 := [rewrite]: #357
+#351 := (iff #332 #350)
+#348 := (= #327 #347)
+#345 := (= #321 #342)
+#339 := (ite #336 #318 uf_7)
+#343 := (= #339 #342)
+#344 := [rewrite]: #343
+#340 := (= #321 #339)
+#337 := (iff #38 #336)
+#338 := [rewrite]: #337
+#341 := [monotonicity #338]: #340
+#346 := [trans #341 #344]: #345
+#349 := [monotonicity #346]: #348
+#352 := [monotonicity #349]: #351
+#360 := [trans #352 #358]: #359
+#333 := (iff #42 #332)
+#330 := (= #41 #327)
+#324 := (- #321 uf_6)
+#328 := (= #324 #327)
+#329 := [rewrite]: #328
+#325 := (= #41 #324)
+#322 := (= #40 #321)
+#319 := (= #39 #318)
+#320 := [rewrite]: #319
+#323 := [monotonicity #320]: #322
+#326 := [monotonicity #323]: #325
+#331 := [trans #326 #329]: #330
+#334 := [monotonicity #331]: #333
+#362 := [trans #334 #360]: #361
+#317 := [asserted]: #42
+#363 := [mp #317 #362]: #356
+#595 := [mp #363 #594]: #592
+#597 := [not-or-elim #595]: #588
+#802 := [mp~ #597 #801]: #799
+#1343 := (not #825)
+#1350 := (not #799)
+#1351 := (or #288 #1075 #1350 #429 #1113 #1343)
+#1352 := [th-lemma]: #1351
+#1689 := [unit-resolution #1352 #802 #1447 #828]: #1688
+#2046 := [unit-resolution #1689 #1405 #1870]: #429
+#430 := (not #429)
+#1156 := (or #430 #1153)
+#1161 := (>= #1159 0::int)
+#1163 := (not #1161)
+#1162 := (not #1160)
+#1164 := (or #1162 #1163)
+#1165 := (not #1164)
+#1168 := (or #429 #1165)
+#1175 := (not #1168)
+#1174 := (not #1156)
+#1176 := (or #1174 #1175)
+#1177 := (not #1176)
+#412 := (* -1::int uf_9)
+#832 := (= z3name!7 #412)
+#833 := (or #429 #832)
+#830 := (= z3name!7 uf_9)
+#831 := (or #430 #830)
+#834 := (and #831 #833)
+#1180 := (iff #834 #1177)
+#1171 := (and #1156 #1168)
+#1178 := (iff #1171 #1177)
+#1179 := [rewrite]: #1178
+#1172 := (iff #834 #1171)
+#1169 := (iff #833 #1168)
+#1166 := (iff #832 #1165)
+#1167 := [rewrite]: #1166
+#1170 := [monotonicity #1167]: #1169
+#1157 := (iff #831 #1156)
+#1154 := (iff #830 #1153)
+#1155 := [rewrite]: #1154
+#1158 := [monotonicity #1155]: #1157
+#1173 := [monotonicity #1158 #1170]: #1172
+#1181 := [trans #1173 #1179]: #1180
+#835 := [intro-def]: #834
+#1182 := [mp #835 #1181]: #1177
+#1183 := [not-or-elim #1182]: #1156
+#2047 := [unit-resolution #1183 #2046]: #1153
+#1307 := (or #1152 #1147)
+#1308 := [def-axiom]: #1307
+#2112 := [unit-resolution #1308 #2047]: #1147
+#2009 := (or #288 #382)
+#1998 := (or #1036 #288)
+#1045 := (+ uf_6 z3name!4)
+#1047 := (>= #1045 0::int)
+#1049 := (not #1047)
+#1046 := (<= #1045 0::int)
+#1048 := (not #1046)
+#1050 := (or #1048 #1049)
+#1460 := [hypothesis]: #1049
+#1279 := (or #1050 #1047)
+#1280 := [def-axiom]: #1279
+#1461 := [unit-resolution #1280 #1460]: #1050
+#1464 := (or #1047 #289)
+#1051 := (not #1050)
+#1448 := [hypothesis]: #1037
+#1273 := (or #1038 #1035)
+#1274 := [def-axiom]: #1273
+#1449 := [unit-resolution #1274 #1448]: #1038
+#1042 := (or #289 #1039)
+#1054 := (or #288 #1051)
+#1061 := (not #1054)
+#1060 := (not #1042)
+#1062 := (or #1060 #1061)
+#1063 := (not #1062)
+#754 := (= z3name!4 #271)
+#755 := (or #288 #754)
+#752 := (= z3name!4 uf_6)
+#753 := (or #289 #752)
+#756 := (and #753 #755)
+#1066 := (iff #756 #1063)
+#1057 := (and #1042 #1054)
+#1064 := (iff #1057 #1063)
+#1065 := [rewrite]: #1064
+#1058 := (iff #756 #1057)
+#1055 := (iff #755 #1054)
+#1052 := (iff #754 #1051)
+#1053 := [rewrite]: #1052
+#1056 := [monotonicity #1053]: #1055
+#1043 := (iff #753 #1042)
+#1040 := (iff #752 #1039)
+#1041 := [rewrite]: #1040
+#1044 := [monotonicity #1041]: #1043
+#1059 := [monotonicity #1044 #1056]: #1058
+#1067 := [trans #1059 #1065]: #1066
+#757 := [intro-def]: #756
+#1068 := [mp #757 #1067]: #1063
+#1069 := [not-or-elim #1068]: #1042
+#1450 := [unit-resolution #1069 #1449]: #289
+#1070 := [not-or-elim #1068]: #1054
+#1451 := [unit-resolution #1070 #1450]: #1051
+#1452 := (or #1035 #1033)
+#1453 := [th-lemma]: #1452
+#1454 := [unit-resolution #1453 #1448]: #1033
+#1455 := (or #1036 #288 #1049)
+#1456 := [th-lemma]: #1455
+#1457 := [unit-resolution #1456 #1450 #1454]: #1049
+#1458 := [unit-resolution #1280 #1457 #1451]: false
+#1459 := [lemma #1458]: #1035
+#1462 := (or #1047 #1037 #289)
+#1463 := [th-lemma]: #1462
+#1465 := [unit-resolution #1463 #1459]: #1464
+#1466 := [unit-resolution #1465 #1460]: #289
+#1467 := [unit-resolution #1070 #1466 #1461]: false
+#1468 := [lemma #1467]: #1047
+#1999 := [unit-resolution #1456 #1468]: #1998
+#2000 := [unit-resolution #1999 #1405]: #1036
+#1407 := [unit-resolution #1070 #1405]: #1051
+#1277 := (or #1050 #1046)
+#1278 := [def-axiom]: #1277
+#1497 := [unit-resolution #1278 #1407]: #1046
+#2001 := (or #336 #1048 #1033 #382 #1350 #1075)
+#2002 := [th-lemma]: #2001
+#2003 := [unit-resolution #2002 #1497 #2000 #1447 #802 #1428]: #336
+#2004 := (or #1087 #1075 #1048 #1033 #382 #1350)
+#2005 := [th-lemma]: #2004
+#2006 := [unit-resolution #2005 #1497 #1447 #2000 #802 #1428]: #1087
+#2007 := [unit-resolution #1292 #2006]: #1088
+#2008 := [unit-resolution #1108 #2007 #2003]: false
+#2010 := [lemma #2008]: #2009
+#2113 := [unit-resolution #2010 #1405]: #382
+#2114 := [unit-resolution #1145 #2113]: #1115
+#1295 := (or #1114 #1109)
+#1296 := [def-axiom]: #1295
+#2115 := [unit-resolution #1296 #2114]: #1109
+decl z3name!2 :: int
+#699 := z3name!2
+#708 := (* -1::int z3name!2)
+#958 := (+ uf_4 #708)
+#957 := (>= #958 0::int)
+#959 := (<= #958 0::int)
+#961 := (not #959)
+#960 := (not #957)
+#962 := (or #960 #961)
+#963 := (not #962)
+decl uf_5 :: int
+#19 := uf_5
+#241 := (>= uf_5 0::int)
+#242 := (not #241)
+#1406 := [hypothesis]: #242
+#1579 := (or #1048 #241)
+#516 := (>= #514 0::int)
+#476 := (>= uf_10 0::int)
+#477 := (not #476)
+#1484 := (or #382 #241)
+#1430 := (or #382 #241 #1075 #1037)
+#1421 := [hypothesis]: #1035
+#1427 := [hypothesis]: #1073
+#763 := (+ uf_7 #760)
+#766 := (+ uf_5 #763)
+#773 := (>= #766 0::int)
+#295 := (ite #288 uf_6 #271)
+#306 := (* -1::int #295)
+#307 := (+ uf_7 #306)
+#308 := (+ uf_5 #307)
+#577 := (>= #308 0::int)
+#774 := (= #577 #773)
+#767 := (~ #308 #766)
+#764 := (~ #307 #763)
+#761 := (~ #306 #760)
+#758 := (~ #295 z3name!4)
+#759 := [apply-def #757]: #758
+#762 := [monotonicity #759]: #761
+#765 := [monotonicity #762]: #764
+#768 := [monotonicity #765]: #767
+#775 := [monotonicity #768]: #774
+#579 := (not #577)
+#576 := (<= #308 0::int)
+#578 := (not #576)
+#580 := (or #578 #579)
+#581 := (not #580)
+#309 := (= #308 0::int)
+#582 := (iff #309 #581)
+#583 := [rewrite]: #582
+#33 := (- uf_6)
+#32 := (< uf_6 0::int)
+#34 := (ite #32 #33 uf_6)
+#35 := (- #34 uf_5)
+#36 := (= uf_7 #35)
+#314 := (iff #36 #309)
+#274 := (ite #32 #271 uf_6)
+#224 := (* -1::int uf_5)
+#280 := (+ #224 #274)
+#285 := (= uf_7 #280)
+#312 := (iff #285 #309)
+#300 := (+ #224 #295)
+#303 := (= uf_7 #300)
+#310 := (iff #303 #309)
+#311 := [rewrite]: #310
+#304 := (iff #285 #303)
+#301 := (= #280 #300)
+#298 := (= #274 #295)
+#292 := (ite #289 #271 uf_6)
+#296 := (= #292 #295)
+#297 := [rewrite]: #296
+#293 := (= #274 #292)
+#290 := (iff #32 #289)
+#291 := [rewrite]: #290
+#294 := [monotonicity #291]: #293
+#299 := [trans #294 #297]: #298
+#302 := [monotonicity #299]: #301
+#305 := [monotonicity #302]: #304
+#313 := [trans #305 #311]: #312
+#286 := (iff #36 #285)
+#283 := (= #35 #280)
+#277 := (- #274 uf_5)
+#281 := (= #277 #280)
+#282 := [rewrite]: #281
+#278 := (= #35 #277)
+#275 := (= #34 #274)
+#272 := (= #33 #271)
+#273 := [rewrite]: #272
+#276 := [monotonicity #273]: #275
+#279 := [monotonicity #276]: #278
+#284 := [trans #279 #282]: #283
+#287 := [monotonicity #284]: #286
+#315 := [trans #287 #313]: #314
+#270 := [asserted]: #36
+#316 := [mp #270 #315]: #309
+#584 := [mp #316 #583]: #581
+#586 := [not-or-elim #584]: #577
+#776 := [mp~ #586 #775]: #773
+#1429 := [th-lemma #776 #1406 #1428 #1427 #802 #1421]: false
+#1431 := [lemma #1429]: #1430
+#1485 := [unit-resolution #1431 #1447 #1459]: #1484
+#1486 := [unit-resolution #1485 #1406]: #382
+#1487 := [unit-resolution #1145 #1486]: #1115
+#1496 := [unit-resolution #1298 #1487]: #1111
+#1545 := [hypothesis]: #1046
+#1548 := (or #1048 #1113 #429)
+#1546 := (or #1048 #1113 #429 #1343 #1075 #1350 #1037)
+#1547 := [th-lemma]: #1546
+#1549 := [unit-resolution #1547 #1447 #802 #1459 #828]: #1548
+#1550 := [unit-resolution #1549 #1545 #1496]: #429
+#1551 := [unit-resolution #1183 #1550]: #1153
+#1552 := [unit-resolution #1308 #1551]: #1147
+#1543 := (or #477 #241 #1150)
+#1488 := [unit-resolution #1296 #1487]: #1109
+#821 := (<= #818 0::int)
+#822 := (= #598 #821)
+#823 := [monotonicity #820]: #822
+#607 := [not-or-elim #606]: #598
+#824 := [mp~ #607 #823]: #821
+#841 := (+ uf_10 #838)
+#844 := (+ uf_8 #841)
+#847 := (<= #844 0::int)
+#436 := (ite #429 uf_9 #412)
+#447 := (* -1::int #436)
+#448 := (+ uf_10 #447)
+#449 := (+ uf_8 #448)
+#609 := (<= #449 0::int)
+#848 := (= #609 #847)
+#845 := (~ #449 #844)
+#842 := (~ #448 #841)
+#839 := (~ #447 #838)
+#836 := (~ #436 z3name!7)
+#837 := [apply-def #835]: #836
+#840 := [monotonicity #837]: #839
+#843 := [monotonicity #840]: #842
+#846 := [monotonicity #843]: #845
+#849 := [monotonicity #846]: #848
+#610 := (>= #449 0::int)
+#612 := (not #610)
+#611 := (not #609)
+#613 := (or #611 #612)
+#614 := (not #613)
+#450 := (= #449 0::int)
+#615 := (iff #450 #614)
+#616 := [rewrite]: #615
+#51 := (- uf_9)
+#50 := (< uf_9 0::int)
+#52 := (ite #50 #51 uf_9)
+#53 := (- #52 uf_8)
+#54 := (= uf_10 #53)
+#455 := (iff #54 #450)
+#415 := (ite #50 #412 uf_9)
+#421 := (+ #365 #415)
+#426 := (= uf_10 #421)
+#453 := (iff #426 #450)
+#441 := (+ #365 #436)
+#444 := (= uf_10 #441)
+#451 := (iff #444 #450)
+#452 := [rewrite]: #451
+#445 := (iff #426 #444)
+#442 := (= #421 #441)
+#439 := (= #415 #436)
+#433 := (ite #430 #412 uf_9)
+#437 := (= #433 #436)
+#438 := [rewrite]: #437
+#434 := (= #415 #433)
+#431 := (iff #50 #430)
+#432 := [rewrite]: #431
+#435 := [monotonicity #432]: #434
+#440 := [trans #435 #438]: #439
+#443 := [monotonicity #440]: #442
+#446 := [monotonicity #443]: #445
+#454 := [trans #446 #452]: #453
+#427 := (iff #54 #426)
+#424 := (= #53 #421)
+#418 := (- #415 uf_8)
+#422 := (= #418 #421)
+#423 := [rewrite]: #422
+#419 := (= #53 #418)
+#416 := (= #52 #415)
+#413 := (= #51 #412)
+#414 := [rewrite]: #413
+#417 := [monotonicity #414]: #416
+#420 := [monotonicity #417]: #419
+#425 := [trans #420 #423]: #424
+#428 := [monotonicity #425]: #427
+#456 := [trans #428 #454]: #455
+#411 := [asserted]: #54
+#457 := [mp #411 #456]: #450
+#617 := [mp #457 #616]: #614
+#618 := [not-or-elim #617]: #609
+#850 := [mp~ #618 #849]: #847
+#1540 := [hypothesis]: #1147
+#1541 := [hypothesis]: #476
+#1542 := [th-lemma #1468 #1406 #1541 #1540 #850 #824 #1488 #776 #1459]: false
+#1544 := [lemma #1542]: #1543
+#1553 := [unit-resolution #1544 #1552 #1406]: #477
+#851 := (>= #844 0::int)
+#852 := (= #610 #851)
+#853 := [monotonicity #846]: #852
+#619 := [not-or-elim #617]: #610
+#854 := [mp~ #619 #853]: #851
+#1309 := (or #1152 #1149)
+#1310 := [def-axiom]: #1309
+#1554 := [unit-resolution #1310 #1551]: #1149
+#769 := (<= #766 0::int)
+#770 := (= #576 #769)
+#771 := [monotonicity #768]: #770
+#585 := [not-or-elim #584]: #576
+#772 := [mp~ #585 #771]: #769
+decl z3name!3 :: int
+#725 := z3name!3
+#1007 := (+ uf_5 z3name!3)
+#1009 := (>= #1007 0::int)
+#1011 := (not #1009)
+#1398 := [hypothesis]: #1011
+#734 := (* -1::int z3name!3)
+#996 := (+ uf_5 #734)
+#997 := (<= #996 0::int)
+#999 := (not #997)
+#995 := (>= #996 0::int)
+#998 := (not #995)
+#1000 := (or #998 #999)
+#1001 := (not #1000)
+#1008 := (<= #1007 0::int)
+#1010 := (not #1008)
+#1012 := (or #1010 #1011)
+#1267 := (or #1012 #1009)
+#1268 := [def-axiom]: #1267
+#1399 := [unit-resolution #1268 #1398]: #1012
+#1013 := (not #1012)
+#1016 := (or #241 #1013)
+#1023 := (not #1016)
+#1004 := (or #242 #1001)
+#1022 := (not #1004)
+#1024 := (or #1022 #1023)
+#1025 := (not #1024)
+#728 := (= z3name!3 #224)
+#729 := (or #241 #728)
+#726 := (= z3name!3 uf_5)
+#727 := (or #242 #726)
+#730 := (and #727 #729)
+#1028 := (iff #730 #1025)
+#1019 := (and #1004 #1016)
+#1026 := (iff #1019 #1025)
+#1027 := [rewrite]: #1026
+#1020 := (iff #730 #1019)
+#1017 := (iff #729 #1016)
+#1014 := (iff #728 #1013)
+#1015 := [rewrite]: #1014
+#1018 := [monotonicity #1015]: #1017
+#1005 := (iff #727 #1004)
+#1002 := (iff #726 #1001)
+#1003 := [rewrite]: #1002
+#1006 := [monotonicity #1003]: #1005
+#1021 := [monotonicity #1006 #1018]: #1020
+#1029 := [trans #1021 #1027]: #1028
+#731 := [intro-def]: #730
+#1030 := [mp #731 #1029]: #1025
+#1032 := [not-or-elim #1030]: #1016
+#1400 := [unit-resolution #1032 #1399]: #241
+#1031 := [not-or-elim #1030]: #1004
+#1401 := [unit-resolution #1031 #1400]: #1001
+#1261 := (or #1000 #997)
+#1262 := [def-axiom]: #1261
+#1402 := [unit-resolution #1262 #1401]: #997
+#1403 := [th-lemma #1400 #1402 #1398]: false
+#1404 := [lemma #1403]: #1009
+#737 := (+ uf_6 #734)
+#740 := (+ uf_4 #737)
+#747 := (>= #740 0::int)
+#248 := (ite #241 uf_5 #224)
+#259 := (* -1::int #248)
+#260 := (+ uf_6 #259)
+#261 := (+ uf_4 #260)
+#566 := (>= #261 0::int)
+#748 := (= #566 #747)
+#741 := (~ #261 #740)
+#738 := (~ #260 #737)
+#735 := (~ #259 #734)
+#732 := (~ #248 z3name!3)
+#733 := [apply-def #731]: #732
+#736 := [monotonicity #733]: #735
+#739 := [monotonicity #736]: #738
+#742 := [monotonicity #739]: #741
+#749 := [monotonicity #742]: #748
+#568 := (not #566)
+#565 := (<= #261 0::int)
+#567 := (not #565)
+#569 := (or #567 #568)
+#570 := (not #569)
+#262 := (= #261 0::int)
+#571 := (iff #262 #570)
+#572 := [rewrite]: #571
+#27 := (- uf_5)
+#26 := (< uf_5 0::int)
+#28 := (ite #26 #27 uf_5)
+#29 := (- #28 uf_4)
+#30 := (= uf_6 #29)
+#267 := (iff #30 #262)
+#227 := (ite #26 #224 uf_5)
+#177 := (* -1::int uf_4)
+#233 := (+ #177 #227)
+#238 := (= uf_6 #233)
+#265 := (iff #238 #262)
+#253 := (+ #177 #248)
+#256 := (= uf_6 #253)
+#263 := (iff #256 #262)
+#264 := [rewrite]: #263
+#257 := (iff #238 #256)
+#254 := (= #233 #253)
+#251 := (= #227 #248)
+#245 := (ite #242 #224 uf_5)
+#249 := (= #245 #248)
+#250 := [rewrite]: #249
+#246 := (= #227 #245)
+#243 := (iff #26 #242)
+#244 := [rewrite]: #243
+#247 := [monotonicity #244]: #246
+#252 := [trans #247 #250]: #251
+#255 := [monotonicity #252]: #254
+#258 := [monotonicity #255]: #257
+#266 := [trans #258 #264]: #265
+#239 := (iff #30 #238)
+#236 := (= #29 #233)
+#230 := (- #227 uf_4)
+#234 := (= #230 #233)
+#235 := [rewrite]: #234
+#231 := (= #29 #230)
+#228 := (= #28 #227)
+#225 := (= #27 #224)
+#226 := [rewrite]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#237 := [trans #232 #235]: #236
+#240 := [monotonicity #237]: #239
+#268 := [trans #240 #266]: #267
+#223 := [asserted]: #30
+#269 := [mp #223 #268]: #262
+#573 := [mp #269 #572]: #570
+#575 := [not-or-elim #573]: #566
+#750 := [mp~ #575 #749]: #747
+#1364 := (not #747)
+#1357 := (not #769)
+#1337 := (not #851)
+#1555 := (or #194 #476 #1151 #1337 #1343 #1113 #1048 #1357 #1364 #1011)
+#1556 := [th-lemma]: #1555
+#1557 := [unit-resolution #1556 #1545 #750 #1404 #772 #1496 #828 #1554 #854 #1553]: #194
+#195 := (not #194)
+#966 := (or #195 #963)
+#969 := (+ uf_4 z3name!2)
+#971 := (>= #969 0::int)
+#973 := (not #971)
+#970 := (<= #969 0::int)
+#972 := (not #970)
+#974 := (or #972 #973)
+#975 := (not #974)
+#978 := (or #194 #975)
+#985 := (not #978)
+#984 := (not #966)
+#986 := (or #984 #985)
+#987 := (not #986)
+#702 := (= z3name!2 #177)
+#703 := (or #194 #702)
+#700 := (= z3name!2 uf_4)
+#701 := (or #195 #700)
+#704 := (and #701 #703)
+#990 := (iff #704 #987)
+#981 := (and #966 #978)
+#988 := (iff #981 #987)
+#989 := [rewrite]: #988
+#982 := (iff #704 #981)
+#979 := (iff #703 #978)
+#976 := (iff #702 #975)
+#977 := [rewrite]: #976
+#980 := [monotonicity #977]: #979
+#967 := (iff #701 #966)
+#964 := (iff #700 #963)
+#965 := [rewrite]: #964
+#968 := [monotonicity #965]: #967
+#983 := [monotonicity #968 #980]: #982
+#991 := [trans #983 #989]: #990
+#705 := [intro-def]: #704
+#992 := [mp #705 #991]: #987
+#993 := [not-or-elim #992]: #966
+#1558 := [unit-resolution #993 #1557]: #963
+#1249 := (or #962 #959)
+#1250 := [def-axiom]: #1249
+#1559 := [unit-resolution #1250 #1558]: #959
+decl z3name!8 :: int
+#855 := z3name!8
+#864 := (* -1::int z3name!8)
+#867 := (+ uf_11 #864)
+#870 := (+ uf_9 #867)
+#873 := (<= #870 0::int)
+#483 := (ite #476 uf_10 #459)
+#494 := (* -1::int #483)
+#495 := (+ uf_11 #494)
+#496 := (+ uf_9 #495)
+#620 := (<= #496 0::int)
+#874 := (= #620 #873)
+#871 := (~ #496 #870)
+#868 := (~ #495 #867)
+#865 := (~ #494 #864)
+#862 := (~ #483 z3name!8)
+#858 := (= z3name!8 #459)
+#859 := (or #476 #858)
+#856 := (= z3name!8 uf_10)
+#857 := (or #477 #856)
+#860 := (and #857 #859)
+#861 := [intro-def]: #860
+#863 := [apply-def #861]: #862
+#866 := [monotonicity #863]: #865
+#869 := [monotonicity #866]: #868
+#872 := [monotonicity #869]: #871
+#875 := [monotonicity #872]: #874
+#621 := (>= #496 0::int)
+#623 := (not #621)
+#622 := (not #620)
+#624 := (or #622 #623)
+#625 := (not #624)
+#497 := (= #496 0::int)
+#626 := (iff #497 #625)
+#627 := [rewrite]: #626
+#57 := (- uf_10)
+#56 := (< uf_10 0::int)
+#58 := (ite #56 #57 uf_10)
+#59 := (- #58 uf_9)
+#60 := (= uf_11 #59)
+#502 := (iff #60 #497)
+#462 := (ite #56 #459 uf_10)
+#468 := (+ #412 #462)
+#473 := (= uf_11 #468)
+#500 := (iff #473 #497)
+#488 := (+ #412 #483)
+#491 := (= uf_11 #488)
+#498 := (iff #491 #497)
+#499 := [rewrite]: #498
+#492 := (iff #473 #491)
+#489 := (= #468 #488)
+#486 := (= #462 #483)
+#480 := (ite #477 #459 uf_10)
+#484 := (= #480 #483)
+#485 := [rewrite]: #484
+#481 := (= #462 #480)
+#478 := (iff #56 #477)
+#479 := [rewrite]: #478
+#482 := [monotonicity #479]: #481
+#487 := [trans #482 #485]: #486
+#490 := [monotonicity #487]: #489
+#493 := [monotonicity #490]: #492
+#501 := [trans #493 #499]: #500
+#474 := (iff #60 #473)
+#471 := (= #59 #468)
+#465 := (- #462 uf_9)
+#469 := (= #465 #468)
+#470 := [rewrite]: #469
+#466 := (= #59 #465)
+#463 := (= #58 #462)
+#460 := (= #57 #459)
+#461 := [rewrite]: #460
+#464 := [monotonicity #461]: #463
+#467 := [monotonicity #464]: #466
+#472 := [trans #467 #470]: #471
+#475 := [monotonicity #472]: #474
+#503 := [trans #475 #501]: #502
+#458 := [asserted]: #60
+#504 := [mp #458 #503]: #497
+#628 := [mp #504 #627]: #625
+#629 := [not-or-elim #628]: #620
+#876 := [mp~ #629 #875]: #873
+#1197 := (+ uf_10 z3name!8)
+#1198 := (<= #1197 0::int)
+#1199 := (>= #1197 0::int)
+#1201 := (not #1199)
+#1200 := (not #1198)
+#1202 := (or #1200 #1201)
+#1203 := (not #1202)
+#1206 := (or #476 #1203)
+#1213 := (not #1206)
+#1186 := (+ uf_10 #864)
+#1187 := (<= #1186 0::int)
+#1189 := (not #1187)
+#1185 := (>= #1186 0::int)
+#1188 := (not #1185)
+#1190 := (or #1188 #1189)
+#1191 := (not #1190)
+#1194 := (or #477 #1191)
+#1212 := (not #1194)
+#1214 := (or #1212 #1213)
+#1215 := (not #1214)
+#1218 := (iff #860 #1215)
+#1209 := (and #1194 #1206)
+#1216 := (iff #1209 #1215)
+#1217 := [rewrite]: #1216
+#1210 := (iff #860 #1209)
+#1207 := (iff #859 #1206)
+#1204 := (iff #858 #1203)
+#1205 := [rewrite]: #1204
+#1208 := [monotonicity #1205]: #1207
+#1195 := (iff #857 #1194)
+#1192 := (iff #856 #1191)
+#1193 := [rewrite]: #1192
+#1196 := [monotonicity #1193]: #1195
+#1211 := [monotonicity #1196 #1208]: #1210
+#1219 := [trans #1211 #1217]: #1218
+#1220 := [mp #861 #1219]: #1215
+#1222 := [not-or-elim #1220]: #1206
+#1560 := [unit-resolution #1222 #1553]: #1203
+#1325 := (or #1202 #1198)
+#1326 := [def-axiom]: #1325
+#1561 := [unit-resolution #1326 #1560]: #1198
+#711 := (+ uf_5 #708)
+#714 := (+ uf_1 #711)
+#721 := (>= #714 0::int)
+#201 := (ite #194 uf_4 #177)
+#212 := (* -1::int #201)
+#213 := (+ uf_5 #212)
+#214 := (+ uf_1 #213)
+#555 := (>= #214 0::int)
+#722 := (= #555 #721)
+#715 := (~ #214 #714)
+#712 := (~ #213 #711)
+#709 := (~ #212 #708)
+#706 := (~ #201 z3name!2)
+#707 := [apply-def #705]: #706
+#710 := [monotonicity #707]: #709
+#713 := [monotonicity #710]: #712
+#716 := [monotonicity #713]: #715
+#723 := [monotonicity #716]: #722
+#557 := (not #555)
+#554 := (<= #214 0::int)
+#556 := (not #554)
+#558 := (or #556 #557)
+#559 := (not #558)
+#215 := (= #214 0::int)
+#560 := (iff #215 #559)
+#561 := [rewrite]: #560
+#21 := (- uf_4)
+#20 := (< uf_4 0::int)
+#22 := (ite #20 #21 uf_4)
+#23 := (- #22 uf_1)
+#24 := (= uf_5 #23)
+#220 := (iff #24 #215)
+#180 := (ite #20 #177 uf_4)
+#186 := (+ #130 #180)
+#191 := (= uf_5 #186)
+#218 := (iff #191 #215)
+#206 := (+ #130 #201)
+#209 := (= uf_5 #206)
+#216 := (iff #209 #215)
+#217 := [rewrite]: #216
+#210 := (iff #191 #209)
+#207 := (= #186 #206)
+#204 := (= #180 #201)
+#198 := (ite #195 #177 uf_4)
+#202 := (= #198 #201)
+#203 := [rewrite]: #202
+#199 := (= #180 #198)
+#196 := (iff #20 #195)
+#197 := [rewrite]: #196
+#200 := [monotonicity #197]: #199
+#205 := [trans #200 #203]: #204
+#208 := [monotonicity #205]: #207
+#211 := [monotonicity #208]: #210
+#219 := [trans #211 #217]: #218
+#192 := (iff #24 #191)
+#189 := (= #23 #186)
+#183 := (- #180 uf_1)
+#187 := (= #183 #186)
+#188 := [rewrite]: #187
+#184 := (= #23 #183)
+#181 := (= #22 #180)
+#178 := (= #21 #177)
+#179 := [rewrite]: #178
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182]: #184
+#190 := [trans #185 #188]: #189
+#193 := [monotonicity #190]: #192
+#221 := [trans #193 #219]: #220
+#176 := [asserted]: #24
+#222 := [mp #176 #221]: #215
+#562 := [mp #222 #561]: #559
+#564 := [not-or-elim #562]: #555
+#724 := [mp~ #564 #723]: #721
+#685 := (+ uf_4 #682)
+#688 := (+ uf_2 #685)
+#695 := (>= #688 0::int)
+#154 := (ite #147 uf_1 #130)
+#165 := (* -1::int #154)
+#166 := (+ uf_4 #165)
+#167 := (+ uf_2 #166)
+#544 := (>= #167 0::int)
+#696 := (= #544 #695)
+#689 := (~ #167 #688)
+#686 := (~ #166 #685)
+#683 := (~ #165 #682)
+#680 := (~ #154 z3name!1)
+#681 := [apply-def #679]: #680
+#684 := [monotonicity #681]: #683
+#687 := [monotonicity #684]: #686
+#690 := [monotonicity #687]: #689
+#697 := [monotonicity #690]: #696
+#546 := (not #544)
+#543 := (<= #167 0::int)
+#545 := (not #543)
+#547 := (or #545 #546)
+#548 := (not #547)
+#168 := (= #167 0::int)
+#549 := (iff #168 #548)
+#550 := [rewrite]: #549
+#15 := (- uf_1)
+#14 := (< uf_1 0::int)
+#16 := (ite #14 #15 uf_1)
+#17 := (- #16 uf_2)
+#18 := (= uf_4 #17)
+#173 := (iff #18 #168)
+#133 := (ite #14 #130 uf_1)
+#139 := (+ #82 #133)
+#144 := (= uf_4 #139)
+#171 := (iff #144 #168)
+#159 := (+ #82 #154)
+#162 := (= uf_4 #159)
+#169 := (iff #162 #168)
+#170 := [rewrite]: #169
+#163 := (iff #144 #162)
+#160 := (= #139 #159)
+#157 := (= #133 #154)
+#151 := (ite #148 #130 uf_1)
+#155 := (= #151 #154)
+#156 := [rewrite]: #155
+#152 := (= #133 #151)
+#149 := (iff #14 #148)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#158 := [trans #153 #156]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#172 := [trans #164 #170]: #171
+#145 := (iff #18 #144)
+#142 := (= #17 #139)
+#136 := (- #133 uf_2)
+#140 := (= #136 #139)
+#141 := [rewrite]: #140
+#137 := (= #17 #136)
+#134 := (= #16 #133)
+#131 := (= #15 #130)
+#132 := [rewrite]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#143 := [trans #138 #141]: #142
+#146 := [monotonicity #143]: #145
+#174 := [trans #146 #172]: #173
+#129 := [asserted]: #18
+#175 := [mp #129 #174]: #168
+#551 := [mp #175 #550]: #548
+#553 := [not-or-elim #551]: #544
+#698 := [mp~ #553 #697]: #695
+#1373 := (not #721)
+#1562 := (or #147 #1373 #961 #241 #195)
+#1563 := [th-lemma]: #1562
+#1564 := [unit-resolution #1563 #1559 #1557 #724 #1406]: #147
+#1565 := [unit-resolution #955 #1564]: #925
+#1566 := [unit-resolution #1238 #1565]: #921
+#1372 := (not #873)
+#1371 := (not #695)
+#1498 := (or #516 #923 #1373 #1371 #1372 #1343 #1200 #1075 #1350 #1113 #961 #1151 #1337 #1048 #1357)
+#1499 := [th-lemma]: #1498
+#1567 := [unit-resolution #1499 #1566 #698 #724 #1545 #772 #1447 #802 #1496 #828 #1554 #854 #1561 #876 #1559]: #516
+#1247 := (or #962 #957)
+#1248 := [def-axiom]: #1247
+#1568 := [unit-resolution #1248 #1558]: #957
+#877 := (>= #870 0::int)
+#878 := (= #621 #877)
+#879 := [monotonicity #872]: #878
+#630 := [not-or-elim #628]: #621
+#880 := [mp~ #630 #879]: #877
+#1327 := (or #1202 #1199)
+#1328 := [def-axiom]: #1327
+#1569 := [unit-resolution #1328 #1560]: #1199
+#795 := (<= #792 0::int)
+#796 := (= #587 #795)
+#797 := [monotonicity #794]: #796
+#596 := [not-or-elim #595]: #587
+#798 := [mp~ #596 #797]: #795
+#1503 := (or #335 #1049 #241)
+#1425 := (or #335 #1049 #241 #1037)
+#1422 := [hypothesis]: #336
+#1423 := [hypothesis]: #1047
+#1424 := [th-lemma #1423 #1422 #776 #1406 #1421]: false
+#1426 := [lemma #1424]: #1425
+#1504 := [unit-resolution #1426 #1459]: #1503
+#1505 := [unit-resolution #1504 #1406 #1468]: #335
+#1506 := [unit-resolution #1107 #1505]: #1077
+#1283 := (or #1076 #1071)
+#1284 := [def-axiom]: #1283
+#1507 := [unit-resolution #1284 #1506]: #1071
+#717 := (<= #714 0::int)
+#718 := (= #554 #717)
+#719 := [monotonicity #716]: #718
+#563 := [not-or-elim #562]: #554
+#720 := [mp~ #563 #719]: #717
+#691 := (<= #688 0::int)
+#692 := (= #543 #691)
+#693 := [monotonicity #690]: #692
+#552 := [not-or-elim #551]: #543
+#694 := [mp~ #552 #693]: #691
+#1235 := (or #924 #919)
+#1236 := [def-axiom]: #1235
+#1570 := [unit-resolution #1236 #1565]: #919
+#1409 := (not #773)
+#1489 := (not #847)
+#1358 := (not #795)
+#1365 := (not #821)
+#1511 := (not #877)
+#1510 := (not #691)
+#1509 := (not #717)
+#1512 := (or #515 #922 #1509 #1510 #1511 #1365 #1201 #1074 #1358 #1112 #960 #1150 #1489 #1049 #1409)
+#1513 := [th-lemma]: #1512
+#1571 := [unit-resolution #1513 #1570 #694 #720 #1468 #776 #1507 #798 #1488 #824 #1552 #850 #1569 #880 #1568]: #515
+#506 := (<= #508 0::int)
+#659 := (+ uf_3 #656)
+#662 := (+ uf_1 #659)
+#665 := (<= #662 0::int)
+#107 := (ite #100 uf_2 #82)
+#118 := (* -1::int #107)
+#119 := (+ uf_3 #118)
+#120 := (+ uf_1 #119)
+#532 := (<= #120 0::int)
+#666 := (= #532 #665)
+#663 := (~ #120 #662)
+#660 := (~ #119 #659)
+#657 := (~ #118 #656)
+#654 := (~ #107 z3name!0)
+#655 := [apply-def #653]: #654
+#658 := [monotonicity #655]: #657
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+#664 := [monotonicity #661]: #663
+#667 := [monotonicity #664]: #666
+#533 := (>= #120 0::int)
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+#534 := (not #532)
+#536 := (or #534 #535)
+#537 := (not #536)
+#121 := (= #120 0::int)
+#538 := (iff #121 #537)
+#539 := [rewrite]: #538
+#8 := (- uf_2)
+#7 := (< uf_2 0::int)
+#9 := (ite #7 #8 uf_2)
+#11 := (- #9 uf_3)
+#12 := (= uf_1 #11)
+#126 := (iff #12 #121)
+#85 := (ite #7 #82 uf_2)
+#91 := (* -1::int uf_3)
+#92 := (+ #91 #85)
+#97 := (= uf_1 #92)
+#124 := (iff #97 #121)
+#112 := (+ #91 #107)
+#115 := (= uf_1 #112)
+#122 := (iff #115 #121)
+#123 := [rewrite]: #122
+#116 := (iff #97 #115)
+#113 := (= #92 #112)
+#110 := (= #85 #107)
+#104 := (ite #101 #82 uf_2)
+#108 := (= #104 #107)
+#109 := [rewrite]: #108
+#105 := (= #85 #104)
+#102 := (iff #7 #101)
+#103 := [rewrite]: #102
+#106 := [monotonicity #103]: #105
+#111 := [trans #106 #109]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#125 := [trans #117 #123]: #124
+#98 := (iff #12 #97)
+#95 := (= #11 #92)
+#88 := (- #85 uf_3)
+#93 := (= #88 #92)
+#94 := [rewrite]: #93
+#89 := (= #11 #88)
+#86 := (= #9 #85)
+#83 := (= #8 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
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+#99 := [monotonicity #96]: #98
+#127 := [trans #99 #125]: #126
+#80 := [asserted]: #12
+#128 := [mp #80 #127]: #121
+#540 := [mp #128 #539]: #537
+#541 := [not-or-elim #540]: #532
+#668 := [mp~ #541 #667]: #665
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+#1516 := [th-lemma]: #1515
+#1572 := [unit-resolution #1516 #1566 #698 #1559 #724 #1406]: #100
+#1573 := [unit-resolution #917 #1572]: #887
+#1223 := (or #886 #881)
+#1224 := [def-axiom]: #1223
+#1574 := [unit-resolution #1224 #1573]: #881
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+#1529 := (or #506 #884 #1528 #1364 #1011 #1343 #1113 #1151 #1337 #1048 #1357 #922 #1510)
+#1530 := [th-lemma]: #1529
+#1575 := [unit-resolution #1530 #1574 #668 #694 #1404 #750 #1545 #772 #1496 #828 #1554 #854 #1570]: #506
+#743 := (<= #740 0::int)
+#744 := (= #565 #743)
+#745 := [monotonicity #742]: #744
+#574 := [not-or-elim #573]: #565
+#746 := [mp~ #574 #745]: #743
+#1520 := [unit-resolution #1032 #1406]: #1013
+#1265 := (or #1012 #1008)
+#1266 := [def-axiom]: #1265
+#1521 := [unit-resolution #1266 #1520]: #1008
+#669 := (>= #662 0::int)
+#670 := (= #533 #669)
+#671 := [monotonicity #664]: #670
+#542 := [not-or-elim #540]: #533
+#672 := [mp~ #542 #671]: #669
+#1576 := [unit-resolution #1226 #1573]: #883
+#1523 := (not #743)
+#1522 := (not #669)
+#1524 := (or #509 #885 #1522 #1523 #1010 #1365 #1112 #1150 #1489 #1049 #1409 #923 #1371)
+#1525 := [th-lemma]: #1524
+#1577 := [unit-resolution #1525 #1576 #672 #698 #1521 #746 #1468 #776 #1488 #824 #1552 #850 #1566]: #509
+#634 := (not #516)
+#633 := (not #515)
+#632 := (not #509)
+#631 := (not #506)
+#635 := (or #631 #632 #633 #634)
+#523 := (and #506 #509 #515 #516)
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+#636 := (not #635)
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+#642 := (iff #639 #635)
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+#640 := (iff #528 #639)
+#637 := (iff #523 #636)
+#638 := [rewrite]: #637
+#641 := [monotonicity #638]: #640
+#645 := [trans #641 #643]: #644
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+#61 := (= uf_3 uf_10)
+#63 := (and #61 #62)
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+#529 := (iff #64 #528)
+#526 := (iff #63 #523)
+#517 := (and #515 #516)
+#510 := (and #506 #509)
+#520 := (and #510 #517)
+#524 := (iff #520 #523)
+#525 := [rewrite]: #524
+#521 := (iff #63 #520)
+#518 := (iff #62 #517)
+#519 := [rewrite]: #518
+#511 := (iff #61 #510)
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+#522 := [monotonicity #512 #519]: #521
+#527 := [trans #522 #525]: #526
+#530 := [monotonicity #527]: #529
+#505 := [asserted]: #64
+#531 := [mp #505 #530]: #528
+#646 := [mp #531 #645]: #635
+#1578 := [unit-resolution #646 #1577 #1575 #1571 #1567]: false
+#1580 := [lemma #1578]: #1579
+#1657 := [unit-resolution #1580 #1406]: #1048
+#1625 := (or #194 #241)
+#1535 := [hypothesis]: #195
+#1538 := (or #194 #960)
+#1432 := [hypothesis]: #973
+#1255 := (or #974 #971)
+#1256 := [def-axiom]: #1255
+#1433 := [unit-resolution #1256 #1432]: #974
+#994 := [not-or-elim #992]: #978
+#1434 := [unit-resolution #994 #1433]: #194
+#1435 := [unit-resolution #993 #1434]: #963
+#1436 := (or #971 #195 #961)
+#1437 := [th-lemma]: #1436
+#1438 := [unit-resolution #1437 #1434 #1432]: #961
+#1439 := [unit-resolution #1250 #1438 #1435]: false
+#1440 := [lemma #1439]: #971
+#1536 := [hypothesis]: #957
+#1537 := [th-lemma #1536 #1535 #1440]: false
+#1539 := [lemma #1537]: #1538
+#1581 := [unit-resolution #1539 #1535]: #960
+#1582 := (or #959 #957)
+#1583 := [th-lemma]: #1582
+#1584 := [unit-resolution #1583 #1581]: #959
+#1585 := (or #147 #1373 #241 #194 #973)
+#1586 := [th-lemma]: #1585
+#1587 := [unit-resolution #1586 #1535 #1440 #724 #1406]: #147
+#1588 := [unit-resolution #955 #1587]: #925
+#1589 := [unit-resolution #1238 #1588]: #921
+#1590 := [unit-resolution #1516 #1589 #698 #1584 #724 #1406]: #100
+#1591 := [unit-resolution #917 #1590]: #887
+#1592 := [unit-resolution #1224 #1591]: #881
+#1593 := (or #430 #1365 #1074 #1358 #1112 #194 #1364 #1011 #241)
+#1594 := [th-lemma]: #1593
+#1595 := [unit-resolution #1594 #1535 #1404 #750 #1507 #798 #1488 #824 #1406]: #430
+#1184 := [not-or-elim #1182]: #1168
+#1596 := [unit-resolution #1184 #1595]: #1165
+#1315 := (or #1164 #1161)
+#1316 := [def-axiom]: #1315
+#1597 := [unit-resolution #1316 #1596]: #1161
+#1533 := (or #288 #241)
+#1471 := (or #194 #288 #241)
+#1469 := (or #194 #288 #241 #1364 #1011)
+#1470 := [th-lemma]: #1469
+#1472 := [unit-resolution #1470 #1404 #750]: #1471
+#1473 := [unit-resolution #1472 #1405 #1406]: #194
+#1474 := [unit-resolution #993 #1473]: #963
+#1475 := [unit-resolution #1250 #1474]: #959
+#1476 := (or #147 #1373 #1364 #1011 #961 #241 #288)
+#1477 := [th-lemma]: #1476
+#1478 := [unit-resolution #1477 #1475 #724 #1406 #1404 #750 #1405]: #147
+#1479 := [unit-resolution #955 #1478]: #925
+#1480 := [unit-resolution #1238 #1479]: #921
+#1419 := (or #288 #241 #429)
+#1333 := [hypothesis]: #430
+#1408 := [unit-resolution #1280 #1407]: #1047
+#1410 := (or #335 #1049 #1409 #288 #241)
+#1411 := [th-lemma]: #1410
+#1412 := [unit-resolution #1411 #1405 #1408 #776 #1406]: #335
+#1413 := [unit-resolution #1107 #1412]: #1077
+#1414 := [unit-resolution #1286 #1413]: #1073
+#1415 := [unit-resolution #1352 #1414 #802 #1405 #828 #1333]: #1113
+#1416 := [unit-resolution #1298 #1415]: #1114
+#1417 := [unit-resolution #1145 #1416]: #383
+#1418 := [th-lemma #1414 #802 #1405 #1408 #776 #1406 #1417]: false
+#1420 := [lemma #1418]: #1419
+#1481 := [unit-resolution #1420 #1405 #1406]: #429
+#1482 := [unit-resolution #1183 #1481]: #1153
+#1483 := [unit-resolution #1308 #1482]: #1147
+#1490 := (or #477 #1150 #1489 #1365 #1112 #1049 #241 #1409 #288)
+#1491 := [th-lemma]: #1490
+#1492 := [unit-resolution #1491 #1405 #1468 #776 #1488 #824 #1483 #850 #1406]: #477
+#1493 := [unit-resolution #1222 #1492]: #1203
+#1494 := [unit-resolution #1326 #1493]: #1198
+#1495 := [unit-resolution #1310 #1482]: #1149
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+#1502 := [unit-resolution #1328 #1493]: #1199
+#1508 := [unit-resolution #1248 #1474]: #957
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+#1518 := [unit-resolution #917 #1517]: #887
+#1519 := [unit-resolution #1226 #1518]: #883
+#1526 := [unit-resolution #1525 #1480 #672 #698 #1521 #746 #1468 #776 #1488 #824 #1483 #850 #1519]: #509
+#1527 := [unit-resolution #1224 #1518]: #881
+#1531 := [unit-resolution #1530 #1501 #668 #694 #1404 #750 #1497 #772 #1496 #828 #1495 #854 #1527]: #506
+#1532 := [unit-resolution #646 #1531 #1526 #1514 #1500]: false
+#1534 := [lemma #1532]: #1533
+#1598 := [unit-resolution #1534 #1406]: #288
+#1599 := [unit-resolution #1069 #1598]: #1039
+#1271 := (or #1038 #1033)
+#1272 := [def-axiom]: #1271
+#1600 := [unit-resolution #1272 #1599]: #1033
+#1601 := [unit-resolution #1236 #1588]: #919
+#1602 := (or #506 #884 #1528 #1364 #1011 #1365 #1112 #1337 #1357 #922 #1510 #1036 #1163 #1074 #1358)
+#1603 := [th-lemma]: #1602
+#1604 := [unit-resolution #1603 #1601 #668 #694 #1404 #750 #1600 #772 #1507 #798 #1488 #824 #1597 #854 #1592]: #506
+#1605 := [unit-resolution #1226 #1591]: #883
+#1313 := (or #1164 #1160)
+#1314 := [def-axiom]: #1313
+#1606 := [unit-resolution #1314 #1596]: #1160
+#1607 := (or #509 #885 #1522 #1523 #1010 #1343 #1113 #1489 #1409 #923 #1371 #1037 #1162 #1075 #1350)
+#1608 := [th-lemma]: #1607
+#1609 := [unit-resolution #1608 #1589 #672 #698 #1521 #746 #1459 #776 #1447 #802 #1496 #828 #1606 #850 #1605]: #509
+#1610 := (or #476 #1036 #1337 #1365 #1112 #1357 #194 #1364 #1011 #1163 #1074 #1358)
+#1611 := [th-lemma]: #1610
+#1612 := [unit-resolution #1611 #1597 #750 #1600 #772 #1507 #798 #1488 #824 #1404 #854 #1535]: #476
+#1221 := [not-or-elim #1220]: #1194
+#1613 := [unit-resolution #1221 #1612]: #1191
+#1319 := (or #1190 #1185)
+#1320 := [def-axiom]: #1319
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+#1615 := (or #516 #923 #1373 #1371 #1372 #1075 #1350 #1489 #1409 #1037 #973 #1162 #1188 #1343 #1113 #1523 #1010)
+#1616 := [th-lemma]: #1615
+#1617 := [unit-resolution #1616 #1606 #1440 #724 #1521 #746 #1459 #776 #1447 #802 #1496 #828 #698 #850 #1614 #876 #1589]: #516
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+#1621 := (or #515 #922 #1509 #1510 #1511 #1074 #1358 #1337 #1357 #1036 #972 #1163 #1189 #1365 #1112 #1364 #1011)
+#1622 := [th-lemma]: #1621
+#1623 := [unit-resolution #1622 #1620 #694 #720 #1404 #750 #1600 #772 #1507 #798 #1488 #824 #1597 #854 #1618 #880 #1601]: #515
+#1624 := [unit-resolution #646 #1623 #1617 #1609 #1604]: false
+#1626 := [lemma #1624]: #1625
+#1658 := [unit-resolution #1626 #1406]: #194
+#1659 := [unit-resolution #993 #1658]: #963
+#1660 := [unit-resolution #1250 #1659]: #959
+#1661 := [unit-resolution #1563 #1660 #1658 #724 #1406]: #147
+#1662 := [unit-resolution #955 #1661]: #925
+#1663 := [unit-resolution #1238 #1662]: #921
+#1664 := [unit-resolution #1516 #1663 #698 #1660 #724 #1406]: #100
+#1665 := [unit-resolution #917 #1664]: #887
+#1666 := [unit-resolution #1226 #1665]: #883
+#1667 := [unit-resolution #1224 #1665]: #881
+#1668 := [unit-resolution #1236 #1662]: #919
+#1669 := [unit-resolution #1248 #1659]: #957
+#1655 := (or #429 #1113 #1010 #960 #1036 #1074 #1112 #922 #923 #884 #885)
+#1632 := [hypothesis]: #919
+#1636 := [hypothesis]: #881
+#1638 := [hypothesis]: #1071
+#1639 := [hypothesis]: #1033
+#1334 := [unit-resolution #1184 #1333]: #1165
+#1335 := [unit-resolution #1316 #1334]: #1161
+#1640 := [unit-resolution #1603 #1335 #668 #694 #1404 #750 #1639 #772 #1638 #798 #1637 #824 #1632 #854 #1636]: #506
+#1641 := [hypothesis]: #883
+#1642 := [hypothesis]: #921
+#1643 := [hypothesis]: #1111
+#1644 := [hypothesis]: #1008
+#1631 := [unit-resolution #1314 #1334]: #1160
+#1645 := [unit-resolution #1608 #1631 #672 #698 #1644 #746 #1459 #776 #1447 #802 #1643 #828 #1642 #850 #1641]: #509
+#1634 := (or #1202 #922 #960 #632 #631 #429)
+#1627 := [hypothesis]: #506
+#1628 := [hypothesis]: #509
+#1384 := [hypothesis]: #1203
+#1396 := (or #1202 #516 #429)
+#1331 := [hypothesis]: #634
+#1385 := [unit-resolution #1326 #1384]: #1198
+#1382 := (or #1189 #1200 #516 #429)
+#1332 := [hypothesis]: #1198
+#1336 := [hypothesis]: #1187
+#1338 := (or #382 #1189 #1337 #429 #1163 #1200)
+#1339 := [th-lemma]: #1338
+#1340 := [unit-resolution #1339 #1336 #1335 #854 #1333 #1332]: #382
+#1341 := [unit-resolution #1145 #1340]: #1115
+#1342 := [unit-resolution #1298 #1341]: #1111
+#1344 := (or #335 #1113 #429 #1343 #1189 #1337 #1163 #1200)
+#1345 := [th-lemma]: #1344
+#1346 := [unit-resolution #1345 #1342 #828 #1333 #1335 #854 #1336 #1332]: #335
+#1347 := [unit-resolution #1107 #1346]: #1077
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+#1353 := [unit-resolution #1352 #1349 #802 #1342 #828 #1333]: #288
+#1354 := [unit-resolution #1069 #1353]: #1039
+#1355 := [unit-resolution #1272 #1354]: #1033
+#1356 := [unit-resolution #1296 #1341]: #1109
+#1359 := (or #242 #1036 #1357 #429 #1189 #1337 #1163 #1200 #1074 #1358)
+#1360 := [th-lemma]: #1359
+#1361 := [unit-resolution #1360 #1355 #772 #1348 #798 #1333 #1335 #854 #1336 #1332]: #242
+#1362 := [unit-resolution #1032 #1361]: #1013
+#1363 := [unit-resolution #1268 #1362]: #1009
+#1366 := (or #194 #1011 #1364 #1074 #1358 #1112 #1365 #1036 #1357 #1189 #1337 #1163 #1200)
+#1367 := [th-lemma]: #1366
+#1368 := [unit-resolution #1367 #1363 #750 #1355 #772 #1348 #798 #1356 #824 #1335 #854 #1336 #1332]: #194
+#1369 := [unit-resolution #993 #1368]: #963
+#1370 := [unit-resolution #1250 #1369]: #959
+#1374 := (or #923 #1371 #516 #1372 #1200 #961 #1373 #1036 #1357 #1337 #1163 #1074 #1358)
+#1375 := [th-lemma]: #1374
+#1376 := [unit-resolution #1375 #1370 #698 #724 #1355 #772 #1348 #798 #1335 #854 #1332 #876 #1331]: #923
+#1377 := (or #147 #195 #961 #1373 #1036 #1357 #429 #1189 #1337 #1163 #1200 #1074 #1358)
+#1378 := [th-lemma]: #1377
+#1379 := [unit-resolution #1378 #1368 #1370 #724 #1355 #772 #1348 #798 #1333 #1335 #854 #1336 #1332]: #147
+#1380 := [unit-resolution #955 #1379]: #925
+#1381 := [unit-resolution #1238 #1380 #1376]: false
+#1383 := [lemma #1381]: #1382
+#1386 := [unit-resolution #1383 #1385 #1331 #1333]: #1189
+#1387 := [unit-resolution #1322 #1386]: #1190
+#1388 := [unit-resolution #1328 #1384]: #1199
+#1389 := (or #1187 #1185)
+#1390 := [th-lemma]: #1389
+#1391 := [unit-resolution #1390 #1386]: #1185
+#1392 := (or #476 #1188 #1201)
+#1393 := [th-lemma]: #1392
+#1394 := [unit-resolution #1393 #1391 #1388]: #476
+#1395 := [unit-resolution #1221 #1394 #1387]: false
+#1397 := [lemma #1395]: #1396
+#1629 := [unit-resolution #1397 #1384 #1333]: #516
+#1630 := [unit-resolution #646 #1629 #1628 #1627]: #633
+#1633 := [th-lemma #1632 #720 #694 #880 #1447 #802 #850 #776 #1459 #1631 #1536 #1388 #1630]: false
+#1635 := [lemma #1633]: #1634
+#1646 := [unit-resolution #1635 #1645 #1536 #1632 #1640 #1333]: #1202
+#1647 := [unit-resolution #1222 #1646]: #476
+#1648 := [unit-resolution #1221 #1647]: #1191
+#1649 := [unit-resolution #1322 #1648]: #1187
+#1650 := [unit-resolution #1320 #1648]: #1185
+#1651 := [unit-resolution #1616 #1650 #1440 #724 #1644 #746 #1459 #776 #1447 #802 #1643 #828 #698 #850 #1631 #876 #1642]: #516
+#1652 := [unit-resolution #646 #1651 #1645 #1640]: #633
+#1653 := [unit-resolution #1622 #1652 #694 #720 #1404 #750 #1639 #772 #1638 #798 #1637 #824 #1335 #854 #1649 #880 #1632]: #972
+#1654 := [th-lemma #1459 #1647 #850 #828 #1643 #776 #746 #1644 #1631 #1447 #802 #1536 #1653]: false
+#1656 := [lemma #1654]: #1655
+#1670 := [unit-resolution #1656 #1496 #1521 #1669 #1600 #1507 #1488 #1668 #1663 #1667 #1666]: #429
+#1671 := [th-lemma #1600 #1670 #824 #1507 #798 #1488 #1657]: false
+#1672 := [lemma #1671]: #241
+#1683 := [unit-resolution #1031 #1672]: #1001
+#1703 := [unit-resolution #1262 #1683]: #997
+#1920 := (or #194 #242 #1364 #999 #288)
+#1921 := [th-lemma]: #1920
+#1922 := [unit-resolution #1921 #1405 #1703 #750 #1672]: #194
+#1923 := [unit-resolution #993 #1922]: #963
+#1924 := [unit-resolution #1248 #1923]: #957
+#1925 := [unit-resolution #1250 #1923]: #959
+#1843 := (or #288 #961 #147)
+#1763 := [hypothesis]: #148
+#1828 := [hypothesis]: #959
+#1842 := [th-lemma #724 #750 #1703 #1828 #1405 #1763]: false
+#1844 := [lemma #1842]: #1843
+#1926 := [unit-resolution #1844 #1925 #1405]: #147
+#1927 := [unit-resolution #955 #1926]: #925
+#1928 := [unit-resolution #1236 #1927]: #919
+#2116 := [unit-resolution #1310 #2047]: #1149
+#2084 := (or #288 #516)
+#2050 := (or #288 #961 #516)
+#2037 := [hypothesis]: #1087
+#2038 := [unit-resolution #1292 #2037]: #1088
+#2041 := (or #1085 #336)
+#2039 := (or #1085 #1075 #336)
+#2040 := [th-lemma]: #2039
+#2042 := [unit-resolution #2040 #1447]: #2041
+#2043 := [unit-resolution #2042 #2037]: #336
+#2044 := [unit-resolution #1108 #2043 #2038]: false
+#2045 := [lemma #2044]: #1085
+#2035 := (or #1087 #1150 #961 #1048 #516)
+#1845 := [hypothesis]: #1085
+#1874 := [hypothesis]: #477
+#1901 := (or #335 #476)
+#1895 := [unit-resolution #1222 #1874]: #1203
+#1896 := [unit-resolution #1326 #1895]: #1198
+#1893 := (or #429 #1200)
+#1880 := (or #335 #1113 #429 #1163 #1200)
+#1857 := [hypothesis]: #1189
+#1858 := [unit-resolution #1322 #1857]: #1190
+#1859 := [unit-resolution #1221 #1858]: #477
+#1860 := [unit-resolution #1222 #1859]: #1203
+#1861 := [unit-resolution #1390 #1857]: #1185
+#1862 := [unit-resolution #1393 #1859 #1861]: #1201
+#1863 := [unit-resolution #1328 #1862 #1860]: false
+#1864 := [lemma #1863]: #1187
+#1878 := (or #335 #1113 #429 #1189 #1163 #1200)
+#1879 := [unit-resolution #1345 #828 #854]: #1878
+#1881 := [unit-resolution #1879 #1864]: #1880
+#1882 := [unit-resolution #1881 #1335 #1870 #1333 #1332]: #335
+#1883 := [unit-resolution #1107 #1882]: #1077
+#1884 := [unit-resolution #1689 #1333 #1870]: #288
+#1885 := [unit-resolution #1069 #1884]: #1039
+#1886 := [unit-resolution #1272 #1885]: #1033
+#1889 := (or #1036 #429 #1163 #1200 #1074)
+#1887 := (or #242 #1036 #429 #1189 #1163 #1200 #1074)
+#1888 := [unit-resolution #1360 #772 #798 #854]: #1887
+#1890 := [unit-resolution #1888 #1672 #1864]: #1889
+#1891 := [unit-resolution #1890 #1886 #1332 #1333 #1335]: #1074
+#1892 := [unit-resolution #1284 #1891 #1883]: false
+#1894 := [lemma #1892]: #1893
+#1897 := [unit-resolution #1894 #1896]: #429
+#1898 := [unit-resolution #1183 #1897]: #1153
+#1899 := [unit-resolution #1310 #1898]: #1149
+#1900 := [th-lemma #854 #1899 #1870 #828 #1422 #1874]: false
+#1902 := [lemma #1900]: #1901
+#1950 := [unit-resolution #1902 #1874]: #335
+#1951 := [unit-resolution #1107 #1950]: #1077
+#1952 := [unit-resolution #1284 #1951]: #1071
+#1953 := [unit-resolution #1328 #1895]: #1199
+#1876 := (or #1109 #476)
+#1673 := [hypothesis]: #1112
+#1760 := (or #429 #1109)
+#1674 := [unit-resolution #1296 #1673]: #1114
+#1675 := [unit-resolution #1145 #1674]: #383
+#1676 := [unit-resolution #1146 #1675]: #1127
+#1677 := [unit-resolution #1304 #1676]: #1123
+#1687 := [unit-resolution #1686 #1673]: #1111
+#1743 := [unit-resolution #1689 #1333 #1687]: #288
+#1744 := [unit-resolution #1069 #1743]: #1039
+#1745 := [unit-resolution #1272 #1744]: #1033
+#1678 := (or #335 #1343 #429 #382 #1125)
+#1679 := [th-lemma]: #1678
+#1746 := [unit-resolution #1679 #1333 #1675 #828 #1677]: #335
+#1747 := [unit-resolution #1107 #1746]: #1077
+#1748 := [unit-resolution #1284 #1747]: #1071
+#1259 := (or #1000 #995)
+#1260 := [def-axiom]: #1259
+#1684 := [unit-resolution #1260 #1683]: #995
+#1693 := (or #147 #1373 #1343 #1074 #1358 #1523 #429 #973 #998 #1036 #1357 #1125)
+#1694 := [th-lemma]: #1693
+#1749 := [unit-resolution #1694 #1745 #724 #1684 #746 #1440 #772 #1748 #798 #1677 #828 #1333]: #147
+#1750 := [unit-resolution #955 #1749]: #925
+#1751 := [unit-resolution #1238 #1750]: #921
+#1714 := (or #100 #923 #1373 #1371 #1343 #1523 #1074 #1358 #973 #429 #382 #1036 #1357 #998 #1125)
+#1715 := [th-lemma]: #1714
+#1752 := [unit-resolution #1715 #1751 #698 #1440 #724 #1684 #746 #1675 #772 #1748 #798 #1745 #1677 #828 #1333]: #100
+#1753 := [unit-resolution #1236 #1750]: #919
+#1727 := (or #1109 #429 #972)
+#1680 := [unit-resolution #1679 #1675 #1677 #828 #1333]: #335
+#1681 := [unit-resolution #1107 #1680]: #1077
+#1682 := [unit-resolution #1284 #1681]: #1071
+#1690 := [unit-resolution #1689 #1687 #1333]: #288
+#1691 := [unit-resolution #1069 #1690]: #1039
+#1692 := [unit-resolution #1272 #1691]: #1033
+#1695 := [unit-resolution #1694 #1692 #724 #1684 #746 #1440 #772 #1682 #798 #1677 #828 #1333]: #147
+#1696 := [unit-resolution #955 #1695]: #925
+#1697 := [unit-resolution #1236 #1696]: #919
+#1698 := (or #476 #429 #1337 #1163 #382)
+#1699 := [th-lemma]: #1698
+#1700 := [unit-resolution #1699 #1675 #1335 #854 #1333]: #476
+#1701 := [unit-resolution #1221 #1700]: #1191
+#1702 := [unit-resolution #1322 #1701]: #1187
+#1704 := [hypothesis]: #970
+#1301 := (or #1126 #1122)
+#1302 := [def-axiom]: #1301
+#1705 := [unit-resolution #1302 #1676]: #1122
+#1706 := (or #515 #922 #1509 #1510 #1511 #1075 #1350 #1337 #1409 #1037 #1163 #1365 #1364 #972 #999 #1124 #1189)
+#1707 := [th-lemma]: #1706
+#1708 := [unit-resolution #1707 #1705 #1704 #720 #1703 #750 #1459 #776 #1447 #802 #694 #824 #1335 #854 #1702 #880 #1697]: #515
+#1709 := [unit-resolution #1238 #1696]: #921
+#1710 := [unit-resolution #1320 #1701]: #1185
+#1711 := (or #516 #923 #1373 #1371 #1372 #1074 #1358 #1489 #1357 #1036 #1162 #1343 #1523 #973 #998 #1125 #1188)
+#1712 := [th-lemma]: #1711
+#1713 := [unit-resolution #1712 #1692 #1440 #724 #1684 #746 #698 #772 #1682 #798 #1677 #828 #1631 #850 #1710 #876 #1709]: #516
+#1716 := [unit-resolution #1715 #1709 #698 #1440 #724 #1684 #746 #1692 #772 #1682 #798 #1675 #1677 #828 #1333]: #100
+#1717 := [unit-resolution #917 #1716]: #887
+#1718 := [unit-resolution #1226 #1717]: #883
+#1719 := (or #509 #885 #1522 #1523 #1343 #1489 #1357 #923 #1371 #1036 #1162 #998 #1125)
+#1720 := [th-lemma]: #1719
+#1721 := [unit-resolution #1720 #1709 #672 #698 #1684 #746 #1692 #772 #1677 #828 #1631 #850 #1718]: #509
+#1722 := [unit-resolution #1224 #1717]: #881
+#1723 := (or #506 #884 #1528 #1364 #1365 #1337 #1409 #922 #1510 #1037 #1163 #999 #1124)
+#1724 := [th-lemma]: #1723
+#1725 := [unit-resolution #1724 #1697 #668 #694 #1703 #750 #1459 #776 #1705 #824 #1335 #854 #1722]: #506
+#1726 := [unit-resolution #646 #1725 #1721 #1713 #1708]: false
+#1728 := [lemma #1726]: #1727
+#1754 := [unit-resolution #1728 #1333 #1673]: #972
+#1755 := [unit-resolution #1254 #1754]: #974
+#1756 := [unit-resolution #994 #1755]: #194
+#1757 := [unit-resolution #993 #1756]: #963
+#1758 := [unit-resolution #1248 #1757]: #957
+#1759 := [th-lemma #1758 #1753 #720 #694 #1675 #1459 #776 #1447 #802 #1752]: false
+#1761 := [lemma #1759]: #1760
+#1871 := [unit-resolution #1761 #1673]: #429
+#1872 := [unit-resolution #1183 #1871]: #1153
+#1873 := [unit-resolution #1310 #1872]: #1149
+#1875 := [th-lemma #1675 #1874 #854 #1873 #1871]: false
+#1877 := [lemma #1875]: #1876
+#1954 := [unit-resolution #1877 #1874]: #1109
+#1948 := (or #288 #1112 #1200 #1201 #1074)
+#1917 := [unit-resolution #1894 #1332]: #429
+#1918 := [unit-resolution #1183 #1917]: #1153
+#1919 := [unit-resolution #1308 #1918]: #1147
+#1929 := [unit-resolution #1310 #1918]: #1149
+#1930 := [unit-resolution #1238 #1927]: #921
+#1931 := [hypothesis]: #1199
+#1932 := (or #515 #922 #1201 #1074 #1112 #960 #1150)
+#1933 := [unit-resolution #1513 #694 #720 #1468 #776 #798 #824 #850 #880]: #1932
+#1934 := [unit-resolution #1933 #1928 #1931 #1637 #1638 #1919 #1924]: #515
+#1935 := (or #516 #923 #1200 #1113 #961 #1151 #1048)
+#1936 := [unit-resolution #1499 #698 #724 #772 #1447 #802 #828 #854 #876]: #1935
+#1937 := [unit-resolution #1936 #1930 #1870 #1332 #1929 #1497 #1925]: #516
+#1915 := (or #898 #634 #633 #923 #961 #1048 #1151 #922 #960 #1112 #1150)
+#1903 := [hypothesis]: #515
+#1904 := [hypothesis]: #516
+#1905 := [hypothesis]: #899
+#1906 := [unit-resolution #1232 #1905]: #895
+#1907 := (or #509 #1522 #1523 #897 #998 #1489 #1150 #960 #1509 #1112 #1365 #1049 #922 #1510 #1409)
+#1908 := [th-lemma]: #1907
+#1909 := [unit-resolution #1908 #1906 #1632 #694 #1536 #720 #1684 #746 #1468 #776 #1637 #824 #1540 #850 #672]: #509
+#1774 := [hypothesis]: #1149
+#1229 := (or #898 #894)
+#1230 := [def-axiom]: #1229
+#1910 := [unit-resolution #1230 #1905]: #894
+#1911 := (or #506 #1528 #1364 #896 #999 #1337 #1151 #961 #1373 #1113 #1343 #1048 #923 #1371 #1357)
+#1912 := [th-lemma]: #1911
+#1913 := [unit-resolution #1912 #1910 #1642 #698 #1828 #724 #1703 #750 #1545 #772 #1870 #828 #1774 #854 #668]: #506
+#1914 := [unit-resolution #646 #1913 #1909 #1904 #1903]: false
+#1916 := [lemma #1914]: #1915
+#1938 := [unit-resolution #1916 #1937 #1934 #1930 #1925 #1497 #1929 #1928 #1924 #1637 #1919]: #898
+#1939 := [unit-resolution #918 #1938]: #100
+#1940 := [unit-resolution #917 #1939]: #887
+#1941 := [unit-resolution #1224 #1940]: #881
+#1942 := (or #506 #884 #1113 #1151 #1048 #922)
+#1943 := [unit-resolution #1530 #668 #694 #1404 #750 #772 #828 #854]: #1942
+#1944 := [unit-resolution #1943 #1941 #1497 #1870 #1929 #1928]: #506
+#1945 := [unit-resolution #646 #1944 #1937 #1934]: #632
+#1946 := [unit-resolution #1908 #1945 #1928 #694 #1924 #720 #1684 #746 #1468 #776 #1637 #824 #1919 #850 #672]: #897
+#1947 := [th-lemma #1946 #1939 #1742]: false
+#1949 := [lemma #1947]: #1948
+#1955 := [unit-resolution #1949 #1954 #1896 #1953 #1952]: #288
+#1956 := [unit-resolution #1069 #1955]: #1039
+#1957 := [unit-resolution #1272 #1956]: #1033
+#1958 := [unit-resolution #1735 #1954]: #382
+#1959 := (or #1123 #383 #1113)
+#1960 := [th-lemma]: #1959
+#1961 := [unit-resolution #1960 #1958 #1870]: #1123
+#1962 := [unit-resolution #1308 #1898]: #1147
+#1965 := (or #1160 #1112 #1074 #289 #1150)
+#1963 := (or #1160 #1365 #1112 #1074 #1358 #289 #1150)
+#1964 := [th-lemma]: #1963
+#1966 := [unit-resolution #1964 #798 #824]: #1965
+#1967 := [unit-resolution #1966 #1955 #1954 #1962 #1952]: #1160
+#1970 := (or #1162 #1151 #1036 #1125 #147 #1074)
+#1968 := (or #1162 #1151 #1343 #1523 #998 #1036 #1357 #1125 #973 #147 #1373 #1074 #1358)
+#1969 := [th-lemma]: #1968
+#1971 := [unit-resolution #1969 #724 #1684 #746 #1440 #772 #798 #828]: #1970
+#1972 := [unit-resolution #1971 #1967 #1952 #1961 #1899 #1957]: #147
+#1973 := [unit-resolution #955 #1972]: #925
+#1974 := [unit-resolution #1236 #1973]: #919
+#1975 := (or #1161 #1151 #430)
+#1976 := [th-lemma]: #1975
+#1977 := [unit-resolution #1976 #1899 #1897]: #1161
+#1978 := (or #476 #1036 #1112 #194 #1163 #1074)
+#1979 := [unit-resolution #1611 #750 #772 #798 #824 #1404 #854]: #1978
+#1980 := [unit-resolution #1979 #1957 #1874 #1954 #1952 #1977]: #194
+#1981 := [unit-resolution #993 #1980]: #963
+#1982 := [unit-resolution #1248 #1981]: #957
+#1983 := [unit-resolution #1933 #1974 #1953 #1954 #1952 #1962 #1982]: #515
+#1984 := [unit-resolution #1238 #1973]: #921
+#1985 := [unit-resolution #1250 #1981]: #959
+#1849 := (or #923 #516 #1200 #961 #1036 #1163 #1074)
+#1850 := [unit-resolution #1375 #698 #724 #772 #798 #854 #876]: #1849
+#1986 := [unit-resolution #1850 #1985 #1896 #1952 #1977 #1957 #1984]: #516
+#1987 := (or #509 #923 #1036 #1162 #1125)
+#1988 := [unit-resolution #1720 #672 #698 #1684 #746 #1742 #772 #828 #850]: #1987
+#1989 := [unit-resolution #1988 #1984 #1961 #1967 #1957]: #509
+#1990 := [unit-resolution #646 #1989 #1986 #1983]: #631
+#1991 := (or #506 #884 #1112 #922 #1036 #1163 #1074)
+#1992 := [unit-resolution #1603 #668 #694 #1404 #750 #772 #798 #824 #854]: #1991
+#1993 := [unit-resolution #1992 #1990 #1977 #1954 #1952 #1957 #1974]: #884
+#1994 := [unit-resolution #1224 #1993]: #886
+#1995 := [unit-resolution #917 #1994]: #101
+#1996 := [th-lemma #746 #1684 #1957 #1874 #854 #1899 #1870 #828 #1984 #1995 #698 #772 #1972]: false
+#1997 := [lemma #1996]: #476
+#2014 := [unit-resolution #1221 #1997]: #1191
+#2015 := [unit-resolution #1320 #2014]: #1185
+#2034 := [th-lemma #876 #850 #1540 #2015 #802 #2033 #698 #772 #1828 #724 #1545 #1845 #1331]: false
+#2036 := [lemma #2034]: #2035
+#2048 := [unit-resolution #2036 #1497 #2045 #1828 #1331]: #1150
+#2049 := [unit-resolution #1308 #2048 #2047]: false
+#2051 := [lemma #2049]: #2050
+#2082 := [unit-resolution #2051 #1405 #1331]: #961
+#2083 := [unit-resolution #1250 #1923 #2082]: false
+#2085 := [lemma #2083]: #2084
+#2089 := [unit-resolution #2085 #1331]: #288
+#2090 := [unit-resolution #1069 #2089]: #1039
+#2091 := [unit-resolution #1272 #2090]: #1033
+#2065 := [hypothesis]: #935
+#2066 := [unit-resolution #1244 #2065]: #936
+#2067 := [unit-resolution #956 #2066]: #147
+#2068 := [th-lemma #2065 #2033 #2067]: false
+#2069 := [lemma #2068]: #933
+#2100 := (or #429 #516)
+#2063 := (or #429 #1086 #516)
+#2052 := [unit-resolution #1761 #1333]: #1109
+#2053 := [unit-resolution #1735 #2052]: #382
+#2054 := [hypothesis]: #1084
+#2055 := (or #1200 #516 #429)
+#2056 := [unit-resolution #1383 #1864]: #2055
+#2057 := [unit-resolution #2056 #1333 #1331]: #1200
+#2060 := (or #1086 #383 #1113 #1188 #1162 #1198)
+#2058 := (or #1086 #383 #1113 #1343 #1188 #1489 #1162 #1198 #1075)
+#2059 := [th-lemma]: #2058
+#2061 := [unit-resolution #2059 #1447 #828 #850]: #2060
+#2062 := [unit-resolution #2061 #1631 #2057 #2015 #1870 #2054 #2053]: false
+#2064 := [lemma #2062]: #2063
+#2086 := [unit-resolution #2064 #1333 #1331]: #1086
+#2087 := [unit-resolution #1290 #2086]: #1088
+#2088 := [unit-resolution #1108 #2087]: #335
+#2080 := (or #1109 #516)
+#2070 := [unit-resolution #1308 #1872]: #1147
+#2020 := (or #194 #1150 #516 #1125 #1151 #1124)
+#1762 := [hypothesis]: #1122
+#1775 := [hypothesis]: #1123
+#1803 := (or #194 #1151 #1150 #1125 #147 #1124)
+#1764 := [unit-resolution #956 #1763]: #937
+#1765 := [unit-resolution #1244 #1764]: #933
+#1766 := (or #509 #885 #1522 #1364 #1365 #1489 #999 #1124 #1371 #1037 #1409 #935 #1150 #972 #1509 #1075 #1350)
+#1767 := [th-lemma]: #1766
+#1768 := [unit-resolution #1767 #1620 #1765 #698 #672 #720 #1703 #750 #1459 #776 #1447 #802 #1762 #824 #1540 #850 #1742]: #509
+#1769 := (or #100 #1371 #935 #194 #147)
+#1770 := [th-lemma]: #1769
+#1771 := [unit-resolution #1770 #1535 #1765 #698 #1763]: #100
+#1772 := [unit-resolution #917 #1771]: #887
+#1773 := [unit-resolution #1224 #1772]: #881
+#1776 := (or #335 #194 #1364 #1037 #1409 #999)
+#1777 := [th-lemma]: #1776
+#1778 := [unit-resolution #1777 #1535 #750 #1459 #776 #1703]: #335
+#1779 := [unit-resolution #1107 #1778]: #1077
+#1780 := [unit-resolution #1284 #1779]: #1071
+#1241 := (or #936 #932)
+#1242 := [def-axiom]: #1241
+#1781 := [unit-resolution #1242 #1764]: #932
+#1782 := (or #288 #1364 #999 #973 #147 #1373 #194)
+#1783 := [th-lemma]: #1782
+#1784 := [unit-resolution #1783 #1535 #1440 #724 #1703 #750 #1763]: #288
+#1785 := [unit-resolution #1069 #1784]: #1039
+#1786 := [unit-resolution #1272 #1785]: #1033
+#1787 := (or #506 #884 #1528 #1523 #1343 #1337 #998 #1125 #1510 #1036 #1357 #934 #1151 #973 #1373 #1074 #1358)
+#1788 := [th-lemma]: #1787
+#1789 := [unit-resolution #1788 #1786 #1781 #694 #1440 #724 #1684 #746 #668 #772 #1780 #798 #1775 #828 #1774 #854 #1773]: #506
+#1790 := (or #476 #1337 #1343 #1523 #1036 #1357 #998 #1125 #973 #147 #1373 #1074 #1358 #1151 #194)
+#1791 := [th-lemma]: #1790
+#1792 := [unit-resolution #1791 #1535 #1440 #724 #1684 #746 #1786 #772 #1780 #798 #1775 #828 #1774 #854 #1763]: #476
+#1793 := [unit-resolution #1221 #1792]: #1191
+#1794 := [unit-resolution #1320 #1793]: #1185
+#1795 := (or #516 #1372 #1489 #1409 #1037 #1188 #1371 #935 #972 #1509 #1075 #1350 #1150)
+#1796 := [th-lemma]: #1795
+#1797 := [unit-resolution #1796 #1620 #698 #720 #1459 #776 #1447 #802 #1540 #850 #1794 #876 #1765]: #516
+#1798 := [unit-resolution #1322 #1793]: #1187
+#1799 := (or #515 #1511 #1337 #1357 #1036 #1189 #1510 #934 #973 #1373 #1074 #1358 #1151)
+#1800 := [th-lemma]: #1799
+#1801 := [unit-resolution #1800 #1786 #1440 #724 #694 #772 #1780 #798 #1774 #854 #1798 #880 #1781]: #515
+#1802 := [unit-resolution #646 #1801 #1797 #1789 #1768]: false
+#1804 := [lemma #1802]: #1803
+#2011 := [unit-resolution #1804 #1535 #1540 #1775 #1774 #1762]: #147
+#2012 := [unit-resolution #955 #2011]: #925
+#2013 := [unit-resolution #1238 #2012]: #921
+#2016 := (or #516 #1188 #935 #972 #1150)
+#2017 := [unit-resolution #1796 #698 #720 #1459 #776 #1447 #802 #850 #876]: #2016
+#2018 := [unit-resolution #2017 #1620 #2015 #1540 #1331]: #935
+#2019 := [th-lemma #2018 #2013 #2011]: false
+#2021 := [lemma #2019]: #2020
+#2071 := [unit-resolution #2021 #2070 #1331 #1677 #1873 #1705]: #194
+#2072 := [unit-resolution #993 #2071]: #963
+#2073 := [unit-resolution #2010 #1675]: #288
+#2074 := [unit-resolution #1069 #2073]: #1039
+#2075 := [unit-resolution #1272 #2074]: #1033
+#2076 := (or #516 #1036 #1188 #935 #1150 #960 #1087)
+#1823 := (or #516 #1372 #1489 #1357 #1036 #1188 #1371 #935 #1509 #1350 #1150 #960 #1523 #998 #1087)
+#1824 := [th-lemma]: #1823
+#2077 := [unit-resolution #1824 #720 #1684 #746 #698 #772 #802 #850 #876]: #2076
+#2078 := [unit-resolution #2077 #2075 #2015 #2045 #2069 #1331 #2070]: #960
+#2079 := [unit-resolution #1248 #2078 #2072]: false
+#2081 := [lemma #2079]: #2080
+#2092 := [unit-resolution #2081 #1331]: #1109
+#2093 := [unit-resolution #1735 #2092]: #382
+#2094 := [unit-resolution #1960 #2093 #1870]: #1123
+#2095 := (or #516 #923 #1074 #1036 #1162 #1125 #1188)
+#2096 := [unit-resolution #1712 #1440 #724 #1684 #746 #698 #772 #798 #828 #850 #876]: #2095
+#2097 := [unit-resolution #2096 #1631 #2015 #2094 #1331 #2091 #2033]: #1074
+#2098 := [unit-resolution #1284 #2097]: #1076
+#2099 := [unit-resolution #1107 #2098 #2088]: false
+#2101 := [lemma #2099]: #2100
+#2102 := [unit-resolution #2101 #1331]: #429
+#2103 := [unit-resolution #1183 #2102]: #1153
+#2104 := [unit-resolution #1308 #2103]: #1147
+#2105 := [unit-resolution #2077 #2104 #2015 #2045 #2069 #1331 #2091]: #960
+#2106 := [unit-resolution #1248 #2105]: #962
+#2107 := [unit-resolution #2017 #2104 #2015 #2069 #1331]: #972
+#2108 := [unit-resolution #1254 #2107]: #974
+#2109 := [unit-resolution #994 #2108]: #194
+#2110 := [unit-resolution #993 #2109 #2106]: false
+#2111 := [lemma #2110]: #516
+#2127 := (or #1199 #1189 #477)
+#2128 := [th-lemma]: #2127
+#2129 := [unit-resolution #2128 #1864 #1997]: #1199
+#2125 := (or #335 #288)
+#1806 := [unit-resolution #1108 #1422]: #1089
+#1829 := [unit-resolution #1290 #1806]: #1084
+#2117 := (or #515 #1511 #1337 #1151 #1189 #1358 #922 #1510 #1409 #960 #1509 #1049 #1086)
+#2118 := [th-lemma]: #2117
+#2119 := [unit-resolution #2118 #1829 #1924 #720 #1468 #776 #694 #798 #2116 #854 #1864 #880 #1928]: #515
+#2120 := (or #101 #922 #1510 #1409 #960 #1509 #1049 #335 #288)
+#2121 := [th-lemma]: #2120
+#2122 := [unit-resolution #2121 #1422 #694 #1924 #720 #1405 #1468 #776 #1928]: #101
+#2123 := [unit-resolution #918 #2122]: #899
+#2124 := [unit-resolution #1916 #2123 #2119 #2111 #1497 #1925 #2033 #2116 #1928 #1924 #2115 #2112]: false
+#2126 := [lemma #2124]: #2125
+#2130 := [unit-resolution #2126 #1405]: #335
+#2131 := [unit-resolution #1107 #2130]: #1077
+#2132 := [unit-resolution #1284 #2131]: #1071
+#2133 := [unit-resolution #1933 #2132 #2129 #2115 #1928 #2112 #1924]: #515
+#2134 := [unit-resolution #1916 #2133 #2111 #1497 #1925 #2033 #2116 #1928 #1924 #2115 #2112]: #898
+#2135 := [unit-resolution #918 #2134]: #100
+#2136 := [unit-resolution #917 #2135]: #887
+#2137 := [unit-resolution #1224 #2136]: #881
+#2138 := [unit-resolution #1943 #2137 #1497 #1870 #2116 #1928]: #506
+#2139 := [unit-resolution #646 #2138 #2111 #2133]: #632
+#2140 := [unit-resolution #1908 #2139 #1928 #694 #1924 #720 #1684 #746 #1468 #776 #2115 #824 #2112 #850 #672]: #897
+#2141 := [th-lemma #2140 #2135 #1742]: false
+#2142 := [lemma #2141]: #288
+#2143 := [unit-resolution #1069 #2142]: #1039
+#2144 := [unit-resolution #1272 #2143]: #1033
+#2145 := [hypothesis]: #1150
+#2146 := [unit-resolution #1308 #2145]: #1152
+#2147 := [unit-resolution #1183 #2146]: #430
+#2148 := [unit-resolution #1184 #2147]: #1165
+#2149 := [unit-resolution #1314 #2148]: #1160
+#2150 := [unit-resolution #1761 #2147]: #1109
+#2151 := [unit-resolution #1735 #2150]: #382
+#2152 := [unit-resolution #1960 #2151 #1870]: #1123
+#2153 := [unit-resolution #1988 #2152 #2149 #2033 #2144]: #509
+#2154 := (or #1149 #1147)
+#2155 := [th-lemma]: #2154
+#2156 := [unit-resolution #2155 #2145]: #1149
+#2157 := [unit-resolution #1894 #2147]: #1200
+#2158 := [unit-resolution #2061 #2149 #2015 #1870 #2157 #2151]: #1086
+#2159 := [unit-resolution #1290 #2158]: #1088
+#2160 := [unit-resolution #1108 #2159]: #335
+#2161 := [unit-resolution #1107 #2160]: #1077
+#2162 := [unit-resolution #1284 #2161]: #1071
+#2163 := [unit-resolution #1971 #2162 #2149 #2152 #2156 #2144]: #147
+#2164 := [unit-resolution #955 #2163]: #925
+#2165 := [unit-resolution #1236 #2164]: #919
+#2166 := [unit-resolution #1316 #2148]: #1161
+#2167 := (or #100 #923 #1371 #1357 #1523 #998 #1036 #383 #429 #1343 #1113 #973 #1373 #1074 #1358)
+#2168 := [th-lemma]: #2167
+#2169 := [unit-resolution #2168 #2162 #698 #1440 #724 #1684 #746 #2144 #772 #2033 #798 #2151 #1870 #828 #2147]: #100
+#2170 := [unit-resolution #917 #2169]: #887
+#2171 := [unit-resolution #1224 #2170]: #881
+#2172 := [unit-resolution #1992 #2171 #2166 #2150 #2162 #2144 #2165]: #506
+#2173 := (or #195 #1357 #1523 #998 #1036 #383 #429 #1343 #1113)
+#2174 := [th-lemma]: #2173
+#2175 := [unit-resolution #2174 #2151 #746 #2144 #772 #1684 #1870 #828 #2147]: #195
+#2176 := [unit-resolution #994 #2175]: #975
+#2177 := [unit-resolution #1254 #2176]: #970
+#2178 := (or #515 #922 #1074 #1036 #972 #1163 #1112)
+#2179 := [unit-resolution #1622 #694 #720 #1404 #750 #772 #1864 #798 #824 #854 #880]: #2178
+#2180 := [unit-resolution #2179 #2177 #2150 #2162 #2166 #2144 #2165]: #515
+#2181 := [unit-resolution #646 #2180 #2172 #2111 #2153]: false
+#2182 := [lemma #2181]: #1147
+#1805 := [unit-resolution #1302 #1729]: #1122
+#2231 := (or #194 #382)
+#2183 := (or #1150 #429 #1163)
+#2184 := [th-lemma]: #2183
+#2185 := [unit-resolution #2184 #1333 #2182]: #1163
+#2186 := [unit-resolution #1316 #2185 #1334]: false
+#2187 := [lemma #2186]: #429
+#2196 := [unit-resolution #1183 #2187]: #1153
+#2197 := [unit-resolution #1310 #2196]: #1149
+#1817 := [unit-resolution #1304 #1729]: #1123
+#2217 := [unit-resolution #1804 #1535 #2182 #1817 #2197 #1805]: #147
+#2218 := [unit-resolution #955 #2217]: #925
+#2219 := [unit-resolution #1236 #2218]: #919
+#2210 := [unit-resolution #1976 #2197 #2187]: #1161
+#2220 := (or #509 #1124 #935 #1150 #972)
+#2221 := [unit-resolution #1767 #698 #672 #720 #1703 #750 #1459 #776 #1447 #802 #824 #850 #1742]: #2220
+#2222 := [unit-resolution #2221 #1620 #2069 #1805 #2182]: #509
+#2223 := (or #515 #922 #1163 #972 #1124)
+#2224 := [unit-resolution #1707 #720 #1703 #750 #1459 #776 #1447 #802 #694 #824 #854 #880 #1864]: #2223
+#2225 := [unit-resolution #2224 #2219 #1805 #1620 #2210]: #515
+#2226 := [unit-resolution #646 #2225 #2111 #2222]: #631
+#2211 := (or #506 #884 #922 #1163 #1124)
+#2212 := [unit-resolution #1724 #668 #694 #1703 #750 #1459 #776 #824 #854]: #2211
+#2227 := [unit-resolution #2212 #2226 #1805 #2210 #2219]: #884
+#2228 := [unit-resolution #1224 #2227]: #886
+#2229 := [unit-resolution #917 #2228]: #101
+#2230 := [th-lemma #1620 #720 #1459 #776 #1447 #802 #2033 #2229 #698 #1428 #2217]: false
+#2232 := [lemma #2230]: #2231
+#2242 := [unit-resolution #2232 #1428]: #194
+#2243 := [unit-resolution #993 #2242]: #963
+#2244 := [unit-resolution #1248 #2243]: #957
+#2193 := (or #509 #1124 #1036 #935 #1150 #960 #1087)
+#1814 := (or #509 #885 #1522 #1523 #1365 #1489 #998 #1124 #1371 #1036 #1357 #935 #1150 #1509 #1350 #960 #1087)
+#1815 := [th-lemma]: #1814
+#2194 := [unit-resolution #1815 #698 #720 #1684 #746 #672 #772 #802 #824 #850 #1742]: #2193
+#2245 := [unit-resolution #2194 #2244 #2069 #2144 #2045 #1805 #2182]: #509
+#2205 := (or #100 #935 #1036 #382 #960 #1087)
+#1834 := (or #100 #1371 #935 #1523 #1036 #1357 #998 #1509 #382 #1350 #960 #1087)
+#1835 := [th-lemma]: #1834
+#2206 := [unit-resolution #1835 #698 #720 #1684 #746 #772 #802]: #2205
+#2246 := [unit-resolution #2206 #2244 #2045 #2069 #2144 #1428]: #100
+#2247 := [unit-resolution #917 #2246]: #887
+#2248 := [unit-resolution #1224 #2247]: #881
+#2215 := (or #335 #382)
+#2188 := (or #335 #194)
+#2189 := [unit-resolution #1777 #750 #1459 #776 #1703]: #2188
+#2190 := [unit-resolution #2189 #1422]: #194
+#2191 := [unit-resolution #993 #2190]: #963
+#2192 := [unit-resolution #1248 #2191]: #957
+#2195 := [unit-resolution #2194 #2192 #2069 #2144 #2045 #1805 #2182]: #509
+#2198 := [unit-resolution #1250 #2191]: #959
+#1840 := (or #335 #934 #1151 #961 #935 #960 #1150 #382)
+#1807 := [unit-resolution #1292 #1806]: #1085
+#1808 := [hypothesis]: #933
+#1809 := (or #288 #382 #1350 #335 #1087)
+#1810 := [th-lemma]: #1809
+#1811 := [unit-resolution #1810 #1422 #1807 #802 #1428]: #288
+#1812 := [unit-resolution #1069 #1811]: #1039
+#1813 := [unit-resolution #1272 #1812]: #1033
+#1816 := [unit-resolution #1815 #1813 #1808 #698 #1536 #720 #1684 #746 #672 #772 #1807 #802 #1805 #824 #1540 #850 #1742]: #509
+#1818 := (or #476 #1337 #1343 #1125 #1151 #335 #382)
+#1819 := [th-lemma]: #1818
+#1820 := [unit-resolution #1819 #1422 #1817 #828 #1774 #854 #1428]: #476
+#1821 := [unit-resolution #1221 #1820]: #1191
+#1822 := [unit-resolution #1320 #1821]: #1185
+#1825 := [unit-resolution #1824 #1813 #1536 #720 #1684 #746 #698 #772 #1807 #802 #1540 #850 #1822 #876 #1808]: #516
+#1826 := [hypothesis]: #932
+#1827 := [unit-resolution #1322 #1821]: #1187
+#1830 := (or #515 #1511 #1337 #1409 #1037 #1189 #1510 #934 #1373 #1358 #1151 #961 #1364 #999 #1086)
+#1831 := [th-lemma]: #1830
+#1832 := [unit-resolution #1831 #1829 #1828 #724 #1703 #750 #1459 #776 #694 #798 #1774 #854 #1827 #880 #1826]: #515
+#1833 := [unit-resolution #646 #1832 #1825 #1816]: #631
+#1836 := [unit-resolution #1835 #1813 #698 #1536 #720 #1684 #746 #1808 #772 #1807 #802 #1428]: #100
+#1837 := [unit-resolution #917 #1836]: #887
+#1838 := [unit-resolution #1224 #1837]: #881
+#1839 := [th-lemma #1838 #668 #750 #828 #854 #1703 #1817 #694 #1459 #776 #1826 #1774 #724 #798 #1828 #1829 #1833]: false
+#1841 := [lemma #1839]: #1840
+#2199 := [unit-resolution #1841 #2198 #2069 #1422 #2197 #2192 #2182 #1428]: #934
+#2200 := [unit-resolution #1242 #2199]: #936
+#2201 := [unit-resolution #956 #2200]: #147
+#2202 := [unit-resolution #955 #2201]: #925
+#2203 := [unit-resolution #1236 #2202]: #919
+#2204 := [unit-resolution #2118 #2203 #1829 #720 #1468 #776 #694 #798 #2197 #854 #1864 #880 #2192]: #515
+#2207 := [unit-resolution #2206 #2192 #2045 #2069 #2144 #1428]: #100
+#2208 := [unit-resolution #917 #2207]: #887
+#2209 := [unit-resolution #1224 #2208]: #881
+#2213 := [unit-resolution #2212 #2203 #1805 #2210 #2209]: #506
+#2214 := [unit-resolution #646 #2213 #2204 #2111 #2195]: false
+#2216 := [lemma #2214]: #2215
+#2249 := [unit-resolution #2216 #1428]: #335
+#2250 := [unit-resolution #1107 #2249]: #1077
+#2251 := [unit-resolution #1284 #2250]: #1071
+#2252 := (or #1084 #1074 #1357 #1523 #998 #1036 #195)
+#2253 := [th-lemma]: #2252
+#2254 := [unit-resolution #2253 #2251 #746 #2144 #772 #1684 #2242]: #1084
+#2255 := [unit-resolution #1250 #2243]: #959
+#2240 := (or #934 #632 #884 #1074 #1125 #961 #1086)
+#2233 := (or #515 #934 #1151 #961 #1086)
+#2234 := [unit-resolution #1831 #1864 #724 #1703 #750 #1459 #776 #694 #798 #854 #880]: #2233
+#2235 := [unit-resolution #2234 #1826 #2197 #1828 #2054]: #515
+#2236 := (or #506 #884 #1125 #1036 #934 #1151 #1074)
+#2237 := [unit-resolution #1788 #694 #1440 #724 #1684 #746 #668 #772 #798 #828 #854]: #2236
+#2238 := [unit-resolution #2237 #1826 #1636 #1638 #1775 #2197 #2144]: #506
+#2239 := [unit-resolution #646 #2238 #2235 #2111 #1628]: false
+#2241 := [lemma #2239]: #2240
+#2256 := [unit-resolution #2241 #2245 #2248 #2251 #1817 #2255 #2254]: #934
+#2257 := [unit-resolution #1242 #2256]: #936
+#2258 := [unit-resolution #956 #2257]: #147
+#2259 := [unit-resolution #955 #2258]: #925
+#2260 := [unit-resolution #1236 #2259]: #919
+#2261 := [unit-resolution #2212 #2260 #1805 #2210 #2248]: #506
+#2262 := [unit-resolution #2118 #2260 #2254 #720 #1468 #776 #694 #798 #2197 #854 #1864 #880 #2244]: #515
+#2263 := [unit-resolution #646 #2262 #2261 #2111 #2245]: false
+#2264 := [lemma #2263]: #382
+#2265 := [unit-resolution #1145 #2264]: #1115
+#2266 := [unit-resolution #1296 #2265]: #1109
+#2267 := [unit-resolution #2189 #1535]: #335
+#2268 := [unit-resolution #1107 #2267]: #1077
+#2269 := [unit-resolution #1284 #2268]: #1071
+#2270 := [unit-resolution #1966 #2269 #2142 #2266 #2182]: #1160
+#2271 := (or #1008 #998 #1036 #1357 #1074 #1358 #383)
+#2272 := [th-lemma]: #2271
+#2273 := [unit-resolution #2272 #2269 #2144 #772 #1684 #798 #2264]: #1008
+#2274 := (or #509 #1010 #1113 #923 #1162)
+#2275 := [unit-resolution #1608 #672 #698 #1742 #746 #1459 #776 #1447 #802 #828 #850]: #2274
+#2276 := [unit-resolution #2275 #2273 #1870 #2270 #2033]: #509
+#2277 := [unit-resolution #1960 #2264 #1870]: #1123
+#2278 := [unit-resolution #1971 #2270 #2269 #2277 #2197 #2144]: #147
+#2279 := [unit-resolution #955 #2278]: #925
+#2280 := [unit-resolution #1236 #2279]: #919
+#2281 := (or #1010 #999 #923 #100 #1371 #961 #1373)
+#2282 := [th-lemma]: #2281
+#2283 := [unit-resolution #2282 #2273 #698 #1584 #724 #1703 #2033]: #100
+#2284 := [unit-resolution #917 #2283]: #887
+#2285 := [unit-resolution #1224 #2284]: #881
+#2286 := [unit-resolution #1992 #2285 #2210 #2266 #2269 #2144 #2280]: #506
+#2287 := [unit-resolution #2179 #2280 #2266 #1620 #2210 #2144 #2269]: #515
+#2288 := [unit-resolution #646 #2287 #2286 #2111 #2276]: false
+#2289 := [lemma #2288]: #194
+#2305 := [unit-resolution #2253 #2302 #746 #2144 #772 #1684 #2289]: #1074
+#2306 := [unit-resolution #1284 #2305]: #1076
+#2307 := [unit-resolution #1107 #2306 #2304]: false
+#2308 := [lemma #2307]: #1084
+#2300 := (or #1086 #515)
+#2290 := [hypothesis]: #633
+#2291 := [unit-resolution #993 #2289]: #963
+#2292 := [unit-resolution #1250 #2291]: #959
+#2293 := [unit-resolution #2234 #2054 #2197 #2292 #2290]: #934
+#2294 := [unit-resolution #1242 #2293]: #936
+#2295 := [unit-resolution #1248 #2291]: #957
+#2296 := [unit-resolution #2118 #2054 #2290 #720 #1468 #776 #694 #798 #2197 #854 #1864 #880 #2295]: #922
+#2297 := [unit-resolution #1236 #2296]: #924
+#2298 := [unit-resolution #955 #2297]: #148
+#2299 := [unit-resolution #956 #2298 #2294]: false
+#2301 := [lemma #2299]: #2300
+#1848 := [unit-resolution #2301 #2308]: #515
+#1851 := [hypothesis]: #632
+#1852 := (or #897 #1522 #509 #1523 #998 #1365 #1489 #1150 #1509 #1350 #633 #1372 #1188 #960 #1087 #1112)
+#1853 := [th-lemma]: #1852
+#1846 := [unit-resolution #1853 #1851 #2295 #720 #1684 #746 #2045 #802 #2266 #824 #2182 #850 #2015 #876 #672 #1848]: #897
+#1847 := [unit-resolution #1232 #1846]: #898
+#1854 := [unit-resolution #918 #1847]: #100
+#1855 := (or #509 #1124)
+#1856 := [unit-resolution #2194 #2069 #2144 #2045 #2295 #2182]: #1855
+#2309 := [unit-resolution #1856 #1851]: #1124
+#2310 := [th-lemma #1848 #876 #850 #2182 #2015 #2309 #2266 #1854]: false
+#2311 := [lemma #2310]: #509
+#2312 := (or #631 #632)
+#2313 := [unit-resolution #646 #2111 #1848]: #2312
+#2314 := [unit-resolution #2313 #2311]: #631
+#2315 := (or #884 #633 #1372 #1188 #1125 #1528 #506 #1364 #999 #1343 #1373 #1358 #961 #1086)
+#2316 := [th-lemma]: #2315
+#2317 := [unit-resolution #2316 #668 #2292 #724 #1703 #750 #2308 #798 #2277 #828 #2015 #876 #2314 #1848]: #884
+#2318 := [unit-resolution #1224 #2317]: #886
+#2319 := (or #896 #1528 #506 #1364 #999 #1343 #1337 #1151 #1373 #1358 #634 #1511 #1189 #961 #1086 #1113)
+#2320 := [th-lemma]: #2319
+#2321 := [unit-resolution #2320 #668 #2292 #724 #1703 #750 #2308 #798 #1870 #828 #2197 #854 #1864 #880 #2314 #2111]: #896
+#2322 := [unit-resolution #1230 #2321]: #898
+#2323 := [unit-resolution #918 #2322]: #100
+[unit-resolution #917 #2323 #2318]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_mono_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,58 @@
+(benchmark Isabelle
+:extrasorts ( T2 T13 T12 T11 T10 T9 T8 T7 T6 T5 T4 T1 T3)
+:extrafuns (
+ (uf_37 T13)
+ (uf_34 T12)
+ (uf_31 T11)
+ (uf_28 T10)
+ (uf_25 T9)
+ (uf_22 T8)
+ (uf_19 T7)
+ (uf_16 T6)
+ (uf_13 T5)
+ (uf_10 T4)
+ (uf_7 T1)
+ (uf_4 T3)
+ (uf_36 Int T13 T13)
+ (uf_33 T13 T12 T12)
+ (uf_30 T12 T11 T11)
+ (uf_27 T11 T10 T10)
+ (uf_24 T10 T9 T9)
+ (uf_21 T9 T8 T8)
+ (uf_18 T8 T7 T7)
+ (uf_15 T7 T6 T6)
+ (uf_12 T6 T5 T5)
+ (uf_9 T5 T4 T4)
+ (uf_6 T4 T1 T1)
+ (uf_3 T1 T3 T3)
+ )
+:extrapreds (
+ (up_35 Int)
+ (up_32 T13)
+ (up_29 T12)
+ (up_26 T11)
+ (up_23 T10)
+ (up_20 T9)
+ (up_17 T8)
+ (up_14 T7)
+ (up_11 T6)
+ (up_8 T5)
+ (up_5 T4)
+ (up_1 T1)
+ (up_2 T3)
+ )
+:assumption (forall (?x1 T1) (and (up_1 ?x1) (or (up_2 (uf_3 ?x1 uf_4)) (not (up_2 (uf_3 ?x1 uf_4))))))
+:assumption (forall (?x2 T4) (and (up_5 ?x2) (or (up_1 (uf_6 ?x2 uf_7)) (not (up_1 (uf_6 ?x2 uf_7))))))
+:assumption (forall (?x3 T5) (and (up_8 ?x3) (or (up_5 (uf_9 ?x3 uf_10)) (not (up_5 (uf_9 ?x3 uf_10))))))
+:assumption (forall (?x4 T6) (and (up_11 ?x4) (or (up_8 (uf_12 ?x4 uf_13)) (not (up_8 (uf_12 ?x4 uf_13))))))
+:assumption (forall (?x5 T7) (and (up_14 ?x5) (or (up_11 (uf_15 ?x5 uf_16)) (not (up_11 (uf_15 ?x5 uf_16))))))
+:assumption (forall (?x6 T8) (and (up_17 ?x6) (or (up_14 (uf_18 ?x6 uf_19)) (not (up_14 (uf_18 ?x6 uf_19))))))
+:assumption (forall (?x7 T9) (and (up_20 ?x7) (or (up_17 (uf_21 ?x7 uf_22)) (not (up_17 (uf_21 ?x7 uf_22))))))
+:assumption (forall (?x8 T10) (and (up_23 ?x8) (or (up_20 (uf_24 ?x8 uf_25)) (not (up_20 (uf_24 ?x8 uf_25))))))
+:assumption (forall (?x9 T11) (and (up_26 ?x9) (or (up_23 (uf_27 ?x9 uf_28)) (not (up_23 (uf_27 ?x9 uf_28))))))
+:assumption (forall (?x10 T12) (and (up_29 ?x10) (or (up_26 (uf_30 ?x10 uf_31)) (not (up_26 (uf_30 ?x10 uf_31))))))
+:assumption (forall (?x11 T13) (and (up_32 ?x11) (or (up_29 (uf_33 ?x11 uf_34)) (not (up_29 (uf_33 ?x11 uf_34))))))
+:assumption (forall (?x12 Int) (and (up_35 ?x12) (or (up_32 (uf_36 ?x12 uf_37)) (not (up_32 (uf_36 ?x12 uf_37))))))
+:assumption (not (up_35 1))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_mono_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,50 @@
+#2 := false
+decl up_35 :: (-> int bool)
+#112 := 1::int
+#113 := (up_35 1::int)
+#114 := (not #113)
+#297 := [asserted]: #114
+#103 := (:var 0 int)
+#104 := (up_35 #103)
+#911 := (pattern #104)
+#912 := (forall (vars (?x12 int)) (:pat #911) #104)
+#294 := (forall (vars (?x12 int)) #104)
+#915 := (iff #294 #912)
+#913 := (iff #104 #104)
+#914 := [refl]: #913
+#916 := [quant-intro #914]: #915
+#320 := (~ #294 #294)
+#361 := (~ #104 #104)
+#362 := [refl]: #361
+#321 := [nnf-pos #362]: #320
+decl up_32 :: (-> T13 bool)
+decl uf_36 :: (-> int T13 T13)
+decl uf_37 :: T13
+#105 := uf_37
+#106 := (uf_36 #103 uf_37)
+#107 := (up_32 #106)
+#108 := (not #107)
+#109 := (or #107 #108)
+#110 := (and #104 #109)
+#111 := (forall (vars (?x12 int)) #110)
+#295 := (iff #111 #294)
+#292 := (iff #110 #104)
+#1 := true
+#287 := (and #104 true)
+#290 := (iff #287 #104)
+#291 := [rewrite]: #290
+#288 := (iff #110 #287)
+#284 := (iff #109 true)
+#286 := [rewrite]: #284
+#289 := [monotonicity #286]: #288
+#293 := [trans #289 #291]: #292
+#296 := [quant-intro #293]: #295
+#283 := [asserted]: #111
+#299 := [mp #283 #296]: #294
+#363 := [mp~ #299 #321]: #294
+#917 := [mp #363 #916]: #912
+#418 := (not #912)
+#504 := (or #418 #113)
+#419 := [quant-inst]: #504
+[unit-resolution #419 #917 #297]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_mono_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,41 @@
+(benchmark Isabelle
+:extrasorts ( T5 T6 T3 T1 T2 T4 T8 T7)
+:extrafuns (
+ (uf_19 T1)
+ (uf_3 Int T3)
+ (uf_7 T2)
+ (uf_8 T4)
+ (uf_2 T1 T2 T2)
+ (uf_6 Int T4 T4)
+ (uf_10 T5 T1 T3)
+ (uf_12 T6 Int T3)
+ (uf_13 T2 T3)
+ (uf_14 T4 T3)
+ (uf_17 T8 T3)
+ (uf_15 T7 T3)
+ (uf_18 T1 T8)
+ (uf_16 Int T7)
+ (uf_9 T5 T2 T3)
+ (uf_11 T6 T4 T3)
+ (uf_1 T2 T3)
+ (uf_5 T4 T3)
+ (uf_4 T3 Int)
+ )
+:assumption (forall (?x1 T1) (?x2 T2) (= (uf_1 (uf_2 ?x1 ?x2)) (uf_3 (+ (uf_4 (uf_1 ?x2)) (uf_4 (uf_3 (+ 0 1)))))))
+:assumption (forall (?x3 Int) (?x4 T4) (= (uf_5 (uf_6 ?x3 ?x4)) (uf_3 (+ (uf_4 (uf_5 ?x4)) (uf_4 (uf_3 (+ 0 1)))))))
+:assumption (= (uf_1 uf_7) (uf_3 0))
+:assumption (= (uf_5 uf_8) (uf_3 0))
+:assumption (forall (?x5 T5) (?x6 T1) (?x7 T2) (= (uf_9 ?x5 (uf_2 ?x6 ?x7)) (uf_3 (+ (+ (uf_4 (uf_10 ?x5 ?x6)) (uf_4 (uf_9 ?x5 ?x7))) (uf_4 (uf_3 (+ 0 1)))))))
+:assumption (forall (?x8 T6) (?x9 Int) (?x10 T4) (= (uf_11 ?x8 (uf_6 ?x9 ?x10)) (uf_3 (+ (+ (uf_4 (uf_12 ?x8 ?x9)) (uf_4 (uf_11 ?x8 ?x10))) (uf_4 (uf_3 (+ 0 1)))))))
+:assumption (forall (?x11 T5) (= (uf_9 ?x11 uf_7) (uf_3 0)))
+:assumption (forall (?x12 T6) (= (uf_11 ?x12 uf_8) (uf_3 0)))
+:assumption (forall (?x13 T2) (= (uf_13 ?x13) (uf_1 ?x13)))
+:assumption (forall (?x14 T4) (= (uf_14 ?x14) (uf_5 ?x14)))
+:assumption (forall (?x15 Int) (= (uf_15 (uf_16 ?x15)) (uf_14 (uf_6 ?x15 uf_8))))
+:assumption (forall (?x16 T1) (= (uf_17 (uf_18 ?x16)) (uf_13 (uf_2 ?x16 uf_7))))
+:assumption (forall (?x17 T3) (= (uf_3 (uf_4 ?x17)) ?x17))
+:assumption (forall (?x18 Int) (implies (<= 0 ?x18) (= (uf_4 (uf_3 ?x18)) ?x18)))
+:assumption (forall (?x19 Int) (implies (< ?x19 0) (= (uf_4 (uf_3 ?x19)) 0)))
+:assumption (not (= (uf_15 (uf_16 3)) (uf_17 (uf_18 uf_19))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_mono_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,492 @@
+#2 := false
+decl uf_17 :: (-> T8 T3)
+decl uf_18 :: (-> T1 T8)
+decl uf_19 :: T1
+#104 := uf_19
+#105 := (uf_18 uf_19)
+#106 := (uf_17 #105)
+decl uf_15 :: (-> T7 T3)
+decl uf_16 :: (-> int T7)
+#101 := 3::int
+#102 := (uf_16 3::int)
+#103 := (uf_15 #102)
+#107 := (= #103 #106)
+decl uf_13 :: (-> T2 T3)
+decl uf_2 :: (-> T1 T2 T2)
+decl uf_7 :: T2
+#29 := uf_7
+#857 := (uf_2 uf_19 uf_7)
+#859 := (uf_13 #857)
+#599 := (= #859 #106)
+#526 := (= #106 #859)
+#79 := (:var 0 T1)
+#82 := (uf_2 #79 uf_7)
+#932 := (pattern #82)
+#80 := (uf_18 #79)
+#931 := (pattern #80)
+#83 := (uf_13 #82)
+#81 := (uf_17 #80)
+#84 := (= #81 #83)
+#933 := (forall (vars (?x16 T1)) (:pat #931 #932) #84)
+#85 := (forall (vars (?x16 T1)) #84)
+#936 := (iff #85 #933)
+#934 := (iff #84 #84)
+#935 := [refl]: #934
+#937 := [quant-intro #935]: #936
+#347 := (~ #85 #85)
+#384 := (~ #84 #84)
+#385 := [refl]: #384
+#348 := [nnf-pos #385]: #347
+#238 := [asserted]: #85
+#386 := [mp~ #238 #348]: #85
+#938 := [mp #386 #937]: #933
+#861 := (not #933)
+#862 := (or #861 #526)
+#863 := [quant-inst]: #862
+#601 := [unit-resolution #863 #938]: #526
+#588 := [symm #601]: #599
+#586 := (= #103 #859)
+decl uf_1 :: (-> T2 T3)
+#558 := (uf_1 #857)
+#832 := (= #558 #859)
+#5 := (:var 0 T2)
+#66 := (uf_13 #5)
+#908 := (pattern #66)
+#8 := (uf_1 #5)
+#907 := (pattern #8)
+#222 := (= #8 #66)
+#909 := (forall (vars (?x13 T2)) (:pat #907 #908) #222)
+#226 := (forall (vars (?x13 T2)) #222)
+#912 := (iff #226 #909)
+#910 := (iff #222 #222)
+#911 := [refl]: #910
+#913 := [quant-intro #911]: #912
+#341 := (~ #226 #226)
+#375 := (~ #222 #222)
+#376 := [refl]: #375
+#342 := [nnf-pos #376]: #341
+#67 := (= #66 #8)
+#68 := (forall (vars (?x13 T2)) #67)
+#227 := (iff #68 #226)
+#224 := (iff #67 #222)
+#225 := [rewrite]: #224
+#228 := [quant-intro #225]: #227
+#221 := [asserted]: #68
+#231 := [mp #221 #228]: #226
+#377 := [mp~ #231 #342]: #226
+#914 := [mp #377 #913]: #909
+#451 := (not #909)
+#837 := (or #451 #832)
+#547 := [quant-inst]: #837
+#615 := [unit-resolution #547 #914]: #832
+#585 := (= #103 #558)
+decl uf_3 :: (-> int T3)
+decl uf_4 :: (-> T3 int)
+#30 := (uf_1 uf_7)
+#806 := (uf_4 #30)
+#11 := 1::int
+#127 := (uf_3 1::int)
+#130 := (uf_4 #127)
+#649 := (+ #130 #806)
+#794 := (uf_3 #649)
+#597 := (= #794 #558)
+#683 := (= #558 #794)
+#4 := (:var 1 T1)
+#6 := (uf_2 #4 #5)
+#865 := (pattern #6)
+#9 := (uf_4 #8)
+#133 := (+ #9 #130)
+#136 := (uf_3 #133)
+#7 := (uf_1 #6)
+#139 := (= #7 #136)
+#866 := (forall (vars (?x1 T1) (?x2 T2)) (:pat #865) #139)
+#142 := (forall (vars (?x1 T1) (?x2 T2)) #139)
+#869 := (iff #142 #866)
+#867 := (iff #139 #139)
+#868 := [refl]: #867
+#870 := [quant-intro #868]: #869
+#361 := (~ #142 #142)
+#359 := (~ #139 #139)
+#360 := [refl]: #359
+#362 := [nnf-pos #360]: #361
+#10 := 0::int
+#12 := (+ 0::int 1::int)
+#13 := (uf_3 #12)
+#14 := (uf_4 #13)
+#15 := (+ #9 #14)
+#16 := (uf_3 #15)
+#17 := (= #7 #16)
+#18 := (forall (vars (?x1 T1) (?x2 T2)) #17)
+#143 := (iff #18 #142)
+#140 := (iff #17 #139)
+#137 := (= #16 #136)
+#134 := (= #15 #133)
+#131 := (= #14 #130)
+#128 := (= #13 #127)
+#125 := (= #12 1::int)
+#126 := [rewrite]: #125
+#129 := [monotonicity #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [quant-intro #141]: #143
+#124 := [asserted]: #18
+#147 := [mp #124 #144]: #142
+#363 := [mp~ #147 #362]: #142
+#871 := [mp #363 #870]: #866
+#701 := (not #866)
+#694 := (or #701 #683)
+#688 := (+ #806 #130)
+#689 := (uf_3 #688)
+#690 := (= #558 #689)
+#702 := (or #701 #690)
+#704 := (iff #702 #694)
+#706 := (iff #694 #694)
+#799 := [rewrite]: #706
+#698 := (iff #690 #683)
+#795 := (= #689 #794)
+#797 := (= #688 #649)
+#699 := [rewrite]: #797
+#798 := [monotonicity #699]: #795
+#700 := [monotonicity #798]: #698
+#705 := [monotonicity #700]: #704
+#796 := [trans #705 #799]: #704
+#703 := [quant-inst]: #702
+#800 := [mp #703 #796]: #694
+#614 := [unit-resolution #800 #871]: #683
+#598 := [symm #614]: #597
+#583 := (= #103 #794)
+#595 := (= #127 #794)
+#605 := (= #794 #127)
+#618 := (= #649 1::int)
+#780 := (<= #806 0::int)
+#778 := (= #806 0::int)
+#31 := (uf_3 0::int)
+#858 := (uf_4 #31)
+#855 := (= #858 0::int)
+#72 := (:var 0 int)
+#92 := (uf_3 #72)
+#947 := (pattern #92)
+#266 := (>= #72 0::int)
+#267 := (not #266)
+#93 := (uf_4 #92)
+#248 := (= #72 #93)
+#273 := (or #248 #267)
+#948 := (forall (vars (?x18 int)) (:pat #947) #273)
+#278 := (forall (vars (?x18 int)) #273)
+#951 := (iff #278 #948)
+#949 := (iff #273 #273)
+#950 := [refl]: #949
+#952 := [quant-intro #950]: #951
+#351 := (~ #278 #278)
+#390 := (~ #273 #273)
+#391 := [refl]: #390
+#352 := [nnf-pos #391]: #351
+#94 := (= #93 #72)
+#91 := (<= 0::int #72)
+#95 := (implies #91 #94)
+#96 := (forall (vars (?x18 int)) #95)
+#281 := (iff #96 #278)
+#255 := (not #91)
+#256 := (or #255 #248)
+#261 := (forall (vars (?x18 int)) #256)
+#279 := (iff #261 #278)
+#276 := (iff #256 #273)
+#270 := (or #267 #248)
+#274 := (iff #270 #273)
+#275 := [rewrite]: #274
+#271 := (iff #256 #270)
+#268 := (iff #255 #267)
+#264 := (iff #91 #266)
+#265 := [rewrite]: #264
+#269 := [monotonicity #265]: #268
+#272 := [monotonicity #269]: #271
+#277 := [trans #272 #275]: #276
+#280 := [quant-intro #277]: #279
+#262 := (iff #96 #261)
+#259 := (iff #95 #256)
+#252 := (implies #91 #248)
+#257 := (iff #252 #256)
+#258 := [rewrite]: #257
+#253 := (iff #95 #252)
+#250 := (iff #94 #248)
+#251 := [rewrite]: #250
+#254 := [monotonicity #251]: #253
+#260 := [trans #254 #258]: #259
+#263 := [quant-intro #260]: #262
+#282 := [trans #263 #280]: #281
+#247 := [asserted]: #96
+#283 := [mp #247 #282]: #278
+#392 := [mp~ #283 #352]: #278
+#953 := [mp #392 #952]: #948
+#848 := (not #948)
+#850 := (or #848 #855)
+#527 := (>= 0::int 0::int)
+#860 := (not #527)
+#864 := (= 0::int #858)
+#854 := (or #864 #860)
+#489 := (or #848 #854)
+#851 := (iff #489 #850)
+#852 := (iff #850 #850)
+#838 := [rewrite]: #852
+#847 := (iff #854 #855)
+#843 := (or #855 false)
+#846 := (iff #843 #855)
+#841 := [rewrite]: #846
+#844 := (iff #854 #843)
+#505 := (iff #860 false)
+#1 := true
+#498 := (not true)
+#503 := (iff #498 false)
+#504 := [rewrite]: #503
+#840 := (iff #860 #498)
+#514 := (iff #527 true)
+#856 := [rewrite]: #514
+#502 := [monotonicity #856]: #840
+#842 := [trans #502 #504]: #505
+#513 := (iff #864 #855)
+#518 := [rewrite]: #513
+#845 := [monotonicity #518 #842]: #844
+#484 := [trans #845 #841]: #847
+#849 := [monotonicity #484]: #851
+#839 := [trans #849 #838]: #851
+#490 := [quant-inst]: #489
+#546 := [mp #490 #839]: #850
+#644 := [unit-resolution #546 #953]: #855
+#621 := (= #806 #858)
+#32 := (= #30 #31)
+#159 := [asserted]: #32
+#626 := [monotonicity #159]: #621
+#616 := [trans #626 #644]: #778
+#606 := (not #778)
+#608 := (or #606 #780)
+#609 := [th-lemma]: #608
+#612 := [unit-resolution #609 #616]: #780
+#790 := (>= #806 0::int)
+#613 := (or #606 #790)
+#617 := [th-lemma]: #613
+#610 := [unit-resolution #617 #616]: #790
+#723 := (<= #130 1::int)
+#746 := (= #130 1::int)
+#713 := (or #848 #746)
+#755 := (>= 1::int 0::int)
+#756 := (not #755)
+#743 := (= 1::int #130)
+#744 := (or #743 #756)
+#714 := (or #848 #744)
+#718 := (iff #714 #713)
+#720 := (iff #713 #713)
+#725 := [rewrite]: #720
+#739 := (iff #744 #746)
+#735 := (or #746 false)
+#738 := (iff #735 #746)
+#733 := [rewrite]: #738
+#736 := (iff #744 #735)
+#731 := (iff #756 false)
+#734 := (iff #756 #498)
+#742 := (iff #755 true)
+#748 := [rewrite]: #742
+#730 := [monotonicity #748]: #734
+#732 := [trans #730 #504]: #731
+#745 := (iff #743 #746)
+#747 := [rewrite]: #745
+#737 := [monotonicity #747 #732]: #736
+#712 := [trans #737 #733]: #739
+#719 := [monotonicity #712]: #718
+#721 := [trans #719 #725]: #718
+#607 := [quant-inst]: #714
+#722 := [mp #607 #721]: #713
+#641 := [unit-resolution #722 #953]: #746
+#620 := (not #746)
+#623 := (or #620 #723)
+#627 := [th-lemma]: #623
+#629 := [unit-resolution #627 #641]: #723
+#726 := (>= #130 1::int)
+#630 := (or #620 #726)
+#628 := [th-lemma]: #630
+#631 := [unit-resolution #628 #641]: #726
+#611 := [th-lemma #631 #629 #610 #612]: #618
+#587 := [monotonicity #611]: #605
+#596 := [symm #587]: #595
+#581 := (= #103 #127)
+decl uf_5 :: (-> T4 T3)
+decl uf_8 :: T4
+#33 := uf_8
+#34 := (uf_5 uf_8)
+#822 := (uf_4 #34)
+#824 := (+ #130 #822)
+#666 := (uf_3 #824)
+#593 := (= #666 #127)
+#589 := (= #127 #666)
+#624 := (= 1::int #824)
+#619 := (= #824 1::int)
+#789 := (<= #822 0::int)
+#787 := (= #822 0::int)
+#632 := (= #822 #858)
+#35 := (= #34 #31)
+#162 := (= #31 #34)
+#163 := (iff #35 #162)
+#164 := [rewrite]: #163
+#160 := [asserted]: #35
+#167 := [mp #160 #164]: #162
+#662 := [symm #167]: #35
+#633 := [monotonicity #662]: #632
+#634 := [trans #633 #644]: #787
+#635 := (not #787)
+#637 := (or #635 #789)
+#638 := [th-lemma]: #637
+#639 := [unit-resolution #638 #634]: #789
+#781 := (>= #822 0::int)
+#481 := (or #635 #781)
+#640 := [th-lemma]: #481
+#636 := [unit-resolution #640 #634]: #781
+#622 := [th-lemma #631 #629 #636 #639]: #619
+#625 := [symm #622]: #624
+#590 := [monotonicity #625]: #589
+#594 := [symm #590]: #593
+#579 := (= #103 #666)
+decl uf_6 :: (-> int T4 T4)
+#539 := (uf_6 3::int uf_8)
+#836 := (uf_5 #539)
+#810 := (= #836 #666)
+#813 := (= #666 #836)
+#20 := (:var 0 T4)
+#19 := (:var 1 int)
+#21 := (uf_6 #19 #20)
+#872 := (pattern #21)
+#23 := (uf_5 #20)
+#24 := (uf_4 #23)
+#146 := (+ #24 #130)
+#150 := (uf_3 #146)
+#22 := (uf_5 #21)
+#153 := (= #22 #150)
+#873 := (forall (vars (?x3 int) (?x4 T4)) (:pat #872) #153)
+#156 := (forall (vars (?x3 int) (?x4 T4)) #153)
+#876 := (iff #156 #873)
+#874 := (iff #153 #153)
+#875 := [refl]: #874
+#877 := [quant-intro #875]: #876
+#328 := (~ #156 #156)
+#364 := (~ #153 #153)
+#365 := [refl]: #364
+#326 := [nnf-pos #365]: #328
+#25 := (+ #24 #14)
+#26 := (uf_3 #25)
+#27 := (= #22 #26)
+#28 := (forall (vars (?x3 int) (?x4 T4)) #27)
+#157 := (iff #28 #156)
+#154 := (iff #27 #153)
+#151 := (= #26 #150)
+#148 := (= #25 #146)
+#149 := [monotonicity #132]: #148
+#152 := [monotonicity #149]: #151
+#155 := [monotonicity #152]: #154
+#158 := [quant-intro #155]: #157
+#145 := [asserted]: #28
+#161 := [mp #145 #158]: #156
+#366 := [mp~ #161 #326]: #156
+#878 := [mp #366 #877]: #873
+#809 := (not #873)
+#816 := (or #809 #813)
+#817 := (+ #822 #130)
+#818 := (uf_3 #817)
+#823 := (= #836 #818)
+#645 := (or #809 #823)
+#648 := (iff #645 #816)
+#802 := (iff #816 #816)
+#804 := [rewrite]: #802
+#814 := (iff #823 #813)
+#807 := (iff #810 #813)
+#808 := [rewrite]: #807
+#811 := (iff #823 #810)
+#667 := (= #818 #666)
+#819 := (= #817 #824)
+#825 := [rewrite]: #819
+#668 := [monotonicity #825]: #667
+#812 := [monotonicity #668]: #811
+#815 := [trans #812 #808]: #814
+#801 := [monotonicity #815]: #648
+#805 := [trans #801 #804]: #648
+#647 := [quant-inst]: #645
+#803 := [mp #647 #805]: #816
+#658 := [unit-resolution #803 #878]: #813
+#592 := [symm #658]: #810
+#600 := (= #103 #836)
+decl uf_14 :: (-> T4 T3)
+#540 := (uf_14 #539)
+#548 := (= #540 #836)
+#69 := (uf_14 #20)
+#916 := (pattern #69)
+#915 := (pattern #23)
+#230 := (= #23 #69)
+#917 := (forall (vars (?x14 T4)) (:pat #915 #916) #230)
+#234 := (forall (vars (?x14 T4)) #230)
+#920 := (iff #234 #917)
+#918 := (iff #230 #230)
+#919 := [refl]: #918
+#921 := [quant-intro #919]: #920
+#343 := (~ #234 #234)
+#378 := (~ #230 #230)
+#379 := [refl]: #378
+#344 := [nnf-pos #379]: #343
+#70 := (= #69 #23)
+#71 := (forall (vars (?x14 T4)) #70)
+#235 := (iff #71 #234)
+#232 := (iff #70 #230)
+#233 := [rewrite]: #232
+#236 := [quant-intro #233]: #235
+#229 := [asserted]: #71
+#239 := [mp #229 #236]: #234
+#380 := [mp~ #239 #344]: #234
+#922 := [mp #380 #921]: #917
+#541 := (not #917)
+#828 := (or #541 #548)
+#833 := (= #836 #540)
+#829 := (or #541 #833)
+#826 := (iff #829 #828)
+#827 := (iff #828 #828)
+#831 := [rewrite]: #827
+#549 := (iff #833 #548)
+#550 := [rewrite]: #549
+#830 := [monotonicity #550]: #826
+#820 := [trans #830 #831]: #826
+#543 := [quant-inst]: #829
+#821 := [mp #543 #820]: #828
+#657 := [unit-resolution #821 #922]: #548
+#521 := (= #103 #540)
+#75 := (uf_6 #72 uf_8)
+#924 := (pattern #75)
+#73 := (uf_16 #72)
+#923 := (pattern #73)
+#76 := (uf_14 #75)
+#74 := (uf_15 #73)
+#77 := (= #74 #76)
+#925 := (forall (vars (?x15 int)) (:pat #923 #924) #77)
+#78 := (forall (vars (?x15 int)) #77)
+#928 := (iff #78 #925)
+#926 := (iff #77 #77)
+#927 := [refl]: #926
+#929 := [quant-intro #927]: #928
+#345 := (~ #78 #78)
+#381 := (~ #77 #77)
+#382 := [refl]: #381
+#346 := [nnf-pos #382]: #345
+#237 := [asserted]: #78
+#383 := [mp~ #237 #346]: #78
+#930 := [mp #383 #929]: #925
+#515 := (not #925)
+#646 := (or #515 #521)
+#853 := [quant-inst]: #646
+#603 := [unit-resolution #853 #930]: #521
+#577 := [trans #603 #657]: #600
+#580 := [trans #577 #592]: #579
+#582 := [trans #580 #594]: #581
+#584 := [trans #582 #596]: #583
+#578 := [trans #584 #598]: #585
+#571 := [trans #578 #615]: #586
+#572 := [trans #571 #588]: #107
+#108 := (not #107)
+#325 := [asserted]: #108
+[unit-resolution #325 #572]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ (uf_3 T1)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (= (uf_1 (* 2 (uf_2 uf_3))) (uf_1 1))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,246 @@
+#2 := false
+#9 := 0::int
+decl uf_2 :: (-> T1 int)
+decl uf_1 :: (-> int T1)
+decl uf_3 :: T1
+#22 := uf_3
+#23 := (uf_2 uf_3)
+#21 := 2::int
+#24 := (* 2::int #23)
+#25 := (uf_1 #24)
+#293 := (uf_2 #25)
+#292 := -1::int
+#296 := (* -1::int #293)
+#275 := (+ #24 #296)
+#258 := (<= #275 0::int)
+#611 := (= #275 0::int)
+#204 := (>= #24 0::int)
+#596 := (= #293 0::int)
+#541 := (not #596)
+#300 := (<= #293 0::int)
+#460 := (not #300)
+#26 := 1::int
+#570 := (>= #293 1::int)
+#569 := (= #293 1::int)
+#27 := (uf_1 1::int)
+#318 := (uf_2 #27)
+#311 := (= #318 1::int)
+#10 := (:var 0 int)
+#12 := (uf_1 #10)
+#627 := (pattern #12)
+#70 := (>= #10 0::int)
+#71 := (not #70)
+#13 := (uf_2 #12)
+#52 := (= #10 #13)
+#77 := (or #52 #71)
+#628 := (forall (vars (?x2 int)) (:pat #627) #77)
+#82 := (forall (vars (?x2 int)) #77)
+#631 := (iff #82 #628)
+#629 := (iff #77 #77)
+#630 := [refl]: #629
+#632 := [quant-intro #630]: #631
+#132 := (~ #82 #82)
+#144 := (~ #77 #77)
+#145 := [refl]: #144
+#130 := [nnf-pos #145]: #132
+#14 := (= #13 #10)
+#11 := (<= 0::int #10)
+#15 := (implies #11 #14)
+#16 := (forall (vars (?x2 int)) #15)
+#85 := (iff #16 #82)
+#59 := (not #11)
+#60 := (or #59 #52)
+#65 := (forall (vars (?x2 int)) #60)
+#83 := (iff #65 #82)
+#80 := (iff #60 #77)
+#74 := (or #71 #52)
+#78 := (iff #74 #77)
+#79 := [rewrite]: #78
+#75 := (iff #60 #74)
+#72 := (iff #59 #71)
+#68 := (iff #11 #70)
+#69 := [rewrite]: #68
+#73 := [monotonicity #69]: #72
+#76 := [monotonicity #73]: #75
+#81 := [trans #76 #79]: #80
+#84 := [quant-intro #81]: #83
+#66 := (iff #16 #65)
+#63 := (iff #15 #60)
+#56 := (implies #11 #52)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #15 #56)
+#54 := (iff #14 #52)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#64 := [trans #58 #62]: #63
+#67 := [quant-intro #64]: #66
+#86 := [trans #67 #84]: #85
+#51 := [asserted]: #16
+#87 := [mp #51 #86]: #82
+#146 := [mp~ #87 #130]: #82
+#633 := [mp #146 #632]: #628
+#612 := (not #628)
+#575 := (or #612 #311)
+#316 := (>= 1::int 0::int)
+#317 := (not #316)
+#211 := (= 1::int #318)
+#588 := (or #211 #317)
+#576 := (or #612 #588)
+#572 := (iff #576 #575)
+#578 := (iff #575 #575)
+#573 := [rewrite]: #578
+#585 := (iff #588 #311)
+#583 := (or #311 false)
+#584 := (iff #583 #311)
+#581 := [rewrite]: #584
+#297 := (iff #588 #583)
+#304 := (iff #317 false)
+#1 := true
+#587 := (not true)
+#302 := (iff #587 false)
+#303 := [rewrite]: #302
+#591 := (iff #317 #587)
+#586 := (iff #316 true)
+#590 := [rewrite]: #586
+#301 := [monotonicity #590]: #591
+#582 := [trans #301 #303]: #304
+#589 := (iff #211 #311)
+#312 := [rewrite]: #589
+#580 := [monotonicity #312 #582]: #297
+#574 := [trans #580 #581]: #585
+#577 := [monotonicity #574]: #572
+#579 := [trans #577 #573]: #572
+#571 := [quant-inst]: #576
+#420 := [mp #571 #579]: #575
+#437 := [unit-resolution #420 #633]: #311
+#452 := (= #293 #318)
+#28 := (= #25 #27)
+#129 := [asserted]: #28
+#454 := [monotonicity #129]: #452
+#455 := [trans #454 #437]: #569
+#448 := (not #569)
+#456 := (or #448 #570)
+#457 := [th-lemma]: #456
+#458 := [unit-resolution #457 #455]: #570
+#459 := (not #570)
+#553 := (or #459 #460)
+#550 := [th-lemma]: #553
+#554 := [unit-resolution #550 #458]: #460
+#543 := (or #541 #300)
+#535 := [th-lemma]: #543
+#532 := [unit-resolution #535 #554]: #541
+#598 := (or #204 #596)
+#18 := (= #13 0::int)
+#118 := (or #18 #70)
+#634 := (forall (vars (?x3 int)) (:pat #627) #118)
+#123 := (forall (vars (?x3 int)) #118)
+#637 := (iff #123 #634)
+#635 := (iff #118 #118)
+#636 := [refl]: #635
+#638 := [quant-intro #636]: #637
+#133 := (~ #123 #123)
+#147 := (~ #118 #118)
+#148 := [refl]: #147
+#134 := [nnf-pos #148]: #133
+#17 := (< #10 0::int)
+#19 := (implies #17 #18)
+#20 := (forall (vars (?x3 int)) #19)
+#126 := (iff #20 #123)
+#89 := (= 0::int #13)
+#95 := (not #17)
+#96 := (or #95 #89)
+#101 := (forall (vars (?x3 int)) #96)
+#124 := (iff #101 #123)
+#121 := (iff #96 #118)
+#115 := (or #70 #18)
+#119 := (iff #115 #118)
+#120 := [rewrite]: #119
+#116 := (iff #96 #115)
+#113 := (iff #89 #18)
+#114 := [rewrite]: #113
+#111 := (iff #95 #70)
+#106 := (not #71)
+#109 := (iff #106 #70)
+#110 := [rewrite]: #109
+#107 := (iff #95 #106)
+#104 := (iff #17 #71)
+#105 := [rewrite]: #104
+#108 := [monotonicity #105]: #107
+#112 := [trans #108 #110]: #111
+#117 := [monotonicity #112 #114]: #116
+#122 := [trans #117 #120]: #121
+#125 := [quant-intro #122]: #124
+#102 := (iff #20 #101)
+#99 := (iff #19 #96)
+#92 := (implies #17 #89)
+#97 := (iff #92 #96)
+#98 := [rewrite]: #97
+#93 := (iff #19 #92)
+#90 := (iff #18 #89)
+#91 := [rewrite]: #90
+#94 := [monotonicity #91]: #93
+#100 := [trans #94 #98]: #99
+#103 := [quant-intro #100]: #102
+#127 := [trans #103 #125]: #126
+#88 := [asserted]: #20
+#128 := [mp #88 #127]: #123
+#149 := [mp~ #128 #134]: #123
+#639 := [mp #149 #638]: #634
+#595 := (not #634)
+#601 := (or #595 #204 #596)
+#597 := (or #596 #204)
+#238 := (or #595 #597)
+#606 := (iff #238 #601)
+#604 := (or #595 #598)
+#605 := (iff #604 #601)
+#603 := [rewrite]: #605
+#243 := (iff #238 #604)
+#599 := (iff #597 #598)
+#600 := [rewrite]: #599
+#244 := [monotonicity #600]: #243
+#592 := [trans #244 #603]: #606
+#602 := [quant-inst]: #238
+#593 := [mp #602 #592]: #601
+#534 := [unit-resolution #593 #639]: #598
+#544 := [unit-resolution #534 #532]: #204
+#290 := (not #204)
+#281 := (or #290 #611)
+#618 := (or #612 #290 #611)
+#294 := (= #24 #293)
+#295 := (or #294 #290)
+#608 := (or #612 #295)
+#594 := (iff #608 #618)
+#272 := (or #612 #281)
+#610 := (iff #272 #618)
+#252 := [rewrite]: #610
+#609 := (iff #608 #272)
+#616 := (iff #295 #281)
+#400 := (or #611 #290)
+#614 := (iff #400 #281)
+#615 := [rewrite]: #614
+#607 := (iff #295 #400)
+#613 := (iff #294 #611)
+#269 := [rewrite]: #613
+#280 := [monotonicity #269]: #607
+#617 := [trans #280 #615]: #616
+#268 := [monotonicity #617]: #609
+#256 := [trans #268 #252]: #594
+#267 := [quant-inst]: #608
+#257 := [mp #267 #256]: #618
+#545 := [unit-resolution #257 #633]: #281
+#546 := [unit-resolution #545 #544]: #611
+#542 := (not #611)
+#547 := (or #542 #258)
+#536 := [th-lemma]: #547
+#537 := [unit-resolution #536 #546]: #258
+#259 := (>= #275 0::int)
+#538 := (or #542 #259)
+#539 := [th-lemma]: #538
+#533 := [unit-resolution #539 #546]: #259
+#563 := (<= #293 1::int)
+#540 := (or #448 #563)
+#524 := [th-lemma]: #540
+#525 := [unit-resolution #524 #455]: #563
+[th-lemma #458 #525 #533 #537]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,14 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ (uf_3 T1)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (< (uf_2 uf_3) 3)
+:assumption (not (< (uf_2 (uf_1 (* 2 (uf_2 uf_3)))) 7))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,199 @@
+#2 := false
+#23 := 3::int
+decl uf_2 :: (-> T1 int)
+decl uf_3 :: T1
+#21 := uf_3
+#22 := (uf_2 uf_3)
+#137 := (>= #22 3::int)
+#135 := (not #137)
+#24 := (< #22 3::int)
+#136 := (iff #24 #135)
+#138 := [rewrite]: #136
+#132 := [asserted]: #24
+#139 := [mp #132 #138]: #135
+#9 := 0::int
+decl uf_1 :: (-> int T1)
+#25 := 2::int
+#26 := (* 2::int #22)
+#27 := (uf_1 #26)
+#28 := (uf_2 #27)
+#297 := -1::int
+#633 := (* -1::int #28)
+#635 := (+ #26 #633)
+#278 := (>= #635 0::int)
+#291 := (= #635 0::int)
+#315 := (>= #26 0::int)
+#279 := (= #28 0::int)
+#627 := (not #279)
+#624 := (<= #28 0::int)
+#281 := (not #624)
+#29 := 7::int
+#143 := (>= #28 7::int)
+#30 := (< #28 7::int)
+#31 := (not #30)
+#150 := (iff #31 #143)
+#141 := (not #143)
+#145 := (not #141)
+#148 := (iff #145 #143)
+#149 := [rewrite]: #148
+#146 := (iff #31 #145)
+#142 := (iff #30 #141)
+#144 := [rewrite]: #142
+#147 := [monotonicity #144]: #146
+#151 := [trans #147 #149]: #150
+#133 := [asserted]: #31
+#152 := [mp #133 #151]: #143
+#618 := (or #281 #141)
+#265 := [th-lemma]: #618
+#266 := [unit-resolution #265 #152]: #281
+#625 := (or #627 #624)
+#628 := [th-lemma]: #625
+#614 := [unit-resolution #628 #266]: #627
+#10 := (:var 0 int)
+#12 := (uf_1 #10)
+#649 := (pattern #12)
+#73 := (>= #10 0::int)
+#13 := (uf_2 #12)
+#18 := (= #13 0::int)
+#121 := (or #18 #73)
+#656 := (forall (vars (?x3 int)) (:pat #649) #121)
+#126 := (forall (vars (?x3 int)) #121)
+#659 := (iff #126 #656)
+#657 := (iff #121 #121)
+#658 := [refl]: #657
+#660 := [quant-intro #658]: #659
+#154 := (~ #126 #126)
+#170 := (~ #121 #121)
+#171 := [refl]: #170
+#155 := [nnf-pos #171]: #154
+#17 := (< #10 0::int)
+#19 := (implies #17 #18)
+#20 := (forall (vars (?x3 int)) #19)
+#129 := (iff #20 #126)
+#92 := (= 0::int #13)
+#98 := (not #17)
+#99 := (or #98 #92)
+#104 := (forall (vars (?x3 int)) #99)
+#127 := (iff #104 #126)
+#124 := (iff #99 #121)
+#118 := (or #73 #18)
+#122 := (iff #118 #121)
+#123 := [rewrite]: #122
+#119 := (iff #99 #118)
+#116 := (iff #92 #18)
+#117 := [rewrite]: #116
+#114 := (iff #98 #73)
+#74 := (not #73)
+#109 := (not #74)
+#112 := (iff #109 #73)
+#113 := [rewrite]: #112
+#110 := (iff #98 #109)
+#107 := (iff #17 #74)
+#108 := [rewrite]: #107
+#111 := [monotonicity #108]: #110
+#115 := [trans #111 #113]: #114
+#120 := [monotonicity #115 #117]: #119
+#125 := [trans #120 #123]: #124
+#128 := [quant-intro #125]: #127
+#105 := (iff #20 #104)
+#102 := (iff #19 #99)
+#95 := (implies #17 #92)
+#100 := (iff #95 #99)
+#101 := [rewrite]: #100
+#96 := (iff #19 #95)
+#93 := (iff #18 #92)
+#94 := [rewrite]: #93
+#97 := [monotonicity #94]: #96
+#103 := [trans #97 #101]: #102
+#106 := [quant-intro #103]: #105
+#130 := [trans #106 #128]: #129
+#91 := [asserted]: #20
+#131 := [mp #91 #130]: #126
+#172 := [mp~ #131 #155]: #126
+#661 := [mp #172 #660]: #656
+#619 := (not #656)
+#620 := (or #619 #279 #315)
+#280 := (or #279 #315)
+#621 := (or #619 #280)
+#617 := (iff #621 #620)
+#623 := [rewrite]: #617
+#622 := [quant-inst]: #621
+#260 := [mp #622 #623]: #620
+#615 := [unit-resolution #260 #661 #614]: #315
+#316 := (not #315)
+#302 := (or #291 #316)
+#55 := (= #10 #13)
+#80 := (or #55 #74)
+#650 := (forall (vars (?x2 int)) (:pat #649) #80)
+#85 := (forall (vars (?x2 int)) #80)
+#653 := (iff #85 #650)
+#651 := (iff #80 #80)
+#652 := [refl]: #651
+#654 := [quant-intro #652]: #653
+#153 := (~ #85 #85)
+#167 := (~ #80 #80)
+#168 := [refl]: #167
+#134 := [nnf-pos #168]: #153
+#14 := (= #13 #10)
+#11 := (<= 0::int #10)
+#15 := (implies #11 #14)
+#16 := (forall (vars (?x2 int)) #15)
+#88 := (iff #16 #85)
+#62 := (not #11)
+#63 := (or #62 #55)
+#68 := (forall (vars (?x2 int)) #63)
+#86 := (iff #68 #85)
+#83 := (iff #63 #80)
+#77 := (or #74 #55)
+#81 := (iff #77 #80)
+#82 := [rewrite]: #81
+#78 := (iff #63 #77)
+#75 := (iff #62 #74)
+#71 := (iff #11 #73)
+#72 := [rewrite]: #71
+#76 := [monotonicity #72]: #75
+#79 := [monotonicity #76]: #78
+#84 := [trans #79 #82]: #83
+#87 := [quant-intro #84]: #86
+#69 := (iff #16 #68)
+#66 := (iff #15 #63)
+#59 := (implies #11 #55)
+#64 := (iff #59 #63)
+#65 := [rewrite]: #64
+#60 := (iff #15 #59)
+#57 := (iff #14 #55)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#67 := [trans #61 #65]: #66
+#70 := [quant-intro #67]: #69
+#89 := [trans #70 #87]: #88
+#54 := [asserted]: #16
+#90 := [mp #54 #89]: #85
+#169 := [mp~ #90 #134]: #85
+#655 := [mp #169 #654]: #650
+#637 := (not #650)
+#638 := (or #637 #291 #316)
+#314 := (= #26 #28)
+#318 := (or #314 #316)
+#639 := (or #637 #318)
+#290 := (iff #639 #638)
+#640 := (or #637 #302)
+#294 := (iff #640 #638)
+#631 := [rewrite]: #294
+#630 := (iff #639 #640)
+#303 := (iff #318 #302)
+#422 := (iff #314 #291)
+#629 := [rewrite]: #422
+#636 := [monotonicity #629]: #303
+#289 := [monotonicity #636]: #630
+#632 := [trans #289 #631]: #290
+#634 := [quant-inst]: #639
+#274 := [mp #634 #632]: #638
+#322 := [unit-resolution #274 #655]: #302
+#337 := [unit-resolution #322 #615]: #291
+#338 := (not #291)
+#339 := (or #338 #278)
+#340 := [th-lemma]: #339
+#232 := [unit-resolution #340 #337]: #278
+[th-lemma #152 #232 #139]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ (uf_3 T1)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (not (let (?x4 (uf_1 (+ 1 (uf_2 uf_3)))) (< (uf_2 (uf_1 (* 0 (uf_2 ?x4)))) (uf_2 (uf_1 (- (uf_2 ?x4) (uf_2 uf_3)))))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,367 @@
+#2 := false
+#9 := 0::int
+decl uf_2 :: (-> T1 int)
+decl uf_3 :: T1
+#22 := uf_3
+#23 := (uf_2 uf_3)
+#469 := (= #23 0::int)
+decl uf_1 :: (-> int T1)
+#251 := (uf_1 #23)
+#557 := (uf_2 #251)
+#558 := (= #557 0::int)
+#556 := (>= #23 0::int)
+#477 := (not #556)
+#144 := -1::int
+#348 := (>= #23 -1::int)
+#628 := (not #348)
+#21 := 1::int
+#24 := (+ 1::int #23)
+#25 := (uf_1 #24)
+#26 := (uf_2 #25)
+#632 := (* -1::int #26)
+#636 := (+ #23 #632)
+#633 := (= #636 -1::int)
+#471 := (not #633)
+#613 := (<= #636 -1::int)
+#527 := (not #613)
+#145 := (* -1::int #23)
+#146 := (+ #145 #26)
+#149 := (uf_1 #146)
+#152 := (uf_2 #149)
+#504 := (+ #632 #152)
+#505 := (+ #23 #504)
+#573 := (>= #505 0::int)
+#502 := (= #505 0::int)
+#599 := (<= #636 0::int)
+#526 := [hypothesis]: #613
+#491 := (or #527 #599)
+#515 := [th-lemma]: #491
+#516 := [unit-resolution #515 #526]: #599
+#587 := (not #599)
+#578 := (or #502 #587)
+#10 := (:var 0 int)
+#12 := (uf_1 #10)
+#673 := (pattern #12)
+#76 := (>= #10 0::int)
+#77 := (not #76)
+#13 := (uf_2 #12)
+#58 := (= #10 #13)
+#83 := (or #58 #77)
+#674 := (forall (vars (?x2 int)) (:pat #673) #83)
+#88 := (forall (vars (?x2 int)) #83)
+#677 := (iff #88 #674)
+#675 := (iff #83 #83)
+#676 := [refl]: #675
+#678 := [quant-intro #676]: #677
+#179 := (~ #88 #88)
+#191 := (~ #83 #83)
+#192 := [refl]: #191
+#177 := [nnf-pos #192]: #179
+#14 := (= #13 #10)
+#11 := (<= 0::int #10)
+#15 := (implies #11 #14)
+#16 := (forall (vars (?x2 int)) #15)
+#91 := (iff #16 #88)
+#65 := (not #11)
+#66 := (or #65 #58)
+#71 := (forall (vars (?x2 int)) #66)
+#89 := (iff #71 #88)
+#86 := (iff #66 #83)
+#80 := (or #77 #58)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #66 #80)
+#78 := (iff #65 #77)
+#74 := (iff #11 #76)
+#75 := [rewrite]: #74
+#79 := [monotonicity #75]: #78
+#82 := [monotonicity #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [quant-intro #87]: #89
+#72 := (iff #16 #71)
+#69 := (iff #15 #66)
+#62 := (implies #11 #58)
+#67 := (iff #62 #66)
+#68 := [rewrite]: #67
+#63 := (iff #15 #62)
+#60 := (iff #14 #58)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#70 := [trans #64 #68]: #69
+#73 := [quant-intro #70]: #72
+#92 := [trans #73 #90]: #91
+#57 := [asserted]: #16
+#93 := [mp #57 #92]: #88
+#193 := [mp~ #93 #177]: #88
+#679 := [mp #193 #678]: #674
+#644 := (not #674)
+#591 := (or #644 #502 #587)
+#498 := (>= #146 0::int)
+#500 := (not #498)
+#501 := (= #146 #152)
+#494 := (or #501 #500)
+#592 := (or #644 #494)
+#579 := (iff #592 #591)
+#593 := (or #644 #578)
+#584 := (iff #593 #591)
+#585 := [rewrite]: #584
+#582 := (iff #592 #593)
+#580 := (iff #494 #578)
+#589 := (iff #500 #587)
+#596 := (iff #498 #599)
+#600 := [rewrite]: #596
+#581 := [monotonicity #600]: #589
+#503 := (iff #501 #502)
+#506 := [rewrite]: #503
+#590 := [monotonicity #506 #581]: #580
+#583 := [monotonicity #590]: #582
+#586 := [trans #583 #585]: #579
+#588 := [quant-inst]: #592
+#570 := [mp #588 #586]: #591
+#511 := [unit-resolution #570 #679]: #578
+#517 := [unit-resolution #511 #516]: #502
+#485 := (not #502)
+#492 := (or #485 #573)
+#451 := [th-lemma]: #492
+#482 := [unit-resolution #451 #517]: #573
+#554 := (<= #152 0::int)
+#163 := (* -1::int #152)
+#138 := (uf_1 0::int)
+#141 := (uf_2 #138)
+#164 := (+ #141 #163)
+#162 := (>= #164 0::int)
+#30 := (- #26 #23)
+#31 := (uf_1 #30)
+#32 := (uf_2 #31)
+#27 := (* 0::int #26)
+#28 := (uf_1 #27)
+#29 := (uf_2 #28)
+#33 := (< #29 #32)
+#34 := (not #33)
+#174 := (iff #34 #162)
+#155 := (< #141 #152)
+#158 := (not #155)
+#172 := (iff #158 #162)
+#161 := (not #162)
+#167 := (not #161)
+#170 := (iff #167 #162)
+#171 := [rewrite]: #170
+#168 := (iff #158 #167)
+#165 := (iff #155 #161)
+#166 := [rewrite]: #165
+#169 := [monotonicity #166]: #168
+#173 := [trans #169 #171]: #172
+#159 := (iff #34 #158)
+#156 := (iff #33 #155)
+#153 := (= #32 #152)
+#150 := (= #31 #149)
+#147 := (= #30 #146)
+#148 := [rewrite]: #147
+#151 := [monotonicity #148]: #150
+#154 := [monotonicity #151]: #153
+#142 := (= #29 #141)
+#139 := (= #28 #138)
+#136 := (= #27 0::int)
+#137 := [rewrite]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#157 := [monotonicity #143 #154]: #156
+#160 := [monotonicity #157]: #159
+#175 := [trans #160 #173]: #174
+#135 := [asserted]: #34
+#176 := [mp #135 #175]: #162
+#651 := (<= #141 0::int)
+#662 := (= #141 0::int)
+#645 := (or #644 #662)
+#316 := (>= 0::int 0::int)
+#446 := (not #316)
+#328 := (= 0::int #141)
+#660 := (or #328 #446)
+#646 := (or #644 #660)
+#647 := (iff #646 #645)
+#648 := (iff #645 #645)
+#650 := [rewrite]: #648
+#642 := (iff #660 #662)
+#640 := (or #662 false)
+#305 := (iff #640 #662)
+#306 := [rewrite]: #305
+#303 := (iff #660 #640)
+#656 := (iff #446 false)
+#1 := true
+#654 := (not true)
+#655 := (iff #654 false)
+#315 := [rewrite]: #655
+#314 := (iff #446 #654)
+#658 := (iff #316 true)
+#664 := [rewrite]: #658
+#319 := [monotonicity #664]: #314
+#299 := [trans #319 #315]: #656
+#661 := (iff #328 #662)
+#663 := [rewrite]: #661
+#304 := [monotonicity #663 #299]: #303
+#643 := [trans #304 #306]: #642
+#285 := [monotonicity #643]: #647
+#290 := [trans #285 #650]: #647
+#641 := [quant-inst]: #646
+#291 := [mp #641 #290]: #645
+#484 := [unit-resolution #291 #679]: #662
+#486 := (not #662)
+#493 := (or #486 #651)
+#495 := [th-lemma]: #493
+#496 := [unit-resolution #495 #484]: #651
+#497 := (not #651)
+#507 := (or #554 #497 #161)
+#487 := [th-lemma]: #507
+#508 := [unit-resolution #487 #496 #176]: #554
+#463 := [th-lemma #508 #526 #482]: false
+#464 := [lemma #463]: #527
+#472 := (or #471 #613)
+#473 := [th-lemma]: #472
+#474 := [unit-resolution #473 #464]: #471
+#631 := (or #628 #633)
+#618 := (or #644 #628 #633)
+#634 := (>= #24 0::int)
+#635 := (not #634)
+#357 := (= #24 #26)
+#358 := (or #357 #635)
+#623 := (or #644 #358)
+#610 := (iff #623 #618)
+#619 := (or #644 #631)
+#467 := (iff #619 #618)
+#468 := [rewrite]: #467
+#625 := (iff #623 #619)
+#622 := (iff #358 #631)
+#626 := (or #633 #628)
+#620 := (iff #626 #631)
+#621 := [rewrite]: #620
+#630 := (iff #358 #626)
+#629 := (iff #635 #628)
+#349 := (iff #634 #348)
+#350 := [rewrite]: #349
+#344 := [monotonicity #350]: #629
+#637 := (iff #357 #633)
+#347 := [rewrite]: #637
+#627 := [monotonicity #347 #344]: #630
+#617 := [trans #627 #621]: #622
+#466 := [monotonicity #617]: #625
+#611 := [trans #466 #468]: #610
+#624 := [quant-inst]: #623
+#612 := [mp #624 #611]: #618
+#475 := [unit-resolution #612 #679]: #631
+#476 := [unit-resolution #475 #474]: #628
+#478 := (or #477 #348)
+#479 := [th-lemma]: #478
+#480 := [unit-resolution #479 #476]: #477
+#560 := (or #556 #558)
+#18 := (= #13 0::int)
+#124 := (or #18 #76)
+#680 := (forall (vars (?x3 int)) (:pat #673) #124)
+#129 := (forall (vars (?x3 int)) #124)
+#683 := (iff #129 #680)
+#681 := (iff #124 #124)
+#682 := [refl]: #681
+#684 := [quant-intro #682]: #683
+#180 := (~ #129 #129)
+#194 := (~ #124 #124)
+#195 := [refl]: #194
+#181 := [nnf-pos #195]: #180
+#17 := (< #10 0::int)
+#19 := (implies #17 #18)
+#20 := (forall (vars (?x3 int)) #19)
+#132 := (iff #20 #129)
+#95 := (= 0::int #13)
+#101 := (not #17)
+#102 := (or #101 #95)
+#107 := (forall (vars (?x3 int)) #102)
+#130 := (iff #107 #129)
+#127 := (iff #102 #124)
+#121 := (or #76 #18)
+#125 := (iff #121 #124)
+#126 := [rewrite]: #125
+#122 := (iff #102 #121)
+#119 := (iff #95 #18)
+#120 := [rewrite]: #119
+#117 := (iff #101 #76)
+#112 := (not #77)
+#115 := (iff #112 #76)
+#116 := [rewrite]: #115
+#113 := (iff #101 #112)
+#110 := (iff #17 #77)
+#111 := [rewrite]: #110
+#114 := [monotonicity #111]: #113
+#118 := [trans #114 #116]: #117
+#123 := [monotonicity #118 #120]: #122
+#128 := [trans #123 #126]: #127
+#131 := [quant-intro #128]: #130
+#108 := (iff #20 #107)
+#105 := (iff #19 #102)
+#98 := (implies #17 #95)
+#103 := (iff #98 #102)
+#104 := [rewrite]: #103
+#99 := (iff #19 #98)
+#96 := (iff #18 #95)
+#97 := [rewrite]: #96
+#100 := [monotonicity #97]: #99
+#106 := [trans #100 #104]: #105
+#109 := [quant-intro #106]: #108
+#133 := [trans #109 #131]: #132
+#94 := [asserted]: #20
+#134 := [mp #94 #133]: #129
+#196 := [mp~ #134 #181]: #129
+#685 := [mp #196 #684]: #680
+#604 := (not #680)
+#562 := (or #604 #556 #558)
+#559 := (or #558 #556)
+#540 := (or #604 #559)
+#542 := (iff #540 #562)
+#543 := (or #604 #560)
+#546 := (iff #543 #562)
+#547 := [rewrite]: #546
+#544 := (iff #540 #543)
+#561 := (iff #559 #560)
+#551 := [rewrite]: #561
+#545 := [monotonicity #551]: #544
+#548 := [trans #545 #547]: #542
+#541 := [quant-inst]: #540
+#534 := [mp #541 #548]: #562
+#465 := [unit-resolution #534 #685]: #560
+#481 := [unit-resolution #465 #480]: #558
+#443 := (= #23 #557)
+#337 := (= uf_3 #251)
+#4 := (:var 0 T1)
+#5 := (uf_2 #4)
+#665 := (pattern #5)
+#6 := (uf_1 #5)
+#51 := (= #4 #6)
+#666 := (forall (vars (?x1 T1)) (:pat #665) #51)
+#54 := (forall (vars (?x1 T1)) #51)
+#667 := (iff #54 #666)
+#669 := (iff #666 #666)
+#670 := [rewrite]: #669
+#668 := [rewrite]: #667
+#671 := [trans #668 #670]: #667
+#188 := (~ #54 #54)
+#186 := (~ #51 #51)
+#187 := [refl]: #186
+#189 := [nnf-pos #187]: #188
+#7 := (= #6 #4)
+#8 := (forall (vars (?x1 T1)) #7)
+#55 := (iff #8 #54)
+#52 := (iff #7 #51)
+#53 := [rewrite]: #52
+#56 := [quant-intro #53]: #55
+#50 := [asserted]: #8
+#59 := [mp #50 #56]: #54
+#190 := [mp~ #59 #189]: #54
+#672 := [mp #190 #671]: #666
+#252 := (not #666)
+#342 := (or #252 #337)
+#339 := [quant-inst]: #342
+#442 := [unit-resolution #339 #672]: #337
+#450 := [monotonicity #442]: #443
+#452 := [trans #450 #481]: #469
+#453 := (not #469)
+#454 := (or #453 #556)
+#456 := [th-lemma]: #454
+[unit-resolution #456 #480 #452]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T1 T2)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ (uf_3 T1)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (not (let (?x4 (uf_1 (+ 1 (uf_2 uf_3)))) (flet ($x5 (if_then_else (< 0 (uf_2 ?x4)) true false)) (or (iff $x5 (= (uf_1 (- (uf_2 ?x4) 1)) uf_3)) $x5))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,302 @@
+#2 := false
+#9 := 0::int
+decl uf_2 :: (-> T1 int)
+decl uf_1 :: (-> int T1)
+decl uf_3 :: T1
+#22 := uf_3
+#23 := (uf_2 uf_3)
+#21 := 1::int
+#24 := (+ 1::int #23)
+#25 := (uf_1 #24)
+#26 := (uf_2 #25)
+#138 := -1::int
+#139 := (+ -1::int #26)
+#142 := (uf_1 #139)
+#289 := (uf_2 #142)
+#383 := (* -1::int #289)
+#542 := (+ #23 #383)
+#544 := (>= #542 0::int)
+#541 := (= #23 #289)
+#148 := (= uf_3 #142)
+#167 := (<= #26 0::int)
+#168 := (not #167)
+#174 := (iff #148 #168)
+#189 := (not #174)
+#220 := (iff #189 #148)
+#210 := (not #148)
+#215 := (not #210)
+#218 := (iff #215 #148)
+#219 := [rewrite]: #218
+#216 := (iff #189 #215)
+#213 := (iff #174 #210)
+#207 := (iff #148 false)
+#211 := (iff #207 #210)
+#212 := [rewrite]: #211
+#208 := (iff #174 #207)
+#205 := (iff #168 false)
+#1 := true
+#200 := (not true)
+#203 := (iff #200 false)
+#204 := [rewrite]: #203
+#201 := (iff #168 #200)
+#198 := (iff #167 true)
+#179 := (or #168 #174)
+#182 := (not #179)
+#27 := (< 0::int #26)
+#28 := (ite #27 true false)
+#29 := (- #26 1::int)
+#30 := (uf_1 #29)
+#31 := (= #30 uf_3)
+#32 := (iff #28 #31)
+#33 := (or #32 #28)
+#34 := (not #33)
+#185 := (iff #34 #182)
+#153 := (iff #27 #148)
+#159 := (or #27 #153)
+#164 := (not #159)
+#183 := (iff #164 #182)
+#180 := (iff #159 #179)
+#177 := (iff #153 #174)
+#171 := (iff #168 #148)
+#175 := (iff #171 #174)
+#176 := [rewrite]: #175
+#172 := (iff #153 #171)
+#169 := (iff #27 #168)
+#170 := [rewrite]: #169
+#173 := [monotonicity #170]: #172
+#178 := [trans #173 #176]: #177
+#181 := [monotonicity #170 #178]: #180
+#184 := [monotonicity #181]: #183
+#165 := (iff #34 #164)
+#162 := (iff #33 #159)
+#156 := (or #153 #27)
+#160 := (iff #156 #159)
+#161 := [rewrite]: #160
+#157 := (iff #33 #156)
+#136 := (iff #28 #27)
+#137 := [rewrite]: #136
+#154 := (iff #32 #153)
+#151 := (iff #31 #148)
+#145 := (= #142 uf_3)
+#149 := (iff #145 #148)
+#150 := [rewrite]: #149
+#146 := (iff #31 #145)
+#143 := (= #30 #142)
+#140 := (= #29 #139)
+#141 := [rewrite]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#152 := [trans #147 #150]: #151
+#155 := [monotonicity #137 #152]: #154
+#158 := [monotonicity #155 #137]: #157
+#163 := [trans #158 #161]: #162
+#166 := [monotonicity #163]: #165
+#186 := [trans #166 #184]: #185
+#135 := [asserted]: #34
+#187 := [mp #135 #186]: #182
+#188 := [not-or-elim #187]: #167
+#199 := [iff-true #188]: #198
+#202 := [monotonicity #199]: #201
+#206 := [trans #202 #204]: #205
+#209 := [monotonicity #206]: #208
+#214 := [trans #209 #212]: #213
+#217 := [monotonicity #214]: #216
+#221 := [trans #217 #219]: #220
+#190 := [not-or-elim #187]: #189
+#222 := [mp #190 #221]: #148
+#624 := [monotonicity #222]: #541
+#618 := (not #541)
+#625 := (or #618 #544)
+#609 := [th-lemma]: #625
+#610 := [unit-resolution #609 #624]: #544
+#698 := (* -1::int #26)
+#355 := (+ #23 #698)
+#324 := (<= #355 -1::int)
+#485 := (= #355 -1::int)
+#367 := (>= #23 -1::int)
+#533 := (>= #289 0::int)
+#643 := (= #289 0::int)
+#659 := (>= #26 1::int)
+#656 := (not #659)
+#612 := (or #656 #168)
+#613 := [th-lemma]: #612
+#614 := [unit-resolution #613 #188]: #656
+#10 := (:var 0 int)
+#12 := (uf_1 #10)
+#712 := (pattern #12)
+#76 := (>= #10 0::int)
+#13 := (uf_2 #12)
+#18 := (= #13 0::int)
+#124 := (or #18 #76)
+#719 := (forall (vars (?x3 int)) (:pat #712) #124)
+#129 := (forall (vars (?x3 int)) #124)
+#722 := (iff #129 #719)
+#720 := (iff #124 #124)
+#721 := [refl]: #720
+#723 := [quant-intro #721]: #722
+#229 := (~ #129 #129)
+#227 := (~ #124 #124)
+#228 := [refl]: #227
+#230 := [nnf-pos #228]: #229
+#17 := (< #10 0::int)
+#19 := (implies #17 #18)
+#20 := (forall (vars (?x3 int)) #19)
+#132 := (iff #20 #129)
+#95 := (= 0::int #13)
+#101 := (not #17)
+#102 := (or #101 #95)
+#107 := (forall (vars (?x3 int)) #102)
+#130 := (iff #107 #129)
+#127 := (iff #102 #124)
+#121 := (or #76 #18)
+#125 := (iff #121 #124)
+#126 := [rewrite]: #125
+#122 := (iff #102 #121)
+#119 := (iff #95 #18)
+#120 := [rewrite]: #119
+#117 := (iff #101 #76)
+#77 := (not #76)
+#112 := (not #77)
+#115 := (iff #112 #76)
+#116 := [rewrite]: #115
+#113 := (iff #101 #112)
+#110 := (iff #17 #77)
+#111 := [rewrite]: #110
+#114 := [monotonicity #111]: #113
+#118 := [trans #114 #116]: #117
+#123 := [monotonicity #118 #120]: #122
+#128 := [trans #123 #126]: #127
+#131 := [quant-intro #128]: #130
+#108 := (iff #20 #107)
+#105 := (iff #19 #102)
+#98 := (implies #17 #95)
+#103 := (iff #98 #102)
+#104 := [rewrite]: #103
+#99 := (iff #19 #98)
+#96 := (iff #18 #95)
+#97 := [rewrite]: #96
+#100 := [monotonicity #97]: #99
+#106 := [trans #100 #104]: #105
+#109 := [quant-intro #106]: #108
+#133 := [trans #109 #131]: #132
+#94 := [asserted]: #20
+#134 := [mp #94 #133]: #129
+#231 := [mp~ #134 #230]: #129
+#724 := [mp #231 #723]: #719
+#402 := (not #719)
+#528 := (or #402 #643 #659)
+#388 := (>= #139 0::int)
+#644 := (or #643 #388)
+#529 := (or #402 #644)
+#522 := (iff #529 #528)
+#642 := (or #643 #659)
+#636 := (or #402 #642)
+#634 := (iff #636 #528)
+#637 := [rewrite]: #634
+#538 := (iff #529 #636)
+#645 := (iff #644 #642)
+#660 := (iff #388 #659)
+#661 := [rewrite]: #660
+#527 := [monotonicity #661]: #645
+#633 := [monotonicity #527]: #538
+#537 := [trans #633 #637]: #522
+#488 := [quant-inst]: #529
+#539 := [mp #488 #537]: #528
+#615 := [unit-resolution #539 #724 #614]: #643
+#611 := (not #643)
+#616 := (or #611 #533)
+#602 := [th-lemma]: #616
+#603 := [unit-resolution #602 #615]: #533
+#606 := (not #544)
+#605 := (not #533)
+#607 := (or #367 #605 #606)
+#604 := [th-lemma]: #607
+#608 := [unit-resolution #604 #603 #610]: #367
+#701 := (not #367)
+#358 := (or #701 #485)
+#58 := (= #10 #13)
+#83 := (or #58 #77)
+#713 := (forall (vars (?x2 int)) (:pat #712) #83)
+#88 := (forall (vars (?x2 int)) #83)
+#716 := (iff #88 #713)
+#714 := (iff #83 #83)
+#715 := [refl]: #714
+#717 := [quant-intro #715]: #716
+#191 := (~ #88 #88)
+#195 := (~ #83 #83)
+#193 := [refl]: #195
+#225 := [nnf-pos #193]: #191
+#14 := (= #13 #10)
+#11 := (<= 0::int #10)
+#15 := (implies #11 #14)
+#16 := (forall (vars (?x2 int)) #15)
+#91 := (iff #16 #88)
+#65 := (not #11)
+#66 := (or #65 #58)
+#71 := (forall (vars (?x2 int)) #66)
+#89 := (iff #71 #88)
+#86 := (iff #66 #83)
+#80 := (or #77 #58)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #66 #80)
+#78 := (iff #65 #77)
+#74 := (iff #11 #76)
+#75 := [rewrite]: #74
+#79 := [monotonicity #75]: #78
+#82 := [monotonicity #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [quant-intro #87]: #89
+#72 := (iff #16 #71)
+#69 := (iff #15 #66)
+#62 := (implies #11 #58)
+#67 := (iff #62 #66)
+#68 := [rewrite]: #67
+#63 := (iff #15 #62)
+#60 := (iff #14 #58)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#70 := [trans #64 #68]: #69
+#73 := [quant-intro #70]: #72
+#92 := [trans #73 #90]: #91
+#57 := [asserted]: #16
+#93 := [mp #57 #92]: #88
+#226 := [mp~ #93 #225]: #88
+#718 := [mp #226 #717]: #713
+#679 := (not #713)
+#342 := (or #679 #701 #485)
+#380 := (>= #24 0::int)
+#381 := (not #380)
+#361 := (= #24 #26)
+#696 := (or #361 #381)
+#343 := (or #679 #696)
+#685 := (iff #343 #342)
+#345 := (or #679 #358)
+#683 := (iff #345 #342)
+#684 := [rewrite]: #683
+#681 := (iff #343 #345)
+#695 := (iff #696 #358)
+#703 := (or #485 #701)
+#694 := (iff #703 #358)
+#354 := [rewrite]: #694
+#693 := (iff #696 #703)
+#702 := (iff #381 #701)
+#699 := (iff #380 #367)
+#700 := [rewrite]: #699
+#697 := [monotonicity #700]: #702
+#692 := (iff #361 #485)
+#366 := [rewrite]: #692
+#353 := [monotonicity #366 #697]: #693
+#338 := [trans #353 #354]: #695
+#682 := [monotonicity #338]: #681
+#680 := [trans #682 #684]: #685
+#344 := [quant-inst]: #343
+#686 := [mp #344 #680]: #342
+#588 := [unit-resolution #686 #718]: #358
+#589 := [unit-resolution #588 #608]: #485
+#591 := (not #485)
+#592 := (or #591 #324)
+#593 := [th-lemma]: #592
+#594 := [unit-resolution #593 #589]: #324
+[th-lemma #603 #188 #594 #610]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_05 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ (uf_3 T1)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (not (distinct (uf_1 (+ (uf_2 uf_3) 1)) (uf_1 (+ (uf_2 (uf_1 (* (uf_2 uf_3) 2))) 3)) (uf_1 (- (uf_2 uf_3) (uf_2 uf_3)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_05.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,525 @@
+#2 := false
+decl uf_2 :: (-> T1 int)
+decl uf_1 :: (-> int T1)
+decl uf_3 :: T1
+#21 := uf_3
+#22 := (uf_2 uf_3)
+#23 := 1::int
+#138 := (+ 1::int #22)
+#141 := (uf_1 #138)
+#656 := (uf_2 #141)
+#26 := 2::int
+#144 := (* 2::int #22)
+#147 := (uf_1 #144)
+#150 := (uf_2 #147)
+#30 := 3::int
+#156 := (+ 3::int #150)
+#161 := (uf_1 #156)
+#494 := (uf_2 #161)
+#288 := (= #494 #656)
+#266 := (= #161 #141)
+#249 := (= #141 #161)
+#9 := 0::int
+#166 := (uf_1 0::int)
+#251 := (= #161 #166)
+#337 := (not #251)
+#567 := (= #494 0::int)
+#543 := (uf_2 #166)
+#547 := (= #543 0::int)
+#10 := (:var 0 int)
+#12 := (uf_1 #10)
+#673 := (pattern #12)
+#78 := (>= #10 0::int)
+#79 := (not #78)
+#13 := (uf_2 #12)
+#60 := (= #10 #13)
+#85 := (or #60 #79)
+#674 := (forall (vars (?x2 int)) (:pat #673) #85)
+#90 := (forall (vars (?x2 int)) #85)
+#677 := (iff #90 #674)
+#675 := (iff #85 #85)
+#676 := [refl]: #675
+#678 := [quant-intro #676]: #677
+#178 := (~ #90 #90)
+#190 := (~ #85 #85)
+#191 := [refl]: #190
+#175 := [nnf-pos #191]: #178
+#14 := (= #13 #10)
+#11 := (<= 0::int #10)
+#15 := (implies #11 #14)
+#16 := (forall (vars (?x2 int)) #15)
+#93 := (iff #16 #90)
+#67 := (not #11)
+#68 := (or #67 #60)
+#73 := (forall (vars (?x2 int)) #68)
+#91 := (iff #73 #90)
+#88 := (iff #68 #85)
+#82 := (or #79 #60)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #68 #82)
+#80 := (iff #67 #79)
+#76 := (iff #11 #78)
+#77 := [rewrite]: #76
+#81 := [monotonicity #77]: #80
+#84 := [monotonicity #81]: #83
+#89 := [trans #84 #87]: #88
+#92 := [quant-intro #89]: #91
+#74 := (iff #16 #73)
+#71 := (iff #15 #68)
+#64 := (implies #11 #60)
+#69 := (iff #64 #68)
+#70 := [rewrite]: #69
+#65 := (iff #15 #64)
+#62 := (iff #14 #60)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#72 := [trans #66 #70]: #71
+#75 := [quant-intro #72]: #74
+#94 := [trans #75 #92]: #93
+#59 := [asserted]: #16
+#95 := [mp #59 #94]: #90
+#192 := [mp~ #95 #175]: #90
+#679 := [mp #192 #678]: #674
+#290 := (not #674)
+#519 := (or #290 #547)
+#540 := (>= 0::int 0::int)
+#541 := (not #540)
+#544 := (= 0::int #543)
+#545 := (or #544 #541)
+#520 := (or #290 #545)
+#521 := (iff #520 #519)
+#523 := (iff #519 #519)
+#526 := [rewrite]: #523
+#407 := (iff #545 #547)
+#533 := (or #547 false)
+#513 := (iff #533 #547)
+#514 := [rewrite]: #513
+#539 := (iff #545 #533)
+#537 := (iff #541 false)
+#1 := true
+#530 := (not true)
+#535 := (iff #530 false)
+#536 := [rewrite]: #535
+#531 := (iff #541 #530)
+#548 := (iff #540 true)
+#534 := [rewrite]: #548
+#532 := [monotonicity #534]: #531
+#538 := [trans #532 #536]: #537
+#546 := (iff #544 #547)
+#542 := [rewrite]: #546
+#512 := [monotonicity #542 #538]: #539
+#518 := [trans #512 #514]: #407
+#522 := [monotonicity #518]: #521
+#527 := [trans #522 #526]: #521
+#525 := [quant-inst]: #520
+#528 := [mp #525 #527]: #519
+#316 := [unit-resolution #528 #679]: #547
+#286 := (= #494 #543)
+#287 := [hypothesis]: #251
+#292 := [monotonicity #287]: #286
+#267 := [trans #292 #316]: #567
+#296 := (not #567)
+#551 := (<= #494 0::int)
+#300 := (not #551)
+#501 := (>= #150 0::int)
+#622 := (>= #144 0::int)
+#302 := -1::int
+#303 := (* -1::int #656)
+#304 := (+ #22 #303)
+#635 := (>= #304 -1::int)
+#305 := (= #304 -1::int)
+#644 := (>= #22 -1::int)
+#511 := (>= #22 0::int)
+#487 := (= #22 0::int)
+#660 := (uf_1 #22)
+#517 := (uf_2 #660)
+#485 := (= #517 0::int)
+#389 := (not #511)
+#390 := [hypothesis]: #389
+#492 := (or #485 #511)
+#18 := (= #13 0::int)
+#126 := (or #18 #78)
+#680 := (forall (vars (?x3 int)) (:pat #673) #126)
+#131 := (forall (vars (?x3 int)) #126)
+#683 := (iff #131 #680)
+#681 := (iff #126 #126)
+#682 := [refl]: #681
+#684 := [quant-intro #682]: #683
+#179 := (~ #131 #131)
+#193 := (~ #126 #126)
+#194 := [refl]: #193
+#180 := [nnf-pos #194]: #179
+#17 := (< #10 0::int)
+#19 := (implies #17 #18)
+#20 := (forall (vars (?x3 int)) #19)
+#134 := (iff #20 #131)
+#97 := (= 0::int #13)
+#103 := (not #17)
+#104 := (or #103 #97)
+#109 := (forall (vars (?x3 int)) #104)
+#132 := (iff #109 #131)
+#129 := (iff #104 #126)
+#123 := (or #78 #18)
+#127 := (iff #123 #126)
+#128 := [rewrite]: #127
+#124 := (iff #104 #123)
+#121 := (iff #97 #18)
+#122 := [rewrite]: #121
+#119 := (iff #103 #78)
+#114 := (not #79)
+#117 := (iff #114 #78)
+#118 := [rewrite]: #117
+#115 := (iff #103 #114)
+#112 := (iff #17 #79)
+#113 := [rewrite]: #112
+#116 := [monotonicity #113]: #115
+#120 := [trans #116 #118]: #119
+#125 := [monotonicity #120 #122]: #124
+#130 := [trans #125 #128]: #129
+#133 := [quant-intro #130]: #132
+#110 := (iff #20 #109)
+#107 := (iff #19 #104)
+#100 := (implies #17 #97)
+#105 := (iff #100 #104)
+#106 := [rewrite]: #105
+#101 := (iff #19 #100)
+#98 := (iff #18 #97)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#108 := [trans #102 #106]: #107
+#111 := [quant-intro #108]: #110
+#135 := [trans #111 #133]: #134
+#96 := [asserted]: #20
+#136 := [mp #96 #135]: #131
+#195 := [mp~ #136 #180]: #131
+#685 := [mp #195 #684]: #680
+#637 := (not #680)
+#484 := (or #637 #485 #511)
+#486 := (or #637 #492)
+#495 := (iff #486 #484)
+#496 := [rewrite]: #495
+#493 := [quant-inst]: #486
+#497 := [mp #493 #496]: #484
+#391 := [unit-resolution #497 #685]: #492
+#392 := [unit-resolution #391 #390]: #485
+#394 := (= #22 #517)
+#661 := (= uf_3 #660)
+#4 := (:var 0 T1)
+#5 := (uf_2 #4)
+#665 := (pattern #5)
+#6 := (uf_1 #5)
+#53 := (= #4 #6)
+#666 := (forall (vars (?x1 T1)) (:pat #665) #53)
+#56 := (forall (vars (?x1 T1)) #53)
+#667 := (iff #56 #666)
+#669 := (iff #666 #666)
+#670 := [rewrite]: #669
+#668 := [rewrite]: #667
+#671 := [trans #668 #670]: #667
+#187 := (~ #56 #56)
+#185 := (~ #53 #53)
+#186 := [refl]: #185
+#188 := [nnf-pos #186]: #187
+#7 := (= #6 #4)
+#8 := (forall (vars (?x1 T1)) #7)
+#57 := (iff #8 #56)
+#54 := (iff #7 #53)
+#55 := [rewrite]: #54
+#58 := [quant-intro #55]: #57
+#52 := [asserted]: #8
+#61 := [mp #52 #58]: #56
+#189 := [mp~ #61 #188]: #56
+#672 := [mp #189 #671]: #666
+#658 := (not #666)
+#664 := (or #658 #661)
+#654 := [quant-inst]: #664
+#393 := [unit-resolution #654 #672]: #661
+#395 := [monotonicity #393]: #394
+#396 := [trans #395 #392]: #487
+#397 := (not #487)
+#398 := (or #397 #511)
+#399 := [th-lemma]: #398
+#388 := [unit-resolution #399 #390 #396]: false
+#400 := [lemma #388]: #511
+#366 := (or #389 #644)
+#367 := [th-lemma]: #366
+#352 := [unit-resolution #367 #400]: #644
+#641 := (not #644)
+#648 := (or #305 #641)
+#651 := (or #290 #305 #641)
+#313 := (>= #138 0::int)
+#318 := (not #313)
+#298 := (= #138 #656)
+#640 := (or #298 #318)
+#649 := (or #290 #640)
+#363 := (iff #649 #651)
+#638 := (or #290 #648)
+#361 := (iff #638 #651)
+#362 := [rewrite]: #361
+#639 := (iff #649 #638)
+#650 := (iff #640 #648)
+#647 := (iff #318 #641)
+#645 := (iff #313 #644)
+#646 := [rewrite]: #645
+#284 := [monotonicity #646]: #647
+#642 := (iff #298 #305)
+#643 := [rewrite]: #642
+#289 := [monotonicity #643 #284]: #650
+#346 := [monotonicity #289]: #639
+#364 := [trans #346 #362]: #363
+#652 := [quant-inst]: #649
+#257 := [mp #652 #364]: #651
+#424 := [unit-resolution #257 #679]: #648
+#353 := [unit-resolution #424 #352]: #305
+#439 := (not #305)
+#281 := (or #439 #635)
+#440 := [th-lemma]: #281
+#330 := [unit-resolution #440 #353]: #635
+#620 := (<= #656 0::int)
+#441 := (not #620)
+#634 := (<= #304 -1::int)
+#344 := (or #439 #634)
+#354 := [th-lemma]: #344
+#355 := [unit-resolution #354 #353]: #634
+#345 := (not #634)
+#356 := (or #441 #389 #345)
+#322 := [th-lemma]: #356
+#324 := [unit-resolution #322 #355 #400]: #441
+#432 := (not #635)
+#331 := (or #622 #432 #620)
+#319 := [th-lemma]: #331
+#320 := [unit-resolution #319 #324 #330]: #622
+#624 := (* -1::int #150)
+#619 := (+ #144 #624)
+#606 := (<= #619 0::int)
+#625 := (= #619 0::int)
+#617 := (not #622)
+#612 := (or #617 #625)
+#615 := (or #290 #617 #625)
+#618 := (= #144 #150)
+#623 := (or #618 #617)
+#609 := (or #290 #623)
+#604 := (iff #609 #615)
+#445 := (or #290 #612)
+#601 := (iff #445 #615)
+#602 := [rewrite]: #601
+#447 := (iff #609 #445)
+#608 := (iff #623 #612)
+#468 := (or #625 #617)
+#613 := (iff #468 #612)
+#607 := [rewrite]: #613
+#610 := (iff #623 #468)
+#466 := (iff #618 #625)
+#467 := [rewrite]: #466
+#611 := [monotonicity #467]: #610
+#614 := [trans #611 #607]: #608
+#448 := [monotonicity #614]: #447
+#605 := [trans #448 #602]: #604
+#616 := [quant-inst]: #609
+#603 := [mp #616 #605]: #615
+#480 := [unit-resolution #603 #679]: #612
+#299 := [unit-resolution #480 #320]: #625
+#406 := (not #625)
+#408 := (or #406 #606)
+#409 := [th-lemma]: #408
+#301 := [unit-resolution #409 #299]: #606
+#413 := (not #606)
+#306 := (or #501 #413 #617)
+#307 := [th-lemma]: #306
+#308 := [unit-resolution #307 #301 #320]: #501
+#506 := -3::int
+#504 := (* -1::int #494)
+#505 := (+ #150 #504)
+#564 := (<= #505 -3::int)
+#599 := (= #505 -3::int)
+#587 := (>= #150 -3::int)
+#417 := (or #587 #413 #617)
+#410 := [th-lemma]: #417
+#309 := [unit-resolution #410 #301 #320]: #587
+#578 := (not #587)
+#593 := (or #578 #599)
+#579 := (or #290 #578 #599)
+#449 := (>= #156 0::int)
+#597 := (not #449)
+#502 := (= #156 #494)
+#503 := (or #502 #597)
+#586 := (or #290 #503)
+#572 := (iff #586 #579)
+#571 := (or #290 #593)
+#575 := (iff #571 #579)
+#576 := [rewrite]: #575
+#573 := (iff #586 #571)
+#584 := (iff #503 #593)
+#591 := (or #599 #578)
+#582 := (iff #591 #593)
+#583 := [rewrite]: #582
+#592 := (iff #503 #591)
+#580 := (iff #597 #578)
+#589 := (iff #449 #587)
+#581 := [rewrite]: #589
+#590 := [monotonicity #581]: #580
+#596 := (iff #502 #599)
+#600 := [rewrite]: #596
+#588 := [monotonicity #600 #590]: #592
+#585 := [trans #588 #583]: #584
+#574 := [monotonicity #585]: #573
+#577 := [trans #574 #576]: #572
+#570 := [quant-inst]: #586
+#563 := [mp #570 #577]: #579
+#458 := [unit-resolution #563 #679]: #593
+#310 := [unit-resolution #458 #309]: #599
+#460 := (not #599)
+#461 := (or #460 #564)
+#444 := [th-lemma]: #461
+#311 := [unit-resolution #444 #310]: #564
+#434 := (not #564)
+#453 := (not #501)
+#312 := (or #300 #453 #434)
+#293 := [th-lemma]: #312
+#295 := [unit-resolution #293 #311 #308]: #300
+#294 := (or #296 #551)
+#297 := [th-lemma]: #294
+#285 := [unit-resolution #297 #295]: #296
+#271 := [unit-resolution #285 #267]: false
+#272 := [lemma #271]: #337
+#282 := (or #249 #251)
+#250 := (= #141 #166)
+#336 := (not #250)
+#357 := (= #656 0::int)
+#332 := (= #656 #543)
+#329 := [hypothesis]: #250
+#333 := [monotonicity #329]: #332
+#323 := [trans #333 #316]: #357
+#429 := (not #357)
+#430 := (or #429 #620)
+#428 := [th-lemma]: #430
+#325 := [unit-resolution #428 #324]: #429
+#334 := [unit-resolution #325 #323]: false
+#317 := [lemma #334]: #336
+#279 := (or #249 #250 #251)
+#335 := (not #249)
+#328 := (and #335 #336 #337)
+#339 := (not #328)
+#169 := (distinct #141 #161 #166)
+#172 := (not #169)
+#33 := (- #22 #22)
+#34 := (uf_1 #33)
+#27 := (* #22 2::int)
+#28 := (uf_1 #27)
+#29 := (uf_2 #28)
+#31 := (+ #29 3::int)
+#32 := (uf_1 #31)
+#24 := (+ #22 1::int)
+#25 := (uf_1 #24)
+#35 := (distinct #25 #32 #34)
+#36 := (not #35)
+#173 := (iff #36 #172)
+#170 := (iff #35 #169)
+#167 := (= #34 #166)
+#164 := (= #33 0::int)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#162 := (= #32 #161)
+#159 := (= #31 #156)
+#153 := (+ #150 3::int)
+#157 := (= #153 #156)
+#158 := [rewrite]: #157
+#154 := (= #31 #153)
+#151 := (= #29 #150)
+#148 := (= #28 #147)
+#145 := (= #27 #144)
+#146 := [rewrite]: #145
+#149 := [monotonicity #146]: #148
+#152 := [monotonicity #149]: #151
+#155 := [monotonicity #152]: #154
+#160 := [trans #155 #158]: #159
+#163 := [monotonicity #160]: #162
+#142 := (= #25 #141)
+#139 := (= #24 #138)
+#140 := [rewrite]: #139
+#143 := [monotonicity #140]: #142
+#171 := [monotonicity #143 #163 #168]: #170
+#174 := [monotonicity #171]: #173
+#137 := [asserted]: #36
+#177 := [mp #137 #174]: #172
+#326 := (or #169 #339)
+#327 := [def-axiom]: #326
+#277 := [unit-resolution #327 #177]: #339
+#659 := (or #328 #249 #250 #251)
+#315 := [def-axiom]: #659
+#280 := [unit-resolution #315 #277]: #279
+#278 := [unit-resolution #280 #317]: #282
+#283 := [unit-resolution #278 #272]: #249
+#269 := [symm #283]: #266
+#270 := [monotonicity #269]: #288
+#508 := (+ #494 #303)
+#473 := (<= #508 0::int)
+#433 := (not #473)
+#477 := [hypothesis]: #473
+#421 := (or #622 #433)
+#489 := (= #150 0::int)
+#478 := [hypothesis]: #617
+#490 := (or #489 #622)
+#499 := (or #637 #489 #622)
+#594 := (or #637 #490)
+#598 := (iff #594 #499)
+#483 := [rewrite]: #598
+#595 := [quant-inst]: #594
+#498 := [mp #595 #483]: #499
+#465 := [unit-resolution #498 #685]: #490
+#481 := [unit-resolution #465 #478]: #489
+#442 := (not #489)
+#443 := (or #442 #501)
+#450 := [th-lemma]: #443
+#452 := [unit-resolution #450 #481]: #501
+#454 := (or #453 #587)
+#456 := [th-lemma]: #454
+#457 := [unit-resolution #456 #452]: #587
+#459 := [unit-resolution #458 #457]: #599
+#462 := [unit-resolution #444 #459]: #564
+#435 := (or #432 #622 #433 #453 #434)
+#437 := [th-lemma]: #435
+#438 := [unit-resolution #437 #478 #452 #462 #477]: #432
+#436 := [unit-resolution #440 #438]: #439
+#420 := (or #441 #433 #453 #434)
+#423 := [th-lemma]: #420
+#427 := [unit-resolution #423 #452 #462 #477]: #441
+#431 := [unit-resolution #428 #427]: #429
+#632 := (or #357 #644)
+#347 := (or #637 #357 #644)
+#358 := (or #357 #313)
+#348 := (or #637 #358)
+#630 := (iff #348 #347)
+#350 := (or #637 #632)
+#343 := (iff #350 #347)
+#626 := [rewrite]: #343
+#628 := (iff #348 #350)
+#636 := (iff #358 #632)
+#633 := [monotonicity #646]: #636
+#629 := [monotonicity #633]: #628
+#627 := [trans #629 #626]: #630
+#349 := [quant-inst]: #348
+#631 := [mp #349 #627]: #347
+#419 := [unit-resolution #631 #685]: #632
+#422 := [unit-resolution #419 #431]: #644
+#425 := [unit-resolution #424 #422 #436]: false
+#426 := [lemma #425]: #421
+#479 := [unit-resolution #426 #477]: #622
+#416 := [unit-resolution #480 #479]: #625
+#412 := [unit-resolution #409 #416]: #606
+#418 := [unit-resolution #410 #412 #479]: #587
+#411 := [unit-resolution #458 #418]: #599
+#414 := [unit-resolution #444 #411]: #564
+#415 := (or #644 #617)
+#401 := [th-lemma]: #415
+#403 := [unit-resolution #401 #479]: #644
+#404 := [unit-resolution #424 #403]: #305
+#402 := [unit-resolution #440 #404]: #635
+#405 := [th-lemma #418 #402 #477 #414 #412]: false
+#387 := [lemma #405]: #433
+#273 := (not #288)
+#274 := (or #273 #473)
+#275 := [th-lemma]: #274
+[unit-resolution #275 #387 #270]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_06 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,13 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ (uf_3 Int)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (not (= (uf_2 (uf_1 (ite (< uf_3 0) (~ uf_3) uf_3))) (ite (< uf_3 0) (~ uf_3) uf_3)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_06.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,161 @@
+#2 := false
+#9 := 0::int
+decl uf_3 :: int
+#21 := uf_3
+#130 := -1::int
+#131 := (* -1::int uf_3)
+#154 := (>= uf_3 0::int)
+#161 := (ite #154 uf_3 #131)
+#648 := (* -1::int #161)
+#651 := (+ #131 #648)
+#657 := (<= #651 0::int)
+#341 := (= #131 #161)
+#155 := (not #154)
+#649 := (+ uf_3 #648)
+#650 := (<= #649 0::int)
+#254 := (= uf_3 #161)
+#646 := [hypothesis]: #154
+#255 := (or #155 #254)
+#342 := [def-axiom]: #255
+#652 := [unit-resolution #342 #646]: #254
+#290 := (not #254)
+#653 := (or #290 #650)
+#655 := [th-lemma]: #653
+#295 := [unit-resolution #655 #652]: #650
+#346 := (>= #161 0::int)
+#274 := (not #346)
+decl uf_2 :: (-> T1 int)
+decl uf_1 :: (-> int T1)
+#166 := (uf_1 #161)
+#169 := (uf_2 #166)
+#172 := (= #161 #169)
+#175 := (not #172)
+#23 := (- uf_3)
+#22 := (< uf_3 0::int)
+#24 := (ite #22 #23 uf_3)
+#25 := (uf_1 #24)
+#26 := (uf_2 #25)
+#27 := (= #26 #24)
+#28 := (not #27)
+#178 := (iff #28 #175)
+#134 := (ite #22 #131 uf_3)
+#137 := (uf_1 #134)
+#140 := (uf_2 #137)
+#146 := (= #134 #140)
+#151 := (not #146)
+#176 := (iff #151 #175)
+#173 := (iff #146 #172)
+#170 := (= #140 #169)
+#167 := (= #137 #166)
+#164 := (= #134 #161)
+#158 := (ite #155 #131 uf_3)
+#162 := (= #158 #161)
+#163 := [rewrite]: #162
+#159 := (= #134 #158)
+#156 := (iff #22 #155)
+#157 := [rewrite]: #156
+#160 := [monotonicity #157]: #159
+#165 := [trans #160 #163]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #165 #171]: #173
+#177 := [monotonicity #174]: #176
+#152 := (iff #28 #151)
+#149 := (iff #27 #146)
+#143 := (= #140 #134)
+#147 := (iff #143 #146)
+#148 := [rewrite]: #147
+#144 := (iff #27 #143)
+#135 := (= #24 #134)
+#132 := (= #23 #131)
+#133 := [rewrite]: #132
+#136 := [monotonicity #133]: #135
+#141 := (= #26 #140)
+#138 := (= #25 #137)
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142 #136]: #144
+#150 := [trans #145 #148]: #149
+#153 := [monotonicity #150]: #152
+#179 := [trans #153 #177]: #178
+#129 := [asserted]: #28
+#180 := [mp #129 #179]: #175
+#10 := (:var 0 int)
+#12 := (uf_1 #10)
+#678 := (pattern #12)
+#70 := (>= #10 0::int)
+#71 := (not #70)
+#13 := (uf_2 #12)
+#52 := (= #10 #13)
+#77 := (or #52 #71)
+#679 := (forall (vars (?x2 int)) (:pat #678) #77)
+#82 := (forall (vars (?x2 int)) #77)
+#682 := (iff #82 #679)
+#680 := (iff #77 #77)
+#681 := [refl]: #680
+#683 := [quant-intro #681]: #682
+#183 := (~ #82 #82)
+#195 := (~ #77 #77)
+#196 := [refl]: #195
+#181 := [nnf-pos #196]: #183
+#14 := (= #13 #10)
+#11 := (<= 0::int #10)
+#15 := (implies #11 #14)
+#16 := (forall (vars (?x2 int)) #15)
+#85 := (iff #16 #82)
+#59 := (not #11)
+#60 := (or #59 #52)
+#65 := (forall (vars (?x2 int)) #60)
+#83 := (iff #65 #82)
+#80 := (iff #60 #77)
+#74 := (or #71 #52)
+#78 := (iff #74 #77)
+#79 := [rewrite]: #78
+#75 := (iff #60 #74)
+#72 := (iff #59 #71)
+#68 := (iff #11 #70)
+#69 := [rewrite]: #68
+#73 := [monotonicity #69]: #72
+#76 := [monotonicity #73]: #75
+#81 := [trans #76 #79]: #80
+#84 := [quant-intro #81]: #83
+#66 := (iff #16 #65)
+#63 := (iff #15 #60)
+#56 := (implies #11 #52)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #15 #56)
+#54 := (iff #14 #52)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#64 := [trans #58 #62]: #63
+#67 := [quant-intro #64]: #66
+#86 := [trans #67 #84]: #85
+#51 := [asserted]: #16
+#87 := [mp #51 #86]: #82
+#197 := [mp~ #87 #181]: #82
+#684 := [mp #197 #683]: #679
+#321 := (not #679)
+#451 := (or #321 #172 #274)
+#327 := (or #172 #274)
+#658 := (or #321 #327)
+#333 := (iff #658 #451)
+#665 := [rewrite]: #333
+#332 := [quant-inst]: #658
+#666 := [mp #332 #665]: #451
+#296 := [unit-resolution #666 #684 #180]: #274
+#656 := [th-lemma #646 #296 #295]: false
+#654 := [lemma #656]: #155
+#256 := (or #154 #341)
+#343 := [def-axiom]: #256
+#644 := [unit-resolution #343 #654]: #341
+#366 := (not #341)
+#367 := (or #366 #657)
+#368 := [th-lemma]: #367
+#369 := [unit-resolution #368 #644]: #657
+#647 := (<= #161 0::int)
+#262 := (or #647 #346)
+#639 := [th-lemma]: #262
+#640 := [unit-resolution #639 #296]: #647
+[th-lemma #654 #640 #369]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_07 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,19 @@
+(benchmark Isabelle
+:extrasorts ( T1 T2)
+:extrafuns (
+ (uf_1 Int T1)
+ (uf_2 T1 Int)
+ (uf_5 T1)
+ )
+:extrapreds (
+ (up_3 T1)
+ (up_4 T1 T1)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1)) ?x1))
+:assumption (forall (?x2 Int) (implies (<= 0 ?x2) (= (uf_2 (uf_1 ?x2)) ?x2)))
+:assumption (forall (?x3 Int) (implies (< ?x3 0) (= (uf_2 (uf_1 ?x3)) 0)))
+:assumption (forall (?x4 T1) (iff (up_3 ?x4) (and (< 1 (uf_2 ?x4)) (forall (?x5 T1) (implies (up_4 ?x5 ?x4) (or (= ?x5 (uf_1 1)) (= ?x5 ?x4)))))))
+:assumption (up_3 (uf_1 (+ (uf_2 (uf_1 (* 4 (uf_2 uf_5)))) 1)))
+:assumption (not (<= 1 (uf_2 uf_5)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nat_arith_07.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,553 @@
+#2 := false
+#9 := 0::int
+decl uf_2 :: (-> T1 int)
+decl uf_1 :: (-> int T1)
+decl uf_5 :: T1
+#36 := uf_5
+#37 := (uf_2 uf_5)
+#35 := 4::int
+#38 := (* 4::int #37)
+#39 := (uf_1 #38)
+#40 := (uf_2 #39)
+#549 := (= #40 0::int)
+#963 := (not #549)
+#537 := (<= #40 0::int)
+#958 := (not #537)
+#22 := 1::int
+#186 := (+ 1::int #40)
+#189 := (uf_1 #186)
+#524 := (uf_2 #189)
+#452 := (<= #524 1::int)
+#874 := (not #452)
+decl up_4 :: (-> T1 T1 bool)
+#4 := (:var 0 T1)
+#456 := (up_4 #4 #189)
+#440 := (pattern #456)
+#446 := (not #456)
+#455 := (= #4 #189)
+#26 := (uf_1 1::int)
+#27 := (= #4 #26)
+#434 := (or #27 #455 #446)
+#416 := (forall (vars (?x5 T1)) (:pat #440) #434)
+#417 := (not #416)
+#409 := (or #417 #452)
+#400 := (not #409)
+decl up_3 :: (-> T1 bool)
+#192 := (up_3 #189)
+#429 := (not #192)
+#405 := (or #429 #400)
+#389 := (not #405)
+decl ?x5!0 :: (-> T1 T1)
+#478 := (?x5!0 #189)
+#479 := (= #26 #478)
+#468 := (= #189 #478)
+#445 := (up_4 #478 #189)
+#447 := (not #445)
+#396 := (or #447 #468 #479)
+#391 := (not #396)
+#386 := (or #192 #391 #452)
+#377 := (not #386)
+#843 := (or #377 #389)
+#848 := (not #843)
+#5 := (uf_2 #4)
+#788 := (pattern #5)
+#21 := (up_3 #4)
+#836 := (pattern #21)
+#210 := (?x5!0 #4)
+#274 := (= #4 #210)
+#271 := (= #26 #210)
+#232 := (up_4 #210 #4)
+#233 := (not #232)
+#277 := (or #233 #271 #274)
+#280 := (not #277)
+#163 := (<= #5 1::int)
+#289 := (or #21 #163 #280)
+#304 := (not #289)
+#24 := (:var 1 T1)
+#25 := (up_4 #4 #24)
+#809 := (pattern #25)
+#28 := (= #4 #24)
+#147 := (not #25)
+#167 := (or #147 #27 #28)
+#810 := (forall (vars (?x5 T1)) (:pat #809) #167)
+#815 := (not #810)
+#818 := (or #163 #815)
+#821 := (not #818)
+#253 := (not #21)
+#824 := (or #253 #821)
+#827 := (not #824)
+#830 := (or #827 #304)
+#833 := (not #830)
+#837 := (forall (vars (?x4 T1)) (:pat #836 #788) #833)
+#170 := (forall (vars (?x5 T1)) #167)
+#236 := (not #170)
+#239 := (or #163 #236)
+#240 := (not #239)
+#215 := (or #253 #240)
+#303 := (not #215)
+#305 := (or #303 #304)
+#306 := (not #305)
+#311 := (forall (vars (?x4 T1)) #306)
+#838 := (iff #311 #837)
+#834 := (iff #306 #833)
+#831 := (iff #305 #830)
+#828 := (iff #303 #827)
+#825 := (iff #215 #824)
+#822 := (iff #240 #821)
+#819 := (iff #239 #818)
+#816 := (iff #236 #815)
+#813 := (iff #170 #810)
+#811 := (iff #167 #167)
+#812 := [refl]: #811
+#814 := [quant-intro #812]: #813
+#817 := [monotonicity #814]: #816
+#820 := [monotonicity #817]: #819
+#823 := [monotonicity #820]: #822
+#826 := [monotonicity #823]: #825
+#829 := [monotonicity #826]: #828
+#832 := [monotonicity #829]: #831
+#835 := [monotonicity #832]: #834
+#839 := [quant-intro #835]: #838
+#164 := (not #163)
+#173 := (and #164 #170)
+#259 := (or #253 #173)
+#294 := (and #259 #289)
+#297 := (forall (vars (?x4 T1)) #294)
+#312 := (iff #297 #311)
+#309 := (iff #294 #306)
+#214 := (and #215 #289)
+#307 := (iff #214 #306)
+#308 := [rewrite]: #307
+#301 := (iff #294 #214)
+#216 := (iff #259 #215)
+#268 := (iff #173 #240)
+#300 := [rewrite]: #268
+#213 := [monotonicity #300]: #216
+#302 := [monotonicity #213]: #301
+#310 := [trans #302 #308]: #309
+#313 := [quant-intro #310]: #312
+#230 := (= #210 #4)
+#231 := (= #210 #26)
+#234 := (or #233 #231 #230)
+#235 := (not #234)
+#228 := (not #164)
+#241 := (or #228 #235)
+#258 := (or #21 #241)
+#260 := (and #259 #258)
+#263 := (forall (vars (?x4 T1)) #260)
+#298 := (iff #263 #297)
+#295 := (iff #260 #294)
+#292 := (iff #258 #289)
+#283 := (or #163 #280)
+#286 := (or #21 #283)
+#290 := (iff #286 #289)
+#291 := [rewrite]: #290
+#287 := (iff #258 #286)
+#284 := (iff #241 #283)
+#281 := (iff #235 #280)
+#278 := (iff #234 #277)
+#275 := (iff #230 #274)
+#276 := [rewrite]: #275
+#272 := (iff #231 #271)
+#273 := [rewrite]: #272
+#279 := [monotonicity #273 #276]: #278
+#282 := [monotonicity #279]: #281
+#269 := (iff #228 #163)
+#270 := [rewrite]: #269
+#285 := [monotonicity #270 #282]: #284
+#288 := [monotonicity #285]: #287
+#293 := [trans #288 #291]: #292
+#296 := [monotonicity #293]: #295
+#299 := [quant-intro #296]: #298
+#176 := (iff #21 #173)
+#179 := (forall (vars (?x4 T1)) #176)
+#264 := (~ #179 #263)
+#261 := (~ #176 #260)
+#251 := (~ #173 #173)
+#249 := (~ #170 #170)
+#247 := (~ #167 #167)
+#248 := [refl]: #247
+#250 := [nnf-pos #248]: #249
+#245 := (~ #164 #164)
+#246 := [refl]: #245
+#252 := [monotonicity #246 #250]: #251
+#242 := (not #173)
+#243 := (~ #242 #241)
+#237 := (~ #236 #235)
+#238 := [sk]: #237
+#229 := (~ #228 #228)
+#209 := [refl]: #229
+#244 := [nnf-neg #209 #238]: #243
+#256 := (~ #21 #21)
+#257 := [refl]: #256
+#254 := (~ #253 #253)
+#255 := [refl]: #254
+#262 := [nnf-pos #255 #257 #244 #252]: #261
+#265 := [nnf-pos #262]: #264
+#29 := (or #27 #28)
+#30 := (implies #25 #29)
+#31 := (forall (vars (?x5 T1)) #30)
+#23 := (< 1::int #5)
+#32 := (and #23 #31)
+#33 := (iff #21 #32)
+#34 := (forall (vars (?x4 T1)) #33)
+#182 := (iff #34 #179)
+#148 := (or #147 #29)
+#151 := (forall (vars (?x5 T1)) #148)
+#154 := (and #23 #151)
+#157 := (iff #21 #154)
+#160 := (forall (vars (?x4 T1)) #157)
+#180 := (iff #160 #179)
+#177 := (iff #157 #176)
+#174 := (iff #154 #173)
+#171 := (iff #151 #170)
+#168 := (iff #148 #167)
+#169 := [rewrite]: #168
+#172 := [quant-intro #169]: #171
+#165 := (iff #23 #164)
+#166 := [rewrite]: #165
+#175 := [monotonicity #166 #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#161 := (iff #34 #160)
+#158 := (iff #33 #157)
+#155 := (iff #32 #154)
+#152 := (iff #31 #151)
+#149 := (iff #30 #148)
+#150 := [rewrite]: #149
+#153 := [quant-intro #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [quant-intro #159]: #161
+#183 := [trans #162 #181]: #182
+#146 := [asserted]: #34
+#184 := [mp #146 #183]: #179
+#266 := [mp~ #184 #265]: #263
+#267 := [mp #266 #299]: #297
+#314 := [mp #267 #313]: #311
+#840 := [mp #314 #839]: #837
+#754 := (not #837)
+#851 := (or #754 #848)
+#448 := (or #447 #479 #468)
+#439 := (not #448)
+#453 := (or #192 #452 #439)
+#454 := (not #453)
+#457 := (or #446 #27 #455)
+#442 := (forall (vars (?x5 T1)) (:pat #440) #457)
+#443 := (not #442)
+#422 := (or #452 #443)
+#424 := (not #422)
+#430 := (or #429 #424)
+#431 := (not #430)
+#432 := (or #431 #454)
+#433 := (not #432)
+#852 := (or #754 #433)
+#854 := (iff #852 #851)
+#856 := (iff #851 #851)
+#857 := [rewrite]: #856
+#849 := (iff #433 #848)
+#846 := (iff #432 #843)
+#379 := (or #389 #377)
+#844 := (iff #379 #843)
+#845 := [rewrite]: #844
+#841 := (iff #432 #379)
+#378 := (iff #454 #377)
+#388 := (iff #453 #386)
+#381 := (or #192 #452 #391)
+#387 := (iff #381 #386)
+#383 := [rewrite]: #387
+#382 := (iff #453 #381)
+#399 := (iff #439 #391)
+#397 := (iff #448 #396)
+#398 := [rewrite]: #397
+#384 := [monotonicity #398]: #399
+#385 := [monotonicity #384]: #382
+#375 := [trans #385 #383]: #388
+#376 := [monotonicity #375]: #378
+#392 := (iff #431 #389)
+#401 := (iff #430 #405)
+#402 := (iff #424 #400)
+#394 := (iff #422 #409)
+#410 := (or #452 #417)
+#415 := (iff #410 #409)
+#390 := [rewrite]: #415
+#411 := (iff #422 #410)
+#420 := (iff #443 #417)
+#418 := (iff #442 #416)
+#423 := (iff #457 #434)
+#435 := [rewrite]: #423
+#419 := [quant-intro #435]: #418
+#408 := [monotonicity #419]: #420
+#414 := [monotonicity #408]: #411
+#395 := [trans #414 #390]: #394
+#403 := [monotonicity #395]: #402
+#406 := [monotonicity #403]: #401
+#393 := [monotonicity #406]: #392
+#842 := [monotonicity #393 #376]: #841
+#847 := [trans #842 #845]: #846
+#850 := [monotonicity #847]: #849
+#855 := [monotonicity #850]: #854
+#858 := [trans #855 #857]: #854
+#853 := [quant-inst]: #852
+#859 := [mp #853 #858]: #851
+#934 := [unit-resolution #859 #840]: #848
+#893 := (or #843 #405)
+#894 := [def-axiom]: #893
+#935 := [unit-resolution #894 #934]: #405
+#938 := (or #389 #400)
+#41 := (+ #40 1::int)
+#42 := (uf_1 #41)
+#43 := (up_3 #42)
+#193 := (iff #43 #192)
+#190 := (= #42 #189)
+#187 := (= #41 #186)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#194 := [monotonicity #191]: #193
+#185 := [asserted]: #43
+#197 := [mp #185 #194]: #192
+#889 := (or #389 #429 #400)
+#890 := [def-axiom]: #889
+#939 := [unit-resolution #890 #197]: #938
+#940 := [unit-resolution #939 #935]: #400
+#881 := (or #409 #874)
+#882 := [def-axiom]: #881
+#941 := [unit-resolution #882 #940]: #874
+#555 := -1::int
+#525 := (* -1::int #524)
+#528 := (+ #40 #525)
+#494 := (>= #528 -1::int)
+#510 := (= #528 -1::int)
+#514 := (>= #40 -1::int)
+#495 := (= #524 0::int)
+#946 := (not #495)
+#467 := (<= #524 0::int)
+#942 := (not #467)
+#943 := (or #942 #452)
+#944 := [th-lemma]: #943
+#945 := [unit-resolution #944 #941]: #942
+#947 := (or #946 #467)
+#948 := [th-lemma]: #947
+#949 := [unit-resolution #948 #945]: #946
+#498 := (or #495 #514)
+#10 := (:var 0 int)
+#12 := (uf_1 #10)
+#796 := (pattern #12)
+#87 := (>= #10 0::int)
+#13 := (uf_2 #12)
+#18 := (= #13 0::int)
+#135 := (or #18 #87)
+#803 := (forall (vars (?x3 int)) (:pat #796) #135)
+#140 := (forall (vars (?x3 int)) #135)
+#806 := (iff #140 #803)
+#804 := (iff #135 #135)
+#805 := [refl]: #804
+#807 := [quant-intro #805]: #806
+#207 := (~ #140 #140)
+#225 := (~ #135 #135)
+#226 := [refl]: #225
+#208 := [nnf-pos #226]: #207
+#17 := (< #10 0::int)
+#19 := (implies #17 #18)
+#20 := (forall (vars (?x3 int)) #19)
+#143 := (iff #20 #140)
+#106 := (= 0::int #13)
+#112 := (not #17)
+#113 := (or #112 #106)
+#118 := (forall (vars (?x3 int)) #113)
+#141 := (iff #118 #140)
+#138 := (iff #113 #135)
+#132 := (or #87 #18)
+#136 := (iff #132 #135)
+#137 := [rewrite]: #136
+#133 := (iff #113 #132)
+#130 := (iff #106 #18)
+#131 := [rewrite]: #130
+#128 := (iff #112 #87)
+#88 := (not #87)
+#123 := (not #88)
+#126 := (iff #123 #87)
+#127 := [rewrite]: #126
+#124 := (iff #112 #123)
+#121 := (iff #17 #88)
+#122 := [rewrite]: #121
+#125 := [monotonicity #122]: #124
+#129 := [trans #125 #127]: #128
+#134 := [monotonicity #129 #131]: #133
+#139 := [trans #134 #137]: #138
+#142 := [quant-intro #139]: #141
+#119 := (iff #20 #118)
+#116 := (iff #19 #113)
+#109 := (implies #17 #106)
+#114 := (iff #109 #113)
+#115 := [rewrite]: #114
+#110 := (iff #19 #109)
+#107 := (iff #18 #106)
+#108 := [rewrite]: #107
+#111 := [monotonicity #108]: #110
+#117 := [trans #111 #115]: #116
+#120 := [quant-intro #117]: #119
+#144 := [trans #120 #142]: #143
+#105 := [asserted]: #20
+#145 := [mp #105 #144]: #140
+#227 := [mp~ #145 #208]: #140
+#808 := [mp #227 #807]: #803
+#532 := (not #803)
+#488 := (or #532 #495 #514)
+#529 := (>= #186 0::int)
+#496 := (or #495 #529)
+#489 := (or #532 #496)
+#474 := (iff #489 #488)
+#482 := (or #532 #498)
+#483 := (iff #482 #488)
+#493 := [rewrite]: #483
+#491 := (iff #489 #482)
+#497 := (iff #496 #498)
+#515 := (iff #529 #514)
+#516 := [rewrite]: #515
+#499 := [monotonicity #516]: #497
+#492 := [monotonicity #499]: #491
+#475 := [trans #492 #493]: #474
+#490 := [quant-inst]: #489
+#476 := [mp #490 #475]: #488
+#950 := [unit-resolution #476 #808]: #498
+#951 := [unit-resolution #950 #949]: #514
+#517 := (not #514)
+#520 := (or #510 #517)
+#69 := (= #10 #13)
+#94 := (or #69 #88)
+#797 := (forall (vars (?x2 int)) (:pat #796) #94)
+#99 := (forall (vars (?x2 int)) #94)
+#800 := (iff #99 #797)
+#798 := (iff #94 #94)
+#799 := [refl]: #798
+#801 := [quant-intro #799]: #800
+#206 := (~ #99 #99)
+#222 := (~ #94 #94)
+#223 := [refl]: #222
+#196 := [nnf-pos #223]: #206
+#14 := (= #13 #10)
+#11 := (<= 0::int #10)
+#15 := (implies #11 #14)
+#16 := (forall (vars (?x2 int)) #15)
+#102 := (iff #16 #99)
+#76 := (not #11)
+#77 := (or #76 #69)
+#82 := (forall (vars (?x2 int)) #77)
+#100 := (iff #82 #99)
+#97 := (iff #77 #94)
+#91 := (or #88 #69)
+#95 := (iff #91 #94)
+#96 := [rewrite]: #95
+#92 := (iff #77 #91)
+#89 := (iff #76 #88)
+#85 := (iff #11 #87)
+#86 := [rewrite]: #85
+#90 := [monotonicity #86]: #89
+#93 := [monotonicity #90]: #92
+#98 := [trans #93 #96]: #97
+#101 := [quant-intro #98]: #100
+#83 := (iff #16 #82)
+#80 := (iff #15 #77)
+#73 := (implies #11 #69)
+#78 := (iff #73 #77)
+#79 := [rewrite]: #78
+#74 := (iff #15 #73)
+#71 := (iff #14 #69)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#81 := [trans #75 #79]: #80
+#84 := [quant-intro #81]: #83
+#103 := [trans #84 #101]: #102
+#68 := [asserted]: #16
+#104 := [mp #68 #103]: #99
+#224 := [mp~ #104 #196]: #99
+#802 := [mp #224 #801]: #797
+#559 := (not #797)
+#511 := (or #559 #510 #517)
+#531 := (not #529)
+#526 := (= #186 #524)
+#527 := (or #526 #531)
+#523 := (or #559 #527)
+#507 := (iff #523 #511)
+#502 := (or #559 #520)
+#505 := (iff #502 #511)
+#506 := [rewrite]: #505
+#503 := (iff #523 #502)
+#521 := (iff #527 #520)
+#518 := (iff #531 #517)
+#519 := [monotonicity #516]: #518
+#512 := (iff #526 #510)
+#513 := [rewrite]: #512
+#522 := [monotonicity #513 #519]: #521
+#504 := [monotonicity #522]: #503
+#508 := [trans #504 #506]: #507
+#500 := [quant-inst]: #523
+#501 := [mp #500 #508]: #511
+#952 := [unit-resolution #501 #802]: #520
+#953 := [unit-resolution #952 #951]: #510
+#954 := (not #510)
+#955 := (or #954 #494)
+#956 := [th-lemma]: #955
+#957 := [unit-resolution #956 #953]: #494
+#959 := (not #494)
+#960 := (or #958 #452 #959)
+#961 := [th-lemma]: #960
+#962 := [unit-resolution #961 #957 #941]: #958
+#964 := (or #963 #537)
+#965 := [th-lemma]: #964
+#966 := [unit-resolution #965 #962]: #963
+#583 := (>= #38 0::int)
+#584 := (not #583)
+#556 := (* -1::int #40)
+#557 := (+ #38 #556)
+#558 := (= #557 0::int)
+#971 := (not #558)
+#544 := (>= #557 0::int)
+#967 := (not #544)
+#201 := (>= #37 1::int)
+#202 := (not #201)
+#44 := (<= 1::int #37)
+#45 := (not #44)
+#203 := (iff #45 #202)
+#199 := (iff #44 #201)
+#200 := [rewrite]: #199
+#204 := [monotonicity #200]: #203
+#195 := [asserted]: #45
+#205 := [mp #195 #204]: #202
+#968 := (or #967 #201 #452 #959)
+#969 := [th-lemma]: #968
+#970 := [unit-resolution #969 #205 #957 #941]: #967
+#972 := (or #971 #544)
+#973 := [th-lemma]: #972
+#974 := [unit-resolution #973 #970]: #971
+#562 := (or #558 #584)
+#564 := (or #559 #558 #584)
+#567 := (= #38 #40)
+#585 := (or #567 #584)
+#543 := (or #559 #585)
+#542 := (iff #543 #564)
+#550 := (or #559 #562)
+#551 := (iff #550 #564)
+#554 := [rewrite]: #551
+#552 := (iff #543 #550)
+#404 := (iff #585 #562)
+#560 := (iff #567 #558)
+#561 := [rewrite]: #560
+#563 := [monotonicity #561]: #404
+#553 := [monotonicity #563]: #552
+#545 := [trans #553 #554]: #542
+#546 := [quant-inst]: #543
+#547 := [mp #546 #545]: #564
+#975 := [unit-resolution #547 #802]: #562
+#976 := [unit-resolution #975 #974]: #584
+#539 := (or #549 #583)
+#535 := (or #532 #549 #583)
+#536 := (or #532 #539)
+#533 := (iff #536 #535)
+#541 := [rewrite]: #533
+#540 := [quant-inst]: #536
+#534 := [mp #540 #541]: #535
+#977 := [unit-resolution #534 #808]: #539
+[unit-resolution #977 #976 #966]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nlarith_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,10 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Int)
+ (uf_2 Int)
+ )
+:assumption (< 0 uf_1)
+:assumption (< 0 (* uf_1 uf_2))
+:assumption (not (< 0 uf_2))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nlarith_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nlarith_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,9 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Int)
+ (uf_2 Int)
+ (uf_3 Int)
+ )
+:assumption (not (= (* uf_1 (+ (+ uf_2 1) uf_3)) (+ (* uf_1 uf_2) (* uf_1 (+ uf_3 1)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nlarith_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,75 @@
+#2 := false
+#6 := 1::int
+decl uf_3 :: int
+#8 := uf_3
+#12 := (+ uf_3 1::int)
+decl uf_1 :: int
+#4 := uf_1
+#13 := (* uf_1 #12)
+decl uf_2 :: int
+#5 := uf_2
+#11 := (* uf_1 uf_2)
+#14 := (+ #11 #13)
+#7 := (+ uf_2 1::int)
+#9 := (+ #7 uf_3)
+#10 := (* uf_1 #9)
+#15 := (= #10 #14)
+#16 := (not #15)
+#85 := (iff #16 false)
+#1 := true
+#80 := (not true)
+#83 := (iff #80 false)
+#84 := [rewrite]: #83
+#81 := (iff #16 #80)
+#78 := (iff #15 true)
+#48 := (* uf_1 uf_3)
+#49 := (+ #11 #48)
+#50 := (+ uf_1 #49)
+#73 := (= #50 #50)
+#76 := (iff #73 true)
+#77 := [rewrite]: #76
+#74 := (iff #15 #73)
+#71 := (= #14 #50)
+#61 := (+ uf_1 #48)
+#66 := (+ #11 #61)
+#69 := (= #66 #50)
+#70 := [rewrite]: #69
+#67 := (= #14 #66)
+#64 := (= #13 #61)
+#55 := (+ 1::int uf_3)
+#58 := (* uf_1 #55)
+#62 := (= #58 #61)
+#63 := [rewrite]: #62
+#59 := (= #13 #58)
+#56 := (= #12 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#65 := [trans #60 #63]: #64
+#68 := [monotonicity #65]: #67
+#72 := [trans #68 #70]: #71
+#53 := (= #10 #50)
+#39 := (+ uf_2 uf_3)
+#40 := (+ 1::int #39)
+#45 := (* uf_1 #40)
+#51 := (= #45 #50)
+#52 := [rewrite]: #51
+#46 := (= #10 #45)
+#43 := (= #9 #40)
+#33 := (+ 1::int uf_2)
+#36 := (+ #33 uf_3)
+#41 := (= #36 #40)
+#42 := [rewrite]: #41
+#37 := (= #9 #36)
+#34 := (= #7 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#44 := [trans #38 #42]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#75 := [monotonicity #54 #72]: #74
+#79 := [trans #75 #77]: #78
+#82 := [monotonicity #79]: #81
+#86 := [trans #82 #84]: #85
+#32 := [asserted]: #16
+[mp #32 #86]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nlarith_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Real)
+ (uf_2 Real)
+ )
+:assumption (not (= (- (* uf_1 (+ 1.0 uf_2)) (* uf_1 (- 1.0 uf_2))) (* (* 2.0 uf_1) uf_2)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nlarith_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,62 @@
+#2 := false
+decl uf_2 :: real
+#6 := uf_2
+decl uf_1 :: real
+#4 := uf_1
+#12 := 2::real
+#13 := (* 2::real uf_1)
+#14 := (* #13 uf_2)
+#5 := 1::real
+#9 := (- 1::real uf_2)
+#10 := (* uf_1 #9)
+#7 := (+ 1::real uf_2)
+#8 := (* uf_1 #7)
+#11 := (- #8 #10)
+#15 := (= #11 #14)
+#16 := (not #15)
+#73 := (iff #16 false)
+#1 := true
+#68 := (not true)
+#71 := (iff #68 false)
+#72 := [rewrite]: #71
+#69 := (iff #16 #68)
+#66 := (iff #15 true)
+#33 := (* uf_1 uf_2)
+#55 := (* 2::real #33)
+#61 := (= #55 #55)
+#64 := (iff #61 true)
+#65 := [rewrite]: #64
+#62 := (iff #15 #61)
+#59 := (= #14 #55)
+#60 := [rewrite]: #59
+#57 := (= #11 #55)
+#37 := -1::real
+#45 := (* -1::real #33)
+#46 := (+ uf_1 #45)
+#34 := (+ uf_1 #33)
+#51 := (- #34 #46)
+#54 := (= #51 #55)
+#56 := [rewrite]: #54
+#52 := (= #11 #51)
+#49 := (= #10 #46)
+#38 := (* -1::real uf_2)
+#39 := (+ 1::real #38)
+#42 := (* uf_1 #39)
+#47 := (= #42 #46)
+#48 := [rewrite]: #47
+#43 := (= #10 #42)
+#40 := (= #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#50 := [trans #44 #48]: #49
+#35 := (= #8 #34)
+#36 := [rewrite]: #35
+#53 := [monotonicity #36 #50]: #52
+#58 := [trans #53 #56]: #57
+#63 := [monotonicity #58 #60]: #62
+#67 := [trans #63 #65]: #66
+#70 := [monotonicity #67]: #69
+#74 := [trans #70 #72]: #73
+#32 := [asserted]: #16
+[mp #32 #74]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nlarith_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,11 @@
+(benchmark Isabelle
+:extrafuns (
+ (uf_1 Int)
+ (uf_3 Int)
+ (uf_5 Int)
+ (uf_4 Int)
+ (uf_2 Int)
+ )
+:assumption (not (= (+ (+ uf_1 (* (+ 1 uf_2) (+ uf_3 uf_4))) (* uf_2 uf_5)) (- (+ uf_1 (+ (+ (* (* 2 (+ 1 uf_2)) (+ uf_3 uf_4)) (* (+ 1 uf_2) uf_5)) (* uf_5 uf_2))) (* (+ 1 uf_2) (+ (+ uf_3 uf_5) uf_4)))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_nlarith_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,141 @@
+#2 := false
+decl uf_4 :: int
+#9 := uf_4
+decl uf_5 :: int
+#13 := uf_5
+decl uf_3 :: int
+#8 := uf_3
+#24 := (+ uf_3 uf_5)
+#25 := (+ #24 uf_4)
+decl uf_2 :: int
+#6 := uf_2
+#5 := 1::int
+#7 := (+ 1::int uf_2)
+#26 := (* #7 #25)
+#21 := (* uf_5 uf_2)
+#19 := (* #7 uf_5)
+#10 := (+ uf_3 uf_4)
+#16 := 2::int
+#17 := (* 2::int #7)
+#18 := (* #17 #10)
+#20 := (+ #18 #19)
+#22 := (+ #20 #21)
+decl uf_1 :: int
+#4 := uf_1
+#23 := (+ uf_1 #22)
+#27 := (- #23 #26)
+#14 := (* uf_2 uf_5)
+#11 := (* #7 #10)
+#12 := (+ uf_1 #11)
+#15 := (+ #12 #14)
+#28 := (= #15 #27)
+#29 := (not #28)
+#149 := (iff #29 false)
+#1 := true
+#144 := (not true)
+#147 := (iff #144 false)
+#148 := [rewrite]: #147
+#145 := (iff #29 #144)
+#142 := (iff #28 true)
+#47 := (* uf_2 uf_4)
+#46 := (* uf_2 uf_3)
+#48 := (+ #46 #47)
+#59 := (+ #14 #48)
+#60 := (+ uf_4 #59)
+#61 := (+ uf_3 #60)
+#62 := (+ uf_1 #61)
+#136 := (= #62 #62)
+#140 := (iff #136 true)
+#141 := [rewrite]: #140
+#135 := (iff #28 #136)
+#138 := (= #27 #62)
+#123 := (+ uf_5 #59)
+#124 := (+ uf_4 #123)
+#125 := (+ uf_3 #124)
+#77 := (* 2::int #47)
+#75 := (* 2::int #46)
+#78 := (+ #75 #77)
+#104 := (* 2::int #14)
+#105 := (+ #104 #78)
+#106 := (+ uf_5 #105)
+#76 := (* 2::int uf_4)
+#107 := (+ #76 #106)
+#74 := (* 2::int uf_3)
+#108 := (+ #74 #107)
+#113 := (+ uf_1 #108)
+#130 := (- #113 #125)
+#133 := (= #130 #62)
+#139 := [rewrite]: #133
+#131 := (= #27 #130)
+#128 := (= #26 #125)
+#116 := (+ uf_4 uf_5)
+#117 := (+ uf_3 #116)
+#120 := (* #7 #117)
+#126 := (= #120 #125)
+#127 := [rewrite]: #126
+#121 := (= #26 #120)
+#118 := (= #25 #117)
+#119 := [rewrite]: #118
+#122 := [monotonicity #119]: #121
+#129 := [trans #122 #127]: #128
+#114 := (= #23 #113)
+#111 := (= #22 #108)
+#91 := (+ #14 #78)
+#92 := (+ uf_5 #91)
+#93 := (+ #76 #92)
+#94 := (+ #74 #93)
+#101 := (+ #94 #14)
+#109 := (= #101 #108)
+#110 := [rewrite]: #109
+#102 := (= #22 #101)
+#99 := (= #21 #14)
+#100 := [rewrite]: #99
+#97 := (= #20 #94)
+#85 := (+ uf_5 #14)
+#79 := (+ #76 #78)
+#80 := (+ #74 #79)
+#88 := (+ #80 #85)
+#95 := (= #88 #94)
+#96 := [rewrite]: #95
+#89 := (= #20 #88)
+#86 := (= #19 #85)
+#87 := [rewrite]: #86
+#83 := (= #18 #80)
+#67 := (* 2::int uf_2)
+#68 := (+ 2::int #67)
+#71 := (* #68 #10)
+#81 := (= #71 #80)
+#82 := [rewrite]: #81
+#72 := (= #18 #71)
+#69 := (= #17 #68)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#84 := [trans #73 #82]: #83
+#90 := [monotonicity #84 #87]: #89
+#98 := [trans #90 #96]: #97
+#103 := [monotonicity #98 #100]: #102
+#112 := [trans #103 #110]: #111
+#115 := [monotonicity #112]: #114
+#132 := [monotonicity #115 #129]: #131
+#137 := [trans #132 #139]: #138
+#65 := (= #15 #62)
+#49 := (+ uf_4 #48)
+#50 := (+ uf_3 #49)
+#53 := (+ uf_1 #50)
+#56 := (+ #53 #14)
+#63 := (= #56 #62)
+#64 := [rewrite]: #63
+#57 := (= #15 #56)
+#54 := (= #12 #53)
+#51 := (= #11 #50)
+#52 := [rewrite]: #51
+#55 := [monotonicity #52]: #54
+#58 := [monotonicity #55]: #57
+#66 := [trans #58 #64]: #65
+#134 := [monotonicity #66 #137]: #135
+#143 := [trans #134 #141]: #142
+#146 := [monotonicity #143]: #145
+#150 := [trans #146 #148]: #149
+#45 := [asserted]: #29
+[mp #45 #150]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_pair_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,17 @@
+(benchmark Isabelle
+:extrasorts ( T2 T3 T1)
+:extrafuns (
+ (uf_2 T1 T2)
+ (uf_3 T1 T3)
+ (uf_1 T2 T3 T1)
+ (uf_6 T2)
+ (uf_4 T2)
+ (uf_5 T3)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1) (uf_3 ?x1)) ?x1))
+:assumption (forall (?x2 T2) (?x3 T3) (= (uf_3 (uf_1 ?x2 ?x3)) ?x3))
+:assumption (forall (?x4 T2) (?x5 T3) (= (uf_2 (uf_1 ?x4 ?x5)) ?x4))
+:assumption (= (uf_2 (uf_1 uf_4 uf_5)) uf_6)
+:assumption (not (= uf_4 uf_6))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_pair_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,50 @@
+#2 := false
+decl uf_6 :: T2
+#23 := uf_6
+decl uf_4 :: T2
+#19 := uf_4
+#25 := (= uf_4 uf_6)
+decl uf_2 :: (-> T1 T2)
+decl uf_1 :: (-> T2 T3 T1)
+decl uf_5 :: T3
+#20 := uf_5
+#21 := (uf_1 uf_4 uf_5)
+#22 := (uf_2 #21)
+#24 := (= #22 uf_6)
+#65 := [asserted]: #24
+#143 := (= uf_4 #22)
+#11 := (:var 0 T3)
+#10 := (:var 1 T2)
+#12 := (uf_1 #10 #11)
+#567 := (pattern #12)
+#16 := (uf_2 #12)
+#58 := (= #10 #16)
+#574 := (forall (vars (?x4 T2) (?x5 T3)) (:pat #567) #58)
+#62 := (forall (vars (?x4 T2) (?x5 T3)) #58)
+#577 := (iff #62 #574)
+#575 := (iff #58 #58)
+#576 := [refl]: #575
+#578 := [quant-intro #576]: #577
+#71 := (~ #62 #62)
+#87 := (~ #58 #58)
+#88 := [refl]: #87
+#72 := [nnf-pos #88]: #71
+#17 := (= #16 #10)
+#18 := (forall (vars (?x4 T2) (?x5 T3)) #17)
+#63 := (iff #18 #62)
+#60 := (iff #17 #58)
+#61 := [rewrite]: #60
+#64 := [quant-intro #61]: #63
+#57 := [asserted]: #18
+#67 := [mp #57 #64]: #62
+#89 := [mp~ #67 #72]: #62
+#579 := [mp #89 #578]: #574
+#214 := (not #574)
+#551 := (or #214 #143)
+#553 := [quant-inst]: #551
+#233 := [unit-resolution #553 #579]: #143
+#235 := [trans #233 #65]: #25
+#26 := (not #25)
+#66 := [asserted]: #26
+[unit-resolution #66 #235]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_pair_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,24 @@
+(benchmark Isabelle
+:extrasorts ( T2 T3 T1 T4)
+:extrafuns (
+ (uf_2 T1 T2)
+ (uf_5 T4 T3)
+ (uf_3 T1 T3)
+ (uf_6 T4 T2)
+ (uf_1 T2 T3 T1)
+ (uf_4 T3 T2 T4)
+ (uf_8 T2)
+ (uf_9 T3)
+ (uf_7 T1)
+ (uf_10 T4)
+ )
+:assumption (forall (?x1 T1) (= (uf_1 (uf_2 ?x1) (uf_3 ?x1)) ?x1))
+:assumption (forall (?x2 T4) (= (uf_4 (uf_5 ?x2) (uf_6 ?x2)) ?x2))
+:assumption (forall (?x3 T2) (?x4 T3) (= (uf_3 (uf_1 ?x3 ?x4)) ?x4))
+:assumption (forall (?x5 T3) (?x6 T2) (= (uf_6 (uf_4 ?x5 ?x6)) ?x6))
+:assumption (forall (?x7 T2) (?x8 T3) (= (uf_2 (uf_1 ?x7 ?x8)) ?x7))
+:assumption (forall (?x9 T3) (?x10 T2) (= (uf_5 (uf_4 ?x9 ?x10)) ?x9))
+:assumption (and (= uf_7 (uf_1 uf_8 uf_9)) (= uf_10 (uf_4 uf_9 uf_8)))
+:assumption (not (= (uf_2 uf_7) (uf_6 uf_10)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_pair_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,105 @@
+#2 := false
+decl uf_6 :: (-> T4 T2)
+decl uf_10 :: T4
+#39 := uf_10
+#44 := (uf_6 uf_10)
+decl uf_2 :: (-> T1 T2)
+decl uf_7 :: T1
+#34 := uf_7
+#43 := (uf_2 uf_7)
+#45 := (= #43 #44)
+decl uf_4 :: (-> T3 T2 T4)
+decl uf_8 :: T2
+#35 := uf_8
+decl uf_9 :: T3
+#36 := uf_9
+#40 := (uf_4 uf_9 uf_8)
+#204 := (uf_6 #40)
+#598 := (= #204 #44)
+#595 := (= #44 #204)
+#41 := (= uf_10 #40)
+decl uf_1 :: (-> T2 T3 T1)
+#37 := (uf_1 uf_8 uf_9)
+#38 := (= uf_7 #37)
+#42 := (and #38 #41)
+#109 := [asserted]: #42
+#114 := [and-elim #109]: #41
+#256 := [monotonicity #114]: #595
+#599 := [symm #256]: #598
+#596 := (= #43 #204)
+#269 := (= uf_8 #204)
+#23 := (:var 0 T2)
+#22 := (:var 1 T3)
+#24 := (uf_4 #22 #23)
+#643 := (pattern #24)
+#25 := (uf_6 #24)
+#86 := (= #23 #25)
+#644 := (forall (vars (?x5 T3) (?x6 T2)) (:pat #643) #86)
+#90 := (forall (vars (?x5 T3) (?x6 T2)) #86)
+#647 := (iff #90 #644)
+#645 := (iff #86 #86)
+#646 := [refl]: #645
+#648 := [quant-intro #646]: #647
+#119 := (~ #90 #90)
+#144 := (~ #86 #86)
+#145 := [refl]: #144
+#120 := [nnf-pos #145]: #119
+#26 := (= #25 #23)
+#27 := (forall (vars (?x5 T3) (?x6 T2)) #26)
+#91 := (iff #27 #90)
+#88 := (iff #26 #86)
+#89 := [rewrite]: #88
+#92 := [quant-intro #89]: #91
+#85 := [asserted]: #27
+#95 := [mp #85 #92]: #90
+#146 := [mp~ #95 #120]: #90
+#649 := [mp #146 #648]: #644
+#613 := (not #644)
+#619 := (or #613 #269)
+#609 := [quant-inst]: #619
+#267 := [unit-resolution #609 #649]: #269
+#600 := (= #43 uf_8)
+#289 := (uf_2 #37)
+#259 := (= #289 uf_8)
+#296 := (= uf_8 #289)
+#17 := (:var 0 T3)
+#16 := (:var 1 T2)
+#18 := (uf_1 #16 #17)
+#636 := (pattern #18)
+#28 := (uf_2 #18)
+#94 := (= #16 #28)
+#650 := (forall (vars (?x7 T2) (?x8 T3)) (:pat #636) #94)
+#98 := (forall (vars (?x7 T2) (?x8 T3)) #94)
+#653 := (iff #98 #650)
+#651 := (iff #94 #94)
+#652 := [refl]: #651
+#654 := [quant-intro #652]: #653
+#121 := (~ #98 #98)
+#147 := (~ #94 #94)
+#148 := [refl]: #147
+#122 := [nnf-pos #148]: #121
+#29 := (= #28 #16)
+#30 := (forall (vars (?x7 T2) (?x8 T3)) #29)
+#99 := (iff #30 #98)
+#96 := (iff #29 #94)
+#97 := [rewrite]: #96
+#100 := [quant-intro #97]: #99
+#93 := [asserted]: #30
+#103 := [mp #93 #100]: #98
+#149 := [mp~ #103 #122]: #98
+#655 := [mp #149 #654]: #650
+#615 := (not #650)
+#616 := (or #615 #296)
+#617 := [quant-inst]: #616
+#618 := [unit-resolution #617 #655]: #296
+#597 := [symm #618]: #259
+#611 := (= #43 #289)
+#113 := [and-elim #109]: #38
+#252 := [monotonicity #113]: #611
+#601 := [trans #252 #597]: #600
+#602 := [trans #601 #267]: #596
+#238 := [trans #602 #599]: #45
+#46 := (not #45)
+#110 := [asserted]: #46
+[unit-resolution #110 #238]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_01 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,4 @@
+(benchmark Isabelle
+:assumption (not true)
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_01.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+#2 := false
+#1 := true
+#4 := (not true)
+#21 := (iff #4 false)
+#22 := [rewrite]: #21
+#20 := [asserted]: #4
+[mp #20 #22]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_02 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1)
+ )
+:assumption (not (or up_1 (not up_1)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_02.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,19 @@
+#2 := false
+decl up_1 :: bool
+#4 := up_1
+#5 := (not up_1)
+#6 := (or up_1 #5)
+#7 := (not #6)
+#31 := (iff #7 false)
+#1 := true
+#26 := (not true)
+#29 := (iff #26 false)
+#30 := [rewrite]: #29
+#27 := (iff #7 #26)
+#24 := (iff #6 true)
+#25 := [rewrite]: #24
+#28 := [monotonicity #25]: #27
+#32 := [trans #28 #30]: #31
+#23 := [asserted]: #7
+[mp #23 #32]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_03 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1)
+ )
+:assumption (not (iff (and up_1 true) up_1))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_03.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,25 @@
+#2 := false
+decl up_1 :: bool
+#4 := up_1
+#1 := true
+#5 := (and up_1 true)
+#6 := (iff #5 up_1)
+#7 := (not #6)
+#37 := (iff #7 false)
+#32 := (not true)
+#35 := (iff #32 false)
+#36 := [rewrite]: #35
+#33 := (iff #7 #32)
+#30 := (iff #6 true)
+#25 := (iff up_1 up_1)
+#28 := (iff #25 true)
+#29 := [rewrite]: #28
+#26 := (iff #6 #25)
+#24 := [rewrite]: #6
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#23 := [asserted]: #7
+[mp #23 #38]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_04 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,10 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1)
+ (up_2)
+ )
+:assumption (and (or up_1 up_2) (not up_1))
+:assumption (not up_2)
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_04.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,38 @@
+#2 := false
+decl up_2 :: bool
+#5 := up_2
+decl up_1 :: bool
+#4 := up_1
+#6 := (or up_1 up_2)
+#51 := (iff #6 false)
+#46 := (or false false)
+#49 := (iff #46 false)
+#50 := [rewrite]: #49
+#47 := (iff #6 #46)
+#40 := (iff up_2 false)
+#9 := (not up_2)
+#43 := (iff #9 #40)
+#41 := (iff #40 #9)
+#42 := [rewrite]: #41
+#44 := [symm #42]: #43
+#32 := [asserted]: #9
+#45 := [mp #32 #44]: #40
+#35 := (iff up_1 false)
+#7 := (not up_1)
+#37 := (iff #7 #35)
+#33 := (iff #35 #7)
+#36 := [rewrite]: #33
+#38 := [symm #36]: #37
+#26 := (and #7 #6)
+#8 := (and #6 #7)
+#27 := (iff #8 #26)
+#28 := [rewrite]: #27
+#25 := [asserted]: #8
+#31 := [mp #25 #28]: #26
+#29 := [and-elim #31]: #7
+#39 := [mp #29 #38]: #35
+#48 := [monotonicity #39 #45]: #47
+#52 := [trans #48 #50]: #51
+#30 := [and-elim #31]: #6
+[mp #30 #52]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_05 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,12 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1)
+ (up_2)
+ (up_3)
+ (up_4)
+ )
+:assumption (or (and up_1 up_2) (and up_3 up_4))
+:assumption (not (or (and up_1 up_2) (and up_3 up_4)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_05.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1 @@
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_06 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,10 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1)
+ (up_2)
+ (up_3)
+ )
+:assumption (not (implies (or (and up_1 up_2) up_3) (or (implies up_1 (or (and up_3 up_2) (and up_1 up_3))) up_1)))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_06.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,71 @@
+#2 := false
+decl up_1 :: bool
+#4 := up_1
+decl up_3 :: bool
+#7 := up_3
+#10 := (and up_1 up_3)
+decl up_2 :: bool
+#5 := up_2
+#9 := (and up_3 up_2)
+#11 := (or #9 #10)
+#12 := (implies up_1 #11)
+#13 := (or #12 up_1)
+#6 := (and up_1 up_2)
+#8 := (or #6 up_3)
+#14 := (implies #8 #13)
+#15 := (not #14)
+#81 := (iff #15 false)
+#32 := (and up_2 up_3)
+#38 := (or #10 #32)
+#46 := (not up_1)
+#47 := (or #46 #38)
+#55 := (or up_1 #47)
+#63 := (not #8)
+#64 := (or #63 #55)
+#69 := (not #64)
+#79 := (iff #69 false)
+#1 := true
+#74 := (not true)
+#77 := (iff #74 false)
+#78 := [rewrite]: #77
+#75 := (iff #69 #74)
+#72 := (iff #64 true)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#70 := (iff #15 #69)
+#67 := (iff #14 #64)
+#60 := (implies #8 #55)
+#65 := (iff #60 #64)
+#66 := [rewrite]: #65
+#61 := (iff #14 #60)
+#58 := (iff #13 #55)
+#52 := (or #47 up_1)
+#56 := (iff #52 #55)
+#57 := [rewrite]: #56
+#53 := (iff #13 #52)
+#50 := (iff #12 #47)
+#43 := (implies up_1 #38)
+#48 := (iff #43 #47)
+#49 := [rewrite]: #48
+#44 := (iff #12 #43)
+#41 := (iff #11 #38)
+#35 := (or #32 #10)
+#39 := (iff #35 #38)
+#40 := [rewrite]: #39
+#36 := (iff #11 #35)
+#33 := (iff #9 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#42 := [trans #37 #40]: #41
+#45 := [monotonicity #42]: #44
+#51 := [trans #45 #49]: #50
+#54 := [monotonicity #51]: #53
+#59 := [trans #54 #57]: #58
+#62 := [monotonicity #59]: #61
+#68 := [trans #62 #66]: #67
+#71 := [monotonicity #68]: #70
+#82 := [trans #71 #80]: #81
+#31 := [asserted]: #15
+[mp #31 #82]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_07 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,8 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1)
+ )
+:assumption (not (iff (iff (iff (iff (iff (iff (iff (iff (iff up_1 up_1) up_1) up_1) up_1) up_1) up_1) up_1) up_1) up_1))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_07.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,57 @@
+#2 := false
+decl up_1 :: bool
+#4 := up_1
+#5 := (iff up_1 up_1)
+#6 := (iff #5 up_1)
+#7 := (iff #6 up_1)
+#8 := (iff #7 up_1)
+#9 := (iff #8 up_1)
+#10 := (iff #9 up_1)
+#11 := (iff #10 up_1)
+#12 := (iff #11 up_1)
+#13 := (iff #12 up_1)
+#14 := (not #13)
+#69 := (iff #14 false)
+#1 := true
+#64 := (not true)
+#67 := (iff #64 false)
+#68 := [rewrite]: #67
+#65 := (iff #14 #64)
+#62 := (iff #13 true)
+#31 := (iff #5 true)
+#32 := [rewrite]: #31
+#60 := (iff #13 #5)
+#33 := (iff true up_1)
+#36 := (iff #33 up_1)
+#37 := [rewrite]: #36
+#57 := (iff #12 #33)
+#55 := (iff #11 true)
+#53 := (iff #11 #5)
+#50 := (iff #10 #33)
+#48 := (iff #9 true)
+#46 := (iff #9 #5)
+#43 := (iff #8 #33)
+#41 := (iff #7 true)
+#39 := (iff #7 #5)
+#34 := (iff #6 #33)
+#35 := [monotonicity #32]: #34
+#38 := [trans #35 #37]: #7
+#40 := [monotonicity #38]: #39
+#42 := [trans #40 #32]: #41
+#44 := [monotonicity #42]: #43
+#45 := [trans #44 #37]: #9
+#47 := [monotonicity #45]: #46
+#49 := [trans #47 #32]: #48
+#51 := [monotonicity #49]: #50
+#52 := [trans #51 #37]: #11
+#54 := [monotonicity #52]: #53
+#56 := [trans #54 #32]: #55
+#58 := [monotonicity #56]: #57
+#59 := [trans #58 #37]: #13
+#61 := [monotonicity #59]: #60
+#63 := [trans #61 #32]: #62
+#66 := [monotonicity #63]: #65
+#70 := [trans #66 #68]: #69
+#30 := [asserted]: #14
+[mp #30 #70]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_08 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,22 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1)
+ (up_2)
+ (up_3)
+ (up_4)
+ (up_5)
+ (up_6)
+ (up_8)
+ (up_9)
+ (up_7)
+ )
+:assumption (or up_1 (or up_2 (or up_3 up_4)))
+:assumption (or up_5 (or up_6 (and up_1 up_4)))
+:assumption (or (not (or up_1 (and up_3 (not up_3)))) up_2)
+:assumption (or (not (and up_2 (or up_7 (not up_7)))) up_3)
+:assumption (or (not (or up_4 false)) up_3)
+:assumption (not (or up_3 (and (not up_8) (or up_8 (and up_9 (not up_9))))))
+:assumption (not false)
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_08.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,194 @@
+#2 := false
+decl up_1 :: bool
+#4 := up_1
+#75 := (not up_1)
+#246 := (iff #75 false)
+#1 := true
+#214 := (not true)
+#217 := (iff #214 false)
+#218 := [rewrite]: #217
+#244 := (iff #75 #214)
+#238 := (iff up_1 true)
+#241 := (iff up_1 #238)
+#239 := (iff #238 up_1)
+#240 := [rewrite]: #239
+#242 := [symm #240]: #241
+decl up_4 :: bool
+#7 := up_4
+decl up_2 :: bool
+#5 := up_2
+#161 := (or up_1 up_2 up_4)
+#200 := (iff #161 up_1)
+#195 := (or up_1 false false)
+#198 := (iff #195 up_1)
+#199 := [rewrite]: #198
+#196 := (iff #161 #195)
+#189 := (iff up_4 false)
+#102 := (not up_4)
+#192 := (iff #102 #189)
+#190 := (iff #189 #102)
+#191 := [rewrite]: #190
+#193 := [symm #191]: #192
+decl up_3 :: bool
+#6 := up_3
+#108 := (or up_3 #102)
+#180 := (iff #108 #102)
+#175 := (or false #102)
+#178 := (iff #175 #102)
+#179 := [rewrite]: #178
+#176 := (iff #108 #175)
+#152 := (iff up_3 false)
+#16 := (not up_3)
+#155 := (iff #16 #152)
+#153 := (iff #152 #16)
+#154 := [rewrite]: #153
+#156 := [symm #154]: #155
+decl up_9 :: bool
+#32 := up_9
+#33 := (not up_9)
+#34 := (and up_9 #33)
+decl up_8 :: bool
+#30 := up_8
+#35 := (or up_8 #34)
+#31 := (not up_8)
+#36 := (and #31 #35)
+#37 := (or up_3 #36)
+#38 := (not #37)
+#138 := (iff #38 #16)
+#136 := (iff #37 up_3)
+#131 := (or up_3 false)
+#134 := (iff #131 up_3)
+#135 := [rewrite]: #134
+#132 := (iff #37 #131)
+#129 := (iff #36 false)
+#124 := (and #31 up_8)
+#127 := (iff #124 false)
+#128 := [rewrite]: #127
+#125 := (iff #36 #124)
+#122 := (iff #35 up_8)
+#117 := (or up_8 false)
+#120 := (iff #117 up_8)
+#121 := [rewrite]: #120
+#118 := (iff #35 #117)
+#114 := (iff #34 false)
+#116 := [rewrite]: #114
+#119 := [monotonicity #116]: #118
+#123 := [trans #119 #121]: #122
+#126 := [monotonicity #123]: #125
+#130 := [trans #126 #128]: #129
+#133 := [monotonicity #130]: #132
+#137 := [trans #133 #135]: #136
+#139 := [monotonicity #137]: #138
+#113 := [asserted]: #38
+#142 := [mp #113 #139]: #16
+#157 := [mp #142 #156]: #152
+#177 := [monotonicity #157]: #176
+#181 := [trans #177 #179]: #180
+#27 := (or up_4 false)
+#28 := (not #27)
+#29 := (or #28 up_3)
+#111 := (iff #29 #108)
+#105 := (or #102 up_3)
+#109 := (iff #105 #108)
+#110 := [rewrite]: #109
+#106 := (iff #29 #105)
+#103 := (iff #28 #102)
+#99 := (iff #27 up_4)
+#101 := [rewrite]: #99
+#104 := [monotonicity #101]: #103
+#107 := [monotonicity #104]: #106
+#112 := [trans #107 #110]: #111
+#98 := [asserted]: #29
+#115 := [mp #98 #112]: #108
+#182 := [mp #115 #181]: #102
+#194 := [mp #182 #193]: #189
+#183 := (iff up_2 false)
+#92 := (not up_2)
+#186 := (iff #92 #183)
+#184 := (iff #183 #92)
+#185 := [rewrite]: #184
+#187 := [symm #185]: #186
+#95 := (or #92 up_3)
+#172 := (iff #95 #92)
+#167 := (or #92 false)
+#170 := (iff #167 #92)
+#171 := [rewrite]: #170
+#168 := (iff #95 #167)
+#169 := [monotonicity #157]: #168
+#173 := [trans #169 #171]: #172
+decl up_7 :: bool
+#21 := up_7
+#22 := (not up_7)
+#23 := (or up_7 #22)
+#24 := (and up_2 #23)
+#25 := (not #24)
+#26 := (or #25 up_3)
+#96 := (iff #26 #95)
+#93 := (iff #25 #92)
+#90 := (iff #24 up_2)
+#85 := (and up_2 true)
+#88 := (iff #85 up_2)
+#89 := [rewrite]: #88
+#86 := (iff #24 #85)
+#82 := (iff #23 true)
+#84 := [rewrite]: #82
+#87 := [monotonicity #84]: #86
+#91 := [trans #87 #89]: #90
+#94 := [monotonicity #91]: #93
+#97 := [monotonicity #94]: #96
+#81 := [asserted]: #26
+#100 := [mp #81 #97]: #95
+#174 := [mp #100 #173]: #92
+#188 := [mp #174 #187]: #183
+#197 := [monotonicity #188 #194]: #196
+#201 := [trans #197 #199]: #200
+#58 := (or up_1 up_2 up_3 up_4)
+#164 := (iff #58 #161)
+#158 := (or up_1 up_2 false up_4)
+#162 := (iff #158 #161)
+#163 := [rewrite]: #162
+#159 := (iff #58 #158)
+#160 := [monotonicity #157]: #159
+#165 := [trans #160 #163]: #164
+#8 := (or up_3 up_4)
+#9 := (or up_2 #8)
+#10 := (or up_1 #9)
+#59 := (iff #10 #58)
+#60 := [rewrite]: #59
+#55 := [asserted]: #10
+#61 := [mp #55 #60]: #58
+#166 := [mp #61 #165]: #161
+#202 := [mp #166 #201]: up_1
+#243 := [mp #202 #242]: #238
+#245 := [monotonicity #243]: #244
+#247 := [trans #245 #218]: #246
+#78 := (or #75 up_2)
+#235 := (iff #78 #75)
+#230 := (or #75 false)
+#233 := (iff #230 #75)
+#234 := [rewrite]: #233
+#231 := (iff #78 #230)
+#232 := [monotonicity #188]: #231
+#236 := [trans #232 #234]: #235
+#17 := (and up_3 #16)
+#18 := (or up_1 #17)
+#19 := (not #18)
+#20 := (or #19 up_2)
+#79 := (iff #20 #78)
+#76 := (iff #19 #75)
+#73 := (iff #18 up_1)
+#68 := (or up_1 false)
+#71 := (iff #68 up_1)
+#72 := [rewrite]: #71
+#69 := (iff #18 #68)
+#62 := (iff #17 false)
+#67 := [rewrite]: #62
+#70 := [monotonicity #67]: #69
+#74 := [trans #70 #72]: #73
+#77 := [monotonicity #74]: #76
+#80 := [monotonicity #77]: #79
+#57 := [asserted]: #20
+#83 := [mp #57 #80]: #78
+#237 := [mp #83 #236]: #75
+[mp #237 #247]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_09 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,11 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrafuns (
+ (uf_1 T1 T1 T1)
+ (uf_2 T1)
+ (uf_3 T1)
+ )
+:assumption (forall (?x1 T1) (?x2 T1) (= (uf_1 ?x1 ?x2) (uf_1 ?x2 ?x1)))
+:assumption (not (and (= uf_2 uf_2) (= (uf_1 uf_2 uf_3) (uf_1 uf_3 uf_2))))
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_09.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,52 @@
+#2 := false
+decl uf_1 :: (-> T1 T1 T1)
+decl uf_2 :: T1
+#10 := uf_2
+decl uf_3 :: T1
+#12 := uf_3
+#14 := (uf_1 uf_3 uf_2)
+#13 := (uf_1 uf_2 uf_3)
+#15 := (= #13 #14)
+#44 := (not #15)
+#11 := (= uf_2 uf_2)
+#16 := (and #11 #15)
+#17 := (not #16)
+#45 := (iff #17 #44)
+#42 := (iff #16 #15)
+#1 := true
+#37 := (and true #15)
+#40 := (iff #37 #15)
+#41 := [rewrite]: #40
+#38 := (iff #16 #37)
+#35 := (iff #11 true)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#34 := [asserted]: #17
+#49 := [mp #34 #46]: #44
+#4 := (:var 1 T1)
+#5 := (:var 0 T1)
+#7 := (uf_1 #5 #4)
+#530 := (pattern #7)
+#6 := (uf_1 #4 #5)
+#529 := (pattern #6)
+#8 := (= #6 #7)
+#531 := (forall (vars (?x1 T1) (?x2 T1)) (:pat #529 #530) #8)
+#9 := (forall (vars (?x1 T1) (?x2 T1)) #8)
+#534 := (iff #9 #531)
+#532 := (iff #8 #8)
+#533 := [refl]: #532
+#535 := [quant-intro #533]: #534
+#55 := (~ #9 #9)
+#53 := (~ #8 #8)
+#54 := [refl]: #53
+#56 := [nnf-pos #54]: #55
+#33 := [asserted]: #9
+#57 := [mp~ #33 #56]: #9
+#536 := [mp #57 #535]: #531
+#112 := (not #531)
+#199 := (or #112 #15)
+#113 := [quant-inst]: #199
+[unit-resolution #113 #536 #49]: false
+unsat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_10 Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,251 @@
+(benchmark Isabelle
+:extrasorts ( T1)
+:extrapreds (
+ (up_1)
+ (up_5)
+ (up_7)
+ (up_9)
+ (up_11)
+ (up_14)
+ (up_16)
+ (up_18)
+ (up_20)
+ (up_22)
+ (up_25)
+ (up_27)
+ (up_29)
+ (up_31)
+ (up_33)
+ (up_36)
+ (up_38)
+ (up_40)
+ (up_42)
+ (up_44)
+ (up_47)
+ (up_49)
+ (up_51)
+ (up_53)
+ (up_55)
+ (up_57)
+ (up_58)
+ (up_59)
+ (up_60)
+ (up_3)
+ (up_2)
+ (up_6)
+ (up_8)
+ (up_10)
+ (up_12)
+ (up_13)
+ (up_15)
+ (up_17)
+ (up_19)
+ (up_21)
+ (up_23)
+ (up_24)
+ (up_26)
+ (up_28)
+ (up_30)
+ (up_32)
+ (up_34)
+ (up_35)
+ (up_37)
+ (up_39)
+ (up_41)
+ (up_43)
+ (up_45)
+ (up_46)
+ (up_48)
+ (up_50)
+ (up_52)
+ (up_54)
+ (up_56)
+ (up_4)
+ )
+:assumption (not up_1)
+:assumption (not up_2)
+:assumption (not up_3)
+:assumption (not up_4)
+:assumption (or up_5 (or up_6 up_1))
+:assumption (or up_7 (or up_8 up_5))
+:assumption (or up_9 (or up_10 up_7))
+:assumption (or up_11 (or up_12 up_9))
+:assumption (or up_13 up_11)
+:assumption (or up_14 (or up_15 up_2))
+:assumption (or up_16 (or up_17 (or up_14 up_6)))
+:assumption (or up_18 (or up_19 (or up_16 up_8)))
+:assumption (or up_20 (or up_21 (or up_18 up_10)))
+:assumption (or up_22 (or up_23 (or up_20 up_12)))
+:assumption (or up_24 (or up_22 up_13))
+:assumption (or up_25 (or up_26 up_15))
+:assumption (or up_27 (or up_28 (or up_25 up_17)))
+:assumption (or up_29 (or up_30 (or up_27 up_19)))
+:assumption (or up_31 (or up_32 (or up_29 up_21)))
+:assumption (or up_33 (or up_34 (or up_31 up_23)))
+:assumption (or up_35 (or up_33 up_24))
+:assumption (or up_36 (or up_37 up_26))
+:assumption (or up_38 (or up_39 (or up_36 up_28)))
+:assumption (or up_40 (or up_41 (or up_38 up_30)))
+:assumption (or up_42 (or up_43 (or up_40 up_32)))
+:assumption (or up_44 (or up_45 (or up_42 up_34)))
+:assumption (or up_46 (or up_44 up_35))
+:assumption (or up_47 (or up_48 up_37))
+:assumption (or up_49 (or up_50 (or up_47 up_39)))
+:assumption (or up_51 (or up_52 (or up_49 up_41)))
+:assumption (or up_53 (or up_54 (or up_51 up_43)))
+:assumption (or up_55 (or up_56 (or up_53 up_45)))
+:assumption (or up_4 (or up_55 up_46))
+:assumption (or up_57 up_48)
+:assumption (or up_58 (or up_57 up_50))
+:assumption (or up_59 (or up_58 up_52))
+:assumption (or up_60 (or up_59 up_54))
+:assumption (or up_3 (or up_60 up_56))
+:assumption (or (not up_5) (not up_6))
+:assumption (or (not up_5) (not up_1))
+:assumption (or (not up_6) (not up_1))
+:assumption (or (not up_7) (not up_8))
+:assumption (or (not up_7) (not up_5))
+:assumption (or (not up_8) (not up_5))
+:assumption (or (not up_9) (not up_10))
+:assumption (or (not up_9) (not up_7))
+:assumption (or (not up_10) (not up_7))
+:assumption (or (not up_11) (not up_12))
+:assumption (or (not up_11) (not up_9))
+:assumption (or (not up_12) (not up_9))
+:assumption (or (not up_13) (not up_11))
+:assumption (or (not up_14) (not up_15))
+:assumption (or (not up_14) (not up_2))
+:assumption (or (not up_15) (not up_2))
+:assumption (or (not up_16) (not up_17))
+:assumption (or (not up_16) (not up_14))
+:assumption (or (not up_16) (not up_6))
+:assumption (or (not up_17) (not up_14))
+:assumption (or (not up_17) (not up_6))
+:assumption (or (not up_14) (not up_6))
+:assumption (or (not up_18) (not up_19))
+:assumption (or (not up_18) (not up_16))
+:assumption (or (not up_18) (not up_8))
+:assumption (or (not up_19) (not up_16))
+:assumption (or (not up_19) (not up_8))
+:assumption (or (not up_16) (not up_8))
+:assumption (or (not up_20) (not up_21))
+:assumption (or (not up_20) (not up_18))
+:assumption (or (not up_20) (not up_10))
+:assumption (or (not up_21) (not up_18))
+:assumption (or (not up_21) (not up_10))
+:assumption (or (not up_18) (not up_10))
+:assumption (or (not up_22) (not up_23))
+:assumption (or (not up_22) (not up_20))
+:assumption (or (not up_22) (not up_12))
+:assumption (or (not up_23) (not up_20))
+:assumption (or (not up_23) (not up_12))
+:assumption (or (not up_20) (not up_12))
+:assumption (or (not up_24) (not up_22))
+:assumption (or (not up_24) (not up_13))
+:assumption (or (not up_22) (not up_13))
+:assumption (or (not up_25) (not up_26))
+:assumption (or (not up_25) (not up_15))
+:assumption (or (not up_26) (not up_15))
+:assumption (or (not up_27) (not up_28))
+:assumption (or (not up_27) (not up_25))
+:assumption (or (not up_27) (not up_17))
+:assumption (or (not up_28) (not up_25))
+:assumption (or (not up_28) (not up_17))
+:assumption (or (not up_25) (not up_17))
+:assumption (or (not up_29) (not up_30))
+:assumption (or (not up_29) (not up_27))
+:assumption (or (not up_29) (not up_19))
+:assumption (or (not up_30) (not up_27))
+:assumption (or (not up_30) (not up_19))
+:assumption (or (not up_27) (not up_19))
+:assumption (or (not up_31) (not up_32))
+:assumption (or (not up_31) (not up_29))
+:assumption (or (not up_31) (not up_21))
+:assumption (or (not up_32) (not up_29))
+:assumption (or (not up_32) (not up_21))
+:assumption (or (not up_29) (not up_21))
+:assumption (or (not up_33) (not up_34))
+:assumption (or (not up_33) (not up_31))
+:assumption (or (not up_33) (not up_23))
+:assumption (or (not up_34) (not up_31))
+:assumption (or (not up_34) (not up_23))
+:assumption (or (not up_31) (not up_23))
+:assumption (or (not up_35) (not up_33))
+:assumption (or (not up_35) (not up_24))
+:assumption (or (not up_33) (not up_24))
+:assumption (or (not up_36) (not up_37))
+:assumption (or (not up_36) (not up_26))
+:assumption (or (not up_37) (not up_26))
+:assumption (or (not up_38) (not up_39))
+:assumption (or (not up_38) (not up_36))
+:assumption (or (not up_38) (not up_28))
+:assumption (or (not up_39) (not up_36))
+:assumption (or (not up_39) (not up_28))
+:assumption (or (not up_36) (not up_28))
+:assumption (or (not up_40) (not up_41))
+:assumption (or (not up_40) (not up_38))
+:assumption (or (not up_40) (not up_30))
+:assumption (or (not up_41) (not up_38))
+:assumption (or (not up_41) (not up_30))
+:assumption (or (not up_38) (not up_30))
+:assumption (or (not up_42) (not up_43))
+:assumption (or (not up_42) (not up_40))
+:assumption (or (not up_42) (not up_32))
+:assumption (or (not up_43) (not up_40))
+:assumption (or (not up_43) (not up_32))
+:assumption (or (not up_40) (not up_32))
+:assumption (or (not up_44) (not up_45))
+:assumption (or (not up_44) (not up_42))
+:assumption (or (not up_44) (not up_34))
+:assumption (or (not up_45) (not up_42))
+:assumption (or (not up_45) (not up_34))
+:assumption (or (not up_42) (not up_34))
+:assumption (or (not up_46) (not up_44))
+:assumption (or (not up_46) (not up_35))
+:assumption (or (not up_44) (not up_35))
+:assumption (or (not up_47) (not up_48))
+:assumption (or (not up_47) (not up_37))
+:assumption (or (not up_48) (not up_37))
+:assumption (or (not up_49) (not up_50))
+:assumption (or (not up_49) (not up_47))
+:assumption (or (not up_49) (not up_39))
+:assumption (or (not up_50) (not up_47))
+:assumption (or (not up_50) (not up_39))
+:assumption (or (not up_47) (not up_39))
+:assumption (or (not up_51) (not up_52))
+:assumption (or (not up_51) (not up_49))
+:assumption (or (not up_51) (not up_41))
+:assumption (or (not up_52) (not up_49))
+:assumption (or (not up_52) (not up_41))
+:assumption (or (not up_49) (not up_41))
+:assumption (or (not up_53) (not up_54))
+:assumption (or (not up_53) (not up_51))
+:assumption (or (not up_53) (not up_43))
+:assumption (or (not up_54) (not up_51))
+:assumption (or (not up_54) (not up_43))
+:assumption (or (not up_51) (not up_43))
+:assumption (or (not up_55) (not up_56))
+:assumption (or (not up_55) (not up_53))
+:assumption (or (not up_55) (not up_45))
+:assumption (or (not up_56) (not up_53))
+:assumption (or (not up_56) (not up_45))
+:assumption (or (not up_53) (not up_45))
+:assumption (or (not up_4) (not up_55))
+:assumption (or (not up_4) (not up_46))
+:assumption (or (not up_55) (not up_46))
+:assumption (or (not up_57) (not up_48))
+:assumption (or (not up_58) (not up_57))
+:assumption (or (not up_58) (not up_50))
+:assumption (or (not up_57) (not up_50))
+:assumption (or (not up_59) (not up_58))
+:assumption (or (not up_59) (not up_52))
+:assumption (or (not up_58) (not up_52))
+:assumption (or (not up_60) (not up_59))
+:assumption (or (not up_60) (not up_54))
+:assumption (or (not up_59) (not up_54))
+:assumption (or (not up_3) (not up_60))
+:assumption (or (not up_3) (not up_56))
+:assumption (or (not up_60) (not up_56))
+:assumption (not false)
+:formula true
+)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Examples/cert/z3_prop_10.proof Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1667 @@
+#2 := false
+decl up_54 :: bool
+#126 := up_54
+#317 := (not up_54)
+decl up_60 :: bool
+#145 := up_60
+decl up_56 :: bool
+#131 := up_56
+#325 := (not up_56)
+decl up_55 :: bool
+#130 := up_55
+decl up_46 :: bool
+#108 := up_46
+#291 := (not up_46)
+decl up_35 :: bool
+#81 := up_35
+decl up_29 :: bool
+#66 := up_29
+decl up_32 :: bool
+#72 := up_32
+#235 := (not up_32)
+decl up_34 :: bool
+#77 := up_34
+#243 := (not up_34)
+decl up_33 :: bool
+#76 := up_33
+#250 := (not up_35)
+#1611 := [hypothesis]: #250
+decl up_24 :: bool
+#54 := up_24
+#209 := (not up_24)
+decl up_13 :: bool
+#28 := up_13
+decl up_11 :: bool
+#24 := up_11
+#165 := (not up_11)
+decl up_12 :: bool
+#25 := up_12
+#2327 := (or up_12 up_35)
+#345 := (not up_60)
+decl up_59 :: bool
+#142 := up_59
+decl up_19 :: bool
+#40 := up_19
+decl up_8 :: bool
+#17 := up_8
+#156 := (not up_8)
+decl up_7 :: bool
+#16 := up_7
+#166 := (not up_12)
+#1457 := [hypothesis]: #166
+#2183 := (or up_7 up_12 up_35)
+#155 := (not up_7)
+#1612 := [hypothesis]: #155
+decl up_10 :: bool
+#21 := up_10
+#161 := (not up_10)
+decl up_20 :: bool
+#44 := up_20
+decl up_23 :: bool
+#50 := up_23
+#202 := (not up_23)
+#2170 := (or up_34 up_7 up_35 up_12)
+#1605 := [hypothesis]: #243
+#2164 := (or up_29 up_34 up_7 up_35 up_12)
+decl up_42 :: bool
+#98 := up_42
+#275 := (not up_42)
+#226 := (not up_29)
+#907 := [hypothesis]: #226
+#2136 := (or up_29 up_12 up_7 up_35 up_32)
+decl up_22 :: bool
+#49 := up_22
+#895 := [hypothesis]: #235
+#1624 := (or up_29 up_22 up_12 up_32 up_35 up_7)
+decl up_21 :: bool
+#45 := up_21
+decl up_31 :: bool
+#71 := up_31
+#234 := (not up_31)
+decl up_9 :: bool
+#20 := up_9
+#201 := (not up_22)
+#1456 := [hypothesis]: #201
+#847 := (or #161 up_32 up_29 up_22 up_12)
+#193 := (not up_20)
+#1400 := [hypothesis]: up_10
+#964 := (or #161 #193)
+#197 := (or #193 #161)
+#966 := (iff #197 #964)
+#967 := [rewrite]: #966
+#963 := [asserted]: #197
+#970 := [mp #963 #967]: #964
+#1399 := [unit-resolution #970 #1400]: #193
+#500 := (or up_12 up_20 up_22 up_23)
+#51 := (or up_20 up_12)
+#52 := (or up_23 #51)
+#53 := (or up_22 #52)
+#503 := (iff #53 #500)
+#491 := (or up_12 up_20)
+#494 := (or up_23 #491)
+#497 := (or up_22 #494)
+#501 := (iff #497 #500)
+#502 := [rewrite]: #501
+#498 := (iff #53 #497)
+#495 := (iff #52 #494)
+#492 := (iff #51 #491)
+#493 := [rewrite]: #492
+#496 := [monotonicity #493]: #495
+#499 := [monotonicity #496]: #498
+#504 := [trans #499 #502]: #503
+#490 := [asserted]: #53
+#505 := [mp #490 #504]: #500
+#900 := [unit-resolution #505 #1399 #1456 #1457]: up_23
+#194 := (not up_21)
+#974 := (or #161 #194)
+#199 := (or #194 #161)
+#976 := (iff #199 #974)
+#977 := [rewrite]: #976
+#973 := [asserted]: #199
+#980 := [mp #973 #977]: #974
+#902 := [unit-resolution #980 #1400]: #194
+#574 := (or up_21 up_29 up_31 up_32)
+#73 := (or up_29 up_21)
+#74 := (or up_32 #73)
+#75 := (or up_31 #74)
+#577 := (iff #75 #574)
+#565 := (or up_21 up_29)
+#568 := (or up_32 #565)
+#571 := (or up_31 #568)
+#575 := (iff #571 #574)
+#576 := [rewrite]: #575
+#572 := (iff #75 #571)
+#569 := (iff #74 #568)
+#566 := (iff #73 #565)
+#567 := [rewrite]: #566
+#570 := [monotonicity #567]: #569
+#573 := [monotonicity #570]: #572
+#578 := [trans #573 #576]: #577
+#564 := [asserted]: #75
+#579 := [mp #564 #578]: #574
+#851 := [unit-resolution #579 #902 #895 #907]: up_31
+#1135 := (or #202 #234)
+#249 := (or #234 #202)
+#1137 := (iff #249 #1135)
+#1138 := [rewrite]: #1137
+#1134 := [asserted]: #249
+#1141 := [mp #1134 #1138]: #1135
+#858 := [unit-resolution #1141 #851 #900]: false
+#853 := [lemma #858]: #847
+#1613 := [unit-resolution #853 #907 #1456 #895 #1457]: #161
+#405 := (or up_7 up_9 up_10)
+#22 := (or up_10 up_7)
+#23 := (or up_9 #22)
+#408 := (iff #23 #405)
+#399 := (or up_7 up_10)
+#402 := (or up_9 #399)
+#406 := (iff #402 #405)
+#407 := [rewrite]: #406
+#403 := (iff #23 #402)
+#400 := (iff #22 #399)
+#401 := [rewrite]: #400
+#404 := [monotonicity #401]: #403
+#409 := [trans #404 #407]: #408
+#398 := [asserted]: #23
+#410 := [mp #398 #409]: #405
+#1614 := [unit-resolution #410 #1613 #1612]: up_9
+#160 := (not up_9)
+#881 := (or #160 #165)
+#168 := (or #165 #160)
+#882 := (iff #168 #881)
+#883 := [rewrite]: #882
+#879 := [asserted]: #168
+#886 := [mp #879 #883]: #881
+#1615 := [unit-resolution #886 #1614]: #165
+#425 := (or up_11 up_13)
+#29 := (or up_13 up_11)
+#426 := (iff #29 #425)
+#427 := [rewrite]: #426
+#424 := [asserted]: #29
+#430 := [mp #424 #427]: #425
+#1616 := [unit-resolution #430 #1615]: up_13
+#170 := (not up_13)
+#1015 := (or #170 #209)
+#211 := (or #209 #170)
+#1017 := (iff #211 #1015)
+#1018 := [rewrite]: #1017
+#1014 := [asserted]: #211
+#1021 := [mp #1014 #1018]: #1015
+#1617 := [unit-resolution #1021 #1616]: #209
+#603 := (or up_24 up_33 up_35)
+#82 := (or up_33 up_24)
+#83 := (or up_35 #82)
+#606 := (iff #83 #603)
+#597 := (or up_24 up_33)
+#600 := (or up_35 #597)
+#604 := (iff #600 #603)
+#605 := [rewrite]: #604
+#601 := (iff #83 #600)
+#598 := (iff #82 #597)
+#599 := [rewrite]: #598
+#602 := [monotonicity #599]: #601
+#607 := [trans #602 #605]: #606
+#596 := [asserted]: #83
+#608 := [mp #596 #607]: #603
+#1618 := [unit-resolution #608 #1617 #1611]: up_33
+#242 := (not up_33)
+#1116 := (or #234 #242)
+#245 := (or #242 #234)
+#1117 := (iff #245 #1116)
+#1118 := [rewrite]: #1117
+#1114 := [asserted]: #245
+#1121 := [mp #1114 #1118]: #1116
+#1619 := [unit-resolution #1121 #1618]: #234
+#1620 := [unit-resolution #579 #1619 #895 #907]: up_21
+#1120 := (or #202 #242)
+#246 := (or #242 #202)
+#1122 := (iff #246 #1120)
+#1123 := [rewrite]: #1122
+#1119 := [asserted]: #246
+#1126 := [mp #1119 #1123]: #1120
+#1621 := [unit-resolution #1126 #1618]: #202
+#1622 := [unit-resolution #505 #1621 #1456 #1457]: up_20
+#195 := (or #193 #194)
+#957 := [asserted]: #195
+#1623 := [unit-resolution #957 #1622 #1620]: false
+#1625 := [lemma #1623]: #1624
+#2132 := [unit-resolution #1625 #907 #1611 #1457 #895 #1612]: up_22
+#1978 := (or up_32 up_35 up_29 up_21 up_12 up_7)
+#1972 := [unit-resolution #1625 #895 #907 #1457 #1611 #1612]: up_22
+#1010 := (or #201 #209)
+#210 := (or #209 #201)
+#1012 := (iff #210 #1010)
+#1013 := [rewrite]: #1012
+#1009 := [asserted]: #210
+#1016 := [mp #1009 #1013]: #1010
+#1973 := [unit-resolution #1016 #1972]: #209
+#1974 := [hypothesis]: #194
+#1975 := [unit-resolution #579 #895 #907 #1974]: up_31
+#1976 := [unit-resolution #1121 #1975]: #242
+#1977 := [unit-resolution #608 #1976 #1973 #1611]: false
+#1979 := [lemma #1977]: #1978
+#2133 := [unit-resolution #1979 #907 #1611 #1457 #895 #1612]: up_21
+#1682 := (or #194 up_7 up_12 up_23)
+#1673 := [hypothesis]: #202
+#1674 := [hypothesis]: up_21
+#1675 := [unit-resolution #957 #1674]: #193
+#1676 := [unit-resolution #505 #1675 #1457 #1673]: up_22
+#1020 := (or #170 #201)
+#212 := (or #201 #170)
+#1022 := (iff #212 #1020)
+#1023 := [rewrite]: #1022
+#1019 := [asserted]: #212
+#1026 := [mp #1019 #1023]: #1020
+#1677 := [unit-resolution #1026 #1676]: #170
+#1678 := [unit-resolution #980 #1674]: #161
+#1679 := [unit-resolution #410 #1678 #1612]: up_9
+#1680 := [unit-resolution #886 #1679]: #165
+#1681 := [unit-resolution #430 #1680 #1677]: false
+#1683 := [lemma #1681]: #1682
+#2134 := [unit-resolution #1683 #2133 #1457 #1612]: up_23
+#203 := (or #201 #202)
+#983 := [asserted]: #203
+#2135 := [unit-resolution #983 #2134 #2132]: false
+#2137 := [lemma #2135]: #2136
+#2156 := [unit-resolution #2137 #907 #1612 #1611 #1457]: up_32
+#1224 := (or #235 #275)
+#279 := (or #275 #235)
+#1226 := (iff #279 #1224)
+#1227 := [rewrite]: #1226
+#1223 := [asserted]: #279
+#1230 := [mp #1223 #1227]: #1224
+#2157 := [unit-resolution #1230 #2156]: #275
+#2158 := (or up_12 up_29 up_7 up_54)
+decl up_26 :: bool
+#58 := up_26
+#214 := (not up_26)
+decl up_15 :: bool
+#31 := up_15
+decl up_14 :: bool
+#30 := up_14
+#172 := (not up_14)
+decl up_6 :: bool
+#13 := up_6
+decl up_5 :: bool
+#12 := up_5
+#150 := (not up_5)
+decl up_25 :: bool
+#57 := up_25
+#2099 := [hypothesis]: up_5
+#859 := (or #150 #155)
+#158 := (or #155 #150)
+#860 := (iff #158 #859)
+#861 := [rewrite]: #860
+#857 := [asserted]: #158
+#864 := [mp #857 #861]: #859
+#2100 := [unit-resolution #864 #2099]: #155
+#863 := (or #150 #156)
+#159 := (or #156 #150)
+#865 := (iff #159 #863)
+#866 := [rewrite]: #865
+#862 := [asserted]: #159
+#869 := [mp #862 #866]: #863
+#2101 := [unit-resolution #869 #2099]: #156
+#2097 := (or up_12 up_7 up_8)
+#1626 := [hypothesis]: #156
+#2054 := (or up_54 up_7 up_8)
+decl up_16 :: bool
+#34 := up_16
+#1597 := [hypothesis]: #317
+#1888 := (or up_16 up_8 up_7 up_54)
+decl up_45 :: bool
+#104 := up_45
+#284 := (not up_45)
+decl up_52 :: bool
+#121 := up_52
+#309 := (not up_52)
+decl up_51 :: bool
+#120 := up_51
+#177 := (not up_16)
+#1627 := [hypothesis]: #177
+#1733 := (or up_51 up_7 up_54 up_8 up_16)
+decl up_53 :: bool
+#125 := up_53
+#308 := (not up_51)
+#1598 := [hypothesis]: #308
+decl up_43 :: bool
+#99 := up_43
+#276 := (not up_43)
+#1710 := (or up_32 up_16 up_8 up_7 up_51 up_54)
+#1671 := (or up_35 up_16 up_8 up_32 up_7)
+#1655 := (or #166 up_32 up_16 up_8 up_35 up_7)
+#1642 := [hypothesis]: up_12
+#885 := (or #160 #166)
+#169 := (or #166 #160)
+#887 := (iff #169 #885)
+#888 := [rewrite]: #887
+#884 := [asserted]: #169
+#891 := [mp #884 #888]: #885
+#1643 := [unit-resolution #891 #1642]: #160
+#1644 := [unit-resolution #410 #1643 #1612]: up_10
+#1645 := [unit-resolution #980 #1644]: #194
+#167 := (or #165 #166)
+#878 := [asserted]: #167
+#1646 := [unit-resolution #878 #1642]: #165
+#1647 := [unit-resolution #430 #1646]: up_13
+#1648 := [unit-resolution #1021 #1647]: #209
+#1649 := [unit-resolution #608 #1648 #1611]: up_33
+#1650 := [unit-resolution #1121 #1649]: #234
+decl up_18 :: bool
+#39 := up_18
+#185 := (not up_18)
+#979 := (or #161 #185)
+#200 := (or #185 #161)
+#981 := (iff #200 #979)
+#982 := [rewrite]: #981
+#978 := [asserted]: #200
+#985 := [mp #978 #982]: #979
+#1651 := [unit-resolution #985 #1644]: #185
+#468 := (or up_8 up_16 up_18 up_19)
+#41 := (or up_16 up_8)
+#42 := (or up_19 #41)
+#43 := (or up_18 #42)
+#471 := (iff #43 #468)
+#459 := (or up_8 up_16)
+#462 := (or up_19 #459)
+#465 := (or up_18 #462)
+#469 := (iff #465 #468)
+#470 := [rewrite]: #469
+#466 := (iff #43 #465)
+#463 := (iff #42 #462)
+#460 := (iff #41 #459)
+#461 := [rewrite]: #460
+#464 := [monotonicity #461]: #463
+#467 := [monotonicity #464]: #466
+#472 := [trans #467 #470]: #471
+#458 := [asserted]: #43
+#473 := [mp #458 #472]: #468
+#1652 := [unit-resolution #473 #1651 #1627 #1626]: up_19
+#186 := (not up_19)
+#1068 := (or #186 #226)
+#230 := (or #226 #186)
+#1070 := (iff #230 #1068)
+#1071 := [rewrite]: #1070
+#1067 := [asserted]: #230
+#1074 := [mp #1067 #1071]: #1068
+#1653 := [unit-resolution #1074 #1652]: #226
+#1654 := [unit-resolution #579 #1653 #1650 #895 #1645]: false
+#1656 := [lemma #1654]: #1655
+#1657 := [unit-resolution #1656 #1611 #1627 #1626 #895 #1612]: #166
+#1640 := (or up_12 up_35 up_7 up_22 up_16 up_8 up_32)
+#1628 := [unit-resolution #1625 #1457 #1456 #895 #1611 #1612]: up_29
+#1629 := [unit-resolution #1074 #1628]: #186
+#1630 := [unit-resolution #473 #1629 #1627 #1626]: up_18
+#960 := (or #185 #193)
+#196 := (or #193 #185)
+#961 := (iff #196 #960)
+#962 := [rewrite]: #961
+#958 := [asserted]: #196
+#965 := [mp #958 #962]: #960
+#1631 := [unit-resolution #965 #1630]: #193
+#1632 := [unit-resolution #505 #1631 #1456 #1457]: up_23
+#1633 := [unit-resolution #1126 #1632]: #242
+#1634 := [unit-resolution #608 #1633 #1611]: up_24
+#1635 := [unit-resolution #985 #1630]: #161
+#1636 := [unit-resolution #410 #1635 #1612]: up_9
+#1637 := [unit-resolution #886 #1636]: #165
+#1638 := [unit-resolution #430 #1637]: up_13
+#1639 := [unit-resolution #1021 #1638 #1634]: false
+#1641 := [lemma #1639]: #1640
+#1658 := [unit-resolution #1641 #1657 #1612 #1611 #1627 #1626 #895]: up_22
+#1659 := [unit-resolution #1016 #1658]: #209
+#1660 := [unit-resolution #608 #1659 #1611]: up_33
+#1661 := [unit-resolution #1121 #1660]: #234
+#1662 := [unit-resolution #1026 #1658]: #170
+#1663 := [unit-resolution #430 #1662]: up_11
+#1664 := [unit-resolution #886 #1663]: #160
+#1665 := [unit-resolution #410 #1664 #1612]: up_10
+#1666 := [unit-resolution #980 #1665]: #194
+#1667 := [unit-resolution #579 #1666 #895 #1661]: up_29
+#1668 := [unit-resolution #985 #1665]: #185
+#1669 := [unit-resolution #473 #1668 #1627 #1626]: up_19
+#1670 := [unit-resolution #1074 #1669 #1667]: false
+#1672 := [lemma #1670]: #1671
+#1698 := [unit-resolution #1672 #895 #1626 #1627 #1612]: up_35
+#1609 := (or #250 up_34 up_51 up_54)
+#316 := (not up_53)
+#1599 := [hypothesis]: up_35
+#1275 := (or #250 #291)
+#293 := (or #291 #250)
+#1277 := (iff #293 #1275)
+#1278 := [rewrite]: #1277
+#1274 := [asserted]: #293
+#1281 := [mp #1274 #1278]: #1275
+#1600 := [unit-resolution #1281 #1599]: #291
+#777 := (or up_46 up_55)
+decl up_4 :: bool
+#10 := up_4
+#783 := (or up_4 up_46 up_55)
+#1514 := (iff #783 #777)
+#1509 := (or false up_46 up_55)
+#1512 := (iff #1509 #777)
+#1513 := [rewrite]: #1512
+#1510 := (iff #783 #1509)
+#1485 := (iff up_4 false)
+#11 := (not up_4)
+#1488 := (iff #11 #1485)
+#1486 := (iff #1485 #11)
+#1487 := [rewrite]: #1486
+#1489 := [symm #1487]: #1488
+#371 := [asserted]: #11
+#1490 := [mp #371 #1489]: #1485
+#1511 := [monotonicity #1490]: #1510
+#1515 := [trans #1511 #1513]: #1514
+#135 := (or up_55 up_46)
+#136 := (or up_4 #135)
+#786 := (iff #136 #783)
+#780 := (or up_4 #777)
+#784 := (iff #780 #783)
+#785 := [rewrite]: #784
+#781 := (iff #136 #780)
+#778 := (iff #135 #777)
+#779 := [rewrite]: #778
+#782 := [monotonicity #779]: #781
+#787 := [trans #782 #785]: #786
+#776 := [asserted]: #136
+#788 := [mp #776 #787]: #783
+#1516 := [mp #788 #1515]: #777
+#1601 := [unit-resolution #1516 #1600]: up_55
+#324 := (not up_55)
+#1376 := (or #316 #324)
+#327 := (or #324 #316)
+#1377 := (iff #327 #1376)
+#1378 := [rewrite]: #1377
+#1374 := [asserted]: #327
+#1381 := [mp #1374 #1378]: #1376
+#1602 := [unit-resolution #1381 #1601]: #316
+#754 := (or up_43 up_51 up_53 up_54)
+#127 := (or up_51 up_43)
+#128 := (or up_54 #127)
+#129 := (or up_53 #128)
+#757 := (iff #129 #754)
+#745 := (or up_43 up_51)
+#748 := (or up_54 #745)
+#751 := (or up_53 #748)
+#755 := (iff #751 #754)
+#756 := [rewrite]: #755
+#752 := (iff #129 #751)
+#749 := (iff #128 #748)
+#746 := (iff #127 #745)
+#747 := [rewrite]: #746
+#750 := [monotonicity #747]: #749
+#753 := [monotonicity #750]: #752
+#758 := [trans #753 #756]: #757
+#744 := [asserted]: #129
+#759 := [mp #744 #758]: #754
+#1603 := [unit-resolution #759 #1602 #1598 #1597]: up_43
+decl up_44 :: bool
+#103 := up_44
+#283 := (not up_44)
+#1280 := (or #250 #283)
+#294 := (or #283 #250)
+#1282 := (iff #294 #1280)
+#1283 := [rewrite]: #1282
+#1279 := [asserted]: #294
+#1286 := [mp #1279 #1283]: #1280
+#1604 := [unit-resolution #1286 #1599]: #283
+#1380 := (or #284 #324)
+#328 := (or #324 #284)
+#1382 := (iff #328 #1380)
+#1383 := [rewrite]: #1382
+#1379 := [asserted]: #328
+#1386 := [mp #1379 #1383]: #1380
+#1606 := [unit-resolution #1386 #1601]: #284
+#680 := (or up_34 up_42 up_44 up_45)
+#105 := (or up_42 up_34)
+#106 := (or up_45 #105)
+#107 := (or up_44 #106)
+#683 := (iff #107 #680)
+#671 := (or up_34 up_42)
+#674 := (or up_45 #671)
+#677 := (or up_44 #674)
+#681 := (iff #677 #680)
+#682 := [rewrite]: #681
+#678 := (iff #107 #677)
+#675 := (iff #106 #674)
+#672 := (iff #105 #671)
+#673 := [rewrite]: #672
+#676 := [monotonicity #673]: #675
+#679 := [monotonicity #676]: #678
+#684 := [trans #679 #682]: #683
+#670 := [asserted]: #107
+#685 := [mp #670 #684]: #680
+#1607 := [unit-resolution #685 #1606 #1605 #1604]: up_42
+#277 := (or #275 #276)
+#1217 := [asserted]: #277
+#1608 := [unit-resolution #1217 #1607 #1603]: false
+#1610 := [lemma #1608]: #1609
+#1699 := [unit-resolution #1610 #1698 #1598 #1597]: up_34
+#1125 := (or #234 #243)
+#247 := (or #243 #234)
+#1127 := (iff #247 #1125)
+#1128 := [rewrite]: #1127
+#1124 := [asserted]: #247
+#1131 := [mp #1124 #1128]: #1125
+#1700 := [unit-resolution #1131 #1699]: #234
+#1130 := (or #202 #243)
+#248 := (or #243 #202)
+#1132 := (iff #248 #1130)
+#1133 := [rewrite]: #1132
+#1129 := [asserted]: #248
+#1136 := [mp #1129 #1133]: #1130
+#1701 := [unit-resolution #1136 #1699]: #202
+#1696 := (or up_12 up_7 up_23 up_16 up_8 up_32 up_31)
+#1684 := [hypothesis]: #234
+#1685 := [unit-resolution #1683 #1457 #1612 #1673]: #194
+#1686 := [unit-resolution #579 #1685 #895 #1684]: up_29
+#1687 := [unit-resolution #1074 #1686]: #186
+#1688 := [unit-resolution #473 #1687 #1627 #1626]: up_18
+#1689 := [unit-resolution #965 #1688]: #193
+#1690 := [unit-resolution #505 #1689 #1457 #1673]: up_22
+#1691 := [unit-resolution #1026 #1690]: #170
+#1692 := [unit-resolution #985 #1688]: #161
+#1693 := [unit-resolution #410 #1692 #1612]: up_9
+#1694 := [unit-resolution #886 #1693]: #165
+#1695 := [unit-resolution #430 #1694 #1691]: false
+#1697 := [lemma #1695]: #1696
+#1702 := [unit-resolution #1697 #1701 #1612 #1627 #1626 #895 #1700]: up_12
+#1703 := [unit-resolution #891 #1702]: #160
+#1704 := [unit-resolution #410 #1703 #1612]: up_10
+#1705 := [unit-resolution #980 #1704]: #194
+#1706 := [unit-resolution #579 #1705 #895 #1700]: up_29
+#1707 := [unit-resolution #985 #1704]: #185
+#1708 := [unit-resolution #473 #1707 #1627 #1626]: up_19
+#1709 := [unit-resolution #1074 #1708 #1706]: false
+#1711 := [lemma #1709]: #1710
+#1712 := [unit-resolution #1711 #1598 #1626 #1612 #1627 #1597]: up_32
+#1234 := (or #235 #276)
+#281 := (or #276 #235)
+#1236 := (iff #281 #1234)
+#1237 := [rewrite]: #1236
+#1233 := [asserted]: #281
+#1240 := [mp #1233 #1237]: #1234
+#1713 := [unit-resolution #1240 #1712]: #276
+#1714 := [unit-resolution #759 #1713 #1598 #1597]: up_53
+#1395 := (or #284 #316)
+#331 := (or #316 #284)
+#1397 := (iff #331 #1395)
+#1398 := [rewrite]: #1397
+#1394 := [asserted]: #331
+#1401 := [mp #1394 #1398]: #1395
+#1715 := [unit-resolution #1401 #1714]: #284
+#1716 := [unit-resolution #1230 #1712]: #275
+#1717 := [unit-resolution #1381 #1714]: #324
+#1718 := [unit-resolution #1516 #1717]: up_46
+#1270 := (or #283 #291)
+#292 := (or #291 #283)
+#1272 := (iff #292 #1270)
+#1273 := [rewrite]: #1272
+#1269 := [asserted]: #292
+#1276 := [mp #1269 #1273]: #1270
+#1719 := [unit-resolution #1276 #1718]: #283
+#1720 := [unit-resolution #685 #1719 #1716 #1715]: up_34
+#1721 := [unit-resolution #1136 #1720]: #202
+#1722 := [unit-resolution #1281 #1718]: #250
+#244 := (or #242 #243)
+#1113 := [asserted]: #244
+#1723 := [unit-resolution #1113 #1720]: #242
+#1724 := [unit-resolution #608 #1723 #1722]: up_24
+#1725 := [unit-resolution #1016 #1724]: #201
+#1726 := [unit-resolution #1021 #1724]: #170
+#1727 := [unit-resolution #430 #1726]: up_11
+#1728 := [unit-resolution #878 #1727]: #166
+#1729 := [unit-resolution #505 #1728 #1725 #1721]: up_20
+#1730 := [unit-resolution #886 #1727]: #160
+#1731 := [unit-resolution #410 #1730 #1612]: up_10
+#1732 := [unit-resolution #970 #1731 #1729]: false
+#1734 := [lemma #1732]: #1733
+#1858 := [unit-resolution #1734 #1627 #1597 #1626 #1612]: up_51
+#310 := (or #308 #309)
+#1321 := [asserted]: #310
+#1859 := [unit-resolution #1321 #1858]: #309
+decl up_58 :: bool
+#139 := up_58
+#337 := (not up_58)
+decl up_49 :: bool
+#115 := up_49
+#300 := (not up_49)
+#1324 := (or #300 #308)
+#311 := (or #308 #300)
+#1325 := (iff #311 #1324)
+#1326 := [rewrite]: #1325
+#1322 := [asserted]: #311
+#1329 := [mp #1322 #1326]: #1324
+#1860 := [unit-resolution #1329 #1858]: #300
+decl up_39 :: bool
+#89 := up_39
+#260 := (not up_39)
+decl up_38 :: bool
+#88 := up_38
+decl up_40 :: bool
+#93 := up_40
+#267 := (not up_40)
+decl up_41 :: bool
+#94 := up_41
+#268 := (not up_41)
+#1328 := (or #268 #308)
+#312 := (or #308 #268)
+#1330 := (iff #312 #1328)
+#1331 := [rewrite]: #1330
+#1327 := [asserted]: #312
+#1334 := [mp #1327 #1331]: #1328
+#1861 := [unit-resolution #1334 #1858]: #268
+#1771 := (or up_32 up_16 up_8 up_41 up_49 up_52 up_7)
+#1735 := [unit-resolution #1281 #1698]: #291
+#1736 := [unit-resolution #1516 #1735]: up_55
+#1737 := [unit-resolution #1386 #1736]: #284
+#1738 := [unit-resolution #1286 #1698]: #283
+#259 := (not up_38)
+decl up_50 :: bool
+#116 := up_50
+#301 := (not up_50)
+#1739 := [hypothesis]: #309
+#341 := (not up_59)
+#326 := (or #324 #325)
+#1373 := [asserted]: #326
+#1740 := [unit-resolution #1373 #1736]: #325
+#834 := (or up_56 up_60)
+decl up_3 :: bool
+#8 := up_3
+#840 := (or up_3 up_56 up_60)
+#1522 := (iff #840 #834)
+#1517 := (or false up_56 up_60)
+#1520 := (iff #1517 #834)
+#1521 := [rewrite]: #1520
+#1518 := (iff #840 #1517)
+#1479 := (iff up_3 false)
+#9 := (not up_3)
+#1482 := (iff #9 #1479)
+#1480 := (iff #1479 #9)
+#1481 := [rewrite]: #1480
+#1483 := [symm #1481]: #1482
+#370 := [asserted]: #9
+#1484 := [mp #370 #1483]: #1479
+#1519 := [monotonicity #1484]: #1518
+#1523 := [trans #1519 #1521]: #1522
+#148 := (or up_60 up_56)
+#149 := (or up_3 #148)
+#843 := (iff #149 #840)
+#837 := (or up_3 #834)
+#841 := (iff #837 #840)
+#842 := [rewrite]: #841
+#838 := (iff #149 #837)
+#835 := (iff #148 #834)
+#836 := [rewrite]: #835
+#839 := [monotonicity #836]: #838
+#844 := [trans #839 #842]: #843
+#833 := [asserted]: #149
+#845 := [mp #833 #844]: #840
+#1524 := [mp #845 #1523]: #834
+#1741 := [unit-resolution #1524 #1740]: up_60
+#1442 := (or #341 #345)
+#346 := (or #345 #341)
+#1444 := (iff #346 #1442)
+#1445 := [rewrite]: #1444
+#1441 := [asserted]: #346
+#1448 := [mp #1441 #1445]: #1442
+#1742 := [unit-resolution #1448 #1741]: #341
+#814 := (or up_52 up_58 up_59)
+#143 := (or up_58 up_52)
+#144 := (or up_59 #143)
+#817 := (iff #144 #814)
+#808 := (or up_52 up_58)
+#811 := (or up_59 #808)
+#815 := (iff #811 #814)
+#816 := [rewrite]: #815
+#812 := (iff #144 #811)
+#809 := (iff #143 #808)
+#810 := [rewrite]: #809
+#813 := [monotonicity #810]: #812
+#818 := [trans #813 #816]: #817
+#807 := [asserted]: #144
+#819 := [mp #807 #818]: #814
+#1743 := [unit-resolution #819 #1742 #1739]: up_58
+#1417 := (or #301 #337)
+#339 := (or #337 #301)
+#1419 := (iff #339 #1417)
+#1420 := [rewrite]: #1419
+#1416 := [asserted]: #339
+#1423 := [mp #1416 #1420]: #1417
+#1744 := [unit-resolution #1423 #1743]: #301
+#1745 := [hypothesis]: #300
+decl up_47 :: bool
+#111 := up_47
+#295 := (not up_47)
+decl up_48 :: bool
+#112 := up_48
+decl up_57 :: bool
+#137 := up_57
+#335 := (not up_57)
+#1412 := (or #335 #337)
+#338 := (or #337 #335)
+#1414 := (iff #338 #1412)
+#1415 := [rewrite]: #1414
+#1411 := [asserted]: #338
+#1418 := [mp #1411 #1415]: #1412
+#1746 := [unit-resolution #1418 #1743]: #335
+#790 := (or up_48 up_57)
+#138 := (or up_57 up_48)
+#791 := (iff #138 #790)
+#792 := [rewrite]: #791
+#789 := [asserted]: #138
+#795 := [mp #789 #792]: #790
+#1747 := [unit-resolution #795 #1746]: up_48
+#296 := (not up_48)
+#297 := (or #295 #296)
+#1284 := [asserted]: #297
+#1748 := [unit-resolution #1284 #1747]: #295
+#722 := (or up_39 up_47 up_49 up_50)
+#117 := (or up_47 up_39)
+#118 := (or up_50 #117)
+#119 := (or up_49 #118)
+#725 := (iff #119 #722)
+#713 := (or up_39 up_47)
+#716 := (or up_50 #713)
+#719 := (or up_49 #716)
+#723 := (iff #719 #722)
+#724 := [rewrite]: #723
+#720 := (iff #119 #719)
+#717 := (iff #118 #716)
+#714 := (iff #117 #713)
+#715 := [rewrite]: #714
+#718 := [monotonicity #715]: #717
+#721 := [monotonicity #718]: #720
+#726 := [trans #721 #724]: #725
+#712 := [asserted]: #119
+#727 := [mp #712 #726]: #722
+#1749 := [unit-resolution #727 #1748 #1745 #1744]: up_39
+#261 := (or #259 #260)
+#1165 := [asserted]: #261
+#1750 := [unit-resolution #1165 #1749]: #259
+#1751 := [hypothesis]: #268
+decl up_30 :: bool
+#67 := up_30
+#227 := (not up_30)
+decl up_27 :: bool
+#61 := up_27
+#213 := (not up_25)
+decl up_37 :: bool
+#85 := up_37
+#255 := (not up_37)
+#1291 := (or #255 #296)
+#299 := (or #296 #255)
+#1293 := (iff #299 #1291)
+#1294 := [rewrite]: #1293
+#1290 := [asserted]: #299
+#1297 := [mp #1290 #1294]: #1291
+#1752 := [unit-resolution #1297 #1747]: #255
+decl up_36 :: bool
+#84 := up_36
+#254 := (not up_36)
+#1177 := (or #254 #260)
+#264 := (or #260 #254)
+#1179 := (iff #264 #1177)
+#1180 := [rewrite]: #1179
+#1176 := [asserted]: #264
+#1183 := [mp #1176 #1180]: #1177
+#1753 := [unit-resolution #1183 #1749]: #254
+#616 := (or up_26 up_36 up_37)
+#86 := (or up_37 up_26)
+#87 := (or up_36 #86)
+#619 := (iff #87 #616)
+#610 := (or up_26 up_37)
+#613 := (or up_36 #610)
+#617 := (iff #613 #616)
+#618 := [rewrite]: #617
+#614 := (iff #87 #613)
+#611 := (iff #86 #610)
+#612 := [rewrite]: #611
+#615 := [monotonicity #612]: #614
+#620 := [trans #615 #618]: #619
+#609 := [asserted]: #87
+#621 := [mp #609 #620]: #616
+#1754 := [unit-resolution #621 #1753 #1752]: up_26
+#215 := (or #213 #214)
+#1024 := [asserted]: #215
+#1755 := [unit-resolution #1024 #1754]: #213
+decl up_28 :: bool
+#62 := up_28
+#219 := (not up_28)
+#1182 := (or #219 #260)
+#265 := (or #260 #219)
+#1184 := (iff #265 #1182)
+#1185 := [rewrite]: #1184
+#1181 := [asserted]: #265
+#1188 := [mp #1181 #1185]: #1182
+#1756 := [unit-resolution #1188 #1749]: #219
+decl up_17 :: bool
+#35 := up_17
+#178 := (not up_17)
+#173 := (not up_15)
+#1031 := (or #173 #214)
+#217 := (or #214 #173)
+#1033 := (iff #217 #1031)
+#1034 := [rewrite]: #1033
+#1030 := [asserted]: #217
+#1037 := [mp #1030 #1034]: #1031
+#1757 := [unit-resolution #1037 #1754]: #173
+#1503 := (or up_14 up_15)
+decl up_2 :: bool
+#6 := up_2
+#436 := (or up_2 up_14 up_15)
+#1506 := (iff #436 #1503)
+#1500 := (or false up_14 up_15)
+#1504 := (iff #1500 #1503)
+#1505 := [rewrite]: #1504
+#1501 := (iff #436 #1500)
+#1473 := (iff up_2 false)
+#7 := (not up_2)
+#1476 := (iff #7 #1473)
+#1474 := (iff #1473 #7)
+#1475 := [rewrite]: #1474
+#1477 := [symm #1475]: #1476
+#369 := [asserted]: #7
+#1478 := [mp #369 #1477]: #1473
+#1502 := [monotonicity #1478]: #1501
+#1507 := [trans #1502 #1505]: #1506
+#32 := (or up_15 up_2)
+#33 := (or up_14 #32)
+#439 := (iff #33 #436)
+#429 := (or up_2 up_15)
+#433 := (or up_14 #429)
+#437 := (iff #433 #436)
+#438 := [rewrite]: #437
+#434 := (iff #33 #433)
+#431 := (iff #32 #429)
+#432 := [rewrite]: #431
+#435 := [monotonicity #432]: #434
+#440 := [trans #435 #438]: #439
+#428 := [asserted]: #33
+#441 := [mp #428 #440]: #436
+#1508 := [mp #441 #1507]: #1503
+#1758 := [unit-resolution #1508 #1757]: up_14
+#917 := (or #172 #178)
+#182 := (or #178 #172)
+#919 := (iff #182 #917)
+#920 := [rewrite]: #919
+#916 := [asserted]: #182
+#923 := [mp #916 #920]: #917
+#1759 := [unit-resolution #923 #1758]: #178
+#542 := (or up_17 up_25 up_27 up_28)
+#63 := (or up_25 up_17)
+#64 := (or up_28 #63)
+#65 := (or up_27 #64)
+#545 := (iff #65 #542)
+#533 := (or up_17 up_25)
+#536 := (or up_28 #533)
+#539 := (or up_27 #536)
+#543 := (iff #539 #542)
+#544 := [rewrite]: #543
+#540 := (iff #65 #539)
+#537 := (iff #64 #536)
+#534 := (iff #63 #533)
+#535 := [rewrite]: #534
+#538 := [monotonicity #535]: #537
+#541 := [monotonicity #538]: #540
+#546 := [trans #541 #544]: #545
+#532 := [asserted]: #65
+#547 := [mp #532 #546]: #542
+#1760 := [unit-resolution #547 #1759 #1756 #1755]: up_27
+#218 := (not up_27)
+#1073 := (or #218 #227)
+#231 := (or #227 #218)
+#1075 := (iff #231 #1073)
+#1076 := [rewrite]: #1075
+#1072 := [asserted]: #231
+#1079 := [mp #1072 #1076]: #1073
+#1761 := [unit-resolution #1079 #1760]: #227
+#648 := (or up_30 up_38 up_40 up_41)
+#95 := (or up_38 up_30)
+#96 := (or up_41 #95)
+#97 := (or up_40 #96)
+#651 := (iff #97 #648)
+#639 := (or up_30 up_38)
+#642 := (or up_41 #639)
+#645 := (or up_40 #642)
+#649 := (iff #645 #648)
+#650 := [rewrite]: #649
+#646 := (iff #97 #645)
+#643 := (iff #96 #642)
+#640 := (iff #95 #639)
+#641 := [rewrite]: #640
+#644 := [monotonicity #641]: #643
+#647 := [monotonicity #644]: #646
+#652 := [trans #647 #650]: #651
+#638 := [asserted]: #97
+#653 := [mp #638 #652]: #648
+#1762 := [unit-resolution #653 #1761 #1751 #1750]: up_40
+#1220 := (or #267 #275)
+#278 := (or #275 #267)
+#1221 := (iff #278 #1220)
+#1222 := [rewrite]: #1221
+#1218 := [asserted]: #278
+#1225 := [mp #1218 #1222]: #1220
+#1763 := [unit-resolution #1225 #1762]: #275
+#1764 := [unit-resolution #685 #1763 #1738 #1737]: up_34
+#1064 := (or #218 #226)
+#229 := (or #226 #218)
+#1065 := (iff #229 #1064)
+#1066 := [rewrite]: #1065
+#1062 := [asserted]: #229
+#1069 := [mp #1062 #1066]: #1064
+#1765 := [unit-resolution #1069 #1760]: #226
+#1083 := (or #186 #218)
+#233 := (or #218 #186)
+#1085 := (iff #233 #1083)
+#1086 := [rewrite]: #1085
+#1082 := [asserted]: #233
+#1089 := [mp #1082 #1086]: #1083
+#1766 := [unit-resolution #1089 #1760]: #186
+#1767 := [unit-resolution #473 #1766 #1627 #1626]: up_18
+#969 := (or #185 #194)
+#198 := (or #194 #185)
+#971 := (iff #198 #969)
+#972 := [rewrite]: #971
+#968 := [asserted]: #198
+#975 := [mp #968 #972]: #969
+#1768 := [unit-resolution #975 #1767]: #194
+#1769 := [unit-resolution #579 #1768 #895 #1765]: up_31
+#1770 := [unit-resolution #1131 #1769 #1764]: false
+#1772 := [lemma #1770]: #1771
+#1862 := [unit-resolution #1772 #1627 #1626 #1861 #1860 #1859 #1612]: up_32
+#1239 := (or #235 #267)
+#282 := (or #267 #235)
+#1241 := (iff #282 #1239)
+#1242 := [rewrite]: #1241
+#1238 := [asserted]: #282
+#1245 := [mp #1238 #1242]: #1239
+#1863 := [unit-resolution #1245 #1862]: #267
+#1856 := (or up_12 up_52 up_49 up_41 up_16 up_8 up_7)
+#1828 := [unit-resolution #1772 #1627 #1626 #1751 #1745 #1739 #1612]: up_32
+#1829 := [unit-resolution #1245 #1828]: #267
+#1830 := [unit-resolution #1230 #1828]: #275
+#1826 := (or #170 up_41 up_40 up_16 up_8 up_49 up_12 up_52 up_42)
+#1804 := [hypothesis]: up_13
+#1805 := [unit-resolution #1026 #1804]: #201
+#1806 := [unit-resolution #1021 #1804]: #209
+#1798 := [hypothesis]: #275
+#1782 := [hypothesis]: #267
+#1802 := (or #242 up_42 up_52 up_49 up_41 up_40 up_16 up_8 up_12 up_22)
+#1783 := [hypothesis]: up_33
+#1784 := [unit-resolution #1126 #1783]: #202
+#1785 := [unit-resolution #505 #1784 #1457 #1456]: up_20
+#1786 := [unit-resolution #965 #1785]: #185
+#1787 := [unit-resolution #473 #1786 #1627 #1626]: up_19
+#1078 := (or #186 #227)
+#232 := (or #227 #186)
+#1080 := (iff #232 #1078)
+#1081 := [rewrite]: #1080
+#1077 := [asserted]: #232
+#1084 := [mp #1077 #1081]: #1078
+#1788 := [unit-resolution #1084 #1787]: #227
+#1789 := [unit-resolution #653 #1788 #1751 #1782]: up_38
+#1790 := [unit-resolution #1165 #1789]: #260
+#1780 := (or #337 up_49 up_39)
+#1773 := [hypothesis]: up_58
+#1774 := [unit-resolution #1418 #1773]: #335
+#1775 := [unit-resolution #795 #1774]: up_48
+#1776 := [hypothesis]: #260
+#1777 := [unit-resolution #1423 #1773]: #301
+#1778 := [unit-resolution #727 #1777 #1745 #1776]: up_47
+#1779 := [unit-resolution #1284 #1778 #1775]: false
+#1781 := [lemma #1779]: #1780
+#1791 := [unit-resolution #1781 #1790 #1745]: #337
+#1792 := [unit-resolution #819 #1791 #1739]: up_59
+#1793 := [unit-resolution #1448 #1792]: #345
+#1794 := [unit-resolution #1524 #1793]: up_56
+#1795 := [unit-resolution #1373 #1794]: #324
+#1796 := [unit-resolution #1516 #1795]: up_46
+#1797 := [unit-resolution #1113 #1783]: #243
+#1390 := (or #284 #325)
+#330 := (or #325 #284)
+#1392 := (iff #330 #1390)
+#1393 := [rewrite]: #1392
+#1389 := [asserted]: #330
+#1396 := [mp #1389 #1393]: #1390
+#1799 := [unit-resolution #1396 #1794]: #284
+#1800 := [unit-resolution #685 #1799 #1798 #1797]: up_44
+#1801 := [unit-resolution #1276 #1800 #1796]: false
+#1803 := [lemma #1801]: #1802
+#1807 := [unit-resolution #1803 #1805 #1739 #1745 #1751 #1782 #1627 #1626 #1457 #1798]: #242
+#1808 := [unit-resolution #608 #1807 #1806]: up_35
+#1809 := [unit-resolution #1286 #1808]: #283
+#1810 := [unit-resolution #1281 #1808]: #291
+#1811 := [unit-resolution #1516 #1810]: up_55
+#1812 := [unit-resolution #1386 #1811]: #284
+#1813 := [unit-resolution #685 #1812 #1798 #1809]: up_34
+#1814 := [unit-resolution #1136 #1813]: #202
+#1815 := [unit-resolution #505 #1814 #1457 #1805]: up_20
+#1816 := [unit-resolution #965 #1815]: #185
+#1817 := [unit-resolution #473 #1816 #1627 #1626]: up_19
+#1818 := [unit-resolution #1373 #1811]: #325
+#1819 := [unit-resolution #1524 #1818]: up_60
+#1820 := [unit-resolution #1448 #1819]: #341
+#1821 := [unit-resolution #819 #1820 #1739]: up_58
+#1822 := [unit-resolution #1781 #1821 #1745]: up_39
+#1823 := [unit-resolution #1165 #1822]: #259
+#1824 := [unit-resolution #653 #1823 #1751 #1782]: up_30
+#1825 := [unit-resolution #1084 #1824 #1817]: false
+#1827 := [lemma #1825]: #1826
+#1831 := [unit-resolution #1827 #1457 #1829 #1627 #1626 #1745 #1751 #1739 #1830]: #170
+#1832 := [unit-resolution #430 #1831]: up_11
+#1833 := [unit-resolution #886 #1832]: #160
+#1834 := [unit-resolution #410 #1833 #1612]: up_10
+#1835 := [unit-resolution #985 #1834]: #185
+#1836 := [unit-resolution #473 #1835 #1627 #1626]: up_19
+#1837 := [unit-resolution #1084 #1836]: #227
+#1838 := [unit-resolution #653 #1837 #1751 #1829]: up_38
+#1839 := [unit-resolution #1165 #1838]: #260
+#1840 := [unit-resolution #1781 #1839 #1745]: #337
+#1841 := [unit-resolution #819 #1840 #1739]: up_59
+#1842 := [unit-resolution #1448 #1841]: #345
+#1843 := [unit-resolution #1524 #1842]: up_56
+#1844 := [unit-resolution #1373 #1843]: #324
+#1845 := [unit-resolution #1516 #1844]: up_46
+#1846 := [unit-resolution #1281 #1845]: #250
+#1847 := [unit-resolution #1396 #1843]: #284
+#1848 := [unit-resolution #1276 #1845]: #283
+#1849 := [unit-resolution #685 #1848 #1830 #1847]: up_34
+#1850 := [unit-resolution #1113 #1849]: #242
+#1851 := [unit-resolution #608 #1850 #1846]: up_24
+#1852 := [unit-resolution #970 #1834]: #193
+#1853 := [unit-resolution #1136 #1849]: #202
+#1854 := [unit-resolution #505 #1853 #1457 #1852]: up_22
+#1855 := [unit-resolution #1016 #1854 #1851]: false
+#1857 := [lemma #1855]: #1856
+#1864 := [unit-resolution #1857 #1859 #1860 #1861 #1627 #1626 #1612]: up_12
+#1865 := [unit-resolution #891 #1864]: #160
+#1866 := [unit-resolution #410 #1865 #1612]: up_10
+#1867 := [unit-resolution #985 #1866]: #185
+#1868 := [unit-resolution #473 #1867 #1627 #1626]: up_19
+#1869 := [unit-resolution #1084 #1868]: #227
+#1870 := [unit-resolution #653 #1869 #1861 #1863]: up_38
+#1871 := [unit-resolution #1165 #1870]: #260
+#1872 := [unit-resolution #1781 #1871 #1860]: #337
+#1873 := [unit-resolution #819 #1872 #1859]: up_59
+#1874 := [unit-resolution #1448 #1873]: #345
+#1875 := [unit-resolution #1524 #1874]: up_56
+#1876 := [unit-resolution #1396 #1875]: #284
+#1877 := [unit-resolution #1230 #1862]: #275
+#1878 := [unit-resolution #1373 #1875]: #324
+#1879 := [unit-resolution #1516 #1878]: up_46
+#1880 := [unit-resolution #1276 #1879]: #283
+#1881 := [unit-resolution #685 #1880 #1877 #1876]: up_34
+#1882 := [unit-resolution #878 #1864]: #165
+#1883 := [unit-resolution #430 #1882]: up_13
+#1884 := [unit-resolution #1021 #1883]: #209
+#1885 := [unit-resolution #1281 #1879]: #250
+#1886 := [unit-resolution #608 #1885 #1884]: up_33
+#1887 := [unit-resolution #1113 #1886 #1881]: false
+#1889 := [lemma #1887]: #1888
+#2026 := [unit-resolution #1889 #1597 #1612 #1626]: up_16
+#908 := (or #172 #177)
+#180 := (or #177 #172)
+#909 := (iff #180 #908)
+#910 := [rewrite]: #909
+#906 := [asserted]: #180
+#913 := [mp #906 #910]: #908
+#2027 := [unit-resolution #913 #2026]: #172
+#2028 := [unit-resolution #1508 #2027]: up_15
+#2029 := [unit-resolution #1037 #2028]: #214
+#1027 := (or #173 #213)
+#216 := (or #213 #173)
+#1028 := (iff #216 #1027)
+#1029 := [rewrite]: #1028
+#1025 := [asserted]: #216
+#1032 := [mp #1025 #1029]: #1027
+#2030 := [unit-resolution #1032 #2028]: #213
+#179 := (or #177 #178)
+#905 := [asserted]: #179
+#2031 := [unit-resolution #905 #2026]: #178
+#1917 := (or #226 up_54 up_26 up_17 up_25)
+#1890 := [hypothesis]: #214
+#1891 := [hypothesis]: #213
+#1892 := [hypothesis]: #178
+#1893 := [hypothesis]: up_29
+#1894 := [unit-resolution #1069 #1893]: #218
+#1895 := [unit-resolution #547 #1894 #1892 #1891]: up_28
+#1187 := (or #219 #254)
+#266 := (or #254 #219)
+#1189 := (iff #266 #1187)
+#1190 := [rewrite]: #1189
+#1186 := [asserted]: #266
+#1193 := [mp #1186 #1190]: #1187
+#1896 := [unit-resolution #1193 #1895]: #254
+#1897 := [unit-resolution #621 #1896 #1890]: up_37
+#1898 := [unit-resolution #1297 #1897]: #296
+#1899 := [unit-resolution #795 #1898]: up_57
+#1900 := [unit-resolution #1418 #1899]: #337
+#1901 := [unit-resolution #1188 #1895]: #260
+#1287 := (or #255 #295)
+#298 := (or #295 #255)
+#1288 := (iff #298 #1287)
+#1289 := [rewrite]: #1288
+#1285 := [asserted]: #298
+#1292 := [mp #1285 #1289]: #1287
+#1902 := [unit-resolution #1292 #1897]: #295
+#1422 := (or #301 #335)
+#340 := (or #335 #301)
+#1424 := (iff #340 #1422)
+#1425 := [rewrite]: #1424
+#1421 := [asserted]: #340
+#1428 := [mp #1421 #1425]: #1422
+#1903 := [unit-resolution #1428 #1899]: #301
+#1904 := [unit-resolution #727 #1903 #1902 #1901]: up_49
+#1333 := (or #300 #309)
+#313 := (or #309 #300)
+#1335 := (iff #313 #1333)
+#1336 := [rewrite]: #1335
+#1332 := [asserted]: #313
+#1339 := [mp #1332 #1336]: #1333
+#1905 := [unit-resolution #1339 #1904]: #309
+#1906 := [unit-resolution #819 #1905 #1900]: up_59
+#1907 := [unit-resolution #1448 #1906]: #345
+#1908 := [unit-resolution #1524 #1907]: up_56
+#1909 := [unit-resolution #1329 #1904]: #308
+#1172 := (or #219 #259)
+#263 := (or #259 #219)
+#1174 := (iff #263 #1172)
+#1175 := [rewrite]: #1174
+#1171 := [asserted]: #263
+#1178 := [mp #1171 #1175]: #1172
+#1910 := [unit-resolution #1178 #1895]: #259
+#228 := (or #226 #227)
+#1061 := [asserted]: #228
+#1911 := [unit-resolution #1061 #1893]: #227
+#1343 := (or #268 #300)
+#315 := (or #300 #268)
+#1345 := (iff #315 #1343)
+#1346 := [rewrite]: #1345
+#1342 := [asserted]: #315
+#1349 := [mp #1342 #1346]: #1343
+#1912 := [unit-resolution #1349 #1904]: #268
+#1913 := [unit-resolution #653 #1912 #1911 #1910]: up_40
+#1229 := (or #267 #276)
+#280 := (or #276 #267)
+#1231 := (iff #280 #1229)
+#1232 := [rewrite]: #1231
+#1228 := [asserted]: #280
+#1235 := [mp #1228 #1232]: #1229
+#1914 := [unit-resolution #1235 #1913]: #276
+#1915 := [unit-resolution #759 #1914 #1909 #1597]: up_53
+#1385 := (or #316 #325)
+#329 := (or #325 #316)
+#1387 := (iff #329 #1385)
+#1388 := [rewrite]: #1387
+#1384 := [asserted]: #329
+#1391 := [mp #1384 #1388]: #1385
+#1916 := [unit-resolution #1391 #1915 #1908]: false
+#1918 := [lemma #1916]: #1917
+#2032 := [unit-resolution #1918 #1597 #2029 #2031 #2030]: #226
+#2010 := (or up_12 up_29 up_7 up_54 up_26)
+#1993 := (or up_35 up_12 up_54 up_26 up_29 up_7)
+#1955 := (or #170 up_54 up_26 up_29 up_12 up_35 up_7)
+#1940 := [unit-resolution #1625 #1805 #907 #1457 #1611 #1612]: up_32
+#1941 := [unit-resolution #1240 #1940]: #276
+#1942 := [unit-resolution #1230 #1940]: #275
+#1943 := [unit-resolution #608 #1806 #1611]: up_33
+#1944 := [unit-resolution #1113 #1943]: #243
+#1925 := (or #325 up_34 up_42)
+#1919 := [hypothesis]: up_56
+#1920 := [unit-resolution #1373 #1919]: #324
+#1921 := [unit-resolution #1516 #1920]: up_46
+#1922 := [unit-resolution #1396 #1919]: #284
+#1923 := [unit-resolution #685 #1922 #1605 #1798]: up_44
+#1924 := [unit-resolution #1276 #1923 #1921]: false
+#1926 := [lemma #1924]: #1925
+#1945 := [unit-resolution #1926 #1944 #1942]: #325
+#1946 := [unit-resolution #1524 #1945]: up_60
+#1947 := [unit-resolution #1448 #1946]: #341
+#1938 := (or #308 up_26 up_59)
+#1927 := [hypothesis]: up_51
+#1928 := [unit-resolution #1329 #1927]: #300
+#1929 := [hypothesis]: #341
+#1930 := [unit-resolution #1321 #1927]: #309
+#1931 := [unit-resolution #819 #1930 #1929]: up_58
+#1932 := [unit-resolution #1781 #1931 #1928]: up_39
+#1933 := [unit-resolution #1183 #1932]: #254
+#1934 := [unit-resolution #1418 #1931]: #335
+#1935 := [unit-resolution #795 #1934]: up_48
+#1936 := [unit-resolution #1297 #1935]: #255
+#1937 := [unit-resolution #621 #1936 #1933 #1890]: false
+#1939 := [lemma #1937]: #1938
+#1948 := [unit-resolution #1939 #1947 #1890]: #308
+#1949 := [unit-resolution #759 #1948 #1941 #1597]: up_53
+#1950 := [unit-resolution #1381 #1949]: #324
+#1951 := [unit-resolution #1516 #1950]: up_46
+#1952 := [unit-resolution #1401 #1949]: #284
+#1953 := [unit-resolution #685 #1952 #1944 #1942]: up_44
+#1954 := [unit-resolution #1276 #1953 #1951]: false
+#1956 := [lemma #1954]: #1955
+#1980 := [unit-resolution #1956 #1611 #1890 #907 #1457 #1597 #1612]: #170
+#1981 := [unit-resolution #430 #1980]: up_11
+#1982 := [unit-resolution #886 #1981]: #160
+#1983 := [unit-resolution #410 #1982 #1612]: up_10
+#1984 := [unit-resolution #980 #1983]: #194
+#1985 := [unit-resolution #1979 #1611 #907 #1984 #1457 #1612]: up_32
+#1970 := (or #235 up_34 up_54 up_26)
+#1957 := [hypothesis]: up_32
+#1958 := [unit-resolution #1240 #1957]: #276
+#1959 := [unit-resolution #1230 #1957]: #275
+#1960 := [unit-resolution #1926 #1959 #1605]: #325
+#1961 := [unit-resolution #1524 #1960]: up_60
+#1962 := [unit-resolution #1448 #1961]: #341
+#1963 := [unit-resolution #1939 #1962 #1890]: #308
+#1964 := [unit-resolution #759 #1963 #1958 #1597]: up_53
+#1965 := [unit-resolution #1381 #1964]: #324
+#1966 := [unit-resolution #1516 #1965]: up_46
+#1967 := [unit-resolution #1401 #1964]: #284
+#1968 := [unit-resolution #685 #1967 #1605 #1959]: up_44
+#1969 := [unit-resolution #1276 #1968 #1966]: false
+#1971 := [lemma #1969]: #1970
+#1986 := [unit-resolution #1971 #1985 #1597 #1890]: up_34
+#1987 := [unit-resolution #1113 #1986]: #242
+#1988 := [unit-resolution #608 #1987 #1611]: up_24
+#1989 := [unit-resolution #970 #1983]: #193
+#1990 := [unit-resolution #1136 #1986]: #202
+#1991 := [unit-resolution #505 #1990 #1457 #1989]: up_22
+#1992 := [unit-resolution #1016 #1991 #1988]: false
+#1994 := [lemma #1992]: #1993
+#1995 := [unit-resolution #1994 #1457 #1597 #1890 #907 #1612]: up_35
+#1996 := [unit-resolution #1281 #1995]: #291
+#1997 := [unit-resolution #1516 #1996]: up_55
+#1998 := [unit-resolution #1373 #1997]: #325
+#1999 := [unit-resolution #1524 #1998]: up_60
+#2000 := [unit-resolution #1448 #1999]: #341
+#2001 := [unit-resolution #1939 #2000 #1890]: #308
+#2002 := [unit-resolution #1610 #2001 #1995 #1597]: up_34
+#2003 := [unit-resolution #1131 #2002]: #234
+#2004 := [unit-resolution #1381 #1997]: #316
+#2005 := [unit-resolution #759 #2001 #2004 #1597]: up_43
+#2006 := [unit-resolution #1240 #2005]: #235
+#2007 := [unit-resolution #1136 #2002]: #202
+#2008 := [unit-resolution #1683 #2007 #1612 #1457]: #194
+#2009 := [unit-resolution #579 #2008 #2006 #907 #2003]: false
+#2011 := [lemma #2009]: #2010
+#2033 := [unit-resolution #2011 #2032 #1612 #1597 #2029]: up_12
+#2034 := [unit-resolution #891 #2033]: #160
+#2035 := [unit-resolution #410 #2034 #1612]: up_10
+#2036 := [unit-resolution #980 #2035]: #194
+#2037 := [unit-resolution #878 #2033]: #165
+#2038 := [unit-resolution #430 #2037]: up_13
+#2039 := [unit-resolution #1021 #2038]: #209
+#2024 := (or #234 up_26 up_54 up_24)
+#2012 := [hypothesis]: #209
+#2013 := [hypothesis]: up_31
+#2014 := [unit-resolution #1121 #2013]: #242
+#2015 := [unit-resolution #608 #2014 #2012]: up_35
+#2016 := [unit-resolution #1131 #2013]: #243
+#2017 := [unit-resolution #1610 #2016 #2015 #1597]: up_51
+#2018 := [unit-resolution #1939 #2017 #1890]: up_59
+#2019 := [unit-resolution #1448 #2018]: #345
+#2020 := [unit-resolution #1281 #2015]: #291
+#2021 := [unit-resolution #1516 #2020]: up_55
+#2022 := [unit-resolution #1373 #2021]: #325
+#2023 := [unit-resolution #1524 #2022 #2019]: false
+#2025 := [lemma #2023]: #2024
+#2040 := [unit-resolution #2025 #2029 #1597 #2039]: #234
+#2041 := [unit-resolution #579 #2040 #2032 #2036]: up_32
+#2042 := [unit-resolution #1240 #2041]: #276
+#2043 := [unit-resolution #1971 #2041 #1597 #2029]: up_34
+#2044 := [unit-resolution #1113 #2043]: #242
+#2045 := [unit-resolution #608 #2044 #2039]: up_35
+#2046 := [unit-resolution #1281 #2045]: #291
+#2047 := [unit-resolution #1516 #2046]: up_55
+#2048 := [unit-resolution #1381 #2047]: #316
+#2049 := [unit-resolution #759 #2048 #2042 #1597]: up_51
+#2050 := [unit-resolution #1373 #2047]: #325
+#2051 := [unit-resolution #1524 #2050]: up_60
+#2052 := [unit-resolution #1448 #2051]: #341
+#2053 := [unit-resolution #1939 #2052 #2049 #2029]: false
+#2055 := [lemma #2053]: #2054
+#2065 := [unit-resolution #2055 #1612 #1626]: up_54
+#1447 := (or #317 #345)
+#347 := (or #345 #317)
+#1449 := (iff #347 #1447)
+#1450 := [rewrite]: #1449
+#1446 := [asserted]: #347
+#1453 := [mp #1446 #1450]: #1447
+#2066 := [unit-resolution #1453 #2065]: #345
+#2067 := [unit-resolution #1524 #2066]: up_56
+#2083 := (or #275 up_7 up_12 up_8)
+#2063 := [hypothesis]: up_42
+#2064 := [unit-resolution #1230 #2063]: #235
+#2068 := [unit-resolution #1373 #2067]: #324
+#2069 := [unit-resolution #1516 #2068]: up_46
+#2070 := [unit-resolution #1281 #2069]: #250
+#2071 := [unit-resolution #1672 #2064 #1626 #2070 #1612]: up_16
+#2072 := [unit-resolution #913 #2071]: #172
+#2073 := [unit-resolution #1508 #2072]: up_15
+#2074 := [unit-resolution #1032 #2073]: #213
+#2075 := [unit-resolution #905 #2071]: #178
+#1452 := (or #317 #341)
+#348 := (or #341 #317)
+#1454 := (iff #348 #1452)
+#1455 := [rewrite]: #1454
+#1451 := [asserted]: #348
+#1458 := [mp #1451 #1455]: #1452
+#2076 := [unit-resolution #1458 #2065]: #341
+#2077 := [unit-resolution #1225 #2063]: #267
+#2061 := (or #226 up_59 up_40 up_17 up_25)
+#2056 := [unit-resolution #653 #1910 #1782 #1911]: up_41
+#2057 := [unit-resolution #1349 #2056]: #300
+#1338 := (or #268 #309)
+#314 := (or #309 #268)
+#1340 := (iff #314 #1338)
+#1341 := [rewrite]: #1340
+#1337 := [asserted]: #314
+#1344 := [mp #1337 #1341]: #1338
+#2058 := [unit-resolution #1344 #2056]: #309
+#2059 := [unit-resolution #819 #2058 #1929]: up_58
+#2060 := [unit-resolution #1781 #2059 #2057 #1901]: false
+#2062 := [lemma #2060]: #2061
+#2078 := [unit-resolution #2062 #2077 #2076 #2075 #2074]: #226
+#2079 := [unit-resolution #1625 #2078 #2070 #1457 #2064 #1612]: up_22
+#2080 := [unit-resolution #1979 #2078 #2070 #1457 #2064 #1612]: up_21
+#2081 := [unit-resolution #1683 #2080 #1612 #1457]: up_23
+#2082 := [unit-resolution #983 #2081 #2079]: false
+#2084 := [lemma #2082]: #2083
+#2085 := [unit-resolution #2084 #1457 #1612 #1626]: #275
+#2086 := [unit-resolution #1926 #2085 #2067]: up_34
+#2087 := [unit-resolution #1136 #2086]: #202
+#2088 := [unit-resolution #1113 #2086]: #242
+#2089 := [unit-resolution #608 #2088 #2070]: up_24
+#2090 := [unit-resolution #1016 #2089]: #201
+#2091 := [unit-resolution #505 #2090 #1457 #2087]: up_20
+#2092 := [unit-resolution #970 #2091]: #161
+#2093 := [unit-resolution #1021 #2089]: #170
+#2094 := [unit-resolution #430 #2093]: up_11
+#2095 := [unit-resolution #886 #2094]: #160
+#2096 := [unit-resolution #410 #2095 #2092 #1612]: false
+#2098 := [lemma #2096]: #2097
+#2102 := [unit-resolution #2098 #2100 #2101]: up_12
+#2103 := [unit-resolution #891 #2102]: #160
+#2104 := [unit-resolution #410 #2103 #2100]: up_10
+#2105 := [unit-resolution #980 #2104]: #194
+#2106 := [unit-resolution #2055 #2100 #2101]: up_54
+#2107 := [unit-resolution #1453 #2106]: #345
+#2108 := [unit-resolution #1524 #2107]: up_56
+#2109 := [unit-resolution #1373 #2108]: #324
+#2110 := [unit-resolution #1516 #2109]: up_46
+#2111 := [unit-resolution #1281 #2110]: #250
+#2112 := [unit-resolution #878 #2102]: #165
+#2113 := [unit-resolution #430 #2112]: up_13
+#2114 := [unit-resolution #1021 #2113]: #209
+#2115 := [unit-resolution #608 #2114 #2111]: up_33
+#2116 := [unit-resolution #1121 #2115]: #234
+#2117 := [unit-resolution #1276 #2110]: #283
+#2118 := [unit-resolution #1396 #2108]: #284
+#2119 := [unit-resolution #1113 #2115]: #243
+#2120 := [unit-resolution #685 #2119 #2118 #2117]: up_42
+#2121 := [unit-resolution #1230 #2120]: #235
+#2122 := [unit-resolution #579 #2121 #2116 #2105]: up_29
+#2123 := [unit-resolution #1225 #2120]: #267
+#2124 := [unit-resolution #1458 #2106]: #341
+#2125 := [unit-resolution #1672 #2121 #2101 #2111 #2100]: up_16
+#2126 := [unit-resolution #905 #2125]: #178
+#2127 := [unit-resolution #2062 #2126 #2124 #2123 #2122]: up_25
+#2128 := [unit-resolution #913 #2125]: #172
+#2129 := [unit-resolution #1508 #2128]: up_15
+#2130 := [unit-resolution #1032 #2129 #2127]: false
+#2131 := [lemma #2130]: #150
+#1494 := (or up_5 up_6)
+decl up_1 :: bool
+#4 := up_1
+#379 := (or up_1 up_5 up_6)
+#1497 := (iff #379 #1494)
+#1491 := (or false up_5 up_6)
+#1495 := (iff #1491 #1494)
+#1496 := [rewrite]: #1495
+#1492 := (iff #379 #1491)
+#1467 := (iff up_1 false)
+#5 := (not up_1)
+#1470 := (iff #5 #1467)
+#1463 := (iff #1467 #5)
+#1468 := [rewrite]: #1463
+#1471 := [symm #1468]: #1470
+#368 := [asserted]: #5
+#1472 := [mp #368 #1471]: #1467
+#1493 := [monotonicity #1472]: #1492
+#1498 := [trans #1493 #1496]: #1497
+#14 := (or up_6 up_1)
+#15 := (or up_5 #14)
+#382 := (iff #15 #379)
+#373 := (or up_1 up_6)
+#376 := (or up_5 #373)
+#380 := (iff #376 #379)
+#381 := [rewrite]: #380
+#377 := (iff #15 #376)
+#374 := (iff #14 #373)
+#375 := [rewrite]: #374
+#378 := [monotonicity #375]: #377
+#383 := [trans #378 #381]: #382
+#372 := [asserted]: #15
+#384 := [mp #372 #383]: #379
+#1499 := [mp #384 #1498]: #1494
+#2138 := [unit-resolution #1499 #2131]: up_6
+#151 := (not up_6)
+#927 := (or #151 #172)
+#184 := (or #172 #151)
+#929 := (iff #184 #927)
+#930 := [rewrite]: #929
+#926 := [asserted]: #184
+#933 := [mp #926 #930]: #927
+#2139 := [unit-resolution #933 #2138]: #172
+#2140 := [unit-resolution #1508 #2139]: up_15
+#2147 := [unit-resolution #1037 #2140]: #214
+#2159 := [unit-resolution #2011 #2147]: #2158
+#2160 := [unit-resolution #2159 #907 #1612 #1457]: up_54
+#2161 := [unit-resolution #1453 #2160]: #345
+#2162 := [unit-resolution #1524 #2161]: up_56
+#2163 := [unit-resolution #1926 #2162 #2157 #1605]: false
+#2165 := [lemma #2163]: #2164
+#2166 := [unit-resolution #2165 #1605 #1612 #1611 #1457]: up_29
+#2148 := (or #226 up_54)
+#2141 := [unit-resolution #1032 #2140]: #213
+#922 := (or #151 #178)
+#183 := (or #178 #151)
+#924 := (iff #183 #922)
+#925 := [rewrite]: #924
+#921 := [asserted]: #183
+#928 := [mp #921 #925]: #922
+#2142 := [unit-resolution #928 #2138]: #178
+#2149 := [unit-resolution #1918 #2147 #2142 #2141]: #2148
+#2167 := [unit-resolution #2149 #2166]: up_54
+#2154 := (or #226 up_34 up_59)
+#2143 := (or #226 up_59 up_40)
+#2144 := [unit-resolution #2062 #2142 #2141]: #2143
+#2145 := [unit-resolution #2144 #1893 #1929]: up_40
+#2146 := [unit-resolution #1225 #2145]: #275
+#2150 := [unit-resolution #2149 #1893]: up_54
+#2151 := [unit-resolution #1453 #2150]: #345
+#2152 := [unit-resolution #1524 #2151]: up_56
+#2153 := [unit-resolution #1926 #2152 #2146 #1605]: false
+#2155 := [lemma #2153]: #2154
+#2168 := [unit-resolution #2155 #2166 #1605]: up_59
+#2169 := [unit-resolution #1458 #2168 #2167]: false
+#2171 := [lemma #2169]: #2170
+#2172 := [unit-resolution #2171 #1612 #1611 #1457]: up_34
+#2173 := [unit-resolution #1136 #2172]: #202
+#2174 := [unit-resolution #1113 #2172]: #242
+#2175 := [unit-resolution #608 #2174 #1611]: up_24
+#2176 := [unit-resolution #1016 #2175]: #201
+#2177 := [unit-resolution #505 #2176 #1457 #2173]: up_20
+#2178 := [unit-resolution #970 #2177]: #161
+#2179 := [unit-resolution #1021 #2175]: #170
+#2180 := [unit-resolution #430 #2179]: up_11
+#2181 := [unit-resolution #886 #2180]: #160
+#2182 := [unit-resolution #410 #2181 #2178 #1612]: false
+#2184 := [lemma #2182]: #2183
+#2235 := [unit-resolution #2184 #1457 #1611]: up_7
+#157 := (or #155 #156)
+#856 := [asserted]: #157
+#2236 := [unit-resolution #856 #2235]: #156
+#2299 := (or up_34 up_35 up_12)
+#2283 := (or #186 up_34)
+#2185 := [hypothesis]: up_19
+#2191 := [unit-resolution #1084 #2185]: #227
+#2186 := [unit-resolution #1089 #2185]: #218
+#2187 := (or up_27 up_28)
+#2188 := [unit-resolution #547 #2142 #2141]: #2187
+#2189 := [unit-resolution #2188 #2186]: up_28
+#2192 := [unit-resolution #1178 #2189]: #259
+#2265 := [unit-resolution #1193 #2189]: #254
+#2266 := (or up_36 up_37)
+#2267 := [unit-resolution #621 #2147]: #2266
+#2268 := [unit-resolution #2267 #2265]: up_37
+#2269 := [unit-resolution #1292 #2268]: #295
+#2190 := [unit-resolution #1188 #2189]: #260
+#2270 := [unit-resolution #1297 #2268]: #296
+#2271 := [unit-resolution #795 #2270]: up_57
+#2272 := [unit-resolution #1428 #2271]: #301
+#2273 := [unit-resolution #727 #2272 #2190 #2269]: up_49
+#2274 := [unit-resolution #1349 #2273]: #268
+#2275 := [unit-resolution #653 #2274 #2192 #2191]: up_40
+#2276 := [unit-resolution #1225 #2275]: #275
+#2277 := [unit-resolution #1418 #2271]: #337
+#2278 := [unit-resolution #1339 #2273]: #309
+#2279 := [unit-resolution #819 #2278 #2277]: up_59
+#2280 := [unit-resolution #1448 #2279]: #345
+#2281 := [unit-resolution #1524 #2280]: up_56
+#2282 := [unit-resolution #1926 #2281 #2276 #1605]: false
+#2284 := [lemma #2282]: #2283
+#2292 := [unit-resolution #2284 #1605]: #186
+#2223 := (or up_8 up_18 up_19)
+#912 := (or #151 #177)
+#181 := (or #177 #151)
+#914 := (iff #181 #912)
+#915 := [rewrite]: #914
+#911 := [asserted]: #181
+#918 := [mp #911 #915]: #912
+#2222 := [unit-resolution #918 #2138]: #177
+#2224 := [unit-resolution #473 #2222]: #2223
+#2293 := [unit-resolution #2224 #2292 #2236]: up_18
+#2257 := (or #235 up_34)
+#2252 := (or #235 up_34 up_54)
+#2253 := [unit-resolution #1971 #2147]: #2252
+#2254 := [unit-resolution #2253 #1957 #1605]: up_54
+#2255 := [unit-resolution #1453 #2254]: #345
+#2256 := [unit-resolution #1524 #2255 #1960]: false
+#2258 := [lemma #2256]: #2257
+#2294 := [unit-resolution #2258 #1605]: #235
+#2290 := (or up_29 up_35 up_32 up_12 #185)
+#2200 := [hypothesis]: up_18
+#2206 := (or #185 up_29 up_32 up_12 up_22)
+#2201 := [unit-resolution #965 #2200]: #193
+#2202 := [unit-resolution #505 #2201 #1457 #1456]: up_23
+#2203 := [unit-resolution #975 #2200]: #194
+#2204 := [unit-resolution #579 #2203 #907 #895]: up_31
+#2205 := [unit-resolution #1141 #2204 #2202]: false
+#2207 := [lemma #2205]: #2206
+#2285 := [unit-resolution #2207 #907 #895 #1457 #2200]: up_22
+#2286 := [unit-resolution #1016 #2285]: #209
+#2287 := [unit-resolution #579 #907 #895 #2203]: up_31
+#2288 := [unit-resolution #1121 #2287]: #242
+#2289 := [unit-resolution #608 #2288 #2286 #1611]: false
+#2291 := [lemma #2289]: #2290
+#2295 := [unit-resolution #2291 #2294 #1611 #1457 #2293]: up_29
+#2296 := [unit-resolution #2149 #2295]: up_54
+#2297 := [unit-resolution #2155 #2295 #1605]: up_59
+#2298 := [unit-resolution #1458 #2297 #2296]: false
+#2300 := [lemma #2298]: #2299
+#2301 := [unit-resolution #2300 #1457 #1611]: up_34
+#2302 := [unit-resolution #1136 #2301]: #202
+#2303 := [unit-resolution #1113 #2301]: #242
+#2304 := [unit-resolution #608 #2303 #1611]: up_24
+#2305 := [unit-resolution #1016 #2304]: #201
+#2306 := [unit-resolution #505 #2305 #1457 #2302]: up_20
+#2307 := [unit-resolution #965 #2306]: #185
+#2308 := [unit-resolution #2224 #2307 #2236]: up_19
+#2309 := [unit-resolution #957 #2306]: #194
+#2310 := [unit-resolution #1131 #2301]: #234
+#2311 := [unit-resolution #1074 #2308]: #226
+#2312 := [unit-resolution #579 #2311 #2310 #2309]: up_32
+#2313 := [unit-resolution #1245 #2312]: #267
+#2198 := (or #186 up_59 up_40)
+#2193 := [unit-resolution #653 #2192 #1782 #2191]: up_41
+#2194 := [unit-resolution #1349 #2193]: #300
+#2195 := [unit-resolution #1344 #2193]: #309
+#2196 := [unit-resolution #819 #2195 #1929]: up_58
+#2197 := [unit-resolution #1781 #2196 #2194 #2190]: false
+#2199 := [lemma #2197]: #2198
+#2314 := [unit-resolution #2199 #2313 #2308]: up_59
+#2315 := [unit-resolution #1448 #2314]: #345
+#2316 := [unit-resolution #1524 #2315]: up_56
+#2317 := [unit-resolution #1084 #2308]: #227
+#2318 := [unit-resolution #1089 #2308]: #218
+#2319 := [unit-resolution #2188 #2318]: up_28
+#2320 := [unit-resolution #1178 #2319]: #259
+#2321 := [unit-resolution #653 #2313 #2320 #2317]: up_41
+#2322 := [unit-resolution #1334 #2321]: #308
+#2323 := [unit-resolution #1240 #2312]: #276
+#2324 := [unit-resolution #1458 #2314]: #317
+#2325 := [unit-resolution #759 #2324 #2323 #2322]: up_53
+#2326 := [unit-resolution #1391 #2325 #2316]: false
+#2328 := [lemma #2326]: #2327
+#2337 := [unit-resolution #2328 #1611]: up_12
+#2338 := [unit-resolution #878 #2337]: #165
+#2339 := [unit-resolution #430 #2338]: up_13
+#2340 := [unit-resolution #1021 #2339]: #209
+#2341 := [unit-resolution #608 #2340 #1611]: up_33
+#2342 := [unit-resolution #1113 #2341]: #243
+#2343 := [unit-resolution #2258 #2342]: #235
+#2344 := [unit-resolution #1121 #2341]: #234
+#2345 := [unit-resolution #2284 #2342]: #186
+#2346 := [unit-resolution #891 #2337]: #160
+#2335 := (or #194 up_9 up_19)
+#2329 := [hypothesis]: #186
+#2330 := [unit-resolution #975 #1674]: #185
+#2331 := [unit-resolution #2224 #2330 #2329]: up_8
+#2332 := [hypothesis]: #160
+#2333 := [unit-resolution #410 #1678 #2332]: up_7
+#2334 := [unit-resolution #856 #2333 #2331]: false
+#2336 := [lemma #2334]: #2335
+#2347 := [unit-resolution #2336 #2346 #2345]: #194
+#2348 := [unit-resolution #579 #2347 #2344 #2343]: up_29
+#2349 := [unit-resolution #2149 #2348]: up_54
+#2350 := [unit-resolution #2155 #2348 #2342]: up_59
+#2351 := [unit-resolution #1458 #2350 #2349]: false
+#2352 := [lemma #2351]: up_35
+#2353 := [unit-resolution #1281 #2352]: #291
+#2354 := [unit-resolution #1516 #2353]: up_55
+#2355 := [unit-resolution #1373 #2354]: #325
+#2356 := [unit-resolution #1524 #2355]: up_60
+#2357 := [unit-resolution #1453 #2356]: #317
+#2358 := [unit-resolution #2149 #2357]: #226
+#2359 := [unit-resolution #1448 #2356]: #341
+#2217 := (or #308 up_59)
+#2218 := [unit-resolution #1939 #2147]: #2217
+#2360 := [unit-resolution #2218 #2359]: #308
+#2361 := [unit-resolution #1381 #2354]: #316
+#2362 := [unit-resolution #759 #2357 #2361 #2360]: up_43
+#2363 := [unit-resolution #1235 #2362]: #267
+#2364 := [unit-resolution #2199 #2363 #2359]: #186
+#1145 := (or #209 #250)
+#252 := (or #250 #209)
+#1147 := (iff #252 #1145)
+#1148 := [rewrite]: #1147
+#1144 := [asserted]: #252
+#1151 := [mp #1144 #1148]: #1145
+#2365 := [unit-resolution #1151 #2352]: #209
+#2230 := (or #234 up_54 up_24)
+#2231 := [unit-resolution #2025 #2147]: #2230
+#2366 := [unit-resolution #2231 #2357 #2365]: #234
+#2367 := [unit-resolution #1240 #2362]: #235
+#2368 := [unit-resolution #579 #2367 #2366 #2358]: up_21
+#2369 := [unit-resolution #2336 #2368 #2364]: up_9
+#870 := (or #155 #160)
+#163 := (or #160 #155)
+#871 := (iff #163 #870)
+#872 := [rewrite]: #871
+#868 := [asserted]: #163
+#875 := [mp #868 #872]: #870
+#2370 := [unit-resolution #875 #2369]: #155
+#2371 := [unit-resolution #891 #2369]: #166
+[unit-resolution #2159 #2371 #2370 #2358 #2357]: false
+unsat
--- a/src/HOL/SMT/SMT.thy Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/SMT.thy Tue Oct 20 10:11:30 2009 +0200
@@ -2,50 +2,20 @@
Author: Sascha Boehme, TU Muenchen
*)
-header {* SMT method using external SMT solvers (CVC3, Yices, Z3) *}
+header {* Bindings to several SMT solvers *}
theory SMT
-imports SMT_Definitions
+imports SMT_Base Z3
uses
- "Tools/smt_normalize.ML"
- "Tools/smt_monomorph.ML"
- "Tools/smt_translate.ML"
- "Tools/smt_solver.ML"
- "Tools/smtlib_interface.ML"
"Tools/cvc3_solver.ML"
"Tools/yices_solver.ML"
- "Tools/z3_model.ML"
- "Tools/z3_interface.ML"
- "Tools/z3_solver.ML"
begin
-setup {*
- SMT_Normalize.setup #>
- SMT_Solver.setup #>
- CVC3_Solver.setup #>
- Yices_Solver.setup #>
- Z3_Solver.setup
-*}
+setup {* CVC3_Solver.setup #> Yices_Solver.setup *}
-ML {*
-OuterSyntax.improper_command "smt_status"
- "Show the available SMT solvers and the currently selected solver."
- OuterKeyword.diag
- (Scan.succeed (Toplevel.no_timing o Toplevel.keep (fn state =>
- SMT_Solver.print_setup (Context.Proof (Toplevel.context_of state)))))
-*}
-
-method_setup smt = {*
- let fun solver thms ctxt = SMT_Solver.smt_tac ctxt thms
- in
- Scan.optional (Scan.lift (Args.add -- Args.colon) |-- Attrib.thms) [] >>
- (Method.SIMPLE_METHOD' oo solver)
- end
-*} "Applies an SMT solver to the current goal."
-
-declare [[ smt_solver = z3, smt_timeout = 20, smt_trace = false ]]
+declare [[ smt_solver = z3, smt_timeout = 20 ]]
declare [[ smt_unfold_defs = true ]]
-declare [[ z3_proofs = false ]]
+declare [[ smt_trace = false, smt_keep = "", smt_cert = "" ]]
+declare [[ z3_proofs = false, z3_options = "" ]]
end
-
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/SMT_Base.thy Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,131 @@
+(* Title: HOL/SMT/SMT_Base.thy
+ Author: Sascha Boehme, TU Muenchen
+*)
+
+header {* SMT-specific definitions and basic tools *}
+
+theory SMT_Base
+imports Real Word "~~/src/HOL/Decision_Procs/Dense_Linear_Order"
+uses
+ ("Tools/smt_normalize.ML")
+ ("Tools/smt_monomorph.ML")
+ ("Tools/smt_translate.ML")
+ ("Tools/smt_solver.ML")
+ ("Tools/smtlib_interface.ML")
+begin
+
+section {* Triggers for quantifier instantiation *}
+
+text {*
+Some SMT solvers support triggers for quantifier instantiation. Each trigger
+consists of one ore more patterns. A pattern may either be a list of positive
+subterms (the first being tagged by "pat" and the consecutive subterms tagged
+by "andpat"), or a list of negative subterms (the first being tagged by "nopat"
+and the consecutive subterms tagged by "andpat").
+*}
+
+datatype pattern = Pattern
+
+definition pat :: "'a \<Rightarrow> pattern"
+where "pat _ = Pattern"
+
+definition nopat :: "bool \<Rightarrow> pattern"
+where "nopat _ = Pattern"
+
+definition andpat :: "pattern \<Rightarrow> 'a \<Rightarrow> pattern" (infixl "andpat" 60)
+where "_ andpat _ = Pattern"
+
+definition trigger :: "pattern list \<Rightarrow> bool \<Rightarrow> bool"
+where "trigger _ P = P"
+
+
+section {* Arithmetic *}
+
+text {*
+The sign of @{term "op mod :: int \<Rightarrow> int \<Rightarrow> int"} follows the sign of the
+divisor. In contrast to that, the sign of the following operation is that of
+the dividend.
+*}
+
+definition rem :: "int \<Rightarrow> int \<Rightarrow> int" (infixl "rem" 70)
+where "a rem b =
+ (if (a \<ge> 0 \<and> b < 0) \<or> (a < 0 \<and> b \<ge> 0) then - (a mod b) else a mod b)"
+
+text {* A decision procedure for linear real arithmetic: *}
+
+setup {*
+ Arith_Data.add_tactic "Ferrante-Rackoff" (K FerranteRackoff.dlo_tac)
+*}
+
+
+section {* Bitvectors *}
+
+text {*
+The following definitions provide additional functions not found in HOL-Word.
+*}
+
+definition sdiv :: "'a::len word \<Rightarrow> 'a word \<Rightarrow> 'a word" (infix "sdiv" 70)
+where "w1 sdiv w2 = word_of_int (sint w1 div sint w2)"
+
+definition smod :: "'a::len word \<Rightarrow> 'a word \<Rightarrow> 'a word" (infix "smod" 70)
+ (* sign follows divisor *)
+where "w1 smod w2 = word_of_int (sint w1 mod sint w2)"
+
+definition srem :: "'a::len word \<Rightarrow> 'a word \<Rightarrow> 'a word" (infix "srem" 70)
+ (* sign follows dividend *)
+where "w1 srem w2 = word_of_int (sint w1 rem sint w2)"
+
+definition bv_shl :: "'a::len0 word \<Rightarrow> 'a word \<Rightarrow> 'a word"
+where "bv_shl w1 w2 = (w1 << unat w2)"
+
+definition bv_lshr :: "'a::len0 word \<Rightarrow> 'a word \<Rightarrow> 'a word"
+where "bv_lshr w1 w2 = (w1 >> unat w2)"
+
+definition bv_ashr :: "'a::len word \<Rightarrow> 'a word \<Rightarrow> 'a word"
+where "bv_ashr w1 w2 = (w1 >>> unat w2)"
+
+
+section {* Higher-Order Encoding *}
+
+definition "apply" where "apply f x = f x"
+
+lemmas array_rules = apply_def fun_upd_same fun_upd_other fun_upd_upd ext
+
+
+section {* First-order logic *}
+
+text {*
+Some SMT solver formats require a strict separation between formulas and terms.
+The following marker symbols are used internally to separate those categories:
+*}
+
+definition formula :: "bool \<Rightarrow> bool" where "formula x = x"
+definition "term" where "term x = x"
+
+text {*
+Predicate symbols also occurring as function symbols are turned into function
+symbols by translating atomic formulas into terms:
+*}
+
+abbreviation holds :: "bool \<Rightarrow> bool" where "holds \<equiv> (\<lambda>P. term P = term True)"
+
+text {*
+The following constant represents equivalence, to be treated differently than
+the (polymorphic) equality predicate:
+*}
+
+definition iff :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infix "iff" 50) where
+ "(x iff y) = (x = y)"
+
+
+section {* Setup *}
+
+use "Tools/smt_normalize.ML"
+use "Tools/smt_monomorph.ML"
+use "Tools/smt_translate.ML"
+use "Tools/smt_solver.ML"
+use "Tools/smtlib_interface.ML"
+
+setup {* SMT_Normalize.setup #> SMT_Solver.setup *}
+
+end
--- a/src/HOL/SMT/SMT_Definitions.thy Tue Oct 20 08:10:47 2009 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,113 +0,0 @@
-(* Title: HOL/SMT/SMT_Definitions.thy
- Author: Sascha Boehme, TU Muenchen
-*)
-
-header {* SMT-specific definitions *}
-
-theory SMT_Definitions
-imports Real Word "~~/src/HOL/Decision_Procs/Dense_Linear_Order"
-begin
-
-section {* Triggers for quantifier instantiation *}
-
-text {*
-Some SMT solvers support triggers for quantifier instantiation. Each trigger
-consists of one ore more patterns. A pattern may either be a list of positive
-subterms (the first being tagged by "pat" and the consecutive subterms tagged
-by "andpat"), or a list of negative subterms (the first being tagged by "nopat"
-and the consecutive subterms tagged by "andpat").
-*}
-
-datatype pattern = Pattern
-
-definition pat :: "'a \<Rightarrow> pattern"
-where "pat _ = Pattern"
-
-definition nopat :: "bool \<Rightarrow> pattern"
-where "nopat _ = Pattern"
-
-definition andpat :: "pattern \<Rightarrow> 'a \<Rightarrow> pattern" (infixl "andpat" 60)
-where "_ andpat _ = Pattern"
-
-definition trigger :: "pattern list \<Rightarrow> bool \<Rightarrow> bool"
-where "trigger _ P = P"
-
-
-section {* Arithmetic *}
-
-text {*
-The sign of @{term "op mod :: int \<Rightarrow> int \<Rightarrow> int"} follows the sign of the
-divisor. In contrast to that, the sign of the following operation is that of
-the dividend.
-*}
-
-definition rem :: "int \<Rightarrow> int \<Rightarrow> int" (infixl "rem" 70)
-where "a rem b =
- (if (a \<ge> 0 \<and> b < 0) \<or> (a < 0 \<and> b \<ge> 0) then - (a mod b) else a mod b)"
-
-text {* A decision procedure for linear real arithmetic: *}
-
-setup {*
- Arith_Data.add_tactic "Ferrante-Rackoff" (K FerranteRackoff.dlo_tac)
-*}
-
-
-section {* Bitvectors *}
-
-text {*
-The following definitions provide additional functions not found in HOL-Word.
-*}
-
-definition sdiv :: "'a::len word \<Rightarrow> 'a word \<Rightarrow> 'a word" (infix "sdiv" 70)
-where "w1 sdiv w2 = word_of_int (sint w1 div sint w2)"
-
-definition smod :: "'a::len word \<Rightarrow> 'a word \<Rightarrow> 'a word" (infix "smod" 70)
- (* sign follows divisor *)
-where "w1 smod w2 = word_of_int (sint w1 mod sint w2)"
-
-definition srem :: "'a::len word \<Rightarrow> 'a word \<Rightarrow> 'a word" (infix "srem" 70)
- (* sign follows dividend *)
-where "w1 srem w2 = word_of_int (sint w1 rem sint w2)"
-
-definition bv_shl :: "'a::len0 word \<Rightarrow> 'a word \<Rightarrow> 'a word"
-where "bv_shl w1 w2 = (w1 << unat w2)"
-
-definition bv_lshr :: "'a::len0 word \<Rightarrow> 'a word \<Rightarrow> 'a word"
-where "bv_lshr w1 w2 = (w1 >> unat w2)"
-
-definition bv_ashr :: "'a::len word \<Rightarrow> 'a word \<Rightarrow> 'a word"
-where "bv_ashr w1 w2 = (w1 >>> unat w2)"
-
-
-section {* Higher-order encoding *}
-
-definition "apply" where "apply f x = f x"
-
-
-section {* First-order logic *}
-
-text {*
-Some SMT solver formats require a strict separation between formulas and terms.
-The following marker symbols are used internally to separate those categories:
-*}
-
-definition formula :: "bool \<Rightarrow> bool" where "formula x = x"
-definition "term" where "term x = x"
-
-text {*
-Predicate symbols also occurring as function symbols are turned into function
-symbols by translating atomic formulas into terms:
-*}
-
-abbreviation holds :: "bool \<Rightarrow> bool" where "holds \<equiv> (\<lambda>P. term P = term True)"
-
-text {*
-The following constant represents equivalence, to be treated differently than
-the (polymorphic) equality predicate:
-*}
-
-definition iff :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infix "iff" 50) where
- "(x iff y) = (x = y)"
-
-end
-
--- a/src/HOL/SMT/Tools/cvc3_solver.ML Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/Tools/cvc3_solver.ML Tue Oct 20 10:11:30 2009 +0200
@@ -27,10 +27,8 @@
fun raise_cex real ctxt recon ls =
let
- val start = String.isPrefix "%Satisfiable Variable Assignment: %"
- val index = find_index start ls
- val ls = if index > 0 then Library.drop (index + 1, ls) else []
- val p = Pretty.big_list (cex_kind real ^ " found:") (map Pretty.str ls)
+ val ls' = filter_out (String.isPrefix "%") ls
+ val p = Pretty.big_list (cex_kind real ^ " found:") (map Pretty.str ls')
in error (Pretty.string_of p) end
fun core_oracle (SMT_Solver.ProofData {context, output, recon, ...}) =
@@ -47,9 +45,9 @@
fun smtlib_solver oracle _ =
SMT_Solver.SolverConfig {
- name = {env_var=env_var, remote_name=solver_name},
+ command = {env_var=env_var, remote_name=solver_name},
+ arguments = options,
interface = SMTLIB_Interface.interface,
- arguments = options,
reconstruct = oracle }
val setup =
--- a/src/HOL/SMT/Tools/smt_normalize.ML Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/Tools/smt_normalize.ML Tue Oct 20 10:11:30 2009 +0200
@@ -273,59 +273,78 @@
fun inst_meta cT = Thm.instantiate_cterm ([(meta_eqT, cT)], []) meta_eq
fun mk_meta_eq ct cu = Thm.mk_binop (inst_meta (Thm.ctyp_of_term ct)) ct cu
- fun lambda_conv conv =
- let
- fun sub_conv cvs ctxt ct =
- (case Thm.term_of ct of
- Const (@{const_name All}, _) $ Abs _ => quant_conv cvs ctxt
- | Const (@{const_name Ex}, _) $ Abs _ => quant_conv cvs ctxt
- | Const _ $ Abs _ => Conv.arg_conv (at_lambda_conv cvs ctxt)
- | Const (@{const_name Let}, _) $ _ $ Abs _ => Conv.combination_conv
- (Conv.arg_conv (sub_conv cvs ctxt)) (abs_conv cvs ctxt)
- | Abs _ => at_lambda_conv cvs ctxt
- | _ $ _ => Conv.comb_conv (sub_conv cvs ctxt)
- | _ => Conv.all_conv) ct
- and abs_conv cvs = Conv.abs_conv (fn (cv, cx) => sub_conv (cv::cvs) cx)
- and quant_conv cvs ctxt = Conv.arg_conv (abs_conv cvs ctxt)
- and at_lambda_conv cvs ctxt = abs_conv cvs ctxt then_conv conv cvs ctxt
- in sub_conv [] end
+ val fresh_name = yield_singleton Name.variants
fun used_vars cvs ct =
let
val lookup = AList.lookup (op aconv) (map (` Thm.term_of) cvs)
val add = (fn (SOME ct) => insert (op aconvc) ct | _ => I)
in Term.fold_aterms (add o lookup) (Thm.term_of ct) [] end
+ fun make_def cvs eq = Thm.symmetric (fold norm_meta_def cvs eq)
+ fun add_def ct thm = Termtab.update (Thm.term_of ct, (serial (), thm))
- val rev_int_fst_ord = rev_order o int_ord o pairself fst
- fun ordered_values tab =
- Termtab.fold (fn (_, x) => OrdList.insert rev_int_fst_ord x) tab []
- |> map snd
+ fun replace ctxt cvs ct (cx as (nctxt, defs)) =
+ let
+ val cvs' = used_vars cvs ct
+ val ct' = fold Thm.cabs cvs' ct
+ val mk_repl = fold (fn ct => fn cu => Thm.capply cu ct) cvs'
+ in
+ (case Termtab.lookup defs (Thm.term_of ct') of
+ SOME (_, eq) => (make_def cvs' eq, cx)
+ | NONE =>
+ let
+ val {t, T, ...} = Thm.rep_cterm ct'
+ val (n, nctxt') = fresh_name "" nctxt
+ val eq = Thm.assume (mk_meta_eq (cert ctxt (Free (n, T))) ct')
+ in (make_def cvs' eq, (nctxt', add_def ct' eq defs)) end)
+ end
+
+ fun none ct cx = (Thm.reflexive ct, cx)
+ fun in_comb f g ct cx =
+ let val (cu1, cu2) = Thm.dest_comb ct
+ in cx |> f cu1 ||>> g cu2 |>> uncurry Thm.combination end
+ fun in_arg f = in_comb none f
+ fun in_abs f cvs ct (nctxt, defs) =
+ let
+ val (n, nctxt') = fresh_name Name.uu nctxt
+ val (cv, cu) = Thm.dest_abs (SOME n) ct
+ in f (cv :: cvs) cu (nctxt', defs) |>> Thm.abstract_rule n cv end
+
+ fun replace_lambdas ctxt =
+ let
+ fun repl cvs ct =
+ (case Thm.term_of ct of
+ Const (@{const_name All}, _) $ Abs _ => in_arg (in_abs repl cvs)
+ | Const (@{const_name Ex}, _) $ Abs _ => in_arg (in_abs repl cvs)
+ | Const _ $ Abs _ => in_arg (at_lambda cvs)
+ | Const (@{const_name Let}, _) $ _ $ Abs _ =>
+ in_comb (in_arg (repl cvs)) (in_abs repl cvs)
+ | Abs _ => at_lambda cvs
+ | _ $ _ => in_comb (repl cvs) (repl cvs)
+ | _ => none) ct
+ and at_lambda cvs ct cx =
+ let
+ val (thm1, cx') = in_abs repl cvs ct cx
+ val (thm2, cx'') = replace ctxt cvs (Thm.rhs_of thm1) cx'
+ in (Thm.transitive thm1 thm2, cx'') end
+ in repl [] end
in
fun lift_lambdas ctxt thms =
let
val declare_frees = fold (Thm.fold_terms Term.declare_term_frees)
- val names = Unsynchronized.ref (declare_frees thms (Name.make_context []))
- val fresh_name = Unsynchronized.change_result names o yield_singleton Name.variants
+ fun rewrite f thm cx =
+ let val (thm', cx') = f (Thm.cprop_of thm) cx
+ in (Thm.equal_elim thm' thm, cx') end
- val defs = Unsynchronized.ref (Termtab.empty : (int * thm) Termtab.table)
- fun add_def t thm = Unsynchronized.change defs (Termtab.update (t, (serial (), thm)))
- fun make_def cvs eq = Thm.symmetric (fold norm_meta_def cvs eq)
- fun def_conv cvs ctxt ct =
- let
- val cvs' = used_vars cvs ct
- val ct' = fold Thm.cabs cvs' ct
- in
- (case Termtab.lookup (!defs) (Thm.term_of ct') of
- SOME (_, eq) => make_def cvs' eq
- | NONE =>
- let
- val {t, T, ...} = Thm.rep_cterm ct'
- val eq = mk_meta_eq (cert ctxt (Free (fresh_name "", T))) ct'
- val thm = Thm.assume eq
- in (add_def t thm; make_def cvs' thm) end)
- end
- val thms' = map (Conv.fconv_rule (lambda_conv def_conv ctxt)) thms
- val eqs = ordered_values (!defs)
+ val rev_int_fst_ord = rev_order o int_ord o pairself fst
+ fun ordered_values tab =
+ Termtab.fold (fn (_, x) => OrdList.insert rev_int_fst_ord x) tab []
+ |> map snd
+
+ val (thms', (_, defs)) =
+ (declare_frees thms (Name.make_context []), Termtab.empty)
+ |> fold_map (rewrite (replace_lambdas ctxt)) thms
+ val eqs = ordered_values defs
in
(maps (#hyps o Thm.crep_thm) eqs, map (normalize_rule ctxt) eqs @ thms')
end
--- a/src/HOL/SMT/Tools/smt_solver.ML Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/Tools/smt_solver.ML Tue Oct 20 10:11:30 2009 +0200
@@ -19,9 +19,9 @@
assms: thm list option }
datatype solver_config = SolverConfig of {
- name: {env_var: string, remote_name: string},
+ command: {env_var: string, remote_name: string},
+ arguments: string list,
interface: interface,
- arguments: string list,
reconstruct: proof_data -> thm }
(*options*)
@@ -29,6 +29,8 @@
val with_timeout: Proof.context -> ('a -> 'b) -> 'a -> 'b
val trace: bool Config.T
val trace_msg: Proof.context -> ('a -> string) -> 'a -> unit
+ val keep: string Config.T
+ val cert: string Config.T
(*solvers*)
type solver = Proof.context -> thm list -> thm
@@ -67,9 +69,9 @@
assms: thm list option }
datatype solver_config = SolverConfig of {
- name: {env_var: string, remote_name: string},
+ command: {env_var: string, remote_name: string},
+ arguments: string list,
interface: interface,
- arguments: string list,
reconstruct: proof_data -> thm }
@@ -86,17 +88,28 @@
fun trace_msg ctxt f x =
if Config.get ctxt trace then tracing (f x) else ()
+val (keep, setup_keep) = Attrib.config_string "smt_keep" ""
+val (cert, setup_cert) = Attrib.config_string "smt_cert" ""
+
(* interface to external solvers *)
local
-fun with_tmp_files f x =
+fun with_files ctxt f x =
let
- fun tmp_path () = File.tmp_path (Path.explode ("smt-" ^ serial_string ()))
- val in_path = tmp_path () and out_path = tmp_path ()
- val y = Exn.capture (f in_path out_path) x
- val _ = try File.rm in_path and _ = try File.rm out_path
+ fun make_names n = (n, n ^ ".proof")
+
+ val keep' = Config.get ctxt keep
+ val paths as (problem_path, proof_path) =
+ if keep' <> "" andalso File.exists (Path.dir (Path.explode keep'))
+ then pairself Path.explode (make_names keep')
+ else pairself (File.tmp_path o Path.explode)
+ (make_names ("smt-" ^ serial_string ()))
+
+ val y = Exn.capture (f problem_path proof_path) x
+
+ val _ = if keep' = "" then (pairself (try File.rm) paths; ()) else ()
in Exn.release y end
fun run in_path out_path (ctxt, cmd, output) =
@@ -115,12 +128,18 @@
fun run_solver ctxt {env_var, remote_name} args output =
let
val qf = File.shell_path and qq = File.shell_quote
- val path = getenv env_var and remote = getenv "REMOTE_SMT_SOLVER"
+ val qs = qf o Path.explode
+ val local_name = getenv env_var
+ val cert_name = Config.get ctxt cert
+ val remote = qs (getenv "REMOTE_SMT_SOLVER")
+ val cert_script = qs (getenv "CERT_SMT_SOLVER")
fun cmd f1 f2 =
- if path <> ""
- then map qq (path :: args) @ [qf f1, ">", qf f2]
- else "perl -w" :: map qq (remote :: remote_name :: args) @ [qf f1, qf f2]
- in with_tmp_files run (ctxt, space_implode " " oo cmd, output) end
+ if cert_name <> ""
+ then "perl -w" :: [cert_script, qs cert_name, qf f1, ">", qf f2]
+ else if local_name <> ""
+ then qs local_name :: map qq args @ [qf f1, ">", qf f2]
+ else "perl -w" :: remote :: map qq (remote_name :: args) @ [qf f1, qf f2]
+ in with_files ctxt run (ctxt, space_implode " " oo cmd, output) end
end
@@ -129,12 +148,12 @@
fun gen_solver solver ctxt prems =
let
- val SolverConfig {name, interface, arguments, reconstruct} = solver ctxt
+ val SolverConfig {command, arguments, interface, reconstruct} = solver ctxt
val Interface {normalize=nc, translate=tc} = interface
val thy = ProofContext.theory_of ctxt
in
SMT_Normalize.normalize nc ctxt prems
- ||> run_solver ctxt name arguments o SMT_Translate.translate tc thy
+ ||> run_solver ctxt command arguments o SMT_Translate.translate tc thy
||> reconstruct o make_proof_data ctxt
|-> fold SMT_Normalize.discharge_definition
end
@@ -196,8 +215,8 @@
fun pretty_counterex ctxt (real, ex) =
let
- val msg = if real then "Counterexample found:"
- else "Potential counterexample found:"
+ val msg = if real then "SMT: counterexample found:"
+ else "SMT: potential counterexample found:"
val cex = if null ex then [Pretty.str "(no assignments)"]
else map (Syntax.pretty_term ctxt) ex
in Pretty.string_of (Pretty.big_list msg cex) end
@@ -212,6 +231,11 @@
val smt_tac = smt_tac' false
+val smt_method =
+ Scan.optional (Scan.lift (Args.add -- Args.colon) |-- Attrib.thms) [] >>
+ (fn thms => fn ctxt => METHOD (fn facts =>
+ HEADGOAL (smt_tac ctxt (thms @ facts))))
+
(* setup *)
@@ -221,7 +245,11 @@
(Thm.declaration_attribute o K o select_solver))
"SMT solver configuration" #>
setup_timeout #>
- setup_trace
+ setup_trace #>
+ setup_keep #>
+ setup_cert #>
+ Method.setup (Binding.name "smt") smt_method
+ "Applies an SMT solver to the current goal."
fun print_setup gen =
let
@@ -243,4 +271,10 @@
Pretty.big_list "Solver-specific settings:" infos])
end
+val _ = OuterSyntax.improper_command "smt_status"
+ "Show the available SMT solvers and the currently selected solver."
+ OuterKeyword.diag
+ (Scan.succeed (Toplevel.no_timing o Toplevel.keep (fn state =>
+ print_setup (Context.Proof (Toplevel.context_of state)))))
+
end
--- a/src/HOL/SMT/Tools/yices_solver.ML Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/Tools/yices_solver.ML Tue Oct 20 10:11:30 2009 +0200
@@ -40,9 +40,9 @@
fun smtlib_solver oracle _ =
SMT_Solver.SolverConfig {
- name = {env_var=env_var, remote_name=solver_name},
+ command = {env_var=env_var, remote_name=solver_name},
+ arguments = options,
interface = SMTLIB_Interface.interface,
- arguments = options,
reconstruct = oracle }
val setup =
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Tools/z3_proof.ML Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,247 @@
+(* Title: HOL/SMT/Tools/z3_proof.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Proof reconstruction for proofs found by Z3.
+*)
+
+signature Z3_PROOF =
+sig
+ val reconstruct: Proof.context -> thm list option -> SMT_Translate.recon ->
+ string list -> thm
+end
+
+structure Z3_Proof: Z3_PROOF =
+struct
+
+structure T = Z3_Proof_Terms
+structure R = Z3_Proof_Rules
+
+fun z3_exn msg = error ("Z3 proof reconstruction: " ^ msg)
+
+
+fun lift f (x, y) = apsnd (pair x) (f y)
+fun lift' f v (x, y) = apsnd (rpair y) (f v x)
+
+fun $$ s = lift (Scan.$$ s)
+fun this s = lift (Scan.this_string s)
+
+fun blank s = lift (Scan.many1 Symbol.is_ascii_blank) s
+
+fun par scan = $$ "(" |-- scan --| $$ ")"
+fun bra scan = $$ "[" |-- scan --| $$ "]"
+
+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 = Scan.repeat1 (Scan.some digit) >>
+ (fn ds => fold (fn d => fn i => i * 10 + d) ds 0)
+val int_num = Scan.optional (Scan.$$ "-" >> 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 =) (explode "_+*-/%~=<>$&|?!.@^#")
+val name = Scan.many1 is_char >> implode
+
+datatype sym = Sym of string * sym list
+
+datatype context = Context of {
+ Ttab: typ Symtab.table,
+ ttab: Thm.cterm Symtab.table,
+ etab: T.preterm Inttab.table,
+ ptab: R.proof Inttab.table,
+ nctxt: Name.context }
+
+fun make_context (Ttab, ttab, etab, ptab, nctxt) =
+ Context {Ttab=Ttab, ttab=ttab, etab=etab, ptab=ptab, nctxt=nctxt}
+
+fun empty_context thy (SMT_Translate.Recon {typs, terms=ttab}) =
+ let
+ val ttab' = Symtab.map (fn @{term True} => @{term "~False"} | t => t) ttab
+ val ns = Symtab.fold (Term.add_free_names o snd) ttab' []
+ val nctxt = Name.make_context ns
+ val tt = Symtab.map (Thm.cterm_of thy) ttab'
+ in make_context (typs, tt, Inttab.empty, Inttab.empty, nctxt) end
+
+fun map_context f (Context {Ttab, ttab, etab, ptab, nctxt}) =
+ make_context (f (Ttab, ttab, etab, ptab, nctxt))
+
+fun map_type_tab f = map_context (fn (Ttab, ttab, etab, ptab, nctxt) =>
+ (f Ttab, ttab, etab, ptab, nctxt))
+
+fun map_term_tab f = map_context (fn (Ttab, ttab, etab, ptab, nctxt) =>
+ (Ttab, f ttab, etab, ptab, nctxt))
+
+fun map_expr_tab f = map_context (fn (Ttab, ttab, etab, ptab, nctxt) =>
+ (Ttab, ttab, f etab, ptab, nctxt))
+
+fun map_proof_tab f = map_context (fn (Ttab, ttab, etab, ptab, nctxt) =>
+ (Ttab, ttab, etab, f ptab, nctxt))
+
+val free_prefix = "f"
+
+fun fresh_name (cx as Context {nctxt, ...}) =
+ let val (n, nctxt') = yield_singleton Name.variants free_prefix nctxt
+ in
+ (n, map_context (fn (Ttab, ttab, etab, ptab, _) =>
+ (Ttab, ttab, etab, ptab, nctxt')) cx)
+ end
+
+fun typ_of_sort name (cx as Context {Ttab, ...}) =
+ (case Symtab.lookup Ttab name of
+ SOME T => (T, cx)
+ | _ => cx |> fresh_name |-> (fn n =>
+ let val T = TFree ("'" ^ n, @{sort type})
+ in pair T o map_type_tab (Symtab.update (name, T)) end))
+
+fun lookup_expr id (cx as Context {etab, ...}) =
+ (case Inttab.lookup etab id of
+ SOME e => (e, cx)
+ | _ => z3_exn ("unknown term id: " ^ quote (string_of_int id)))
+
+fun add_expr k t = map_expr_tab (Inttab.update (k, t))
+
+fun add_proof thy k ((r, ps), t) (cx as Context {nctxt, ...}) =
+ let val p = R.make_proof r ps (T.compile thy nctxt t)
+ in (k, map_proof_tab (Inttab.update (k, p)) cx) end
+
+fun mk_app app (cx as Context {ttab, ...}) =
+ let
+ val mk =
+ (fn
+ (Sym ("true", _), _) => T.mk_true
+ | (Sym ("false", _), _) => T.mk_false
+ | (Sym ("=", _), [t, u]) => T.mk_eq t u
+ | (Sym ("distinct", _), ts) => T.mk_distinct ts
+ | (Sym ("ite", _), [s, t, u]) => T.mk_if s t u
+ | (Sym ("and", _), ts) => T.mk_and ts
+ | (Sym ("or", _), ts) => T.mk_or ts
+ | (Sym ("iff", _), [t, u]) => T.mk_iff t u
+ | (Sym ("xor", _), [t, u]) => T.mk_not (T.mk_iff t u)
+ | (Sym ("not", _), [t]) => T.mk_not t
+ | (Sym ("implies", _), [t, u]) => T.mk_implies t u
+ | (Sym ("~", _), [t, u]) => T.mk_eq t u
+ | (Sym ("<", _), [t, u]) => T.mk_lt t u
+ | (Sym ("<=", _), [t, u]) => T.mk_le t u
+ | (Sym (">", _), [t, u]) => T.mk_lt u t
+ | (Sym (">=", _), [t, u]) => T.mk_le u t
+ | (Sym ("+", _), [t, u]) => T.mk_add t u
+ | (Sym ("-", _), [t, u]) => T.mk_sub t u
+ | (Sym ("-", _), [t]) => T.mk_uminus t
+ | (Sym ("*", _), [t, u]) => T.mk_mul t u
+ | (Sym ("/", _), [t, u]) => T.mk_real_div t u
+ | (Sym ("div", _), [t, u]) => T.mk_int_div t u
+ | (Sym ("mod", _), [t, u]) => T.mk_mod t u
+ | (Sym ("rem", _), [t, u]) => T.mk_rem t u
+ | (Sym ("select", _), [m, k]) => T.mk_access m k
+ | (Sym ("store", _), [m, k, v]) => T.mk_update m k v
+ | (Sym ("pattern", _), _) => T.mk_true
+ | (Sym (n, _), ts) =>
+ (case Symtab.lookup ttab n of
+ SOME ct => T.mk_fun ct ts
+ | NONE => z3_exn ("unknown function: " ^ quote n)))
+ in (mk app, cx) end
+
+fun add_decl thy (n, T) (cx as Context {ttab, ...}) =
+ (case Symtab.lookup ttab n of
+ SOME _ => cx
+ | _ => cx |> fresh_name |-> (fn n' =>
+ map_term_tab (Symtab.update (n, Thm.cterm_of thy (Free (n', T))))))
+
+
+fun sep scan_sep scan = scan ::: Scan.repeat (scan_sep |-- scan)
+fun bsep scan = Scan.repeat (blank |-- scan)
+fun bsep1 scan = Scan.repeat1 (blank |-- scan)
+
+val id = Scan.$$ "#" |-- int_num
+
+fun sym s =
+ (lift name -- Scan.optional (bra (sep ($$ ":") sym)) [] >> Sym) s
+
+fun sort st = Scan.first [
+ this "bool" >> K @{typ bool},
+ this "int" >> K @{typ int},
+ this "real" >> K @{typ real},
+ this "bv" |-- bra (lift int_num) >> T.wordT,
+ this "array" |-- bra (sort --| $$ ":" -- sort) >> (op -->),
+ par (this "->" |-- bsep1 sort) >> ((op --->) o split_last),
+ lift name #-> lift' typ_of_sort] st
+
+fun bound thy =
+ par (this ":var" -- blank |-- lift int_num --| blank -- sort) >>
+ uncurry (T.mk_bound thy)
+
+val number =
+ int_num -- Scan.option (Scan.$$ "/" |-- int_num) --|
+ Scan.this_string "::" :|-- (fn num as (n, _) =>
+ Scan.this_string "int" >> K (T.mk_int_num n) ||
+ Scan.this_string "real" >> K (T.mk_real_frac_num num))
+
+fun bv_number thy =
+ this "bv" |-- bra (lift (int_num --| Scan.$$ ":" -- int_num)) >>
+ uncurry (T.mk_bv_num thy)
+
+val constant = sym #-> lift' (mk_app o rpair [])
+
+fun arg thy = Scan.first [lift id #-> lift' lookup_expr,
+ lift number, bv_number thy, constant]
+
+fun application thy =
+ par (sym -- bsep1 (arg thy)) #-> lift' mk_app
+
+val variables =
+ par (this "vars" |-- bsep1 (par ((lift name >> K "x") --| blank -- sort)))
+val patterns = bsep (par ((this ":pat" || this ":nopat") |-- bsep1 (lift id)))
+val quant_kind =
+ this "forall" >> K T.mk_forall || this "exists" >> K T.mk_exists
+fun quantifier thy = par (quant_kind --| blank --
+ variables --| patterns --| blank -- arg thy) >>
+ (fn ((q, vs), body) => fold_rev (q thy) vs body)
+
+fun expr thy k = Scan.first [bound thy, quantifier thy, application thy,
+ lift number, bv_number thy, constant] #-> apfst o add_expr k
+
+fun rule_name name =
+ (case R.rule_of_string name of
+ SOME r => r
+ | NONE => z3_exn ("unknown proof rule: " ^ quote name))
+
+fun rule thy k =
+ bra (lift (name >> rule_name) -- bsep (lift id)) --|
+ ($$ ":" -- blank) -- arg thy #-> lift' (add_proof thy k)
+
+fun decl thy = ((this "decl" -- blank) |-- lift name --|
+ (blank -- this "::" -- blank) -- sort) #-> apfst o add_decl thy
+
+fun def st = (lift id --| (blank -- this ":=" -- blank)) st
+
+fun node thy =
+ decl thy #> pair NONE ||
+ def :|-- (fn k => expr thy k #> pair NONE || rule thy k #>> K NONE) ||
+ rule thy ~1 #>> SOME
+
+fun parse_error line_no ((_, xs), _) =
+ "parse error at line " ^ string_of_int line_no ^ ": " ^ quote (implode xs)
+
+fun handle_errors ln scan = Scan.error (Scan.!! (parse_error ln) scan)
+
+fun parse_line thy l (st as (stop, line_no, cx)) =
+ if is_some stop then st
+ else
+ (cx, explode l)
+ |> handle_errors line_no (Scan.finite' Symbol.stopper (node thy))
+ |> (fn (stop', (cx', _)) => (stop', line_no + 1, cx'))
+
+fun reconstruct ctxt assms recon output =
+ let
+ val _ = T.var_prefix <> free_prefix orelse error "Same prefixes"
+
+ val thy = ProofContext.theory_of ctxt
+ in
+ (case fold (parse_line thy) output (NONE, 1, empty_context thy recon) of
+ (SOME p, _, Context {ptab, ...}) => R.prove ctxt assms ptab p
+ | _ => z3_exn "bad proof")
+ end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Tools/z3_proof_rules.ML Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,1319 @@
+(* Title: HOL/SMT/Tools/z3_proof_rules.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Z3 proof rules and their reconstruction.
+*)
+
+signature Z3_PROOF_RULES =
+sig
+ (*proof rule names*)
+ type rule
+ val rule_of_string: string -> rule option
+ val string_of_rule: rule -> string
+
+ (*proof reconstruction*)
+ type proof
+ val make_proof: rule -> int list -> Thm.cterm * Thm.cterm list -> proof
+ val prove: Proof.context -> thm list option -> proof Inttab.table -> int ->
+ thm
+
+ (*setup*)
+ val setup: theory -> theory
+end
+
+structure Z3_Proof_Rules: Z3_PROOF_RULES =
+struct
+
+structure T = Z3_Proof_Terms
+
+fun z3_exn msg = error ("Z3 proof reconstruction: " ^ msg)
+
+
+(* proof rule names *)
+
+datatype rule = TrueAxiom | Asserted | Goal | ModusPonens | Reflexivity |
+ Symmetry | Transitivity | TransitivityStar | Monotonicity | QuantIntro |
+ Distributivity | AndElim | NotOrElim | Rewrite | RewriteStar | PullQuant |
+ PullQuantStar | PushQuant | ElimUnusedVars | DestEqRes | QuantInst |
+ Hypothesis | Lemma | UnitResolution | IffTrue | IffFalse | Commutativity |
+ DefAxiom | IntroDef | ApplyDef | IffOeq | NnfPos | NnfNeg | NnfStar |
+ CnfStar | Skolemize | ModusPonensOeq | ThLemma
+
+val rule_names = Symtab.make [
+ ("true-axiom", TrueAxiom),
+ ("asserted", Asserted),
+ ("goal", Goal),
+ ("mp", ModusPonens),
+ ("refl", Reflexivity),
+ ("symm", Symmetry),
+ ("trans", Transitivity),
+ ("trans*", TransitivityStar),
+ ("monotonicity", Monotonicity),
+ ("quant-intro", QuantIntro),
+ ("distributivity", Distributivity),
+ ("and-elim", AndElim),
+ ("not-or-elim", NotOrElim),
+ ("rewrite", Rewrite),
+ ("rewrite*", RewriteStar),
+ ("pull-quant", PullQuant),
+ ("pull-quant*", PullQuantStar),
+ ("push-quant", PushQuant),
+ ("elim-unused", ElimUnusedVars),
+ ("der", DestEqRes),
+ ("quant-inst", QuantInst),
+ ("hypothesis", Hypothesis),
+ ("lemma", Lemma),
+ ("unit-resolution", UnitResolution),
+ ("iff-true", IffTrue),
+ ("iff-false", IffFalse),
+ ("commutativity", Commutativity),
+ ("def-axiom", DefAxiom),
+ ("intro-def", IntroDef),
+ ("apply-def", ApplyDef),
+ ("iff~", IffOeq),
+ ("nnf-pos", NnfPos),
+ ("nnf-neg", NnfNeg),
+ ("nnf*", NnfStar),
+ ("cnf*", CnfStar),
+ ("sk", Skolemize),
+ ("mp~", ModusPonensOeq),
+ ("th-lemma", ThLemma)]
+
+val rule_of_string = Symtab.lookup rule_names
+fun string_of_rule r =
+ let fun fit (s, r') = if r = r' then SOME s else NONE
+ in the (Symtab.get_first NONE fit rule_names) end
+
+
+(* proof representation *)
+
+datatype theorem =
+ Thm of thm |
+ MetaEq of thm |
+ Literals of thm * thm Termtab.table
+
+fun thm_of (Thm thm) = thm
+ | thm_of (MetaEq thm) = thm COMP @{thm meta_eq_to_obj_eq}
+ | thm_of (Literals (thm, _)) = thm
+
+fun meta_eq_of (MetaEq thm) = thm
+ | meta_eq_of p = thm_of p COMP @{thm eq_reflection}
+
+datatype proof =
+ Unproved of {
+ rule: rule,
+ subs: int list,
+ prop: Thm.cterm,
+ vars: Thm.cterm list } |
+ Sequent of {
+ hyps: Thm.cterm list,
+ vars: Thm.cterm list,
+ thm: theorem }
+
+fun make_proof r ps (ct, cvs) = Unproved {rule=r, subs=ps, prop=ct, vars=cvs}
+
+
+(* proof reconstruction utilities *)
+
+fun try_apply ctxt name nfs ct =
+ let
+ val trace = SMT_Solver.trace_msg ctxt I
+
+ fun first [] = z3_exn (name ^ " failed")
+ | first ((n, f) :: nfs) =
+ (case try f ct of
+ SOME thm => (trace (n ^ " succeeded"); thm)
+ | NONE => (trace (n ^ " failed"); first nfs))
+ in first nfs end
+
+fun prop_of thm = (case Thm.prop_of thm of @{term Trueprop} $ t => t | t => t)
+
+fun as_meta_eq ct = uncurry T.mk_meta_eq (Thm.dest_binop ct)
+
+fun by_tac' tac ct = Goal.norm_result (Goal.prove_internal [] ct (K (tac 1)))
+fun by_tac tac ct = by_tac' tac (T.mk_prop ct)
+
+fun match_instantiate' f ct thm =
+ Thm.instantiate (Thm.match (f (Thm.cprop_of thm), ct)) thm
+val match_instantiate = match_instantiate' I
+
+local
+ fun maybe_instantiate ct thm =
+ try Thm.first_order_match (Thm.cprop_of thm, ct)
+ |> Option.map (fn inst => Thm.instantiate inst thm)
+in
+fun thm_net_of thms =
+ let fun insert thm = Net.insert_term (K false) (Thm.prop_of thm, thm)
+ in fold insert thms Net.empty end
+
+fun first_of thms ct = get_first (maybe_instantiate ct) thms
+fun net_instance net ct = first_of (Net.match_term net (Thm.term_of ct)) ct
+end
+
+fun certify ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
+fun certify_var ctxt idx T = certify ctxt (Var (("x", idx), T))
+
+fun varify ctxt =
+ let
+ fun varify1 cv thm =
+ let
+ val T = Thm.typ_of (Thm.ctyp_of_term cv)
+ val v = certify_var ctxt (Thm.maxidx_of thm + 1) T
+ in SMT_Normalize.instantiate_free (cv, v) thm end
+ in fold varify1 end
+
+fun under_assumption f ct =
+ let val ct' = T.mk_prop ct
+ in Thm.implies_intr ct' (f (Thm.assume ct')) end
+
+fun with_conv conv prove ct =
+ let val eq = Thm.symmetric (conv ct)
+ in Thm.equal_elim eq (prove (Thm.lhs_of eq)) end
+
+fun list2 (x, y) = [x, y]
+
+fun precompose f rule = (f (Thm.cprem_of rule 1), f, rule)
+
+fun discharge p pq = Thm.implies_elim pq p
+
+fun compose (cvs, f, rule) thm =
+ let fun inst thm = Thm.instantiate ([], cvs ~~ f (Thm.cprop_of thm))
+ in discharge thm (inst thm rule) end
+
+fun make_hyp_def thm = (* |- c x == t x ==> P (c x) ~~> c == t |- P (c x) *)
+ let
+ val (lhs, rhs) = Thm.dest_binop (Thm.cprem_of thm 1)
+ val (cf, cvs) = Drule.strip_comb lhs
+ val eq = T.mk_meta_eq cf (fold_rev Thm.cabs cvs rhs)
+ fun apply cv th =
+ Thm.combination th (Thm.reflexive cv)
+ |> Conv.fconv_rule (Conv.arg_conv (Thm.beta_conversion false))
+ in ([eq], Thm.implies_elim thm (fold apply cvs (Thm.assume eq))) end
+
+val true_thm = @{lemma "~False" by simp}
+
+val is_neg = (fn @{term Not} $ _ => true | _ => false)
+fun is_neg' f = (fn @{term Not} $ t => f t | _ => false)
+val is_conj = (fn @{term "op &"} $ _ $ _ => true | _ => false)
+val is_disj = (fn @{term "op |"} $ _ $ _ => true | _ => false)
+
+(** explosion of conjunctions and disjunctions **)
+
+local
+ val dest_conj_term = (fn @{term "op &"} $ t $ u => SOME (t, u) | _ => NONE)
+
+ val negate_term = (fn @{term Not} $ t => t | t => @{term Not} $ t)
+ fun dest_disj_term' f = (fn
+ @{term Not} $ (@{term "op |"} $ t $ u) => SOME (f t, f u)
+ | _ => NONE)
+ val dest_disj_term = dest_disj_term' negate_term
+
+ fun destc ct = list2 (Thm.dest_binop (Thm.dest_arg ct))
+ val dest_conj1 = precompose destc @{thm conjunct1}
+ val dest_conj2 = precompose destc @{thm conjunct2}
+ fun dest_conj_rules t =
+ dest_conj_term t |> Option.map (K (dest_conj1, dest_conj2))
+
+ fun destd f ct = list2 (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 = precompose (destd I) @{lemma "~(P | Q) ==> ~P" by fast}
+ and dest_disj2 = precompose (destd dn1) @{lemma "~(~P | Q) ==> P" by fast}
+ and dest_disj3 = precompose (destd I) @{lemma "~(P | Q) ==> ~Q" by fast}
+ and dest_disj4 = precompose (destd dn2) @{lemma "~(P | ~Q) ==> Q" by fast}
+
+ val is_neg = (fn @{term Not} $ _ => true | _ => false)
+ 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)
+
+ val is_dneg = is_neg' is_neg
+ fun destn ct = [Thm.dest_arg (Thm.dest_arg (Thm.dest_arg ct))]
+ val dneg_rule = precompose destn @{thm notnotD}
+in
+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
+
+fun explode_term is_conj keep_intermediate =
+ 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 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 #>
+ keep_intermediate ? cons (t, rev rules)
+ end
+ | NONE => cons (t, rev rules))
+ fun explode0 (@{term Not} $ (@{term Not} $ t)) = [(t, [dneg_rule])]
+ | explode0 t = explode1 [] t []
+ in explode0 end
+
+fun extract_lit thm rules = fold compose rules thm
+
+fun explode_thm 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 (prop_of thm) then cons thm
+ else
+ (case dest_rules (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) (prop_of thm)
+ then explode1 (compose dest_rule thm)
+ else cons (compose dest_rule thm)
+ fun explode0 thm =
+ if not is_conj andalso is_dneg (prop_of thm) then [compose dneg_rule thm]
+ else explode1 thm []
+ in explode0 end
+end
+
+(** joining of literals to conjunctions or disjunctions **)
+
+local
+ fun precomp2 f g thm =
+ (f (Thm.cprem_of thm 1), g (Thm.cprem_of thm 2), f, g, thm)
+ fun comp2 (cv1, cv2, f, g, rule) thm1 thm2 =
+ let val inst = [(cv1, f (Thm.cprop_of thm1)), (cv2, g (Thm.cprop_of thm2))]
+ in Thm.instantiate ([], inst) rule |> discharge thm1 |> discharge thm2 end
+
+ 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 (@{term "op &"} $ t $ u) = ((false, t), (false, u))
+ | dest_conj t = raise TERM ("dest_conj", [t])
+
+ val neg = (fn @{term Not} $ t => (true, t) | t => (false, @{term Not} $ t))
+ fun dest_disj (@{term Not} $ (@{term "op |"} $ t $ u)) = (neg t, neg u)
+ | dest_disj t = raise TERM ("dest_disj", [t])
+
+ val dnegE = precompose (single o d2 o d1) @{thm notnotD}
+ val dnegI = precompose (single o d1) @{lemma "P ==> ~~P" by fast}
+ fun as_dneg f t = f (@{term Not} $ (@{term Not} $ t))
+
+ fun dni f = list2 o apsnd f o Thm.dest_binop o f o d1
+ val negIffE = precompose (dni d1) @{lemma "~(P = (~Q)) ==> Q = P" by fast}
+ val negIffI = precompose (dni I) @{lemma "P = Q ==> ~(Q = (~P))" by fast}
+ val iff_const = @{term "op = :: bool => _"}
+ fun as_negIff f (@{term "op = :: bool => _"} $ t $ u) =
+ f (@{term Not} $ (iff_const $ u $ (@{term Not} $ t)))
+ | as_negIff _ _ = NONE
+in
+fun make_lit_tab thms = fold (Termtab.update o ` prop_of) thms Termtab.empty
+
+fun join is_conj tab 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_lit = Termtab.lookup tab
+ fun lookup_lit' t =
+ (case t of
+ @{term Not} $ (@{term Not} $ t) => (compose dnegI, lookup_lit t)
+ | @{term Not} $ (@{term "op = :: bool => _"} $ t $ (@{term Not} $ u)) =>
+ (compose negIffI, lookup_lit (iff_const $ u $ t))
+ | @{term Not} $ ((eq as Const (@{const_name "op ="}, _)) $ t $ u) =>
+ let fun rewr lit = lit COMP @{thm not_sym}
+ in (rewr, lookup_lit (@{term Not} $ (eq $ u $ t))) end
+ | _ =>
+ (case as_dneg lookup_lit t of
+ NONE => (compose negIffE, as_negIff lookup_lit t)
+ | x => (compose dnegE, x)))
+ fun join1 (s, t) =
+ (case lookup_lit t of
+ SOME lit => (s, lit)
+ | NONE =>
+ (case lookup_lit' 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 fastsimp}
+ val cp3 = @{lemma "P = (~Q) ==> (~P) = Q" by simp}
+ val neg = Thm.capply @{cterm Not}
+in
+fun contrapos1 prove (ct, cu) = prove (neg ct, neg cu) COMP cp1
+fun contrapos2 prove (ct, cu) = prove (neg ct, Thm.dest_arg cu) COMP cp2
+fun contrapos3 prove (ct, cu) = prove (Thm.dest_arg ct, neg cu) COMP cp3
+end
+
+local
+ fun prove_eq l r (cl, cr) =
+ let
+ fun explode is_conj = explode_thm is_conj true (l <> r) []
+ fun make_tab is_conj thm = make_lit_tab (true_thm :: explode is_conj thm)
+ fun prove is_conj ct tab = join is_conj tab (Thm.term_of ct)
+
+ val thm1 = under_assumption (prove r cr o make_tab l) cl
+ val thm2 = 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 CONJ
+ else if is_disj t then DISJ
+ else if is_neg' is_conj t then NCON
+ else if is_neg' is_disj t then NDIS
+ else CONJ (*allows to prove equalities with single literals on each side*)
+in
+fun prove_conj_disj_eq ct =
+ let val cp = Thm.dest_binop ct
+ in
+ (case pairself (kind_of o Thm.term_of) cp of
+ (CONJ, CONJ) => prove_eq true true cp
+ | (CONJ, NDIS) => prove_eq true false cp
+ | (DISJ, DISJ) => contrapos1 (prove_eq false false) cp
+ | (DISJ, NCON) => contrapos2 (prove_eq false true) cp
+ | (NCON, NCON) => contrapos1 (prove_eq true true) cp
+ | (NCON, DISJ) => contrapos3 (prove_eq true false) cp
+ | (NDIS, NDIS) => prove_eq false false cp
+ | (NDIS, CONJ) => prove_eq false true cp)
+ end
+end
+
+(** unfolding of distinct **)
+
+local
+ val distinct1 = @{lemma "distinct [] == ~False" by simp}
+ val distinct2 = @{lemma "distinct [x] == ~False" by simp}
+ val distinct3 = @{lemma "distinct (x # xs) == x ~: set xs & distinct xs"
+ by simp}
+
+ val set1 = @{lemma "x ~: set [] == ~False" by simp}
+ val set2 = @{lemma "x ~: set [y] == x ~= y" by simp}
+ val set3 = @{lemma "x ~: set (y # ys) == x ~= y & x ~: set ys" by simp}
+
+ fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
+
+ fun unfold_conv rule1 rule2 rule3 sub_conv =
+ let
+ fun uconv ct =
+ (Conv.rewr_conv rule1 else_conv
+ Conv.rewr_conv rule2 else_conv
+ (Conv.rewr_conv rule3 then_conv binop_conv sub_conv uconv)) ct
+ in uconv end
+
+ val set_conv = unfold_conv set1 set2 set3 Conv.all_conv
+in
+val unfold_distinct_conv = unfold_conv distinct1 distinct2 distinct3 set_conv
+end
+
+
+(* core proof rules *)
+
+datatype assms = Some of thm list | Many of thm Net.net
+
+val true_false = @{lemma "True == ~ False" by simp}
+
+local
+ val TT_eq = @{lemma "(P = (~False)) == P" by simp}
+ val remove_trigger = @{lemma "trigger t p == p"
+ by (rule eq_reflection, rule trigger_def)}
+ val remove_iff = @{lemma "p iff q == p = q"
+ by (rule eq_reflection, rule iff_def)}
+
+ fun with_context simpset ctxt = Simplifier.context ctxt simpset
+
+ val prep_ss = with_context (Simplifier.empty_ss addsimps
+ [@{thm Let_def}, remove_trigger, remove_iff, true_false, TT_eq])
+
+ val TT_eq_conv = Conv.rewr_conv TT_eq
+ val norm_conv = More_Conv.bottom_conv (K (Conv.try_conv TT_eq_conv))
+
+ val threshold = 10
+
+ val lookup = (fn Some thms => first_of thms | Many net => net_instance net)
+ fun lookup_assm ctxt assms ct =
+ (case lookup assms ct of
+ SOME thm => thm
+ | _ => z3_exn ("not asserted: " ^
+ quote (Syntax.string_of_term ctxt (Thm.term_of ct))))
+in
+fun prepare_assms ctxt assms =
+ let
+ val rewrite = Conv.fconv_rule (Simplifier.rewrite (prep_ss ctxt))
+ val thms = map rewrite assms
+ in if length assms < threshold then Some thms else Many (thm_net_of thms) end
+
+fun asserted _ NONE ct = Thm (Thm.assume (T.mk_prop ct))
+ | asserted ctxt (SOME assms) ct =
+ Thm (with_conv (norm_conv ctxt) (lookup_assm ctxt assms) (T.mk_prop ct))
+end
+
+
+(** P ==> P = Q ==> Q or P ==> P --> Q ==> Q **)
+local
+ val meta_iffD1 = @{lemma "P == Q ==> P ==> (Q::bool)" by simp}
+ val meta_iffD1_c = precompose (list2 o Thm.dest_binop) meta_iffD1
+
+ val iffD1_c = precompose (list2 o Thm.dest_binop o Thm.dest_arg) @{thm iffD1}
+ val mp_c = precompose (list2 o Thm.dest_binop o Thm.dest_arg) @{thm mp}
+in
+fun mp (MetaEq thm) p = Thm (Thm.implies_elim (compose meta_iffD1_c thm) p)
+ | mp p_q p =
+ let
+ val pq = thm_of p_q
+ val thm = compose iffD1_c pq handle THM _ => compose mp_c pq
+ in Thm (Thm.implies_elim thm p) end
+end
+
+
+(** and_elim: P1 & ... & Pn ==> Pi **)
+(** not_or_elim: ~(P1 | ... | Pn) ==> ~Pi **)
+local
+ fun get_lit conj t (l, thm) =
+ let val is_sublit_of = exists_lit conj (fn u => u aconv t)
+ in if is_sublit_of (prop_of thm) then SOME (l, thm) else NONE end
+
+ fun derive conj t lits idx ptab =
+ let
+ val (l, lit) = the (Termtab.get_first NONE (get_lit conj t) lits)
+ val ls = explode_thm conj false false [t] lit
+ val lits' = fold (Termtab.update o ` prop_of) ls (Termtab.delete l lits)
+ fun upd (Sequent {hyps, vars, thm}) =
+ Sequent {hyps=hyps, vars=vars, thm = Literals (thm_of thm, lits')}
+ | upd p = p
+ in (the (Termtab.lookup lits' t), Inttab.map_entry idx upd ptab) end
+
+ val mk_tab = make_lit_tab o single
+ val literals_of = (fn Literals (_, lits) => lits | p => mk_tab (thm_of p))
+ fun lit_elim conj (p, idx) ct ptab =
+ let val lits = literals_of p
+ in
+ (case Termtab.lookup lits (Thm.term_of ct) of
+ SOME lit => (Thm lit, ptab)
+ | NONE => apfst Thm (derive conj (Thm.term_of ct) lits idx ptab))
+ end
+in
+val and_elim = lit_elim true
+val not_or_elim = lit_elim false
+end
+
+
+(** P1 ... Pn |- False ==> |- ~P1 | ... | ~Pn **)
+local
+ fun step lit thm =
+ Thm.implies_elim (Thm.implies_intr (Thm.cprop_of lit) thm) lit
+ val explode_disj = explode_thm false false false
+ fun intro hyps thm th = fold step (explode_disj hyps th) thm
+
+ fun dest_ccontr ct = [Thm.dest_arg (Thm.dest_arg (Thm.dest_arg1 ct))]
+ val ccontr = precompose dest_ccontr @{thm ccontr}
+in
+fun lemma thm ct =
+ let
+ val cu = Thm.capply @{cterm Not} ct
+ val hyps = map_filter (try HOLogic.dest_Trueprop) (#hyps (Thm.rep_thm thm))
+ in Thm (compose ccontr (under_assumption (intro hyps thm) cu)) end
+end
+
+
+(** \/{P1, ..., Pn, Q1, ..., Qn} & ~P1 & ... & ~Pn ==> \/{Q1, ..., Qn} **)
+local
+ val explode_disj = explode_thm false true false and join_disj = join false
+ fun unit thm thms th =
+ let val t = @{term Not} $ prop_of thm and ts = map prop_of thms
+ in join_disj (make_lit_tab (thms @ explode_disj ts th)) t end
+
+ fun dest_arg2 ct = Thm.dest_arg (Thm.dest_arg ct)
+ fun dest ct = list2 (pairself dest_arg2 (Thm.dest_binop ct))
+ val contrapos = precompose dest @{lemma "(~P ==> ~Q) ==> Q ==> P" by fast}
+in
+fun unit_resolution thm thms ct =
+ under_assumption (unit thm thms) (Thm.capply @{cterm Not} ct)
+ |> Thm o discharge thm o compose contrapos
+end
+
+
+local
+ val iff1 = @{lemma "P ==> P == (~ False)" by simp}
+ val iff2 = @{lemma "~P ==> P == False" by simp}
+in
+fun iff_true thm = MetaEq (thm COMP iff1)
+fun iff_false thm = MetaEq (thm COMP iff2)
+end
+
+
+(** distributivity of | over & **)
+val distributivity = Thm o by_tac (Classical.fast_tac HOL_cs)
+
+
+(** Tseitin-like axioms **)
+local
+ val disjI1 = @{lemma "(P ==> Q) ==> ~P | Q" by fast}
+ val disjI2 = @{lemma "(~P ==> Q) ==> P | Q" by fast}
+ val disjI3 = @{lemma "(~Q ==> P) ==> P | Q" by fast}
+ val disjI4 = @{lemma "(Q ==> P) ==> P | ~Q" by fast}
+
+ fun prove' conj1 conj2 ct2 thm =
+ let val tab =
+ make_lit_tab (true_thm :: explode_thm conj1 true (conj1 <> conj2) [] thm)
+ in join conj2 tab (Thm.term_of ct2) end
+
+ fun prove rule (ct1, conj1) (ct2, conj2) =
+ under_assumption (prove' conj1 conj2 ct2) ct1 COMP rule
+
+ fun prove_def_axiom ct =
+ let val (ct1, ct2) = Thm.dest_binop ct
+ in
+ (case Thm.term_of ct1 of
+ @{term Not} $ (@{term "op &"} $ _ $ _) =>
+ prove disjI1 (Thm.dest_arg ct1, true) (ct2, true)
+ | @{term "op &"} $ _ $ _ =>
+ prove disjI3 (Thm.capply @{cterm Not} ct2, false) (ct1, true)
+ | @{term Not} $ (@{term "op |"} $ _ $ _) =>
+ prove disjI3 (Thm.capply @{cterm Not} ct2, false) (ct1, false)
+ | @{term "op |"} $ _ $ _ =>
+ prove disjI2 (Thm.capply @{cterm Not} ct1, false) (ct2, true)
+ | Const (@{const_name distinct}, _) $ _ =>
+ let
+ fun dis_conv cv = Conv.arg_conv (Conv.arg1_conv cv)
+ fun prv cu =
+ let val (cu1, cu2) = Thm.dest_binop (Thm.dest_arg cu)
+ in prove disjI4 (Thm.dest_arg cu2, true) (cu1, true) end
+ in with_conv (dis_conv unfold_distinct_conv) prv (T.mk_prop ct) end
+ | @{term Not} $ (Const (@{const_name distinct}, _) $ _) =>
+ let
+ fun dis_conv cv = Conv.arg_conv (Conv.arg1_conv (Conv.arg_conv cv))
+ fun prv cu =
+ let val (cu1, cu2) = Thm.dest_binop (Thm.dest_arg cu)
+ in prove disjI1 (Thm.dest_arg cu1, true) (cu2, true) end
+ in with_conv (dis_conv unfold_distinct_conv) prv (T.mk_prop ct) end
+ | _ => raise CTERM ("prove_def_axiom", [ct]))
+ end
+
+ val ifI = @{lemma "(P ==> Q1) ==> (~P ==> Q2) ==> if P then Q1 else Q2"
+ by simp}
+ val ifE = @{lemma
+ "(if P then Q1 else Q2) ==> (P --> Q1 ==> ~P --> Q2 ==> R) ==> R" by simp}
+ val claset = HOL_cs addIs [ifI] addEs [ifE]
+in
+fun def_axiom ctxt ct =
+ Thm (try_apply ctxt "def_axiom" [
+ ("conj/disj", prove_def_axiom),
+ ("fast", by_tac (Classical.fast_tac claset)),
+ ("simp+fast", by_tac (Simplifier.simp_tac HOL_ss THEN_ALL_NEW
+ Classical.fast_tac claset))] ct)
+end
+
+
+(** local definitions **)
+local
+ val intro_rules = [
+ @{lemma "n == P ==> (~n | P) & (n | ~P)" by simp},
+ @{lemma "n == (if P then s else t) ==> (~P | n = s) & (P | n = t)"
+ by simp},
+ @{lemma "n == P ==> n = P" by (rule meta_eq_to_obj_eq)} ]
+
+ val apply_rules = [
+ @{lemma "(~n | P) & (n | ~P) ==> P == n" by (atomize(full)) fast},
+ @{lemma "(~P | n = s) & (P | n = t) ==> (if P then s else t) == n"
+ by (atomize(full)) fastsimp} ]
+
+ val inst_rule = match_instantiate' Thm.dest_arg
+
+ fun apply_rule ct =
+ (case get_first (try (inst_rule (T.mk_prop ct))) intro_rules of
+ SOME thm => thm
+ | NONE => raise CTERM ("intro_def", [ct]))
+in
+fun intro_def ct = apsnd Thm (make_hyp_def (apply_rule ct))
+
+fun apply_def thm =
+ get_first (try (fn rule => MetaEq (thm COMP rule))) apply_rules
+ |> the_default (Thm thm)
+end
+
+
+local
+ val quant_rules1 = ([
+ @{lemma "(!!x. P x == Q) ==> ALL x. P x == Q" by simp},
+ @{lemma "(!!x. P x == Q) ==> EX x. P x == Q" by simp}], [
+ @{lemma "(!!x. P x == Q x) ==> ALL x. P x == ALL x. Q x" by simp},
+ @{lemma "(!!x. P x == Q x) ==> EX x. P x == EX x. Q x" by simp}])
+
+ val quant_rules2 = ([
+ @{lemma "(!!x. ~P x == Q) ==> ~(ALL x. P x) == Q" by simp},
+ @{lemma "(!!x. ~P x == Q) ==> ~(EX x. P x) == Q" by simp}], [
+ @{lemma "(!!x. ~P x == Q x) ==> ~(ALL x. P x) == EX x. Q x" by simp},
+ @{lemma "(!!x. ~P x == Q x) ==> ~(EX x. P x) == ALL x. Q x" by simp}])
+
+ fun nnf_quant_tac thm (qs as (qs1, qs2)) i st = (
+ Tactic.rtac thm ORELSE'
+ (Tactic.match_tac qs1 THEN' nnf_quant_tac thm qs) ORELSE'
+ (Tactic.match_tac qs2 THEN' nnf_quant_tac thm qs)) i st
+
+ fun nnf_quant ctxt qs (p, (vars, _)) ct =
+ as_meta_eq ct
+ |> by_tac' (nnf_quant_tac (varify ctxt vars (meta_eq_of p)) qs)
+
+ val nnf_rules = thm_net_of [@{thm not_not}]
+
+ fun prove_nnf ctxt =
+ try_apply ctxt "nnf" [
+ ("conj/disj", prove_conj_disj_eq o Thm.dest_arg),
+ ("rule", the o net_instance nnf_rules),
+ ("tactic", by_tac' (Classical.best_tac HOL_cs))]
+in
+fun nnf ctxt ps ct =
+ (case Thm.term_of ct of
+ _ $ (l as Const _ $ Abs _) $ (r as Const _ $ Abs _) =>
+ if l aconv r then MetaEq (Thm.reflexive (Thm.dest_arg ct))
+ else MetaEq (nnf_quant ctxt quant_rules1 (hd ps) ct)
+ | _ $ (@{term Not} $ (Const _ $ Abs _)) $ (Const _ $ Abs _) =>
+ MetaEq (nnf_quant ctxt quant_rules2 (hd ps) ct)
+ | _ =>
+ let
+ val eqs = map (Thm.symmetric o meta_eq_of o fst) ps
+ val nnf_rewr_conv = Conv.arg_conv (Conv.arg_conv
+ (More_Conv.top_sweep_conv (K (More_Conv.rewrs_conv eqs)) ctxt))
+ in Thm (with_conv nnf_rewr_conv (prove_nnf ctxt) (T.mk_prop ct)) end)
+end
+
+
+(* equality proof rules *)
+
+(** t = t **)
+fun refl ct = MetaEq (Thm.reflexive (Thm.dest_arg ct))
+
+
+(** s = t ==> t = s **)
+local
+ val symm_rule = @{lemma "s = t ==> t == s" by simp}
+in
+fun symm (MetaEq thm) = MetaEq (Thm.symmetric thm)
+ | symm p = MetaEq (thm_of p COMP symm_rule)
+end
+
+
+(** s = t ==> t = u ==> s = u **)
+local
+ val trans_rule = @{lemma "s = t ==> t = u ==> s == u" by simp}
+in
+fun trans (MetaEq thm) q = MetaEq (Thm.transitive thm (meta_eq_of q))
+ | trans p (MetaEq thm) = MetaEq (Thm.transitive (meta_eq_of p) thm)
+ | trans p q = MetaEq (thm_of q COMP (thm_of p COMP trans_rule))
+end
+
+
+(** t1 = s1 & ... & tn = sn ==> f t1 ... tn = f s1 .. sn
+ (reflexive antecendents are droppped) **)
+local
+ exception MONO
+
+ fun prove_refl (ct, _) = Thm.reflexive ct
+ fun prove_comb f g cp =
+ let val ((ct1, ct2), (cu1, cu2)) = pairself Thm.dest_comb cp
+ in Thm.combination (f (ct1, cu1)) (g (ct2, cu2)) end
+ fun prove_arg f = prove_comb prove_refl f
+
+ fun prove f cp = prove_comb (prove f) f cp handle CTERM _ => prove_refl cp
+
+ fun prove_nary is_comb f =
+ let
+ fun prove (cp as (ct, _)) = f cp handle MONO =>
+ if is_comb (Thm.term_of ct)
+ then prove_comb (prove_arg prove) prove cp
+ else prove_refl cp
+ in prove end
+
+ fun prove_list f n cp =
+ if n = 0 then prove_refl cp
+ else prove_comb (prove_arg f) (prove_list f (n-1)) cp
+
+ fun with_length f (cp as (cl, _)) =
+ f (length (HOLogic.dest_list (Thm.term_of cl))) cp
+
+ fun prove_distinct f = prove_arg (with_length (prove_list f))
+
+ fun prove_eq exn lookup cp =
+ (case lookup (Logic.mk_equals (pairself Thm.term_of cp)) of
+ SOME eq => eq
+ | NONE => if exn then raise MONO else prove_refl cp)
+ val prove_eq_exn = prove_eq true and prove_eq_safe = prove_eq false
+
+ fun mono f (cp as (cl, _)) =
+ (case Term.head_of (Thm.term_of cl) of
+ @{term "op &"} => prove_nary is_conj (prove_eq_exn f)
+ | @{term "op |"} => prove_nary is_disj (prove_eq_exn f)
+ | Const (@{const_name distinct}, _) => prove_distinct (prove_eq_safe f)
+ | _ => prove (prove_eq_safe f)) cp
+in
+fun monotonicity eqs ct =
+ let
+ val tab = map (` Thm.prop_of o meta_eq_of) eqs
+ val lookup = AList.lookup (op aconv) tab
+ val cp = Thm.dest_binop ct
+ in MetaEq (prove_eq_exn lookup cp handle MONO => mono lookup cp) end
+end
+
+
+(** f a b = f b a **)
+local
+ val rule = @{lemma "a = b == b = a" by (atomize(full)) (rule eq_commute)}
+in
+fun commutativity ct = MetaEq (match_instantiate (as_meta_eq ct) rule)
+end
+
+
+(* quantifier proof rules *)
+
+(** P ?x = Q ?x ==> (ALL x. P x) = (ALL x. Q x)
+ P ?x = Q ?x ==> (EX x. P x) = (EX x. Q x) **)
+local
+ val rules = [
+ @{lemma "(!!x. P x == Q x) ==> (EX x. P x) == (EX x. Q x)" by simp},
+ @{lemma "(!!x. P x == Q x) ==> (ALL x. P x) == (ALL x. Q x)" by simp}]
+in
+fun quant_intro ctxt (p, (vars, _)) ct =
+ let
+ val rules' = varify ctxt vars (meta_eq_of p) :: rules
+ val cu = as_meta_eq ct
+ in MetaEq (by_tac' (REPEAT_ALL_NEW (Tactic.match_tac rules')) cu) end
+end
+
+
+(** |- ((ALL x. P x) | Q) = (ALL x. P x | Q) **)
+val pull_quant =
+ Thm o by_tac (Tactic.rtac @{thm refl} ORELSE' Simplifier.simp_tac HOL_ss)
+
+
+(** |- (ALL x. P x & Q x) = ((ALL x. P x) & (ALL x. Q x)) **)
+val push_quant =
+ Thm o by_tac (Tactic.rtac @{thm refl} ORELSE' Simplifier.simp_tac HOL_ss)
+
+
+(**
+ |- (ALL x1 ... xn y1 ... yn. P x1 ... xn) = (ALL x1 ... xn. P x1 ... xn)
+**)
+local
+ val elim_all = @{lemma "ALL x. P == P" by simp}
+ val elim_ex = @{lemma "EX x. P == P" by simp}
+
+ val rule = (fn @{const_name All} => elim_all | _ => elim_ex)
+
+ fun collect xs tp =
+ if (op aconv) tp then rev xs
+ else
+ (case tp of
+ (Const (q, _) $ Abs (_, _, l), r' as Const _ $ Abs (_, _, r)) =>
+ if l aconv r then rev xs
+ else if Term.loose_bvar1 (l, 0) then collect (NONE :: xs) (l, r)
+ else collect (SOME (rule q) :: xs) (Term.incr_bv (~1, 0, l), r')
+ | (Const (q, _) $ Abs (_, _, l), r) =>
+ collect (SOME (rule q) :: xs) (Term.incr_bv (~1, 0, l), r)
+ | (l, r) => raise TERM ("elim_unused", [l, r]))
+
+ fun elim _ [] ct = Conv.all_conv ct
+ | elim ctxt (x::xs) ct =
+ (case x of
+ SOME rule => Conv.rewr_conv rule then_conv elim ctxt xs
+ | _ => Conv.arg_conv (Conv.abs_conv (fn (_,cx) => elim cx xs) ctxt)) ct
+in
+fun elim_unused_vars ctxt ct =
+ let val (lhs, rhs) = Thm.dest_binop ct
+ in MetaEq (elim ctxt (collect [] (Thm.term_of lhs, Thm.term_of rhs)) lhs) end
+end
+
+
+(**
+ |- (ALL x1 ... xn. ~(x1 = t1 & ... xn = tn) | P x1 ... xn) = P t1 ... tn
+**)
+val dest_eq_res = Thm o by_tac (Simplifier.simp_tac HOL_ss)
+
+
+(** |- ~(ALL x1...xn. P x1...xn) | P a1...an **)
+local
+ val rule = @{lemma "~ P x | Q ==> ~(ALL x. P x) | Q" by fast}
+in
+val quant_inst = Thm o by_tac (
+ REPEAT_ALL_NEW (Tactic.match_tac [rule])
+ THEN' Tactic.rtac @{thm excluded_middle})
+end
+
+
+(** c = SOME x. P x |- (EX x. P x) = P c
+ c = SOME x. ~ P x |- ~(ALL x. P x) = ~ P c **)
+local
+ val elim_ex = @{lemma "EX x. P == P" by simp}
+ val elim_all = @{lemma "~ (ALL x. P) == ~P" by simp}
+ val sk_ex = @{lemma "c == SOME x. P x ==> EX x. P x == P c"
+ by simp (intro eq_reflection some_eq_ex[symmetric])}
+ val sk_all = @{lemma "c == SOME x. ~ P x ==> ~(ALL x. P x) == ~ P c"
+ by (simp only: not_all) (intro eq_reflection some_eq_ex[symmetric])}
+ val sk_ex_rule = ((sk_ex, I), elim_ex)
+ and sk_all_rule = ((sk_all, Thm.dest_arg), elim_all)
+
+ fun dest f sk_rule =
+ Thm.dest_comb (f (Thm.dest_arg (Thm.dest_arg (Thm.cprop_of sk_rule))))
+ fun type_of f sk_rule = Thm.ctyp_of_term (snd (dest f sk_rule))
+ fun inst_sk (sk_rule, f) p c =
+ Thm.instantiate ([(type_of f sk_rule, Thm.ctyp_of_term c)], []) sk_rule
+ |> (fn sk' => Thm.instantiate ([], (list2 (dest f sk') ~~ [p, c])) sk')
+ |> Conv.fconv_rule (Thm.beta_conversion true)
+
+ fun kind (Const (q as @{const_name Ex}, _) $ _) = (sk_ex_rule, q, I, I)
+ | kind (@{term Not} $ (Const (q as @{const_name All}, _) $ _)) =
+ (sk_all_rule, q, Thm.dest_arg, Thm.capply @{cterm Not})
+ | kind _ = z3_exn "skolemize: no quantifier"
+
+ fun bodies_of ctxt ct =
+ let
+ val (rule, q, dest, make) = kind (Thm.term_of ct)
+
+ fun inst_abs idx T cbs ct =
+ let
+ val cv = certify_var ctxt idx T
+ val cu = Drule.beta_conv (Thm.dest_arg ct) cv
+ in dest_body (idx + 1) ((cv, Thm.dest_arg ct) :: cbs) cu end
+ and dest_body idx cbs ct =
+ (case Thm.term_of ct of
+ Const (qname, _) $ Abs (_, T, _) =>
+ if q = qname then inst_abs idx T cbs ct else (make ct, rev cbs)
+ | _ => (make ct, rev cbs))
+ in (rule, dest_body (#maxidx (Thm.rep_cterm ct) + 1) [] (dest ct)) end
+
+ fun transitive f thm = Thm.transitive thm (f (Thm.rhs_of thm))
+
+ fun sk_step (rule, elim) (cv, mct, cb) (is, thm) =
+ (case mct of
+ SOME ct =>
+ make_hyp_def (inst_sk rule (Thm.instantiate_cterm ([], is) cb) ct)
+ |> apsnd (pair ((cv, ct) :: is) o Thm.transitive thm)
+ | NONE => ([], (is, transitive (Conv.rewr_conv elim) thm)))
+in
+fun skolemize ctxt ct =
+ let
+ val (lhs, rhs) = Thm.dest_binop ct
+ val (rule, (cu, cbs)) = bodies_of ctxt lhs
+ val ctab = snd (Thm.first_order_match (cu, rhs))
+ fun lookup_var (cv, cb) = (cv, AList.lookup (op aconvc) ctab cv, cb)
+ in
+ ([], Thm.reflexive lhs)
+ |> fold_map (sk_step rule) (map lookup_var cbs)
+ |> apfst (rev o flat) o apsnd (MetaEq o snd)
+ end
+end
+
+
+(* theory proof rules *)
+
+(** prove linear arithmetic problems via generalization **)
+local
+ val is_numeral = can HOLogic.dest_number
+ fun is_number (Const (@{const_name uminus}, _) $ t) = is_numeral t
+ | is_number t = is_numeral t
+
+ local
+ val int_distrib = @{lemma "n * (x + y) == n * x + n * (y::int)"
+ by (simp add: int_distrib)}
+ val real_distrib = @{lemma "n * (x + y) == n * x + n * (y::real)"
+ by (simp add: mult.add_right)}
+ val int_assoc = @{lemma "n * (m * x) == (n * m) * (x::int)" by linarith}
+ val real_assoc = @{lemma "n * (m * x) == (n * m) * (x::real)" by linarith}
+
+ val number_of_cong = @{lemma
+ "number_of x * number_of y == (number_of (x * y) :: int)"
+ "number_of x * number_of y == (number_of (x * y) :: real)"
+ by simp_all}
+ val reduce_ss = HOL_ss addsimps @{thms mult_bin_simps}
+ addsimps @{thms add_bin_simps} addsimps @{thms succ_bin_simps}
+ addsimps @{thms minus_bin_simps} addsimps @{thms pred_bin_simps}
+ addsimps number_of_cong
+ val reduce_conv = Simplifier.rewrite reduce_ss
+
+ fun apply_conv distrib assoc u ct =
+ ((case u of
+ Const (@{const_name times}, _) $ n $ _ =>
+ if is_number n
+ then Conv.rewr_conv assoc then_conv Conv.arg1_conv reduce_conv
+ else Conv.rewr_conv distrib
+ | _ => Conv.rewr_conv distrib)
+ then_conv Conv.binop_conv (Conv.try_conv distrib_conv)) ct
+
+ and distrib_conv ct =
+ (case Thm.term_of ct of
+ @{term "op * :: int => _"} $ n $ u =>
+ if is_number n then apply_conv int_distrib int_assoc u
+ else Conv.no_conv
+ | @{term "op * :: real => _"} $ n $ u =>
+ if is_number n then apply_conv real_distrib real_assoc u
+ else Conv.no_conv
+ | _ => Conv.no_conv) ct
+ in
+ val all_distrib_conv = More_Conv.top_sweep_conv (K distrib_conv)
+ end
+
+ local
+ fun make_ctxt ctxt = (ctxt, Ctermtab.empty, 1)
+ fun fresh ct (cx as (ctxt, tab, idx)) =
+ (case Ctermtab.lookup tab ct of
+ SOME cv => (cv, cx)
+ | NONE =>
+ let val cv = certify_var ctxt idx (#T (Thm.rep_cterm ct))
+ in (cv, (ctxt, Ctermtab.update (ct, cv) tab, idx + 1)) end)
+
+ fun fold_map_op f ct =
+ let val (cf, cu) = Thm.dest_comb ct
+ in f cu #>> Thm.capply cf end
+
+ fun fold_map_binop f1 f2 ct =
+ let val ((cf, cu1), cu2) = apfst Thm.dest_comb (Thm.dest_comb ct)
+ in f1 cu1 ##>> f2 cu2 #>> uncurry (Thm.mk_binop cf) end
+
+ fun mult f1 f2 ct t u =
+ if is_number t
+ then if is_number u then pair ct else fold_map_binop f1 f2 ct
+ else fresh ct
+
+ fun poly ct =
+ (case Thm.term_of ct of
+ Const (@{const_name plus}, _) $ _ $ _ => fold_map_binop poly poly ct
+ | Const (@{const_name minus}, _) $ _ $ _ => fold_map_binop poly poly ct
+ | Const (@{const_name times}, _) $ t $ u => mult pair fresh ct t u
+ | Const (@{const_name div}, _) $ t $ u => mult fresh pair ct t u
+ | Const (@{const_name mod}, _) $ t $ u => mult fresh pair ct t u
+ | t => if is_number t then pair ct else fresh ct)
+
+ val ineq_ops = [@{term "op = :: int => _"}, @{term "op < :: int => _"},
+ @{term "op <= :: int => _"}, @{term "op = :: real => _"},
+ @{term "op < :: real => _"}, @{term "op <= :: real => _"}]
+ fun ineq ct =
+ (case Thm.term_of ct of
+ t $ _ $ _ =>
+ if member (op =) ineq_ops t then fold_map_binop poly poly ct
+ else raise CTERM ("arith_lemma", [ct])
+ | @{term Not} $ (t $ _ $ _) =>
+ if member (op =) ineq_ops t
+ then fold_map_op (fold_map_binop poly poly) ct
+ else raise CTERM ("arith_lemma", [ct])
+ | _ => raise CTERM ("arith_lemma", [ct]))
+
+ fun conj ct =
+ (case Thm.term_of ct of
+ @{term "op &"} $ _ $ _ => fold_map_binop conj conj ct
+ | @{term "~False"} => pair ct
+ | _ => ineq ct)
+
+ fun disj ct =
+ (case Thm.term_of ct of
+ @{term "op |"} $ _ $ _ => fold_map_binop disj disj ct
+ | @{term False} => pair ct
+ | _ => conj ct)
+ in
+ fun prove_arith ctxt thms ct =
+ let
+ val (goal, (_, tab, _)) =
+ make_ctxt ctxt
+ |> fold_map (fold_map_op ineq o Thm.cprop_of) thms
+ ||>> fold_map_op disj ct
+ |>> uncurry (fold_rev (Thm.mk_binop @{cterm "op ==>"}))
+ in
+ Goal.prove_internal [] goal (fn _ => Arith_Data.arith_tac ctxt 1)
+ |> Thm.instantiate ([], map swap (Ctermtab.dest tab))
+ |> fold (fn th1 => fn th2 => Thm.implies_elim th2 th1) thms
+ end
+ end
+in
+fun arith_lemma ctxt thms ct =
+ let val thms' = map (Conv.fconv_rule (all_distrib_conv ctxt)) thms
+ in with_conv (all_distrib_conv ctxt) (prove_arith ctxt thms') ct end
+end
+
+(** theory lemmas: linear arithmetic, arrays **)
+local
+ val array_ss = HOL_ss addsimps @{thms array_rules}
+ fun array_tac thms =
+ Tactic.cut_facts_tac thms
+ THEN' Simplifier.asm_full_simp_tac array_ss
+
+ fun full_arith_tac ctxt thms =
+ Tactic.cut_facts_tac thms
+ THEN' Arith_Data.arith_tac ctxt
+in
+fun th_lemma ctxt thms ct =
+ Thm (try_apply ctxt "th-lemma" [
+ ("abstract arith", arith_lemma ctxt thms),
+ ("array", by_tac' (array_tac thms)),
+ ("full arith", by_tac' (full_arith_tac ctxt thms))] (T.mk_prop ct))
+end
+
+
+(** rewriting: prove equalities:
+ * ACI of conjunction/disjunction
+ * contradiction, excluded middle
+ * logical rewriting rules (for negation, implication, equivalence,
+ distinct)
+ * normal forms for polynoms (integer/real arithmetic)
+ * quantifier elimination over linear arithmetic
+ * ... ? **)
+structure Z3_Rewrite_Rules =
+struct
+ val name = "z3_rewrite"
+ val descr = "Z3 rewrite rules used in proof reconstruction"
+
+ structure Data = GenericDataFun
+ (
+ type T = thm Net.net
+ val empty = Net.empty
+ val extend = I
+ fun merge _ = Net.merge Thm.eq_thm_prop
+ )
+ val get = Data.get o Context.Proof
+
+ val entry = ` Thm.prop_of o Simplifier.rewrite_rule [true_false]
+ val eq = Thm.eq_thm_prop
+ val ins = Net.insert_term eq o entry and del = Net.delete_term eq o entry
+ fun insert thm net = ins thm net handle Net.INSERT => net
+ fun delete thm net = del thm net handle Net.DELETE => net
+
+ val add = Thm.declaration_attribute (Data.map o insert)
+ val del = Thm.declaration_attribute (Data.map o delete)
+ val setup = Attrib.setup (Binding.name name) (Attrib.add_del add del) descr
+end
+
+local
+ val contra_rule = @{lemma "P ==> ~P ==> False" by (rule notE)}
+ fun contra_left conj thm =
+ let
+ fun make_tab xs = fold Termtab.update xs Termtab.empty
+ val tab = make_tab (explode_term conj true (prop_of thm))
+ fun pnlits (t, nrs) =
+ (case t of
+ @{term Not} $ u => Termtab.lookup tab u |> Option.map (pair nrs)
+ | _ => NONE)
+ in
+ (case Termtab.lookup tab @{term False} of
+ SOME rs => extract_lit thm rs
+ | NONE =>
+ pairself (extract_lit thm) (the (Termtab.get_first NONE pnlits tab))
+ |> (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}
+ fun contradiction conj ct =
+ iff_intro (under_assumption (contra_left conj) ct) (contra_right ct)
+
+ fun conj_disj ct =
+ let
+ val cp as (cl, _) = Thm.dest_binop (Thm.dest_arg ct)
+ val (lhs, rhs) = pairself Thm.term_of cp
+ in
+ if is_conj lhs andalso rhs = @{term False}
+ then contradiction true cl
+ else if is_disj lhs andalso rhs = @{term "~False"}
+ then contrapos2 (contradiction false o fst) cp
+ else prove_conj_disj_eq (Thm.dest_arg ct)
+ end
+
+ val distinct =
+ let val try_unfold = Conv.try_conv unfold_distinct_conv
+ in with_conv (Conv.arg_conv (Conv.binop_conv try_unfold)) conj_disj end
+
+ val nnf_neg_rule = @{lemma "~~P == P" by fastsimp}
+ val nnf_cd_rules = @{lemma "~(P | Q) == ~P & ~Q" "~(P & Q) == ~P | ~Q"
+ by fastsimp+}
+
+ fun nnf_conv ct = Conv.try_conv (
+ (Conv.rewr_conv nnf_neg_rule then_conv nnf_conv) else_conv
+ (More_Conv.rewrs_conv nnf_cd_rules then_conv Conv.binop_conv nnf_conv)) ct
+ val iffI_rule = @{lemma "~P | Q ==> ~Q | P ==> P = Q" by fast}
+ fun arith_tac ctxt = CSUBGOAL (fn (goal, i) =>
+ let val prep_then = with_conv (Conv.arg_conv (Conv.binop_conv nnf_conv))
+ in Tactic.rtac (prep_then (arith_lemma ctxt []) goal) i end)
+ fun arith_eq_tac ctxt =
+ Tactic.rtac iffI_rule THEN_ALL_NEW arith_tac ctxt
+ ORELSE' arith_tac ctxt
+
+ val simpset = HOL_ss addsimps @{thms array_rules}
+ addsimps @{thms ring_distribs} addsimps @{thms field_eq_simps}
+ addsimps @{thms arith_special} addsimps @{thms less_bin_simps}
+ addsimps @{thms le_bin_simps} addsimps @{thms eq_bin_simps}
+ addsimps @{thms add_bin_simps} addsimps @{thms succ_bin_simps}
+ addsimps @{thms minus_bin_simps} addsimps @{thms pred_bin_simps}
+ addsimps @{thms mult_bin_simps} addsimps @{thms iszero_simps}
+ addsimprocs [
+ Simplifier.simproc @{theory} "fast_int_arith" [
+ "(m::int) < n", "(m::int) <= n", "(m::int) = n"] (K Lin_Arith.simproc),
+ Simplifier.simproc @{theory} "fast_real_arith" [
+ "(m::real) < n", "(m::real) <= n", "(m::real) = n"]
+ (K Lin_Arith.simproc)]
+ val simp_tac = CHANGED o Simplifier.simp_tac simpset
+ ORELSE' Classical.best_tac HOL_cs
+in
+fun rewrite ctxt thms ct =
+ let val rules_net = Z3_Rewrite_Rules.get ctxt
+ in
+ Thm (try_apply ctxt "rewrite" [
+ ("schematic rule", the o net_instance rules_net),
+ ("conj/disj", conj_disj),
+ ("distinct", distinct),
+ ("arith", by_tac' (arith_eq_tac ctxt)),
+ ("classical", by_tac' (Classical.best_tac HOL_cs)),
+ ("simp", by_tac' simp_tac),
+ ("full arith", by_tac' (Arith_Data.arith_tac ctxt))] (T.mk_prop ct))
+ end
+end
+
+
+(* tracing and debugging *)
+
+fun check idx r ct ((_, p), _) =
+ let val thm = thm_of p |> tap (Thm.join_proofs o single)
+ in
+ if (Thm.cprop_of thm) aconvc (T.mk_prop ct) then ()
+ else z3_exn ("proof step failed: " ^ quote (string_of_rule r) ^
+ " (#" ^ string_of_int idx ^ ")")
+ end
+
+local
+ fun trace_before ctxt idx (r, ps, ct) =
+ Pretty.string_of (
+ Pretty.big_list ("#" ^ string_of_int idx ^ ": " ^ string_of_rule r) [
+ Pretty.big_list "assumptions:"
+ (map (Display.pretty_thm ctxt o thm_of o fst) ps),
+ Pretty.block [Pretty.str "goal: ",
+ Syntax.pretty_term ctxt (Thm.term_of ct)]])
+
+ fun trace_after ctxt ((_, p), _) = Pretty.string_of (Pretty.block
+ [Pretty.str "result: ", Display.pretty_thm ctxt (thm_of p)])
+in
+fun trace_rule ctxt idx prove r ps ct ptab =
+ let
+ val _ = SMT_Solver.trace_msg ctxt (trace_before ctxt idx) (r, ps, ct)
+ val result = prove r ps ct ptab
+ val _ = SMT_Solver.trace_msg ctxt (trace_after ctxt) result
+ in result end
+end
+
+
+(* overall reconstruction procedure *)
+
+fun not_supported r =
+ z3_exn ("proof rule not implemented: " ^ quote (string_of_rule r))
+
+fun prove ctxt assms =
+ let
+ val prems = Option.map (prepare_assms ctxt) assms
+
+ fun step r ps ct ptab =
+ (case (r, ps) of
+ (* core rules *)
+ (TrueAxiom, _) => (([], Thm true_thm), ptab)
+ | (Asserted, _) => (([], asserted ctxt prems ct), ptab)
+ | (Goal, _) => (([], asserted ctxt prems ct), ptab)
+ | (ModusPonens, [(p, _), (q, _)]) => (([], mp q (thm_of p)), ptab)
+ | (ModusPonensOeq, [(p, _), (q, _)]) => (([], mp q (thm_of p)), ptab)
+ | (AndElim, [(p, (_, i))]) => apfst (pair []) (and_elim (p, i) ct ptab)
+ | (NotOrElim, [(p, (_, i))]) =>
+ apfst (pair []) (not_or_elim (p, i) ct ptab)
+ | (Hypothesis, _) => (([], Thm (Thm.assume (T.mk_prop ct))), ptab)
+ | (Lemma, [(p, _)]) => (([], lemma (thm_of p) ct), ptab)
+ | (UnitResolution, (p, _) :: ps) =>
+ (([], unit_resolution (thm_of p) (map (thm_of o fst) ps) ct), ptab)
+ | (IffTrue, [(p, _)]) => (([], iff_true (thm_of p)), ptab)
+ | (IffFalse, [(p, _)]) => (([], iff_false (thm_of p)), ptab)
+ | (Distributivity, _) => (([], distributivity ct), ptab)
+ | (DefAxiom, _) => (([], def_axiom ctxt ct), ptab)
+ | (IntroDef, _) => (intro_def ct, ptab)
+ | (ApplyDef, [(p, _)]) => (([], apply_def (thm_of p)), ptab)
+ | (IffOeq, [(p, _)]) => (([], p), ptab)
+ | (NnfPos, _) => (([], nnf ctxt ps ct), ptab)
+ | (NnfNeg, _) => (([], nnf ctxt ps ct), ptab)
+
+ (* equality rules *)
+ | (Reflexivity, _) => (([], refl ct), ptab)
+ | (Symmetry, [(p, _)]) => (([], symm p), ptab)
+ | (Transitivity, [(p, _), (q, _)]) => (([], trans p q), ptab)
+ | (Monotonicity, _) => (([], monotonicity (map fst ps) ct), ptab)
+ | (Commutativity, _) => (([], commutativity ct), ptab)
+
+ (* quantifier rules *)
+ | (QuantIntro, [p]) => (([], quant_intro ctxt p ct), ptab)
+ | (PullQuant, _) => (([], pull_quant ct), ptab)
+ | (PushQuant, _) => (([], push_quant ct), ptab)
+ | (ElimUnusedVars, _) => (([], elim_unused_vars ctxt ct), ptab)
+ | (DestEqRes, _) => (([], dest_eq_res ct), ptab)
+ | (QuantInst, _) => (([], quant_inst ct), ptab)
+ | (Skolemize, _) => (skolemize ctxt ct, ptab)
+
+ (* theory rules *)
+ | (ThLemma, _) => (([], th_lemma ctxt (map (thm_of o fst) ps) ct), ptab)
+ | (Rewrite, _) => (([], rewrite ctxt [] ct), ptab)
+ | (RewriteStar, ps) =>
+ (([], rewrite ctxt (map (thm_of o fst) ps) ct), ptab)
+
+ | (NnfStar, _) => not_supported r
+ | (CnfStar, _) => not_supported r
+ | (TransitivityStar, _) => not_supported r
+ | (PullQuantStar, _) => not_supported r
+
+ | _ => z3_exn ("Proof rule " ^ quote (string_of_rule r) ^
+ " has an unexpected number of arguments."))
+
+ fun eq_hyp (ct, cu) = Thm.dest_arg1 ct aconvc Thm.dest_arg1 cu
+
+ fun conclude idx rule prop ((hypss, ps), ptab) =
+ trace_rule ctxt idx step rule ps prop ptab
+ |> Config.get ctxt SMT_Solver.trace ? tap (check idx rule prop)
+ |>> apfst (distinct eq_hyp o fold append hypss)
+
+ fun add_sequent idx vars (hyps, thm) ptab =
+ let val s = Sequent {hyps=hyps, vars=vars, thm=thm}
+ in ((hyps, (thm, vars)), Inttab.update (idx, s) ptab) end
+
+ fun lookup idx ptab =
+ (case Inttab.lookup ptab idx of
+ SOME (Unproved {rule, subs, vars, prop}) =>
+ fold_map lookup subs ptab
+ |>> split_list
+ |>> apsnd (map2 (fn idx => fn (p, vs) => (p, (vs, idx))) subs)
+ |> conclude idx rule prop
+ |-> add_sequent idx vars
+ | SOME (Sequent {hyps, vars, thm}) => ((hyps, (thm, vars)), ptab)
+ | NONE => z3_exn ("unknown proof id: " ^ quote (string_of_int idx)))
+
+ fun result (hyps, (thm, _)) =
+ fold SMT_Normalize.discharge_definition hyps (thm_of thm)
+
+ in (fn ptab => fn idx => result (fst (lookup idx ptab))) end
+
+val setup = Z3_Rewrite_Rules.setup
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Tools/z3_proof_terms.ML Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,246 @@
+(* Title: HOL/SMT/Tools/z3_proof_terms.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Reconstruction functions for terms occurring in Z3 proofs.
+*)
+
+signature Z3_PROOF_TERMS =
+sig
+ val mk_prop: Thm.cterm -> Thm.cterm
+ val mk_meta_eq: Thm.cterm -> Thm.cterm -> Thm.cterm
+
+ type preterm
+
+ val compile: theory -> Name.context -> preterm -> Thm.cterm * Thm.cterm list
+
+ val mk_bound: theory -> int -> typ -> preterm
+ val mk_fun: Thm.cterm -> preterm list -> preterm
+ val mk_forall: theory -> string * typ -> preterm -> preterm
+ val mk_exists: theory -> string * typ -> preterm -> preterm
+
+ val mk_true: preterm
+ val mk_false: preterm
+ val mk_not: preterm -> preterm
+ val mk_and: preterm list -> preterm
+ val mk_or: preterm list -> preterm
+ val mk_implies: preterm -> preterm -> preterm
+ val mk_iff: preterm -> preterm -> preterm
+
+ val mk_eq: preterm -> preterm -> preterm
+ val mk_if: preterm -> preterm -> preterm -> preterm
+ val mk_distinct: preterm list -> preterm
+
+ val mk_pat: preterm list -> preterm
+ val mk_nopat: preterm list -> preterm
+ val mk_trigger: preterm list -> preterm -> preterm
+
+ val mk_access: preterm -> preterm -> preterm
+ val mk_update: preterm -> preterm -> preterm -> preterm
+
+ val mk_int_num: int -> preterm
+ val mk_real_frac_num: int * int option -> preterm
+ val mk_uminus: preterm -> preterm
+ val mk_add: preterm -> preterm -> preterm
+ val mk_sub: preterm -> preterm -> preterm
+ val mk_mul: preterm -> preterm -> preterm
+ val mk_int_div: preterm -> preterm -> preterm
+ val mk_real_div: preterm -> preterm -> preterm
+ val mk_rem: preterm -> preterm -> preterm
+ val mk_mod: preterm -> preterm -> preterm
+ val mk_lt: preterm -> preterm -> preterm
+ val mk_le: preterm -> preterm -> preterm
+
+ val wordT : int -> typ
+ val mk_bv_num : theory -> int -> int -> preterm
+
+ val var_prefix: string
+end
+
+structure Z3_Proof_Terms: Z3_PROOF_TERMS =
+struct
+
+fun instTs cUs (cTs, ct) = Thm.instantiate_cterm (cTs ~~ cUs, []) ct
+fun instT cU (cT, ct) = instTs [cU] ([cT], ct)
+fun mk_inst_pair destT cpat = (destT (Thm.ctyp_of_term cpat), cpat)
+val destT1 = hd o Thm.dest_ctyp
+val destT2 = hd o tl o Thm.dest_ctyp
+
+
+val mk_prop = Thm.capply @{cterm Trueprop}
+
+val meta_eq = mk_inst_pair destT1 @{cpat "op =="}
+fun mk_meta_eq ct = Thm.mk_binop (instT (Thm.ctyp_of_term ct) meta_eq) ct
+
+
+datatype preterm = Preterm of {
+ cterm: Thm.cterm,
+ vars: (int * Thm.cterm) list }
+
+fun mk_preterm (ct, vs) = Preterm {cterm=ct, vars=vs}
+fun dest_preterm (Preterm {cterm, vars}) = (cterm, vars)
+fun ctyp_of_preterm (Preterm {cterm, ...}) = Thm.ctyp_of_term cterm
+
+fun instT' e = instT (ctyp_of_preterm e)
+
+val maxidx_of = #maxidx o Thm.rep_cterm
+
+val var_prefix = "v"
+
+local
+fun mk_inst nctxt cert vs =
+ let
+ val max = fold (curry Int.max o fst) vs 0
+ val names = fst (Name.variants (replicate (max + 1) var_prefix) nctxt)
+ fun mk (i, v) = (v, cert (Free (nth names i, #T (Thm.rep_cterm v))))
+ in map mk vs end
+
+fun fix_vars _ _ ct [] = (ct, [])
+ | fix_vars thy nctxt ct vs =
+ let
+ val cert = Thm.cterm_of thy
+ val inst = mk_inst nctxt cert vs
+ in (Thm.instantiate_cterm ([], inst) ct, map snd inst) end
+in
+fun compile thy nctxt (Preterm {cterm, vars}) = fix_vars thy nctxt cterm vars
+end
+
+local
+fun app e (ct1, vs1) =
+ let
+ fun part (var as (i, v)) (inst, vs) =
+ (case AList.lookup (op =) vs1 i of
+ NONE => (inst, var :: vs)
+ | SOME v' => ((v, v') :: inst, vs))
+
+ val (ct2, vs2) = dest_preterm e
+ val incr =
+ if maxidx_of ct1 < 0 orelse maxidx_of ct2 < 0 then I
+ else Thm.incr_indexes_cterm (maxidx_of ct1 + 1)
+
+ val (inst, vs) = fold (part o apsnd incr) vs2 ([], vs1)
+ val ct2' = Thm.instantiate_cterm ([], inst) (incr ct2)
+ in (Thm.capply ct1 ct2', vs) end
+in
+fun mk_fun ct es = mk_preterm (fold app es (ct, []))
+fun mk_binop f t u = mk_fun f [t, u]
+fun mk_nary _ e [] = e
+ | mk_nary ct _ es = uncurry (fold_rev (mk_binop ct)) (split_last es)
+end
+
+fun mk_bound thy i T =
+ let val ct = Thm.cterm_of thy (Var ((Name.uu, 0), T))
+ in mk_preterm (ct, [(i, ct)]) end
+
+local
+fun mk_quant q thy (n, T) e =
+ let
+ val (ct, vs) = dest_preterm e
+ val cv =
+ (case AList.lookup (op =) vs 0 of
+ SOME cv => cv
+ | _ => Thm.cterm_of thy (Var ((Name.uu, maxidx_of ct + 1), T)))
+ val cq = instT (Thm.ctyp_of_term cv) q
+ fun dec (i, v) = if i = 0 then NONE else SOME (i - 1, v)
+ in mk_preterm (Thm.capply cq (Thm.cabs cv ct), map_filter dec vs) end
+in
+val mk_forall = mk_quant (mk_inst_pair (destT1 o destT1) @{cpat All})
+val mk_exists = mk_quant (mk_inst_pair (destT1 o destT1) @{cpat Ex})
+end
+
+
+val mk_false = mk_fun @{cterm False} []
+val mk_not = mk_fun @{cterm Not} o single
+val mk_true = mk_not mk_false
+val mk_and = mk_nary @{cterm "op &"} mk_true
+val mk_or = mk_nary @{cterm "op |"} mk_false
+val mk_implies = mk_binop @{cterm "op -->"}
+val mk_iff = mk_binop @{cterm "op = :: bool => _"}
+
+val eq = mk_inst_pair destT1 @{cpat "op ="}
+fun mk_eq t u = mk_binop (instT' t eq) t u
+
+val if_term = mk_inst_pair (destT1 o destT2) @{cpat If}
+fun mk_if c t u = mk_fun (instT' t if_term) [c, t, u]
+
+val nil_term = mk_inst_pair destT1 @{cpat Nil}
+val cons_term = mk_inst_pair destT1 @{cpat Cons}
+fun mk_list cT es =
+ fold_rev (mk_binop (instT cT cons_term)) es (mk_fun (instT cT nil_term) [])
+
+val distinct = mk_inst_pair (destT1 o destT1) @{cpat distinct}
+fun mk_distinct [] = mk_true
+ | mk_distinct (es as (e :: _)) =
+ mk_fun (instT' e distinct) [mk_list (ctyp_of_preterm e) es]
+
+val pat = mk_inst_pair destT1 @{cpat pat}
+val nopat = mk_inst_pair destT1 @{cpat nopat}
+val andpat = mk_inst_pair (destT1 o destT2) @{cpat "op andpat"}
+fun mk_gen_pat _ [] = raise TERM ("mk_gen_pat: empty pattern", [])
+ | mk_gen_pat pat (e :: es) =
+ let fun mk t p = mk_fun (instT' t andpat) [p, t]
+ in fold mk es (mk_fun (instT' e pat) [e]) end
+val mk_pat = mk_gen_pat pat
+val mk_nopat = mk_gen_pat nopat
+
+fun mk_trigger es e = mk_fun @{cterm trigger} [mk_list @{ctyp pattern} es, e]
+
+
+val access = mk_inst_pair (Thm.dest_ctyp o destT1) @{cpat apply}
+fun mk_access array index =
+ let val cTs = Thm.dest_ctyp (ctyp_of_preterm array)
+ in mk_fun (instTs cTs access) [array, index] end
+
+val update = mk_inst_pair (Thm.dest_ctyp o destT1) @{cpat fun_upd}
+fun mk_update array index value =
+ let val cTs = Thm.dest_ctyp (ctyp_of_preterm array)
+ in mk_fun (instTs cTs update) [array, index, value] end
+
+
+fun mk_int_num i = mk_fun (Numeral.mk_cnumber @{ctyp int} i) []
+fun mk_real_num i = mk_fun (Numeral.mk_cnumber @{ctyp real} i) []
+
+fun mk_real_frac_num (e, NONE) = mk_real_num e
+ | mk_real_frac_num (e, SOME d) =
+ mk_binop @{cterm "op / :: real => _"} (mk_real_num e) (mk_real_num d)
+
+fun has_int_type e = (Thm.typ_of (ctyp_of_preterm e) = @{typ int})
+fun choose e i r = if has_int_type e then i else r
+
+val uminus_i = @{cterm "uminus :: int => _"}
+val uminus_r = @{cterm "uminus :: real => _"}
+fun mk_uminus e = mk_fun (choose e uminus_i uminus_r) [e]
+
+fun arith_op int_op real_op t u = mk_binop (choose t int_op real_op) t u
+
+val mk_add = arith_op @{cterm "op + :: int => _"} @{cterm "op + :: real => _"}
+val mk_sub = arith_op @{cterm "op - :: int => _"} @{cterm "op - :: real => _"}
+val mk_mul = arith_op @{cterm "op * :: int => _"} @{cterm "op * :: real => _"}
+val mk_int_div = mk_binop @{cterm "op div :: int => _"}
+val mk_real_div = mk_binop @{cterm "op / :: real => _"}
+val mk_rem = mk_binop @{cterm "op rem :: int => _"}
+val mk_mod = mk_binop @{cterm "op mod :: int => _"}
+val mk_lt = arith_op @{cterm "op < :: int => _"} @{cterm "op < :: real => _"}
+val mk_le = arith_op @{cterm "op <= :: int => _"} @{cterm "op <= :: real => _"}
+
+fun binT size =
+ let
+ fun bitT i T =
+ if i = 0
+ then Type (@{type_name "Numeral_Type.bit0"}, [T])
+ else Type (@{type_name "Numeral_Type.bit1"}, [T])
+
+ fun binT i =
+ if i = 0 then @{typ "Numeral_Type.num0"}
+ else if i = 1 then @{typ "Numeral_Type.num1"}
+ else let val (q, r) = Integer.div_mod i 2 in bitT r (binT q) end
+ in
+ if size >= 0 then binT size
+ else raise TYPE ("mk_binT: " ^ string_of_int size, [], [])
+ end
+
+fun wordT size = Type (@{type_name "word"}, [binT size])
+
+fun mk_bv_num thy num size =
+ mk_fun (Numeral.mk_cnumber (Thm.ctyp_of thy (wordT size)) num) []
+
+end
--- a/src/HOL/SMT/Tools/z3_solver.ML Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/Tools/z3_solver.ML Tue Oct 20 10:11:30 2009 +0200
@@ -8,7 +8,6 @@
sig
val proofs: bool Config.T
val options: string Config.T
-
val setup: theory -> theory
end
@@ -57,20 +56,18 @@
check_unsat recon output
|> K @{cprop False}
-(* FIXME
fun prover (SMT_Solver.ProofData {context, output, recon, assms}) =
check_unsat recon output
|> Z3_Proof.reconstruct context assms recon
-*)
fun solver oracle ctxt =
let val with_proof = Config.get ctxt proofs
in
SMT_Solver.SolverConfig {
- name = {env_var=env_var, remote_name=solver_name},
+ command = {env_var=env_var, remote_name=solver_name},
+ arguments = cmdline_options ctxt,
interface = Z3_Interface.interface,
- arguments = cmdline_options ctxt,
- reconstruct = (*FIXME:if with_proof then prover else*) oracle }
+ reconstruct = if with_proof then prover else oracle }
end
val setup =
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/Z3.thy Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,24 @@
+(* Title: HOL/SMT/Z3.thy
+ Author: Sascha Boehme, TU Muenchen
+*)
+
+header {* Binding to the SMT solver Z3, with proof reconstruction *}
+
+theory Z3
+imports SMT_Base
+uses
+ "Tools/z3_proof_terms.ML"
+ "Tools/z3_proof_rules.ML"
+ "Tools/z3_proof.ML"
+ "Tools/z3_model.ML"
+ "Tools/z3_interface.ML"
+ "Tools/z3_solver.ML"
+begin
+
+setup {* Z3_Proof_Rules.setup #> Z3_Solver.setup *}
+
+lemmas [z3_rewrite] =
+ refl eq_commute conj_commute disj_commute simp_thms nnf_simps
+ ring_distribs field_eq_simps
+
+end
--- a/src/HOL/SMT/etc/settings Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/etc/settings Tue Oct 20 10:11:30 2009 +0200
@@ -1,9 +1,11 @@
ISABELLE_SMT="$COMPONENT"
-REMOTE_SMT_SOLVER="$ISABELLE_SMT/lib/scripts/remote_smt.pl"
+REMOTE_SMT_SOLVER="$COMPONENT/lib/scripts/remote_smt.pl"
REMOTE_SMT_URL="http://www4.in.tum.de/smt/smt"
+CERT_SMT_SOLVER="$COMPONENT/lib/scripts/cert_smt.pl"
+
#
# Paths to local SMT solvers:
#
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT/lib/scripts/cert_smt.pl Tue Oct 20 10:11:30 2009 +0200
@@ -0,0 +1,33 @@
+#
+# Author: Sascha Boehme, TU Muenchen
+#
+# Fake SMT solver: check that input matches previously computed input and
+# and return previously computed output.
+#
+
+use strict;
+use File::Compare;
+
+
+# arguments
+
+my $cert_path = $ARGV[0];
+my $new_problem = $ARGV[1];
+
+
+# check content of new problem file against old problem file
+
+my $old_problem = $cert_path;
+my $old_proof = $cert_path . ".proof";
+
+if (-e $old_problem and compare($old_problem, $new_problem) == 0) {
+ if (-e $old_proof) {
+ open FILE, "<$old_proof";
+ foreach (<FILE>) {
+ print $_;
+ }
+ close FILE;
+ }
+ else { print "ERROR: unable to open proof file\n"; }
+}
+else { print "ERROR: bad problem\n"; }
--- a/src/HOL/SMT/lib/scripts/remote_smt.pl Tue Oct 20 08:10:47 2009 +0200
+++ b/src/HOL/SMT/lib/scripts/remote_smt.pl Tue Oct 20 10:11:30 2009 +0200
@@ -1,7 +1,8 @@
#
-# Script to invoke remote SMT solvers.
# Author: Sascha Boehme, TU Muenchen
#
+# Invoke remote SMT solvers.
+#
use strict;
use LWP;