--- a/etc/components Wed May 12 23:54:01 2010 +0200
+++ b/etc/components Wed May 12 23:54:02 2010 +0200
@@ -16,4 +16,4 @@
src/HOL/Tools/ATP_Manager
src/HOL/Mirabelle
src/HOL/Library/Sum_Of_Squares
-src/HOL/SMT
+src/HOL/Tools/SMT
--- a/src/HOL/IsaMakefile Wed May 12 23:54:01 2010 +0200
+++ b/src/HOL/IsaMakefile Wed May 12 23:54:02 2010 +0200
@@ -20,7 +20,6 @@
HOL-Plain \
HOL-Probability \
HOL-Proofs \
- HOL-SMT \
HOL-Word \
HOL4 \
TLA
@@ -61,7 +60,7 @@
HOL-Proofs-Extraction \
HOL-Proofs-Lambda \
HOL-SET_Protocol \
- HOL-SMT-Examples \
+ HOL-SMT_Examples \
HOL-Statespace \
HOL-Subst \
TLA-Buffer \
@@ -274,6 +273,7 @@
Semiring_Normalization.thy \
SetInterval.thy \
Sledgehammer.thy \
+ SMT.thy \
String.thy \
Typerep.thy \
$(SRC)/Provers/Arith/assoc_fold.ML \
@@ -281,6 +281,7 @@
$(SRC)/Provers/Arith/cancel_numerals.ML \
$(SRC)/Provers/Arith/combine_numerals.ML \
$(SRC)/Provers/Arith/extract_common_term.ML \
+ $(SRC)/Tools/cache_io.ML \
$(SRC)/Tools/Metis/metis.ML \
Tools/ATP_Manager/atp_manager.ML \
Tools/ATP_Manager/atp_systems.ML \
@@ -322,6 +323,20 @@
Tools/Sledgehammer/sledgehammer_isar.ML \
Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML \
Tools/Sledgehammer/sledgehammer_util.ML \
+ Tools/SMT/cvc3_solver.ML \
+ Tools/SMT/smtlib_interface.ML \
+ Tools/SMT/smt_monomorph.ML \
+ Tools/SMT/smt_normalize.ML \
+ Tools/SMT/smt_solver.ML \
+ Tools/SMT/smt_translate.ML \
+ Tools/SMT/yices_solver.ML \
+ Tools/SMT/z3_interface.ML \
+ Tools/SMT/z3_model.ML \
+ Tools/SMT/z3_proof_literals.ML \
+ Tools/SMT/z3_proof_parser.ML \
+ Tools/SMT/z3_proof_reconstruction.ML \
+ Tools/SMT/z3_proof_tools.ML \
+ Tools/SMT/z3_solver.ML \
Tools/string_code.ML \
Tools/string_syntax.ML \
Tools/transfer.ML \
@@ -1070,9 +1085,9 @@
## HOL-Multivariate_Analysis
-HOL-Multivariate_Analysis: HOL-SMT $(OUT)/HOL-Multivariate_Analysis
+HOL-Multivariate_Analysis: HOL $(OUT)/HOL-Multivariate_Analysis
-$(OUT)/HOL-Multivariate_Analysis: $(OUT)/HOL-SMT \
+$(OUT)/HOL-Multivariate_Analysis: $(OUT)/HOL \
Multivariate_Analysis/ROOT.ML \
Multivariate_Analysis/document/root.tex \
Multivariate_Analysis/Brouwer_Fixpoint.thy \
@@ -1094,7 +1109,7 @@
Library/Inner_Product.thy Library/Numeral_Type.thy \
Library/Convex.thy Library/FrechetDeriv.thy \
Library/Product_Vector.thy Library/Product_plus.thy
- @cd Multivariate_Analysis; $(ISABELLE_TOOL) usedir -b -g true $(OUT)/HOL-SMT HOL-Multivariate_Analysis
+ @cd Multivariate_Analysis; $(ISABELLE_TOOL) usedir -b -g true $(OUT)/HOL HOL-Multivariate_Analysis
## HOL-Probability
@@ -1238,39 +1253,23 @@
@$(ISABELLE_TOOL) usedir $(OUT)/HOL Mirabelle
-## HOL-SMT
+## HOL-SMT_Examples
-HOL-SMT: HOL-Word $(OUT)/HOL-SMT
+HOL-SMT_Examples: HOL $(LOG)/HOL-SMT_Examples.gz
-$(OUT)/HOL-SMT: $(OUT)/HOL-Word SMT/ROOT.ML 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/smtlib_interface.ML \
- SMT/Tools/z3_interface.ML SMT/Tools/smt_additional_facts.ML \
- SMT/Tools/smt_solver.ML SMT/Tools/cvc3_solver.ML \
- SMT/Tools/yices_solver.ML SMT/Tools/z3_proof_parser.ML \
- SMT/Tools/z3_proof_tools.ML SMT/Tools/z3_proof_literals.ML \
- SMT/Tools/z3_proof_reconstruction.ML SMT/Tools/z3_model.ML \
- SMT/Tools/z3_solver.ML $(SRC)/Tools/cache_io.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/SMT_Examples.certs
- @cd SMT; $(ISABELLE_TOOL) usedir $(OUT)/HOL-SMT Examples
+$(LOG)/HOL-SMT_Examples.gz: $(OUT)/HOL-SMT SMT_Examples/ROOT.ML \
+ SMT_Examples/SMT_Examples.thy SMT_Examples/SMT_Examples.certs
+ @cd SMT; $(ISABELLE_TOOL) usedir $(OUT)/HOL Examples
## HOL-Boogie
-HOL-Boogie: HOL-SMT $(OUT)/HOL-Boogie
+HOL-Boogie: HOL $(OUT)/HOL-Boogie
-$(OUT)/HOL-Boogie: $(OUT)/HOL-SMT Boogie/ROOT.ML Boogie/Boogie.thy \
+$(OUT)/HOL-Boogie: $(OUT)/HOL Boogie/ROOT.ML Boogie/Boogie.thy \
Boogie/Tools/boogie_vcs.ML Boogie/Tools/boogie_loader.ML \
Boogie/Tools/boogie_commands.ML Boogie/Tools/boogie_tactics.ML
- @cd Boogie; $(ISABELLE_TOOL) usedir -b -g true $(OUT)/HOL-SMT HOL-Boogie
+ @cd Boogie; $(ISABELLE_TOOL) usedir -b -g true $(OUT)/HOL HOL-Boogie
## HOL-Boogie_Examples
@@ -1344,15 +1343,15 @@
$(LOG)/HOL-Probability.gz $(LOG)/HOL-Prolog.gz \
$(LOG)/HOL-Proofs.gz $(LOG)/HOL-Proofs-Extraction.gz \
$(LOG)/HOL-Proofs-Lambda.gz $(LOG)/HOL-SET_Protocol.gz \
- $(LOG)/HOL-SMT-Examples.gz $(LOG)/HOL-SMT.gz \
- $(LOG)/HOL-Statespace.gz $(LOG)/HOL-Subst.gz \
- $(LOG)/HOL-UNITY.gz $(LOG)/HOL-Unix.gz \
- $(LOG)/HOL-Word-Examples.gz $(LOG)/HOL-Word.gz \
- $(LOG)/HOL-ZF.gz $(LOG)/HOL-ex.gz $(LOG)/HOL.gz \
- $(LOG)/HOL4.gz $(LOG)/TLA-Buffer.gz $(LOG)/TLA-Inc.gz \
- $(LOG)/TLA-Memory.gz $(LOG)/TLA.gz $(OUT)/HOL \
- $(OUT)/HOL-Algebra $(OUT)/HOL-Base $(OUT)/HOL-Boogie \
- $(OUT)/HOL-Main $(OUT)/HOL-Multivariate_Analysis \
- $(OUT)/HOL-NSA $(OUT)/HOL-Nominal $(OUT)/HOL-Plain \
+ $(LOG)/HOL-SMT_Examples.gz $(LOG)/HOL-Statespace.gz \
+ $(LOG)/HOL-Subst.gz $(LOG)/HOL-UNITY.gz \
+ $(LOG)/HOL-Unix.gz $(LOG)/HOL-Word-Examples.gz \
+ $(LOG)/HOL-Word.gz $(LOG)/HOL-ZF.gz $(LOG)/HOL-ex.gz \
+ $(LOG)/HOL.gz $(LOG)/HOL4.gz $(LOG)/TLA-Buffer.gz \
+ $(LOG)/TLA-Inc.gz $(LOG)/TLA-Memory.gz $(LOG)/TLA.gz \
+ $(OUT)/HOL $(OUT)/HOL-Algebra $(OUT)/HOL-Base \
+ $(OUT)/HOL-Boogie $(OUT)/HOL-Main \
+ $(OUT)/HOL-Multivariate_Analysis $(OUT)/HOL-NSA \
+ $(OUT)/HOL-Nominal $(OUT)/HOL-Plain \
$(OUT)/HOL-Probability $(OUT)/HOL-Proofs \
- $(OUT)/HOL-SMT $(OUT)/HOL-Word $(OUT)/HOL4 $(OUT)/TLA
+ $(OUT)/HOL-Word $(OUT)/HOL4 $(OUT)/TLA
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT.thy Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,306 @@
+(* Title: HOL/SMT.thy
+ Author: Sascha Boehme, TU Muenchen
+*)
+
+header {* Bindings to Satisfiability Modulo Theories (SMT) solvers *}
+
+theory SMT
+imports List
+uses
+ "~~/src/Tools/cache_io.ML"
+ ("Tools/SMT/smt_additional_facts.ML")
+ ("Tools/SMT/smt_monomorph.ML")
+ ("Tools/SMT/smt_normalize.ML")
+ ("Tools/SMT/smt_translate.ML")
+ ("Tools/SMT/smt_solver.ML")
+ ("Tools/SMT/smtlib_interface.ML")
+ ("Tools/SMT/z3_proof_parser.ML")
+ ("Tools/SMT/z3_proof_tools.ML")
+ ("Tools/SMT/z3_proof_literals.ML")
+ ("Tools/SMT/z3_proof_reconstruction.ML")
+ ("Tools/SMT/z3_model.ML")
+ ("Tools/SMT/z3_interface.ML")
+ ("Tools/SMT/z3_solver.ML")
+ ("Tools/SMT/cvc3_solver.ML")
+ ("Tools/SMT/yices_solver.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 :: "'a \<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 {* Higher-order encoding *}
+
+text {*
+Application is made explicit for constants occurring with varying
+numbers of arguments. This is achieved by the introduction of the
+following constant.
+*}
+
+definition "apply" where "apply f x = f x"
+
+text {*
+Some solvers support a theory of arrays which can be used to encode
+higher-order functions. The following set of lemmas specifies the
+properties of such (extensional) arrays.
+*}
+
+lemmas array_rules = ext fun_upd_apply fun_upd_same fun_upd_other
+ fun_upd_upd
+
+
+
+section {* First-order logic *}
+
+text {*
+Some SMT solvers require a strict separation between formulas and
+terms. When translating higher-order into first-order problems,
+all uninterpreted constants (those not builtin in the target solver)
+are treated as function symbols in the first-order sense. Their
+occurrences as head symbols in atoms (i.e., as predicate symbols) is
+turned into terms by equating such atoms with @{term True} using the
+following term-level equation symbol.
+*}
+
+definition term_eq :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infix "term'_eq" 50)
+ where "(x term_eq y) = (x = y)"
+
+
+
+section {* Setup *}
+
+use "Tools/SMT/smt_monomorph.ML"
+use "Tools/SMT/smt_normalize.ML"
+use "Tools/SMT/smt_translate.ML"
+use "Tools/SMT/smt_solver.ML"
+use "Tools/SMT/smtlib_interface.ML"
+use "Tools/SMT/z3_interface.ML"
+use "Tools/SMT/z3_proof_parser.ML"
+use "Tools/SMT/z3_proof_tools.ML"
+use "Tools/SMT/z3_proof_literals.ML"
+use "Tools/SMT/z3_proof_reconstruction.ML"
+use "Tools/SMT/z3_model.ML"
+use "Tools/SMT/z3_solver.ML"
+use "Tools/SMT/cvc3_solver.ML"
+use "Tools/SMT/yices_solver.ML"
+
+setup {*
+ SMT_Solver.setup #>
+ Z3_Proof_Reconstruction.setup #>
+ Z3_Solver.setup #>
+ CVC3_Solver.setup #>
+ Yices_Solver.setup
+*}
+
+
+
+section {* Configuration *}
+
+text {*
+The current configuration can be printed by the following command
+(which shows the values of most options):
+*}
+
+smt_status
+
+
+
+subsection {* General configuration options *}
+
+text {*
+The option @{text smt_solver} can be used to change the target SMT
+solver. The possible values are @{text cvc3}, @{text yices}, and
+@{text z3}. It is advisable to locally install the selected solver,
+although this is not necessary for @{text cvc3} and @{text z3}, which
+can also be used over an Internet-based service.
+
+When using local SMT solvers, the path to their binaries should be
+declared by setting the following environment variables:
+@{text CVC3_SOLVER}, @{text YICES_SOLVER}, and @{text Z3_SOLVER}.
+*}
+
+declare [[ smt_solver = z3 ]]
+
+text {*
+Since SMT solvers are potentially non-terminating, there is a timeout
+(given in seconds) to restrict their runtime. A value greater than
+120 (seconds) is in most cases not advisable.
+*}
+
+declare [[ smt_timeout = 20 ]]
+
+
+
+subsection {* Certificates *}
+
+text {*
+By setting the option @{text smt_certificates} to the name of a file,
+all following applications of an SMT solver a cached in that file.
+Any further application of the same SMT solver (using the very same
+configuration) re-uses the cached certificate instead of invoking the
+solver. An empty string disables caching certificates.
+
+The filename should be given as an explicit path. It is good
+practice to use the name of the current theory (with ending
+@{text ".certs"} instead of @{text ".thy"}) as the certificates file.
+*}
+
+declare [[ smt_certificates = "" ]]
+
+text {*
+The option @{text smt_fixed} controls whether only stored
+certificates are should be used or invocation of an SMT solver is
+allowed. When set to @{text true}, no SMT solver will ever be
+invoked and only the existing certificates found in the configured
+cache are used; when set to @{text false} and there is no cached
+certificate for some proposition, then the configured SMT solver is
+invoked.
+*}
+
+declare [[ smt_fixed = false ]]
+
+
+
+subsection {* Tracing *}
+
+text {*
+For tracing the generated problem file given to the SMT solver as
+well as the returned result of the solver, the option
+@{text smt_trace} should be set to @{text true}.
+*}
+
+declare [[ smt_trace = false ]]
+
+
+
+subsection {* Z3-specific options *}
+
+text {*
+Z3 is the only SMT solver whose proofs are checked (or reconstructed)
+in Isabelle (all other solvers are implemented as oracles). Enabling
+or disabling proof reconstruction for Z3 is controlled by the option
+@{text z3_proofs}.
+*}
+
+declare [[ z3_proofs = true ]]
+
+text {*
+From the set of assumptions given to Z3, those assumptions used in
+the proof are traced when the option @{text z3_trace_assms} is set to
+@{term true}.
+*}
+
+declare [[ z3_trace_assms = false ]]
+
+text {*
+Z3 provides several commandline options to tweak its behaviour. They
+can be configured by writing them literally as value for the option
+@{text z3_options}.
+*}
+
+declare [[ z3_options = "" ]]
+
+
+
+section {* Schematic rules for Z3 proof reconstruction *}
+
+text {*
+Several prof rules of Z3 are not very well documented. There are two
+lemma groups which can turn failing Z3 proof reconstruction attempts
+into succeeding ones: the facts in @{text z3_rule} are tried prior to
+any implemented reconstruction procedure for all uncertain Z3 proof
+rules; the facts in @{text z3_simp} are only fed to invocations of
+the simplifier when reconstructing theory-specific proof steps.
+*}
+
+lemmas [z3_rule] =
+ refl eq_commute conj_commute disj_commute simp_thms nnf_simps
+ ring_distribs field_simps times_divide_eq_right times_divide_eq_left
+ if_True if_False not_not
+
+lemma [z3_rule]:
+ "(P \<longrightarrow> Q) = (Q \<or> \<not>P)"
+ "(\<not>P \<longrightarrow> Q) = (P \<or> Q)"
+ "(\<not>P \<longrightarrow> Q) = (Q \<or> P)"
+ by auto
+
+lemma [z3_rule]:
+ "((P = Q) \<longrightarrow> R) = (R | (Q = (\<not>P)))"
+ by auto
+
+lemma [z3_rule]:
+ "((\<not>P) = P) = False"
+ "(P = (\<not>P)) = False"
+ "(P \<noteq> Q) = (Q = (\<not>P))"
+ "(P = Q) = ((\<not>P \<or> Q) \<and> (P \<or> \<not>Q))"
+ "(P \<noteq> Q) = ((\<not>P \<or> \<not>Q) \<and> (P \<or> Q))"
+ by auto
+
+lemma [z3_rule]:
+ "(if P then P else \<not>P) = True"
+ "(if \<not>P then \<not>P else P) = True"
+ "(if P then True else False) = P"
+ "(if P then False else True) = (\<not>P)"
+ "(if \<not>P then x else y) = (if P then y else x)"
+ by auto
+
+lemma [z3_rule]:
+ "P = Q \<or> P \<or> Q"
+ "P = Q \<or> \<not>P \<or> \<not>Q"
+ "(\<not>P) = Q \<or> \<not>P \<or> Q"
+ "(\<not>P) = Q \<or> P \<or> \<not>Q"
+ "P = (\<not>Q) \<or> \<not>P \<or> Q"
+ "P = (\<not>Q) \<or> P \<or> \<not>Q"
+ "P \<noteq> Q \<or> P \<or> \<not>Q"
+ "P \<noteq> Q \<or> \<not>P \<or> Q"
+ "P \<noteq> (\<not>Q) \<or> P \<or> Q"
+ "(\<not>P) \<noteq> Q \<or> P \<or> Q"
+ "P \<or> Q \<or> P \<noteq> (\<not>Q)"
+ "P \<or> Q \<or> (\<not>P) \<noteq> Q"
+ "P \<or> \<not>Q \<or> P \<noteq> Q"
+ "\<not>P \<or> Q \<or> P \<noteq> Q"
+ by auto
+
+lemma [z3_rule]:
+ "0 + (x::int) = x"
+ "x + 0 = x"
+ "0 * x = 0"
+ "1 * x = x"
+ "x + y = y + x"
+ by auto
+
+lemma [z3_rule]:
+ "0 + (x::real) = x"
+ "x + 0 = x"
+ "0 * x = 0"
+ "1 * x = x"
+ "x + y = y + x"
+ by auto
+
+
+end
--- a/src/HOL/SMT/Examples/ROOT.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1 +0,0 @@
-use_thys ["SMT_Examples"];
--- a/src/HOL/SMT/Examples/SMT_Examples.certs Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,13471 +0,0 @@
-bb06851c317eb8b672e27364b0ae34a4e39eb880 8 0
-#2 := false
-#1 := true
-#4 := (not true)
-#21 := (iff #4 false)
-#22 := [rewrite]: #21
-#20 := [asserted]: #4
-[mp #20 #22]: false
-unsat
-70d1f77bec207467bc0306af0d98a71fa8328274 19 0
-#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
-148012a9e9d44fe30a0c79e3344bdb805124f661 25 0
-#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
-bc9a25b7f6dc3ac2431ee71b6e71c5a7b25e89d1 38 0
-#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
-9b3db6ce34c8a1806160f1349b898b6c5ca40ba0 1 0
-unsat
-912e9b7fb52f4a71d232354b3bb53c11e5a41ccd 71 0
-#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
-4d063d3cdf6657ddb4258379f900ef18e9042978 57 0
-#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
-212c7825456dae820eef6b1fa0cb8c5ceeff8780 194 0
-#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
-42890f9fa7c18237798ca55d0cf9dfff6f2f868a 52 0
-#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
-62bff2883948b13c19c4cd52ed250bf0afc3ec90 1667 0
-#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
-d8841d120b7cf772be783d793f759fb6353b9fcd 78 0
-#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
-bc722e6a73140d95a8643a8d8a522de8bf529dea 135 0
-#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
-3ad10572aa4268ecfd73368c6cc15680136648a3 136 0
-WARNING: failed to find a pattern for quantifier (quantifier id: k!12)
-#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
-0e958e27514643bb596851e6dbb61a23f6b348b0 56 0
-#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
-6ecefa4023d224e6c51226d5bee17e2a19cc4333 17 0
-#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
-5e0256133fc82f0e2fea6597b863483e4e61d3c6 17 0
-#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
-55cf32b061b843ac5bcaefb74005a7dd3a24386f 26 0
-#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
-e81d17ec85af9db5ec6ba5bf4ced62daaa719ef3 41 0
-#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
-448f188ebf9d7fbd2920c0a51a8f105192e6af1a 35 0
-#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
-c3751ecae7701923f4ba6a90c6c6eee35ee1b13d 250 0
-#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
-a67db8da0b1a1104d4370e2e261e8521096f24e1 124 0
-#2 := false
-decl uf_1 :: (-> T1 T2)
-decl uf_3 :: T1
-#8 := uf_3
-#9 := (uf_1 uf_3)
-decl uf_2 :: (-> int int T1)
-#5 := 3::int
-#4 := 2::int
-#6 := (uf_2 2::int 3::int)
-#7 := (uf_1 #6)
-#10 := (= #7 #9)
-#225 := (= #6 uf_3)
-#13 := (:var 0 int)
-#12 := (:var 1 int)
-#14 := (uf_2 #12 #13)
-#549 := (pattern #14)
-#52 := 0::int
-#50 := -1::int
-#54 := (* -1::int #13)
-#55 := (+ #12 #54)
-#53 := (>= #55 0::int)
-#51 := (not #53)
-#36 := (= uf_3 #14)
-#61 := (iff #36 #51)
-#550 := (forall (vars (?x1 int) (?x2 int)) (:pat #549) #61)
-#66 := (forall (vars (?x1 int) (?x2 int)) #61)
-#553 := (iff #66 #550)
-#551 := (iff #61 #61)
-#552 := [refl]: #551
-#554 := [quant-intro #552]: #553
-#79 := (~ #66 #66)
-#77 := (~ #61 #61)
-#78 := [refl]: #77
-#80 := [nnf-pos #78]: #79
-#16 := (< #12 #13)
-#15 := (= #14 uf_3)
-#17 := (iff #15 #16)
-#18 := (forall (vars (?x1 int) (?x2 int)) #17)
-#69 := (iff #18 #66)
-#42 := (iff #16 #36)
-#47 := (forall (vars (?x1 int) (?x2 int)) #42)
-#67 := (iff #47 #66)
-#64 := (iff #42 #61)
-#58 := (iff #51 #36)
-#62 := (iff #58 #61)
-#63 := [rewrite]: #62
-#59 := (iff #42 #58)
-#56 := (iff #16 #51)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#65 := [trans #60 #63]: #64
-#68 := [quant-intro #65]: #67
-#48 := (iff #18 #47)
-#45 := (iff #17 #42)
-#39 := (iff #36 #16)
-#43 := (iff #39 #42)
-#44 := [rewrite]: #43
-#40 := (iff #17 #39)
-#37 := (iff #15 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#46 := [trans #41 #44]: #45
-#49 := [quant-intro #46]: #48
-#70 := [trans #49 #68]: #69
-#35 := [asserted]: #18
-#71 := [mp #35 #70]: #66
-#74 := [mp~ #71 #80]: #66
-#555 := [mp #74 #554]: #550
-#529 := (not #550)
-#530 := (or #529 #225)
-#220 := (* -1::int 3::int)
-#221 := (+ 2::int #220)
-#222 := (>= #221 0::int)
-#213 := (not #222)
-#135 := (= uf_3 #6)
-#224 := (iff #135 #213)
-#525 := (or #529 #224)
-#169 := (iff #525 #530)
-#534 := (iff #530 #530)
-#174 := [rewrite]: #534
-#527 := (iff #224 #225)
-#1 := true
-#187 := (iff #225 true)
-#190 := (iff #187 #225)
-#526 := [rewrite]: #190
-#188 := (iff #224 #187)
-#183 := (iff #213 true)
-#198 := (not false)
-#199 := (iff #198 true)
-#540 := [rewrite]: #199
-#203 := (iff #213 #198)
-#548 := (iff #222 false)
-#544 := (>= -1::int 0::int)
-#547 := (iff #544 false)
-#542 := [rewrite]: #547
-#545 := (iff #222 #544)
-#211 := (= #221 -1::int)
-#223 := -3::int
-#541 := (+ 2::int -3::int)
-#330 := (= #541 -1::int)
-#537 := [rewrite]: #330
-#543 := (= #221 #541)
-#227 := (= #220 -3::int)
-#206 := [rewrite]: #227
-#200 := [monotonicity #206]: #543
-#212 := [trans #200 #537]: #211
-#546 := [monotonicity #212]: #545
-#538 := [trans #546 #542]: #548
-#539 := [monotonicity #538]: #203
-#524 := [trans #539 #540]: #183
-#153 := (iff #135 #225)
-#226 := [rewrite]: #153
-#189 := [monotonicity #226 #524]: #188
-#528 := [trans #189 #526]: #527
-#532 := [monotonicity #528]: #169
-#175 := [trans #532 #174]: #169
-#531 := [quant-inst]: #525
-#535 := [mp #531 #175]: #530
-#533 := [unit-resolution #535 #555]: #225
-#536 := [monotonicity #533]: #10
-#11 := (not #10)
-#34 := [asserted]: #11
-[unit-resolution #34 #536]: false
-unsat
-243524c591f6dcfe16a79ddd249c64a337ff3612 54 0
-#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
-adfe7d6c2da6653191952bd9673c1274f94c2ab2 63 0
-#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
-3440e29713ba625633b10a2c4fdc186cb6e0cf3e 35 0
-#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
-7a45124c81166760c08802d05bb1a73c01b0f138 45 0
-#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
-f946ff901958cea1a0225dfba1e556060c889a10 59 0
-#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
-88d529b1517abb78e220ec8f58e3b3405bb2453b 212 0
-#2 := false
-decl uf_4 :: T1
-#13 := uf_4
-decl uf_1 :: (-> int int T1)
-#5 := 3::int
-decl uf_2 :: int
-#4 := uf_2
-#6 := (uf_1 uf_2 3::int)
-#559 := (= #6 uf_4)
-decl uf_3 :: (-> int int T1)
-#7 := (uf_3 3::int uf_2)
-#254 := (= #7 uf_4)
-#524 := (iff #254 #559)
-#529 := (iff #559 #254)
-#39 := (= #6 #7)
-#8 := (distinct #6 #7)
-#9 := (not #8)
-#48 := (iff #9 #39)
-#40 := (not #39)
-#43 := (not #40)
-#46 := (iff #43 #39)
-#47 := [rewrite]: #46
-#44 := (iff #9 #43)
-#41 := (iff #8 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#38 := [asserted]: #9
-#52 := [mp #38 #49]: #39
-#523 := [monotonicity #52]: #529
-#530 := [symm #523]: #524
-#547 := (not #559)
-#570 := (not #254)
-#531 := (iff #570 #547)
-#525 := [monotonicity #530]: #531
-#540 := [hypothesis]: #570
-#532 := [mp #540 #525]: #547
-#256 := (>= uf_2 3::int)
-#579 := (not #256)
-#541 := (or #254 #579)
-#258 := (iff #254 #256)
-#11 := (:var 0 int)
-#10 := (:var 1 int)
-#12 := (uf_3 #10 #11)
-#581 := (pattern #12)
-#57 := 0::int
-#54 := -1::int
-#55 := (* -1::int #11)
-#56 := (+ #10 #55)
-#58 := (<= #56 0::int)
-#14 := (= #12 uf_4)
-#61 := (iff #14 #58)
-#582 := (forall (vars (?x1 int) (?x2 int)) (:pat #581) #61)
-#64 := (forall (vars (?x1 int) (?x2 int)) #61)
-#585 := (iff #64 #582)
-#583 := (iff #61 #61)
-#584 := [refl]: #583
-#586 := [quant-intro #584]: #585
-#108 := (~ #64 #64)
-#106 := (~ #61 #61)
-#107 := [refl]: #106
-#109 := [nnf-pos #107]: #108
-#15 := (<= #10 #11)
-#16 := (iff #14 #15)
-#17 := (forall (vars (?x1 int) (?x2 int)) #16)
-#65 := (iff #17 #64)
-#62 := (iff #16 #61)
-#59 := (iff #15 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#66 := [quant-intro #63]: #65
-#50 := [asserted]: #17
-#67 := [mp #50 #66]: #64
-#101 := [mp~ #67 #109]: #64
-#587 := [mp #101 #586]: #582
-#238 := (not #582)
-#573 := (or #238 #258)
-#167 := (* -1::int uf_2)
-#252 := (+ 3::int #167)
-#253 := (<= #252 0::int)
-#245 := (iff #254 #253)
-#575 := (or #238 #245)
-#362 := (iff #575 #573)
-#243 := (iff #573 #573)
-#244 := [rewrite]: #243
-#255 := (iff #245 #258)
-#257 := (iff #253 #256)
-#185 := [rewrite]: #257
-#259 := [monotonicity #185]: #255
-#569 := [monotonicity #259]: #362
-#576 := [trans #569 #244]: #362
-#232 := [quant-inst]: #575
-#577 := [mp #232 #576]: #573
-#535 := [unit-resolution #577 #587]: #258
-#578 := (not #258)
-#574 := (or #578 #254 #579)
-#580 := [def-axiom]: #574
-#382 := [unit-resolution #580 #535]: #541
-#383 := [unit-resolution #382 #540]: #579
-#526 := (or #559 #256)
-#273 := (iff #559 #579)
-#18 := (uf_1 #10 #11)
-#588 := (pattern #18)
-#82 := (>= #56 0::int)
-#81 := (not #82)
-#53 := (= uf_4 #18)
-#88 := (iff #53 #81)
-#589 := (forall (vars (?x3 int) (?x4 int)) (:pat #588) #88)
-#93 := (forall (vars (?x3 int) (?x4 int)) #88)
-#592 := (iff #93 #589)
-#590 := (iff #88 #88)
-#591 := [refl]: #590
-#593 := [quant-intro #591]: #592
-#102 := (~ #93 #93)
-#99 := (~ #88 #88)
-#110 := [refl]: #99
-#103 := [nnf-pos #110]: #102
-#20 := (< #10 #11)
-#19 := (= #18 uf_4)
-#21 := (iff #19 #20)
-#22 := (forall (vars (?x3 int) (?x4 int)) #21)
-#96 := (iff #22 #93)
-#73 := (iff #20 #53)
-#78 := (forall (vars (?x3 int) (?x4 int)) #73)
-#94 := (iff #78 #93)
-#91 := (iff #73 #88)
-#85 := (iff #81 #53)
-#89 := (iff #85 #88)
-#90 := [rewrite]: #89
-#86 := (iff #73 #85)
-#83 := (iff #20 #81)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#92 := [trans #87 #90]: #91
-#95 := [quant-intro #92]: #94
-#79 := (iff #22 #78)
-#76 := (iff #21 #73)
-#70 := (iff #53 #20)
-#74 := (iff #70 #73)
-#75 := [rewrite]: #74
-#71 := (iff #21 #70)
-#68 := (iff #19 #53)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#77 := [trans #72 #75]: #76
-#80 := [quant-intro #77]: #79
-#97 := [trans #80 #95]: #96
-#51 := [asserted]: #22
-#98 := [mp #51 #97]: #93
-#111 := [mp~ #98 #103]: #93
-#594 := [mp #111 #593]: #589
-#552 := (not #589)
-#549 := (or #552 #273)
-#219 := (* -1::int 3::int)
-#220 := (+ uf_2 #219)
-#221 := (>= #220 0::int)
-#222 := (not #221)
-#556 := (= uf_4 #6)
-#558 := (iff #556 #222)
-#553 := (or #552 #558)
-#264 := (iff #553 #549)
-#266 := (iff #549 #549)
-#544 := [rewrite]: #266
-#274 := (iff #558 #273)
-#550 := (iff #222 #579)
-#280 := (iff #221 #256)
-#562 := -3::int
-#206 := (+ -3::int uf_2)
-#554 := (>= #206 0::int)
-#278 := (iff #554 #256)
-#279 := [rewrite]: #278
-#555 := (iff #221 #554)
-#565 := (= #220 #206)
-#201 := (+ uf_2 -3::int)
-#207 := (= #201 #206)
-#567 := [rewrite]: #207
-#564 := (= #220 #201)
-#557 := (= #219 -3::int)
-#563 := [rewrite]: #557
-#566 := [monotonicity #563]: #564
-#568 := [trans #566 #567]: #565
-#277 := [monotonicity #568]: #555
-#173 := [trans #277 #279]: #280
-#551 := [monotonicity #173]: #550
-#560 := (iff #556 #559)
-#561 := [rewrite]: #560
-#548 := [monotonicity #561 #551]: #274
-#265 := [monotonicity #548]: #264
-#545 := [trans #265 #544]: #264
-#263 := [quant-inst]: #553
-#260 := [mp #263 #545]: #549
-#384 := [unit-resolution #260 #594]: #273
-#542 := (not #273)
-#546 := (or #542 #559 #256)
-#543 := [def-axiom]: #546
-#527 := [unit-resolution #543 #384]: #526
-#528 := [unit-resolution #527 #383]: #559
-#361 := [unit-resolution #528 #532]: false
-#363 := [lemma #361]: #254
-#522 := [mp #363 #530]: #559
-#364 := (or #570 #256)
-#230 := (or #578 #570 #256)
-#235 := [def-axiom]: #230
-#517 := [unit-resolution #235 #535]: #364
-#518 := [unit-resolution #517 #363]: #256
-#520 := (or #547 #579)
-#536 := (or #542 #547 #579)
-#537 := [def-axiom]: #536
-#521 := [unit-resolution #537 #384]: #520
-#519 := [unit-resolution #521 #518]: #547
-[unit-resolution #519 #522]: false
-unsat
-bf36938883aa38907d4d00c1860a1d18e7b620d0 86 0
-#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
-d4ecdf21a3d5d758670676ddb9e6e093ea9fcc15 673 0
-#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
-efea5b71ce31ca68241e4ee8755a8335445d88e6 2291 0
-#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
-#661 := [monotonicity #658]: #660
-#664 := [monotonicity #661]: #663
-#667 := [monotonicity #664]: #666
-#533 := (>= #120 0::int)
-#535 := (not #533)
-#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
-#90 := [monotonicity #87]: #89
-#96 := [trans #90 #94]: #95
-#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
-#1515 := (or #100 #241 #923 #1373 #1371 #961)
-#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
-#1528 := (not #665)
-#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)
-#528 := (not #523)
-#644 := (iff #528 #635)
-#636 := (not #635)
-#639 := (not #636)
-#642 := (iff #639 #635)
-#643 := [rewrite]: #642
-#640 := (iff #528 #639)
-#637 := (iff #523 #636)
-#638 := [rewrite]: #637
-#641 := [monotonicity #638]: #640
-#645 := [trans #641 #643]: #644
-#62 := (= uf_2 uf_11)
-#61 := (= uf_3 uf_10)
-#63 := (and #61 #62)
-#64 := (not #63)
-#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)
-#512 := [rewrite]: #511
-#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
-#1500 := [unit-resolution #1499 #1475 #698 #724 #1497 #772 #1447 #802 #1496 #828 #1495 #854 #1494 #876 #1480]: #516
-#1501 := [unit-resolution #1236 #1479]: #919
-#1502 := [unit-resolution #1328 #1493]: #1199
-#1508 := [unit-resolution #1248 #1474]: #957
-#1514 := [unit-resolution #1513 #1508 #694 #720 #1468 #776 #1507 #798 #1488 #824 #1483 #850 #1502 #880 #1501]: #515
-#1517 := [unit-resolution #1516 #1480 #698 #1475 #724 #1406]: #100
-#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
-#1614 := [unit-resolution #1320 #1613]: #1185
-#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
-#1321 := (or #1190 #1187)
-#1322 := [def-axiom]: #1321
-#1618 := [unit-resolution #1322 #1613]: #1187
-#1619 := [unit-resolution #994 #1535]: #975
-#1253 := (or #974 #970)
-#1254 := [def-axiom]: #1253
-#1620 := [unit-resolution #1254 #1619]: #970
-#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
-#1348 := [unit-resolution #1284 #1347]: #1071
-#1349 := [unit-resolution #1286 #1347]: #1073
-#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
-258b6cd4609a61b7800235c7f356739cfb8996c5 52 0
-#2 := false
-#8 := 1::real
-decl uf_1 :: real
-#4 := uf_1
-#6 := 2::real
-#7 := (* 2::real uf_1)
-#9 := (+ #7 1::real)
-#5 := (+ uf_1 uf_1)
-#10 := (< #5 #9)
-#11 := (or false #10)
-#12 := (or #10 #11)
-#13 := (not #12)
-#64 := (iff #13 false)
-#32 := (+ 1::real #7)
-#35 := (< #7 #32)
-#52 := (not #35)
-#62 := (iff #52 false)
-#1 := true
-#57 := (not true)
-#60 := (iff #57 false)
-#61 := [rewrite]: #60
-#58 := (iff #52 #57)
-#55 := (iff #35 true)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#53 := (iff #13 #52)
-#50 := (iff #12 #35)
-#45 := (or #35 #35)
-#48 := (iff #45 #35)
-#49 := [rewrite]: #48
-#46 := (iff #12 #45)
-#43 := (iff #11 #35)
-#38 := (or false #35)
-#41 := (iff #38 #35)
-#42 := [rewrite]: #41
-#39 := (iff #11 #38)
-#36 := (iff #10 #35)
-#33 := (= #9 #32)
-#34 := [rewrite]: #33
-#30 := (= #5 #7)
-#31 := [rewrite]: #30
-#37 := [monotonicity #31 #34]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#47 := [monotonicity #37 #44]: #46
-#51 := [trans #47 #49]: #50
-#54 := [monotonicity #51]: #53
-#65 := [trans #54 #63]: #64
-#29 := [asserted]: #13
-[mp #29 #65]: false
-unsat
-3d1d0473f97c11d6c4d10f6e0313b2e2f4aac879 59 0
-#2 := false
-#55 := 0::int
-#7 := 2::int
-decl uf_1 :: int
-#4 := uf_1
-#8 := (mod uf_1 2::int)
-#58 := (>= #8 0::int)
-#61 := (not #58)
-#5 := 1::int
-#9 := (* 2::int #8)
-#10 := (+ #9 1::int)
-#11 := (+ uf_1 #10)
-#6 := (+ uf_1 1::int)
-#12 := (<= #6 #11)
-#13 := (not #12)
-#66 := (iff #13 #61)
-#39 := (+ uf_1 #9)
-#40 := (+ 1::int #39)
-#30 := (+ 1::int uf_1)
-#45 := (<= #30 #40)
-#48 := (not #45)
-#64 := (iff #48 #61)
-#56 := (>= #9 0::int)
-#51 := (not #56)
-#62 := (iff #51 #61)
-#59 := (iff #56 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#52 := (iff #48 #51)
-#53 := (iff #45 #56)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #52
-#65 := [trans #57 #63]: #64
-#49 := (iff #13 #48)
-#46 := (iff #12 #45)
-#43 := (= #11 #40)
-#33 := (+ 1::int #9)
-#36 := (+ uf_1 #33)
-#41 := (= #36 #40)
-#42 := [rewrite]: #41
-#37 := (= #11 #36)
-#34 := (= #10 #33)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#44 := [trans #38 #42]: #43
-#31 := (= #6 #30)
-#32 := [rewrite]: #31
-#47 := [monotonicity #32 #44]: #46
-#50 := [monotonicity #47]: #49
-#67 := [trans #50 #65]: #66
-#29 := [asserted]: #13
-#68 := [mp #29 #67]: #61
-#1 := true
-#28 := [true-axiom]: true
-#142 := (or false #58)
-#143 := [th-lemma]: #142
-#144 := [unit-resolution #143 #28]: #58
-[unit-resolution #144 #68]: false
-unsat
-f768cbe713eb8031e45b1a78d0f49a07f5398eb8 54 0
-#2 := false
-#5 := 2::int
-decl uf_1 :: int
-#4 := uf_1
-#6 := (mod uf_1 2::int)
-#55 := (>= #6 2::int)
-#9 := 3::int
-#10 := (+ uf_1 3::int)
-#7 := (+ #6 #6)
-#8 := (+ uf_1 #7)
-#11 := (< #8 #10)
-#12 := (not #11)
-#60 := (iff #12 #55)
-#35 := (+ 3::int uf_1)
-#29 := (* 2::int #6)
-#32 := (+ uf_1 #29)
-#38 := (< #32 #35)
-#41 := (not #38)
-#58 := (iff #41 #55)
-#48 := (>= #29 3::int)
-#56 := (iff #48 #55)
-#57 := [rewrite]: #56
-#53 := (iff #41 #48)
-#46 := (not #48)
-#45 := (not #46)
-#51 := (iff #45 #48)
-#52 := [rewrite]: #51
-#49 := (iff #41 #45)
-#47 := (iff #38 #46)
-#44 := [rewrite]: #47
-#50 := [monotonicity #44]: #49
-#54 := [trans #50 #52]: #53
-#59 := [trans #54 #57]: #58
-#42 := (iff #12 #41)
-#39 := (iff #11 #38)
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#33 := (= #8 #32)
-#30 := (= #7 #29)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#40 := [monotonicity #34 #37]: #39
-#43 := [monotonicity #40]: #42
-#61 := [trans #43 #59]: #60
-#28 := [asserted]: #12
-#62 := [mp #28 #61]: #55
-#127 := (not #55)
-#1 := true
-#27 := [true-axiom]: true
-#137 := (or false #127)
-#138 := [th-lemma]: #137
-#139 := [unit-resolution #138 #27]: #127
-[unit-resolution #139 #62]: false
-unsat
-2c2bcacfbe018175dd39ce04dd5cbe02c800a0dd 118 0
-#2 := false
-#5 := 0::real
-decl uf_1 :: real
-#4 := uf_1
-#94 := (<= uf_1 0::real)
-#17 := 2::real
-#40 := (* 2::real uf_1)
-#102 := (<= #40 0::real)
-#103 := (>= #40 0::real)
-#105 := (not #103)
-#104 := (not #102)
-#106 := (or #104 #105)
-#107 := (not #106)
-#88 := (= #40 0::real)
-#108 := (iff #88 #107)
-#109 := [rewrite]: #108
-#16 := 4::real
-#11 := (- uf_1)
-#10 := (< uf_1 0::real)
-#12 := (ite #10 #11 uf_1)
-#9 := 1::real
-#13 := (< 1::real #12)
-#14 := (not #13)
-#15 := (or #13 #14)
-#18 := (ite #15 4::real 2::real)
-#19 := (* #18 uf_1)
-#8 := (+ uf_1 uf_1)
-#20 := (= #8 #19)
-#21 := (not #20)
-#22 := (not #21)
-#89 := (iff #22 #88)
-#70 := (* 4::real uf_1)
-#73 := (= #40 #70)
-#86 := (iff #73 #88)
-#87 := [rewrite]: #86
-#84 := (iff #22 #73)
-#76 := (not #73)
-#79 := (not #76)
-#82 := (iff #79 #73)
-#83 := [rewrite]: #82
-#80 := (iff #22 #79)
-#77 := (iff #21 #76)
-#74 := (iff #20 #73)
-#71 := (= #19 #70)
-#68 := (= #18 4::real)
-#1 := true
-#63 := (ite true 4::real 2::real)
-#66 := (= #63 4::real)
-#67 := [rewrite]: #66
-#64 := (= #18 #63)
-#61 := (iff #15 true)
-#43 := -1::real
-#44 := (* -1::real uf_1)
-#47 := (ite #10 #44 uf_1)
-#50 := (< 1::real #47)
-#53 := (not #50)
-#56 := (or #50 #53)
-#59 := (iff #56 true)
-#60 := [rewrite]: #59
-#57 := (iff #15 #56)
-#54 := (iff #14 #53)
-#51 := (iff #13 #50)
-#48 := (= #12 #47)
-#45 := (= #11 #44)
-#46 := [rewrite]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#55 := [monotonicity #52]: #54
-#58 := [monotonicity #52 #55]: #57
-#62 := [trans #58 #60]: #61
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#72 := [monotonicity #69]: #71
-#41 := (= #8 #40)
-#42 := [rewrite]: #41
-#75 := [monotonicity #42 #72]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#85 := [trans #81 #83]: #84
-#90 := [trans #85 #87]: #89
-#39 := [asserted]: #22
-#91 := [mp #39 #90]: #88
-#110 := [mp #91 #109]: #107
-#111 := [not-or-elim #110]: #102
-#127 := (or #94 #104)
-#128 := [th-lemma]: #127
-#129 := [unit-resolution #128 #111]: #94
-#92 := (>= uf_1 0::real)
-#112 := [not-or-elim #110]: #103
-#130 := (or #92 #105)
-#131 := [th-lemma]: #130
-#132 := [unit-resolution #131 #112]: #92
-#114 := (not #94)
-#113 := (not #92)
-#115 := (or #113 #114)
-#95 := (and #92 #94)
-#98 := (not #95)
-#124 := (iff #98 #115)
-#116 := (not #115)
-#119 := (not #116)
-#122 := (iff #119 #115)
-#123 := [rewrite]: #122
-#120 := (iff #98 #119)
-#117 := (iff #95 #116)
-#118 := [rewrite]: #117
-#121 := [monotonicity #118]: #120
-#125 := [trans #121 #123]: #124
-#6 := (= uf_1 0::real)
-#7 := (not #6)
-#99 := (iff #7 #98)
-#96 := (iff #6 #95)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#38 := [asserted]: #7
-#101 := [mp #38 #100]: #98
-#126 := [mp #101 #125]: #115
-[unit-resolution #126 #132 #129]: false
-unsat
-8bded5c2f0cd48cce9a86100cc4c6ce26ec88a2e 208 0
-#2 := false
-#9 := 0::int
-#11 := 4::int
-decl uf_1 :: int
-#4 := uf_1
-#189 := (div uf_1 4::int)
-#210 := -4::int
-#211 := (* -4::int #189)
-#12 := (mod uf_1 4::int)
-#134 := -1::int
-#209 := (* -1::int #12)
-#212 := (+ #209 #211)
-#213 := (+ uf_1 #212)
-#214 := (<= #213 0::int)
-#215 := (not #214)
-#208 := (>= #213 0::int)
-#207 := (not #208)
-#216 := (or #207 #215)
-#217 := (not #216)
-#1 := true
-#36 := [true-axiom]: true
-#393 := (or false #217)
-#394 := [th-lemma]: #393
-#395 := [unit-resolution #394 #36]: #217
-#224 := (or #216 #214)
-#225 := [def-axiom]: #224
-#396 := [unit-resolution #225 #395]: #214
-#222 := (or #216 #208)
-#223 := [def-axiom]: #222
-#397 := [unit-resolution #223 #395]: #208
-#250 := (>= #12 4::int)
-#251 := (not #250)
-#398 := (or false #251)
-#399 := [th-lemma]: #398
-#400 := [unit-resolution #399 #36]: #251
-#13 := 3::int
-#90 := (>= #12 3::int)
-#92 := (not #90)
-#89 := (<= #12 3::int)
-#91 := (not #89)
-#93 := (or #91 #92)
-#94 := (not #93)
-#14 := (= #12 3::int)
-#95 := (iff #14 #94)
-#96 := [rewrite]: #95
-#38 := [asserted]: #14
-#97 := [mp #38 #96]: #94
-#99 := [not-or-elim #97]: #90
-#7 := 2::int
-#261 := (div uf_1 2::int)
-#140 := -2::int
-#276 := (* -2::int #261)
-#15 := (mod uf_1 2::int)
-#275 := (* -1::int #15)
-#277 := (+ #275 #276)
-#278 := (+ uf_1 #277)
-#279 := (<= #278 0::int)
-#280 := (not #279)
-#274 := (>= #278 0::int)
-#273 := (not #274)
-#281 := (or #273 #280)
-#282 := (not #281)
-#408 := (or false #282)
-#409 := [th-lemma]: #408
-#410 := [unit-resolution #409 #36]: #282
-#289 := (or #281 #279)
-#290 := [def-axiom]: #289
-#411 := [unit-resolution #290 #410]: #279
-#287 := (or #281 #274)
-#288 := [def-axiom]: #287
-#412 := [unit-resolution #288 #410]: #274
-#16 := 1::int
-#55 := (>= #15 1::int)
-#100 := (not #55)
-decl uf_2 :: int
-#5 := uf_2
-#18 := (mod uf_2 2::int)
-#61 := (<= #18 1::int)
-#102 := (not #61)
-#375 := [hypothesis]: #102
-#358 := (>= #18 2::int)
-#359 := (not #358)
-#403 := (or false #359)
-#404 := [th-lemma]: #403
-#405 := [unit-resolution #404 #36]: #359
-#406 := [th-lemma #405 #375]: false
-#407 := [lemma #406]: #61
-#413 := (or #100 #102)
-#62 := (>= #18 1::int)
-#315 := (div uf_2 2::int)
-#330 := (* -2::int #315)
-#329 := (* -1::int #18)
-#331 := (+ #329 #330)
-#332 := (+ uf_2 #331)
-#333 := (<= #332 0::int)
-#334 := (not #333)
-#328 := (>= #332 0::int)
-#327 := (not #328)
-#335 := (or #327 #334)
-#336 := (not #335)
-#376 := (or false #336)
-#377 := [th-lemma]: #376
-#378 := [unit-resolution #377 #36]: #336
-#343 := (or #335 #333)
-#344 := [def-axiom]: #343
-#379 := [unit-resolution #344 #378]: #333
-#341 := (or #335 #328)
-#342 := [def-axiom]: #341
-#380 := [unit-resolution #342 #378]: #328
-#103 := (not #62)
-#381 := [hypothesis]: #103
-#352 := (>= #18 0::int)
-#382 := (or false #352)
-#383 := [th-lemma]: #382
-#384 := [unit-resolution #383 #36]: #352
-#6 := (+ uf_1 uf_2)
-#116 := (div #6 2::int)
-#141 := (* -2::int #116)
-#8 := (mod #6 2::int)
-#139 := (* -1::int #8)
-#142 := (+ #139 #141)
-#143 := (+ uf_2 #142)
-#144 := (+ uf_1 #143)
-#138 := (<= #144 0::int)
-#136 := (not #138)
-#137 := (>= #144 0::int)
-#135 := (not #137)
-#145 := (or #135 #136)
-#146 := (not #145)
-#385 := (or false #146)
-#386 := [th-lemma]: #385
-#387 := [unit-resolution #386 #36]: #146
-#153 := (or #145 #138)
-#154 := [def-axiom]: #153
-#388 := [unit-resolution #154 #387]: #138
-#151 := (or #145 #137)
-#152 := [def-axiom]: #151
-#389 := [unit-resolution #152 #387]: #137
-#78 := (<= #8 0::int)
-#79 := (>= #8 0::int)
-#81 := (not #79)
-#80 := (not #78)
-#82 := (or #80 #81)
-#83 := (not #82)
-#10 := (= #8 0::int)
-#84 := (iff #10 #83)
-#85 := [rewrite]: #84
-#37 := [asserted]: #10
-#86 := [mp #37 #85]: #83
-#87 := [not-or-elim #86]: #78
-#390 := (or false #79)
-#391 := [th-lemma]: #390
-#392 := [unit-resolution #391 #36]: #79
-#401 := [th-lemma #99 #400 #397 #396 #392 #87 #389 #388 #384 #381 #380 #379]: false
-#402 := [lemma #401]: #62
-#57 := (<= #15 1::int)
-#101 := (not #57)
-#369 := [hypothesis]: #101
-#304 := (>= #15 2::int)
-#305 := (not #304)
-#370 := (or false #305)
-#371 := [th-lemma]: #370
-#372 := [unit-resolution #371 #36]: #305
-#373 := [th-lemma #372 #369]: false
-#374 := [lemma #373]: #57
-#104 := (or #100 #101 #102 #103)
-#69 := (and #55 #57 #61 #62)
-#74 := (not #69)
-#113 := (iff #74 #104)
-#105 := (not #104)
-#108 := (not #105)
-#111 := (iff #108 #104)
-#112 := [rewrite]: #111
-#109 := (iff #74 #108)
-#106 := (iff #69 #105)
-#107 := [rewrite]: #106
-#110 := [monotonicity #107]: #109
-#114 := [trans #110 #112]: #113
-#19 := (= #18 1::int)
-#17 := (= #15 1::int)
-#20 := (and #17 #19)
-#21 := (not #20)
-#75 := (iff #21 #74)
-#72 := (iff #20 #69)
-#63 := (and #61 #62)
-#58 := (and #55 #57)
-#66 := (and #58 #63)
-#70 := (iff #66 #69)
-#71 := [rewrite]: #70
-#67 := (iff #20 #66)
-#64 := (iff #19 #63)
-#65 := [rewrite]: #64
-#59 := (iff #17 #58)
-#60 := [rewrite]: #59
-#68 := [monotonicity #60 #65]: #67
-#73 := [trans #68 #71]: #72
-#76 := [monotonicity #73]: #75
-#39 := [asserted]: #21
-#77 := [mp #39 #76]: #74
-#115 := [mp #77 #114]: #104
-#414 := [unit-resolution #115 #374 #402]: #413
-#415 := [unit-resolution #414 #407]: #100
-#298 := (>= #15 0::int)
-#416 := (or false #298)
-#417 := [th-lemma]: #416
-#418 := [unit-resolution #417 #36]: #298
-[th-lemma #418 #415 #412 #411 #99 #400 #397 #396]: false
-unsat
-7beaddc803d2c23197634dc63d56d564292d85fe 24 0
-#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
-723fcd1ecb9fa59a7e0fede642f23063fb499818 24 0
-#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
-a72d0e977596e1fac0cccee600f0bf9d29ed71aa 1 0
-unsat
-70141a690f46561f859d3deed80b9611816f9f81 1 0
-unsat
-41b6ddffa2c7efc9285d0e0a65d74c4325ef6ddb 1 0
-unsat
-a08fcdd29520930b0a940df57c3d8266dbefd10f 73 0
-#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
-470993954e986ab72716000fd7da9fa600b05225 82 0
-#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
-40c93af1a084932780f95bda03b3df7712e01201 78 0
-#2 := false
-#5 := (:var 0 int)
-#7 := 2::int
-#11 := (* 2::int #5)
-#9 := 1::int
-#4 := (:var 1 int)
-#8 := (* 2::int #4)
-#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)
-#91 := (iff #15 false)
-#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)
-#89 := (iff #50 false)
-#1 := true
-#84 := (not true)
-#87 := (iff #84 false)
-#88 := [rewrite]: #87
-#85 := (iff #50 #84)
-#82 := (iff #47 true)
-#77 := (forall (vars (?x1 int) (?x2 int)) true)
-#80 := (iff #77 true)
-#81 := [elim-unused]: #80
-#78 := (iff #47 #77)
-#75 := (iff #42 true)
-#55 := 0::int
-#53 := -1::int
-#57 := (* -1::int #5)
-#58 := (+ #4 #57)
-#56 := (>= #58 0::int)
-#54 := (not #56)
-#69 := (or #56 #54)
-#73 := (iff #69 true)
-#74 := [rewrite]: #73
-#71 := (iff #42 #69)
-#70 := (iff #35 #54)
-#68 := [rewrite]: #70
-#66 := (iff #41 #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
-#72 := [monotonicity #67 #68]: #71
-#76 := [trans #72 #74]: #75
-#79 := [quant-intro #76]: #78
-#83 := [trans #79 #81]: #82
-#86 := [monotonicity #83]: #85
-#90 := [trans #86 #88]: #89
-#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
-#92 := [trans #52 #90]: #91
-#31 := [asserted]: #15
-[mp #31 #92]: false
-unsat
-26b175ea54cef59293a917c6fb083751b00d312a 61 0
-#2 := false
-#9 := (:var 0 int)
-#4 := 2::int
-#10 := (* 2::int #9)
-#7 := 1::int
-#5 := (:var 1 int)
-#6 := (* 2::int #5)
-#8 := (+ #6 1::int)
-#11 := (= #8 #10)
-#12 := (not #11)
-#13 := (forall (vars (?x1 int) (?x2 int)) #12)
-#14 := (not #13)
-#74 := (iff #14 false)
-#31 := (+ 1::int #6)
-#37 := (= #10 #31)
-#42 := (not #37)
-#45 := (forall (vars (?x1 int) (?x2 int)) #42)
-#48 := (not #45)
-#72 := (iff #48 false)
-#1 := true
-#67 := (not true)
-#70 := (iff #67 false)
-#71 := [rewrite]: #70
-#68 := (iff #48 #67)
-#65 := (iff #45 true)
-#60 := (forall (vars (?x1 int) (?x2 int)) true)
-#63 := (iff #60 true)
-#64 := [elim-unused]: #63
-#61 := (iff #45 #60)
-#58 := (iff #42 true)
-#51 := (not false)
-#56 := (iff #51 true)
-#57 := [rewrite]: #56
-#52 := (iff #42 #51)
-#53 := (iff #37 false)
-#54 := [rewrite]: #53
-#55 := [monotonicity #54]: #52
-#59 := [trans #55 #57]: #58
-#62 := [quant-intro #59]: #61
-#66 := [trans #62 #64]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#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
-#75 := [trans #50 #73]: #74
-#30 := [asserted]: #14
-[mp #30 #75]: false
-unsat
-74037c10b4f126275ba21e7140b7f1e159b39ed9 111 0
-#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
-628c1b88ca8fb09c896ae05059a52dc2f8e25db2 89 0
-#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
-b7c4f9440c4594c46eee14ce57f17610bb7e2536 84 0
-WARNING: failed to find a pattern for quantifier (quantifier id: k!2)
-#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)
-#182 := (not #49)
-#118 := (<= 0::int 0::int)
-#204 := (not #118)
-#119 := (>= 0::int 0::int)
-#205 := (not #119)
-#206 := (or #205 #204)
-#187 := (or #182 #206)
-#172 := (iff #187 #182)
-#183 := (or #182 false)
-#509 := (iff #183 #182)
-#171 := [rewrite]: #509
-#525 := (iff #187 #183)
-#533 := (iff #206 false)
-#529 := (or false false)
-#532 := (iff #529 false)
-#527 := [rewrite]: #532
-#530 := (iff #206 #529)
-#195 := (iff #204 false)
-#1 := true
-#209 := (not true)
-#207 := (iff #209 false)
-#211 := [rewrite]: #207
-#315 := (iff #204 #209)
-#528 := (iff #118 true)
-#184 := [rewrite]: #528
-#522 := [monotonicity #184]: #315
-#196 := [trans #522 #211]: #195
-#190 := (iff #205 false)
-#137 := (iff #205 #209)
-#197 := (iff #119 true)
-#208 := [rewrite]: #197
-#210 := [monotonicity #208]: #137
-#526 := [trans #210 #211]: #190
-#531 := [monotonicity #526 #196]: #530
-#523 := [trans #531 #527]: #533
-#167 := [monotonicity #523]: #525
-#173 := [trans #167 #171]: #172
-#524 := [quant-inst]: #187
-#174 := [mp #524 #173]: #182
-#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
-7a9cc3ee85422788d981af84d181bd61d65f774c 181 0
-WARNING: failed to find a pattern for quantifier (quantifier id: k!2)
-#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)
-#263 := (<= 0::int 0::int)
-#268 := (not #263)
-#604 := (>= 0::int 0::int)
-#264 := (not #604)
-#605 := (or #264 #268)
-#588 := (or #86 #605)
-#584 := (iff #588 #86)
-#311 := (or #86 false)
-#207 := (iff #311 #86)
-#583 := [rewrite]: #207
-#312 := (iff #588 #311)
-#601 := (iff #605 false)
-#599 := (or false false)
-#600 := (iff #599 false)
-#598 := [rewrite]: #600
-#239 := (iff #605 #599)
-#234 := (iff #268 false)
-#1 := true
-#252 := (not true)
-#255 := (iff #252 false)
-#591 := [rewrite]: #255
-#590 := (iff #268 #252)
-#594 := (iff #263 true)
-#595 := [rewrite]: #594
-#596 := [monotonicity #595]: #590
-#597 := [trans #596 #591]: #234
-#592 := (iff #264 false)
-#253 := (iff #264 #252)
-#248 := (iff #604 true)
-#589 := [rewrite]: #248
-#254 := [monotonicity #589]: #253
-#593 := [trans #254 #591]: #592
-#240 := [monotonicity #593 #597]: #239
-#587 := [trans #240 #598]: #601
-#313 := [monotonicity #587]: #312
-#306 := [trans #313 #583]: #584
-#310 := [quant-inst]: #588
-#307 := [mp #310 #306]: #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)
-#608 := (>= #92 3::int)
-#265 := (not #608)
-#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
-#395 := (not #95)
-#602 := (or #265 #395)
-#276 := [th-lemma]: #602
-#277 := [unit-resolution #276 #126]: #265
-#609 := [hypothesis]: #290
-#611 := (or #610 #608)
-#612 := [th-lemma]: #611
-#607 := [unit-resolution #612 #609 #277]: false
-#613 := [lemma #607]: #610
-#292 := (or z3name!0 #290)
-#271 := [def-axiom]: #292
-#581 := [unit-resolution #271 #613]: 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
-#585 := [unit-resolution #128 #581]: #55
-[unit-resolution #585 #307]: false
-unsat
-5201b12abd6b3d0f247a34c1fd9f443fc951c55f 68 0
-#2 := false
-#12 := 1::int
-#9 := (:var 1 int)
-#7 := 6::int
-#8 := (- 6::int)
-#10 := (* #8 #9)
-#5 := (:var 2 int)
-#4 := 4::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)
-#82 := (iff #16 false)
-#53 := (:var 0 int)
-#33 := -6::int
-#54 := (* -6::int #53)
-#55 := (* 4::int #9)
-#56 := (+ #55 #54)
-#57 := (= 1::int #56)
-#58 := (exists (vars (?x1 int) (?x2 int)) #57)
-#80 := (iff #58 false)
-#76 := (exists (vars (?x1 int) (?x2 int)) false)
-#78 := (iff #76 false)
-#79 := [elim-unused]: #78
-#77 := (iff #58 #76)
-#73 := (iff #57 false)
-#74 := [rewrite]: #73
-#75 := [quant-intro #74]: #77
-#81 := [trans #75 #79]: #80
-#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
-#83 := [trans #72 #81]: #82
-#32 := [asserted]: #16
-[mp #32 #83]: false
-unsat
-0f9091dc6853772b5280c29fc11ae1382022f24d 107 0
-#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
-a19e2cec45cb985989328595a0e06836a1e0fbc3 117 0
-#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
-34bf666106f50c4ee2e8834de4912d59c6e7d9d9 148 0
-#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
-1d6946d9384f22b76e98f04aff657c54e4fe51ad 67 0
-#2 := false
-#4 := (:var 0 int)
-#5 := (pattern #4)
-decl uf_1 :: int
-#6 := uf_1
-#8 := 2::int
-#10 := (* 2::int uf_1)
-#9 := (* 2::int #4)
-#11 := (< #9 #10)
-#7 := (< #4 uf_1)
-#12 := (implies #7 #11)
-#13 := (forall (vars (?x1 int)) (:pat #5) #12)
-#14 := (not #13)
-#79 := (iff #14 false)
-#31 := (not #7)
-#32 := (or #31 #11)
-#35 := (forall (vars (?x1 int)) (:pat #5) #32)
-#38 := (not #35)
-#77 := (iff #38 false)
-#1 := true
-#72 := (not true)
-#75 := (iff #72 false)
-#76 := [rewrite]: #75
-#73 := (iff #38 #72)
-#70 := (iff #35 true)
-#65 := (forall (vars (?x1 int)) (:pat #5) true)
-#68 := (iff #65 true)
-#69 := [elim-unused]: #68
-#66 := (iff #35 #65)
-#63 := (iff #32 true)
-#43 := 0::int
-#41 := -1::int
-#45 := (* -1::int uf_1)
-#46 := (+ #4 #45)
-#44 := (>= #46 0::int)
-#42 := (not #44)
-#57 := (or #44 #42)
-#61 := (iff #57 true)
-#62 := [rewrite]: #61
-#59 := (iff #32 #57)
-#58 := (iff #11 #42)
-#56 := [rewrite]: #58
-#54 := (iff #31 #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
-#60 := [monotonicity #55 #56]: #59
-#64 := [trans #60 #62]: #63
-#67 := [quant-intro #64]: #66
-#71 := [trans #67 #69]: #70
-#74 := [monotonicity #71]: #73
-#78 := [trans #74 #76]: #77
-#39 := (iff #14 #38)
-#36 := (iff #13 #35)
-#33 := (iff #12 #32)
-#34 := [rewrite]: #33
-#37 := [quant-intro #34]: #36
-#40 := [monotonicity #37]: #39
-#80 := [trans #40 #78]: #79
-#30 := [asserted]: #14
-[mp #30 #80]: false
-unsat
-d938f8b556e86b20a82e4661e3a61bad7d95357d 1 0
-unsat
-dfca84a72c9a54145743ea34eaa7c75e8665fd45 75 0
-#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
-2662a556257bfe403cd3fda75e9fe55964bc9dcd 62 0
-#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
-a89308e99854a72f032798efa6ed32cee1f069ad 141 0
-#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
-2e721ab2035f9845f1e87e78db6dfc67c28f6d40 252 0
-#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)
-#295 := -1::int
-#274 := (* -1::int #293)
-#610 := (+ #24 #274)
-#594 := (<= #610 0::int)
-#612 := (= #610 0::int)
-#606 := (>= #23 0::int)
-#237 := (= #293 0::int)
-#549 := (not #237)
-#588 := (<= #293 0::int)
-#457 := (not #588)
-#26 := 1::int
-#558 := (>= #293 1::int)
-#555 := (= #293 1::int)
-#27 := (uf_1 1::int)
-#589 := (uf_2 #27)
-#301 := (= #589 1::int)
-#10 := (:var 0 int)
-#12 := (uf_1 #10)
-#626 := (pattern #12)
-#70 := (>= #10 0::int)
-#71 := (not #70)
-#13 := (uf_2 #12)
-#52 := (= #10 #13)
-#77 := (or #52 #71)
-#627 := (forall (vars (?x2 int)) (:pat #626) #77)
-#82 := (forall (vars (?x2 int)) #77)
-#630 := (iff #82 #627)
-#628 := (iff #77 #77)
-#629 := [refl]: #628
-#631 := [quant-intro #629]: #630
-#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
-#632 := [mp #146 #631]: #627
-#609 := (not #627)
-#578 := (or #609 #301)
-#311 := (>= 1::int 0::int)
-#585 := (not #311)
-#586 := (= 1::int #589)
-#590 := (or #586 #585)
-#419 := (or #609 #590)
-#421 := (iff #419 #578)
-#564 := (iff #578 #578)
-#565 := [rewrite]: #564
-#577 := (iff #590 #301)
-#574 := (or #301 false)
-#571 := (iff #574 #301)
-#576 := [rewrite]: #571
-#575 := (iff #590 #574)
-#584 := (iff #585 false)
-#1 := true
-#582 := (not true)
-#583 := (iff #582 false)
-#580 := [rewrite]: #583
-#296 := (iff #585 #582)
-#303 := (iff #311 true)
-#581 := [rewrite]: #303
-#579 := [monotonicity #581]: #296
-#573 := [trans #579 #580]: #584
-#300 := (iff #586 #301)
-#302 := [rewrite]: #300
-#570 := [monotonicity #302 #573]: #575
-#572 := [trans #570 #576]: #577
-#563 := [monotonicity #572]: #421
-#566 := [trans #563 #565]: #421
-#420 := [quant-inst]: #419
-#560 := [mp #420 #566]: #578
-#442 := [unit-resolution #560 #632]: #301
-#443 := (= #293 #589)
-#28 := (= #25 #27)
-#129 := [asserted]: #28
-#436 := [monotonicity #129]: #443
-#451 := [trans #436 #442]: #555
-#453 := (not #555)
-#454 := (or #453 #558)
-#447 := [th-lemma]: #454
-#455 := [unit-resolution #447 #451]: #558
-#456 := (not #558)
-#458 := (or #456 #457)
-#459 := [th-lemma]: #458
-#552 := [unit-resolution #459 #455]: #457
-#553 := (or #549 #588)
-#540 := [th-lemma]: #553
-#542 := [unit-resolution #540 #552]: #549
-#603 := (or #237 #606)
-#18 := (= #13 0::int)
-#118 := (or #18 #70)
-#633 := (forall (vars (?x3 int)) (:pat #626) #118)
-#123 := (forall (vars (?x3 int)) #118)
-#636 := (iff #123 #633)
-#634 := (iff #118 #118)
-#635 := [refl]: #634
-#637 := [quant-intro #635]: #636
-#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
-#638 := [mp #149 #637]: #633
-#604 := (not #633)
-#602 := (or #604 #237 #606)
-#204 := (>= #24 0::int)
-#601 := (or #237 #204)
-#605 := (or #604 #601)
-#317 := (iff #605 #602)
-#592 := (or #604 #603)
-#315 := (iff #592 #602)
-#316 := [rewrite]: #315
-#299 := (iff #605 #592)
-#242 := (iff #601 #603)
-#279 := (iff #204 #606)
-#280 := [rewrite]: #279
-#243 := [monotonicity #280]: #242
-#314 := [monotonicity #243]: #299
-#210 := [trans #314 #316]: #317
-#591 := [quant-inst]: #605
-#587 := [mp #591 #210]: #602
-#534 := [unit-resolution #587 #638]: #603
-#531 := [unit-resolution #534 #542]: #606
-#613 := (not #606)
-#607 := (or #613 #612)
-#251 := (or #609 #613 #612)
-#289 := (not #204)
-#294 := (= #24 #293)
-#291 := (or #294 #289)
-#593 := (or #609 #291)
-#597 := (iff #593 #251)
-#256 := (or #609 #607)
-#595 := (iff #256 #251)
-#596 := [rewrite]: #595
-#257 := (iff #593 #256)
-#608 := (iff #291 #607)
-#616 := (or #612 #613)
-#266 := (iff #616 #607)
-#271 := [rewrite]: #266
-#611 := (iff #291 #616)
-#614 := (iff #289 #613)
-#615 := [monotonicity #280]: #614
-#268 := (iff #294 #612)
-#399 := [rewrite]: #268
-#617 := [monotonicity #399 #615]: #611
-#267 := [trans #617 #271]: #608
-#258 := [monotonicity #267]: #257
-#598 := [trans #258 #596]: #597
-#255 := [quant-inst]: #593
-#599 := [mp #255 #598]: #251
-#533 := [unit-resolution #599 #632]: #607
-#543 := [unit-resolution #533 #531]: #612
-#544 := (not #612)
-#545 := (or #544 #594)
-#541 := [th-lemma]: #545
-#546 := [unit-resolution #541 #543]: #594
-#600 := (>= #610 0::int)
-#535 := (or #544 #600)
-#536 := [th-lemma]: #535
-#537 := [unit-resolution #536 #543]: #600
-#557 := (<= #293 1::int)
-#538 := (or #453 #557)
-#532 := [th-lemma]: #538
-#539 := [unit-resolution #532 #451]: #557
-[th-lemma #455 #539 #537 #546]: false
-unsat
-5d4787d5f6bf7b62bda1a48bdd01dc6863801852 223 0
-#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)
-#632 := -1::int
-#634 := (* -1::int #28)
-#290 := (+ #26 #634)
-#623 := (>= #290 0::int)
-#421 := (= #290 0::int)
-#302 := (>= #22 0::int)
-#625 := (= #28 0::int)
-#318 := (not #625)
-#322 := (<= #28 0::int)
-#324 := (not #322)
-#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
-#325 := (or #324 #141)
-#603 := [th-lemma]: #325
-#604 := [unit-resolution #603 #152]: #324
-#601 := (or #318 #322)
-#605 := [th-lemma]: #601
-#602 := [unit-resolution #605 #604]: #318
-#10 := (:var 0 int)
-#12 := (uf_1 #10)
-#648 := (pattern #12)
-#73 := (>= #10 0::int)
-#13 := (uf_2 #12)
-#18 := (= #13 0::int)
-#121 := (or #18 #73)
-#655 := (forall (vars (?x3 int)) (:pat #648) #121)
-#126 := (forall (vars (?x3 int)) #121)
-#658 := (iff #126 #655)
-#656 := (iff #121 #121)
-#657 := [refl]: #656
-#659 := [quant-intro #657]: #658
-#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
-#660 := [mp #172 #659]: #655
-#337 := (not #655)
-#338 := (or #337 #302 #625)
-#315 := (>= #26 0::int)
-#264 := (or #625 #315)
-#339 := (or #337 #264)
-#611 := (iff #339 #338)
-#627 := (or #302 #625)
-#609 := (or #337 #627)
-#333 := (iff #609 #338)
-#607 := [rewrite]: #333
-#610 := (iff #339 #609)
-#321 := (iff #264 #627)
-#265 := (or #625 #302)
-#613 := (iff #265 #627)
-#614 := [rewrite]: #613
-#626 := (iff #264 #265)
-#635 := (iff #315 #302)
-#636 := [rewrite]: #635
-#624 := [monotonicity #636]: #626
-#336 := [trans #624 #614]: #321
-#332 := [monotonicity #336]: #610
-#608 := [trans #332 #607]: #611
-#231 := [quant-inst]: #339
-#612 := [mp #231 #608]: #338
-#606 := [unit-resolution #612 #660 #602]: #302
-#637 := (not #302)
-#293 := (or #637 #421)
-#55 := (= #10 #13)
-#80 := (or #55 #74)
-#649 := (forall (vars (?x2 int)) (:pat #648) #80)
-#85 := (forall (vars (?x2 int)) #80)
-#652 := (iff #85 #649)
-#650 := (iff #80 #80)
-#651 := [refl]: #650
-#653 := [quant-intro #651]: #652
-#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
-#654 := [mp #169 #653]: #649
-#615 := (not #649)
-#277 := (or #615 #637 #421)
-#243 := (not #315)
-#317 := (= #26 #28)
-#296 := (or #317 #243)
-#278 := (or #615 #296)
-#621 := (iff #278 #277)
-#280 := (or #615 #293)
-#619 := (iff #280 #277)
-#620 := [rewrite]: #619
-#617 := (iff #278 #280)
-#631 := (iff #296 #293)
-#639 := (or #421 #637)
-#630 := (iff #639 #293)
-#289 := [rewrite]: #630
-#629 := (iff #296 #639)
-#638 := (iff #243 #637)
-#633 := [monotonicity #636]: #638
-#628 := (iff #317 #421)
-#301 := [rewrite]: #628
-#288 := [monotonicity #301 #633]: #629
-#273 := [trans #288 #289]: #631
-#618 := [monotonicity #273]: #617
-#616 := [trans #618 #620]: #621
-#279 := [quant-inst]: #278
-#622 := [mp #279 #616]: #277
-#595 := [unit-resolution #622 #654]: #293
-#596 := [unit-resolution #595 #606]: #421
-#597 := (not #421)
-#592 := (or #597 #623)
-#593 := [th-lemma]: #592
-#598 := [unit-resolution #593 #596]: #623
-[th-lemma #152 #598 #139]: false
-unsat
-60689c41168db239dbf5f3a98d5f2bce0fef9e02 367 0
-#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)
-#635 := (* -1::int #26)
-#632 := (+ #23 #635)
-#636 := (= #632 -1::int)
-#471 := (not #636)
-#606 := (<= #632 -1::int)
-#527 := (not #606)
-#145 := (* -1::int #23)
-#146 := (+ #145 #26)
-#149 := (uf_1 #146)
-#152 := (uf_2 #149)
-#504 := (+ #635 #152)
-#505 := (+ #23 #504)
-#573 := (>= #505 0::int)
-#502 := (= #505 0::int)
-#595 := (<= #632 0::int)
-#526 := [hypothesis]: #606
-#514 := (or #527 #595)
-#515 := [th-lemma]: #514
-#510 := [unit-resolution #515 #526]: #595
-#588 := (not #595)
-#579 := (or #502 #588)
-#10 := (:var 0 int)
-#12 := (uf_1 #10)
-#672 := (pattern #12)
-#76 := (>= #10 0::int)
-#77 := (not #76)
-#13 := (uf_2 #12)
-#58 := (= #10 #13)
-#83 := (or #58 #77)
-#673 := (forall (vars (?x2 int)) (:pat #672) #83)
-#88 := (forall (vars (?x2 int)) #83)
-#676 := (iff #88 #673)
-#674 := (iff #83 #83)
-#675 := [refl]: #674
-#677 := [quant-intro #675]: #676
-#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
-#678 := [mp #193 #677]: #673
-#644 := (not #673)
-#591 := (or #644 #502 #588)
-#499 := (>= #146 0::int)
-#500 := (not #499)
-#493 := (= #146 #152)
-#501 := (or #493 #500)
-#587 := (or #644 #501)
-#585 := (iff #587 #591)
-#581 := (or #644 #579)
-#584 := (iff #581 #591)
-#578 := [rewrite]: #584
-#582 := (iff #587 #581)
-#589 := (iff #501 #579)
-#580 := (iff #500 #588)
-#599 := (iff #499 #595)
-#586 := [rewrite]: #599
-#577 := [monotonicity #586]: #580
-#503 := (iff #493 #502)
-#598 := [rewrite]: #503
-#590 := [monotonicity #598 #577]: #589
-#583 := [monotonicity #590]: #582
-#569 := [trans #583 #578]: #585
-#592 := [quant-inst]: #587
-#570 := [mp #592 #569]: #591
-#516 := [unit-resolution #570 #678]: #579
-#484 := [unit-resolution #516 #510]: #502
-#491 := (not #502)
-#450 := (or #491 #573)
-#481 := [th-lemma]: #450
-#483 := [unit-resolution #481 #484]: #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
-#648 := (<= #141 0::int)
-#662 := (= #141 0::int)
-#645 := (or #644 #662)
-#445 := (>= 0::int 0::int)
-#652 := (not #445)
-#659 := (= 0::int #141)
-#660 := (or #659 #652)
-#640 := (or #644 #660)
-#284 := (iff #640 #645)
-#649 := (iff #645 #645)
-#289 := [rewrite]: #649
-#642 := (iff #660 #662)
-#302 := (or #662 false)
-#305 := (iff #302 #662)
-#641 := [rewrite]: #305
-#303 := (iff #660 #302)
-#298 := (iff #652 false)
-#1 := true
-#313 := (not true)
-#314 := (iff #313 false)
-#655 := [rewrite]: #314
-#318 := (iff #652 #313)
-#663 := (iff #445 true)
-#653 := [rewrite]: #663
-#654 := [monotonicity #653]: #318
-#639 := [trans #654 #655]: #298
-#661 := (iff #659 #662)
-#657 := [rewrite]: #661
-#304 := [monotonicity #657 #639]: #303
-#643 := [trans #304 #641]: #642
-#647 := [monotonicity #643]: #284
-#290 := [trans #647 #289]: #284
-#646 := [quant-inst]: #640
-#650 := [mp #646 #290]: #645
-#485 := [unit-resolution #650 #678]: #662
-#492 := (not #662)
-#494 := (or #492 #648)
-#495 := [th-lemma]: #494
-#496 := [unit-resolution #495 #485]: #648
-#506 := (not #648)
-#486 := (or #554 #506 #161)
-#507 := [th-lemma]: #486
-#462 := [unit-resolution #507 #496 #176]: #554
-#463 := [th-lemma #462 #526 #483]: false
-#468 := [lemma #463]: #527
-#472 := (or #471 #606)
-#473 := [th-lemma]: #472
-#474 := [unit-resolution #473 #468]: #471
-#619 := (or #628 #636)
-#622 := (or #644 #628 #636)
-#634 := (>= #24 0::int)
-#356 := (not #634)
-#357 := (= #24 #26)
-#631 := (or #357 #356)
-#623 := (or #644 #631)
-#610 := (iff #623 #622)
-#624 := (or #644 #619)
-#467 := (iff #624 #622)
-#609 := [rewrite]: #467
-#465 := (iff #623 #624)
-#616 := (iff #631 #619)
-#629 := (or #636 #628)
-#620 := (iff #629 #619)
-#621 := [rewrite]: #620
-#626 := (iff #631 #629)
-#343 := (iff #356 #628)
-#349 := (iff #634 #348)
-#627 := [rewrite]: #349
-#625 := [monotonicity #627]: #343
-#346 := (iff #357 #636)
-#347 := [rewrite]: #346
-#630 := [monotonicity #347 #625]: #626
-#617 := [trans #630 #621]: #616
-#466 := [monotonicity #617]: #465
-#611 := [trans #466 #609]: #610
-#618 := [quant-inst]: #623
-#612 := [mp #618 #611]: #622
-#475 := [unit-resolution #612 #678]: #619
-#476 := [unit-resolution #475 #474]: #628
-#478 := (or #477 #348)
-#479 := [th-lemma]: #478
-#464 := [unit-resolution #479 #476]: #477
-#560 := (or #556 #558)
-#18 := (= #13 0::int)
-#124 := (or #18 #76)
-#679 := (forall (vars (?x3 int)) (:pat #672) #124)
-#129 := (forall (vars (?x3 int)) #124)
-#682 := (iff #129 #679)
-#680 := (iff #124 #124)
-#681 := [refl]: #680
-#683 := [quant-intro #681]: #682
-#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
-#684 := [mp #196 #683]: #679
-#604 := (not #679)
-#539 := (or #604 #556 #558)
-#559 := (or #558 #556)
-#540 := (or #604 #559)
-#547 := (iff #540 #539)
-#543 := (or #604 #560)
-#546 := (iff #543 #539)
-#541 := [rewrite]: #546
-#544 := (iff #540 #543)
-#550 := (iff #559 #560)
-#561 := [rewrite]: #550
-#545 := [monotonicity #561]: #544
-#533 := [trans #545 #541]: #547
-#542 := [quant-inst]: #540
-#529 := [mp #542 #533]: #539
-#480 := [unit-resolution #529 #684]: #560
-#441 := [unit-resolution #480 #464]: #558
-#449 := (= #23 #557)
-#336 := (= uf_3 #251)
-#4 := (:var 0 T1)
-#5 := (uf_2 #4)
-#664 := (pattern #5)
-#6 := (uf_1 #5)
-#51 := (= #4 #6)
-#665 := (forall (vars (?x1 T1)) (:pat #664) #51)
-#54 := (forall (vars (?x1 T1)) #51)
-#666 := (iff #54 #665)
-#668 := (iff #665 #665)
-#669 := [rewrite]: #668
-#667 := [rewrite]: #666
-#670 := [trans #667 #669]: #666
-#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
-#671 := [mp #190 #670]: #665
-#337 := (not #665)
-#338 := (or #337 #336)
-#342 := [quant-inst]: #338
-#442 := [unit-resolution #342 #671]: #336
-#451 := [monotonicity #442]: #449
-#452 := [trans #451 #441]: #469
-#453 := (not #469)
-#455 := (or #453 #556)
-#456 := [th-lemma]: #455
-[unit-resolution #456 #464 #452]: false
-unsat
-94b7ba760bb9dd467688fc28632e0ae8f6f51951 302 0
-#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)
-#674 := (* -1::int #289)
-#538 := (+ #23 #674)
-#532 := (>= #538 0::int)
-#536 := (= #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
-#543 := [monotonicity #222]: #536
-#544 := (not #536)
-#616 := (or #544 #532)
-#618 := [th-lemma]: #616
-#628 := [unit-resolution #618 #543]: #532
-#354 := (* -1::int #26)
-#484 := (+ #23 #354)
-#683 := (<= #484 -1::int)
-#691 := (= #484 -1::int)
-#698 := (>= #23 -1::int)
-#521 := (>= #289 0::int)
-#652 := (= #289 0::int)
-#387 := (>= #26 1::int)
-#667 := (not #387)
-#629 := (or #667 #168)
-#630 := [th-lemma]: #629
-#626 := [unit-resolution #630 #188]: #667
-#10 := (:var 0 int)
-#12 := (uf_1 #10)
-#711 := (pattern #12)
-#76 := (>= #10 0::int)
-#13 := (uf_2 #12)
-#18 := (= #13 0::int)
-#124 := (or #18 #76)
-#718 := (forall (vars (?x3 int)) (:pat #711) #124)
-#129 := (forall (vars (?x3 int)) #124)
-#721 := (iff #129 #718)
-#719 := (iff #124 #124)
-#720 := [refl]: #719
-#722 := [quant-intro #720]: #721
-#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
-#723 := [mp #231 #722]: #718
-#328 := (not #718)
-#643 := (or #328 #387 #652)
-#673 := (>= #139 0::int)
-#653 := (or #652 #673)
-#641 := (or #328 #653)
-#537 := (iff #641 #643)
-#485 := (or #387 #652)
-#526 := (or #328 #485)
-#487 := (iff #526 #643)
-#635 := [rewrite]: #487
-#527 := (iff #641 #526)
-#640 := (iff #653 #485)
-#647 := (or #652 #387)
-#486 := (iff #647 #485)
-#639 := [rewrite]: #486
-#654 := (iff #653 #647)
-#388 := (iff #673 #387)
-#666 := [rewrite]: #388
-#483 := [monotonicity #666]: #654
-#642 := [trans #483 #639]: #640
-#528 := [monotonicity #642]: #527
-#632 := [trans #528 #635]: #537
-#644 := [quant-inst]: #641
-#633 := [mp #644 #632]: #643
-#631 := [unit-resolution #633 #723 #626]: #652
-#620 := (not #652)
-#621 := (or #620 #521)
-#622 := [th-lemma]: #621
-#623 := [unit-resolution #622 #631]: #521
-#624 := (not #532)
-#617 := (not #521)
-#608 := (or #698 #617 #624)
-#609 := [th-lemma]: #608
-#611 := [unit-resolution #609 #623 #628]: #698
-#701 := (not #698)
-#692 := (or #691 #701)
-#58 := (= #10 #13)
-#83 := (or #58 #77)
-#712 := (forall (vars (?x2 int)) (:pat #711) #83)
-#88 := (forall (vars (?x2 int)) #83)
-#715 := (iff #88 #712)
-#713 := (iff #83 #83)
-#714 := [refl]: #713
-#716 := [quant-intro #714]: #715
-#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
-#717 := [mp #226 #716]: #712
-#693 := (not #712)
-#353 := (or #693 #691 #701)
-#380 := (>= #24 0::int)
-#377 := (not #380)
-#695 := (= #24 #26)
-#697 := (or #695 #377)
-#694 := (or #693 #697)
-#680 := (iff #694 #353)
-#678 := (or #693 #692)
-#343 := (iff #678 #353)
-#344 := [rewrite]: #343
-#341 := (iff #694 #678)
-#352 := (iff #697 #692)
-#696 := (iff #377 #701)
-#699 := (iff #380 #698)
-#700 := [rewrite]: #699
-#702 := [monotonicity #700]: #696
-#365 := (iff #695 #691)
-#366 := [rewrite]: #365
-#357 := [monotonicity #366 #702]: #352
-#342 := [monotonicity #357]: #341
-#681 := [trans #342 #344]: #680
-#337 := [quant-inst]: #694
-#682 := [mp #337 #681]: #353
-#612 := [unit-resolution #682 #717]: #692
-#613 := [unit-resolution #612 #611]: #691
-#614 := (not #691)
-#610 := (or #614 #683)
-#615 := [th-lemma]: #610
-#601 := [unit-resolution #615 #613]: #683
-[th-lemma #623 #188 #601 #628]: false
-unsat
-8d2fca14b1477934a0c7f4f6528bd3be029bba7b 458 0
-#2 := false
-#9 := 0::int
-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)
-#297 := (uf_2 #141)
-#357 := (= #297 0::int)
-#166 := (uf_1 0::int)
-#531 := (uf_2 #166)
-#537 := (= #531 0::int)
-#10 := (:var 0 int)
-#12 := (uf_1 #10)
-#672 := (pattern #12)
-#78 := (>= #10 0::int)
-#79 := (not #78)
-#13 := (uf_2 #12)
-#60 := (= #10 #13)
-#85 := (or #60 #79)
-#673 := (forall (vars (?x2 int)) (:pat #672) #85)
-#90 := (forall (vars (?x2 int)) #85)
-#676 := (iff #90 #673)
-#674 := (iff #85 #85)
-#675 := [refl]: #674
-#677 := [quant-intro #675]: #676
-#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
-#678 := [mp #192 #677]: #673
-#650 := (not #673)
-#528 := (or #650 #537)
-#529 := (>= 0::int 0::int)
-#530 := (not #529)
-#534 := (= 0::int #531)
-#535 := (or #534 #530)
-#508 := (or #650 #535)
-#509 := (iff #508 #528)
-#514 := (iff #528 #528)
-#515 := [rewrite]: #514
-#527 := (iff #535 #537)
-#520 := (or #537 false)
-#525 := (iff #520 #537)
-#526 := [rewrite]: #525
-#521 := (iff #535 #520)
-#519 := (iff #530 false)
-#1 := true
-#512 := (not true)
-#517 := (iff #512 false)
-#518 := [rewrite]: #517
-#513 := (iff #530 #512)
-#538 := (iff #529 true)
-#511 := [rewrite]: #538
-#406 := [monotonicity #511]: #513
-#524 := [trans #406 #518]: #519
-#536 := (iff #534 #537)
-#532 := [rewrite]: #536
-#522 := [monotonicity #532 #524]: #521
-#523 := [trans #522 #526]: #527
-#490 := [monotonicity #523]: #509
-#510 := [trans #490 #515]: #509
-#454 := [quant-inst]: #508
-#516 := [mp #454 #510]: #528
-#394 := [unit-resolution #516 #678]: #537
-#355 := (= #297 #531)
-#250 := (= #141 #166)
-#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)
-#336 := (= #161 #166)
-#327 := (not #336)
-#588 := (uf_2 #161)
-#555 := (= #588 0::int)
-#398 := (= #588 #531)
-#395 := [hypothesis]: #336
-#387 := [monotonicity #395]: #398
-#399 := [trans #387 #394]: #555
-#390 := (not #555)
-#547 := (<= #588 0::int)
-#403 := (not #547)
-#595 := (>= #150 0::int)
-#302 := -1::int
-#618 := (* -1::int #150)
-#624 := (+ #144 #618)
-#488 := (<= #624 0::int)
-#465 := (= #624 0::int)
-#609 := (>= #22 0::int)
-#442 := (= #22 0::int)
-#660 := (uf_1 #22)
-#495 := (uf_2 #660)
-#496 := (= #495 0::int)
-#612 := (not #609)
-#451 := [hypothesis]: #612
-#506 := (or #496 #609)
-#18 := (= #13 0::int)
-#126 := (or #18 #78)
-#679 := (forall (vars (?x3 int)) (:pat #672) #126)
-#131 := (forall (vars (?x3 int)) #126)
-#682 := (iff #131 #679)
-#680 := (iff #126 #126)
-#681 := [refl]: #680
-#683 := [quant-intro #681]: #682
-#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
-#684 := [mp #195 #683]: #679
-#346 := (not #679)
-#462 := (or #346 #496 #609)
-#463 := (or #346 #506)
-#469 := (iff #463 #462)
-#470 := [rewrite]: #469
-#468 := [quant-inst]: #463
-#471 := [mp #468 #470]: #462
-#452 := [unit-resolution #471 #684]: #506
-#453 := [unit-resolution #452 #451]: #496
-#456 := (= #22 #495)
-#661 := (= uf_3 #660)
-#4 := (:var 0 T1)
-#5 := (uf_2 #4)
-#664 := (pattern #5)
-#6 := (uf_1 #5)
-#53 := (= #4 #6)
-#665 := (forall (vars (?x1 T1)) (:pat #664) #53)
-#56 := (forall (vars (?x1 T1)) #53)
-#666 := (iff #56 #665)
-#668 := (iff #665 #665)
-#669 := [rewrite]: #668
-#667 := [rewrite]: #666
-#670 := [trans #667 #669]: #666
-#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
-#671 := [mp #189 #670]: #665
-#663 := (not #665)
-#653 := (or #663 #661)
-#312 := [quant-inst]: #653
-#455 := [unit-resolution #312 #671]: #661
-#457 := [monotonicity #455]: #456
-#458 := [trans #457 #453]: #442
-#459 := (not #442)
-#460 := (or #459 #609)
-#443 := [th-lemma]: #460
-#461 := [unit-resolution #443 #451 #458]: false
-#431 := [lemma #461]: #609
-#613 := (or #465 #612)
-#615 := (or #650 #465 #612)
-#616 := (>= #144 0::int)
-#617 := (not #616)
-#622 := (= #144 #150)
-#623 := (or #622 #617)
-#444 := (or #650 #623)
-#602 := (iff #444 #615)
-#447 := (or #650 #613)
-#603 := (iff #447 #615)
-#604 := [rewrite]: #603
-#600 := (iff #444 #447)
-#614 := (iff #623 #613)
-#606 := (iff #617 #612)
-#610 := (iff #616 #609)
-#611 := [rewrite]: #610
-#607 := [monotonicity #611]: #606
-#466 := (iff #622 #465)
-#467 := [rewrite]: #466
-#608 := [monotonicity #467 #607]: #614
-#601 := [monotonicity #608]: #600
-#605 := [trans #601 #604]: #602
-#446 := [quant-inst]: #444
-#487 := [mp #446 #605]: #615
-#439 := [unit-resolution #487 #678]: #613
-#435 := [unit-resolution #439 #431]: #465
-#440 := (not #465)
-#419 := (or #440 #488)
-#422 := [th-lemma]: #419
-#426 := [unit-resolution #422 #435]: #488
-#430 := (not #488)
-#433 := (or #595 #612 #430)
-#438 := [th-lemma]: #433
-#402 := [unit-resolution #438 #431 #426]: #595
-#590 := -3::int
-#579 := (* -1::int #588)
-#589 := (+ #150 #579)
-#553 := (<= #589 -3::int)
-#591 := (= #589 -3::int)
-#581 := (>= #150 -3::int)
-#644 := (>= #22 -1::int)
-#428 := (or #612 #644)
-#429 := [th-lemma]: #428
-#427 := [unit-resolution #429 #431]: #644
-#646 := (not #644)
-#418 := (or #581 #646 #430)
-#421 := [th-lemma]: #418
-#423 := [unit-resolution #421 #426 #427]: #581
-#584 := (not #581)
-#573 := (or #584 #591)
-#562 := (or #650 #584 #591)
-#599 := (>= #156 0::int)
-#586 := (not #599)
-#580 := (= #156 #588)
-#577 := (or #580 #586)
-#563 := (or #650 #577)
-#549 := (iff #563 #562)
-#566 := (or #650 #573)
-#568 := (iff #566 #562)
-#548 := [rewrite]: #568
-#567 := (iff #563 #566)
-#571 := (iff #577 #573)
-#569 := (or #591 #584)
-#574 := (iff #569 #573)
-#575 := [rewrite]: #574
-#570 := (iff #577 #569)
-#578 := (iff #586 #584)
-#582 := (iff #599 #581)
-#583 := [rewrite]: #582
-#585 := [monotonicity #583]: #578
-#587 := (iff #580 #591)
-#592 := [rewrite]: #587
-#572 := [monotonicity #592 #585]: #570
-#576 := [trans #572 #575]: #571
-#564 := [monotonicity #576]: #567
-#551 := [trans #564 #548]: #549
-#565 := [quant-inst]: #563
-#552 := [mp #565 #551]: #562
-#424 := [unit-resolution #552 #678]: #573
-#420 := [unit-resolution #424 #423]: #591
-#425 := (not #591)
-#415 := (or #425 #553)
-#405 := [th-lemma]: #415
-#407 := [unit-resolution #405 #420]: #553
-#404 := (not #553)
-#401 := (not #595)
-#386 := (or #403 #401 #404)
-#388 := [th-lemma]: #386
-#389 := [unit-resolution #388 #407 #402]: #403
-#391 := (or #390 #547)
-#392 := [th-lemma]: #391
-#393 := [unit-resolution #392 #389]: #390
-#376 := [unit-resolution #393 #399]: false
-#378 := [lemma #376]: #327
-#249 := (= #141 #161)
-#334 := (not #249)
-#396 := (= #297 #588)
-#385 := [hypothesis]: #249
-#370 := [monotonicity #385]: #396
-#380 := (not #396)
-#434 := (+ #297 #579)
-#280 := (>= #434 0::int)
-#414 := (not #280)
-#303 := (* -1::int #297)
-#304 := (+ #22 #303)
-#356 := (>= #304 -1::int)
-#641 := (= #304 -1::int)
-#649 := (or #641 #646)
-#648 := (or #650 #641 #646)
-#317 := (>= #138 0::int)
-#654 := (not #317)
-#639 := (= #138 #297)
-#301 := (or #639 #654)
-#651 := (or #650 #301)
-#363 := (iff #651 #648)
-#638 := (or #650 #649)
-#361 := (iff #638 #648)
-#362 := [rewrite]: #361
-#345 := (iff #651 #638)
-#288 := (iff #301 #649)
-#283 := (iff #654 #646)
-#645 := (iff #317 #644)
-#640 := [rewrite]: #645
-#647 := [monotonicity #640]: #283
-#642 := (iff #639 #641)
-#643 := [rewrite]: #642
-#289 := [monotonicity #643 #647]: #288
-#360 := [monotonicity #289]: #345
-#256 := [trans #360 #362]: #363
-#637 := [quant-inst]: #651
-#633 := [mp #637 #256]: #648
-#408 := [unit-resolution #633 #678]: #649
-#411 := [unit-resolution #408 #427]: #641
-#412 := (not #641)
-#416 := (or #412 #356)
-#409 := [th-lemma]: #416
-#417 := [unit-resolution #409 #411]: #356
-#410 := [hypothesis]: #280
-#413 := [th-lemma #423 #410 #417 #407 #426]: false
-#400 := [lemma #413]: #414
-#381 := (or #380 #280)
-#382 := [th-lemma]: #381
-#377 := [unit-resolution #382 #400]: #380
-#371 := [unit-resolution #377 #370]: false
-#372 := [lemma #371]: #334
-#352 := (or #249 #250 #336)
-#335 := (not #250)
-#338 := (and #334 #335 #327)
-#339 := (not #338)
-#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)
-#659 := [def-axiom]: #326
-#351 := [unit-resolution #659 #177]: #339
-#314 := (or #338 #249 #250 #336)
-#445 := [def-axiom]: #314
-#343 := [unit-resolution #445 #351]: #352
-#353 := [unit-resolution #343 #372 #378]: #250
-#321 := [monotonicity #353]: #355
-#323 := [trans #321 #394]: #357
-#368 := (not #357)
-#620 := (<= #297 0::int)
-#364 := (not #620)
-#634 := (<= #304 -1::int)
-#374 := (or #412 #634)
-#373 := [th-lemma]: #374
-#375 := [unit-resolution #373 #411]: #634
-#365 := (not #634)
-#366 := (or #364 #612 #365)
-#358 := [th-lemma]: #366
-#367 := [unit-resolution #358 #375 #431]: #364
-#359 := (or #368 #620)
-#369 := [th-lemma]: #359
-#350 := [unit-resolution #369 #367]: #368
-[unit-resolution #350 #323]: false
-unsat
-720080123967f7b12d5ac9ba2a5e5203400a16cd 161 0
-#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)
-#645 := (+ #131 #648)
-#642 := (<= #645 0::int)
-#340 := (= #131 #161)
-#155 := (not #154)
-#649 := (+ uf_3 #648)
-#650 := (<= #649 0::int)
-#254 := (= uf_3 #161)
-#651 := [hypothesis]: #154
-#255 := (or #155 #254)
-#341 := [def-axiom]: #255
-#289 := [unit-resolution #341 #651]: #254
-#652 := (not #254)
-#654 := (or #652 #650)
-#294 := [th-lemma]: #654
-#295 := [unit-resolution #294 #289]: #650
-#273 := (>= #161 0::int)
-#346 := (not #273)
-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)
-#677 := (pattern #12)
-#70 := (>= #10 0::int)
-#71 := (not #70)
-#13 := (uf_2 #12)
-#52 := (= #10 #13)
-#77 := (or #52 #71)
-#678 := (forall (vars (?x2 int)) (:pat #677) #77)
-#82 := (forall (vars (?x2 int)) #77)
-#681 := (iff #82 #678)
-#679 := (iff #77 #77)
-#680 := [refl]: #679
-#682 := [quant-intro #680]: #681
-#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
-#683 := [mp #197 #682]: #678
-#450 := (not #678)
-#657 := (or #450 #172 #346)
-#661 := (or #172 #346)
-#331 := (or #450 #661)
-#664 := (iff #331 #657)
-#665 := [rewrite]: #664
-#332 := [quant-inst]: #331
-#666 := [mp #332 #665]: #657
-#655 := [unit-resolution #666 #683 #180]: #346
-#653 := [th-lemma #651 #655 #295]: false
-#656 := [lemma #653]: #155
-#342 := (or #154 #340)
-#333 := [def-axiom]: #342
-#365 := [unit-resolution #333 #656]: #340
-#366 := (not #340)
-#367 := (or #366 #642)
-#368 := [th-lemma]: #367
-#261 := [unit-resolution #368 #365]: #642
-#647 := (<= #161 0::int)
-#638 := (or #647 #273)
-#639 := [th-lemma]: #638
-#361 := [unit-resolution #639 #655]: #647
-[th-lemma #656 #361 #261]: false
-unsat
-201224fffb303874a019c931bc3ddb7a48e74843 557 0
-#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)
-#527 := (= #40 0::int)
-#976 := (not #527)
-#502 := (<= #40 0::int)
-#971 := (not #502)
-#22 := 1::int
-#186 := (+ 1::int #40)
-#189 := (uf_1 #186)
-#506 := (uf_2 #189)
-#407 := (<= #506 1::int)
-#876 := (not #407)
-decl up_4 :: (-> T1 T1 bool)
-#4 := (:var 0 T1)
-#408 := (up_4 #4 #189)
-#393 := (pattern #408)
-#413 := (= #4 #189)
-#414 := (not #408)
-#26 := (uf_1 1::int)
-#27 := (= #4 #26)
-#392 := (or #27 #414 #413)
-#397 := (forall (vars (?x5 T1)) (:pat #393) #392)
-#383 := (not #397)
-#382 := (or #383 #407)
-#375 := (not #382)
-decl up_3 :: (-> T1 bool)
-#192 := (up_3 #189)
-#404 := (not #192)
-#841 := (or #404 #375)
-decl ?x5!0 :: (-> T1 T1)
-#422 := (?x5!0 #189)
-#434 := (= #189 #422)
-#417 := (up_4 #422 #189)
-#418 := (not #417)
-#415 := (= #26 #422)
-#847 := (or #415 #418 #434)
-#850 := (not #847)
-#853 := (or #192 #407 #850)
-#856 := (not #853)
-#844 := (not #841)
-#859 := (or #844 #856)
-#862 := (not #859)
-#5 := (uf_2 #4)
-#787 := (pattern #5)
-#21 := (up_3 #4)
-#835 := (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)
-#808 := (pattern #25)
-#28 := (= #4 #24)
-#147 := (not #25)
-#167 := (or #147 #27 #28)
-#809 := (forall (vars (?x5 T1)) (:pat #808) #167)
-#814 := (not #809)
-#817 := (or #163 #814)
-#820 := (not #817)
-#253 := (not #21)
-#823 := (or #253 #820)
-#826 := (not #823)
-#829 := (or #826 #304)
-#832 := (not #829)
-#836 := (forall (vars (?x4 T1)) (:pat #835 #787) #832)
-#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)
-#837 := (iff #311 #836)
-#833 := (iff #306 #832)
-#830 := (iff #305 #829)
-#827 := (iff #303 #826)
-#824 := (iff #215 #823)
-#821 := (iff #240 #820)
-#818 := (iff #239 #817)
-#815 := (iff #236 #814)
-#812 := (iff #170 #809)
-#810 := (iff #167 #167)
-#811 := [refl]: #810
-#813 := [quant-intro #811]: #812
-#816 := [monotonicity #813]: #815
-#819 := [monotonicity #816]: #818
-#822 := [monotonicity #819]: #821
-#825 := [monotonicity #822]: #824
-#828 := [monotonicity #825]: #827
-#831 := [monotonicity #828]: #830
-#834 := [monotonicity #831]: #833
-#838 := [quant-intro #834]: #837
-#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
-#839 := [mp #314 #838]: #836
-#589 := (not #836)
-#865 := (or #589 #862)
-#416 := (or #418 #415 #434)
-#419 := (not #416)
-#409 := (or #192 #407 #419)
-#410 := (not #409)
-#389 := (or #414 #27 #413)
-#394 := (forall (vars (?x5 T1)) (:pat #393) #389)
-#399 := (not #394)
-#401 := (or #407 #399)
-#402 := (not #401)
-#400 := (or #404 #402)
-#405 := (not #400)
-#388 := (or #405 #410)
-#391 := (not #388)
-#866 := (or #589 #391)
-#868 := (iff #866 #865)
-#870 := (iff #865 #865)
-#871 := [rewrite]: #870
-#863 := (iff #391 #862)
-#860 := (iff #388 #859)
-#857 := (iff #410 #856)
-#854 := (iff #409 #853)
-#851 := (iff #419 #850)
-#848 := (iff #416 #847)
-#849 := [rewrite]: #848
-#852 := [monotonicity #849]: #851
-#855 := [monotonicity #852]: #854
-#858 := [monotonicity #855]: #857
-#845 := (iff #405 #844)
-#842 := (iff #400 #841)
-#378 := (iff #402 #375)
-#376 := (iff #401 #382)
-#384 := (or #407 #383)
-#387 := (iff #384 #382)
-#374 := [rewrite]: #387
-#385 := (iff #401 #384)
-#380 := (iff #399 #383)
-#390 := (iff #394 #397)
-#395 := (iff #389 #392)
-#396 := [rewrite]: #395
-#398 := [quant-intro #396]: #390
-#381 := [monotonicity #398]: #380
-#386 := [monotonicity #381]: #385
-#377 := [trans #386 #374]: #376
-#840 := [monotonicity #377]: #378
-#843 := [monotonicity #840]: #842
-#846 := [monotonicity #843]: #845
-#861 := [monotonicity #846 #858]: #860
-#864 := [monotonicity #861]: #863
-#869 := [monotonicity #864]: #868
-#872 := [trans #869 #871]: #868
-#867 := [quant-inst]: #866
-#873 := [mp #867 #872]: #865
-#947 := [unit-resolution #873 #839]: #862
-#905 := (or #859 #841)
-#906 := [def-axiom]: #905
-#948 := [unit-resolution #906 #947]: #841
-#951 := (or #844 #375)
-#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
-#885 := (or #844 #404 #375)
-#886 := [def-axiom]: #885
-#952 := [unit-resolution #886 #197]: #951
-#953 := [unit-resolution #952 #948]: #375
-#877 := (or #382 #876)
-#878 := [def-axiom]: #877
-#954 := [unit-resolution #878 #953]: #876
-#542 := -1::int
-#508 := (* -1::int #506)
-#493 := (+ #40 #508)
-#438 := (>= #493 -1::int)
-#494 := (= #493 -1::int)
-#496 := (>= #40 -1::int)
-#451 := (= #506 0::int)
-#959 := (not #451)
-#432 := (<= #506 0::int)
-#955 := (not #432)
-#956 := (or #955 #407)
-#957 := [th-lemma]: #956
-#958 := [unit-resolution #957 #954]: #955
-#960 := (or #959 #432)
-#961 := [th-lemma]: #960
-#962 := [unit-resolution #961 #958]: #959
-#453 := (or #451 #496)
-#10 := (:var 0 int)
-#12 := (uf_1 #10)
-#795 := (pattern #12)
-#87 := (>= #10 0::int)
-#13 := (uf_2 #12)
-#18 := (= #13 0::int)
-#135 := (or #18 #87)
-#802 := (forall (vars (?x3 int)) (:pat #795) #135)
-#140 := (forall (vars (?x3 int)) #135)
-#805 := (iff #140 #802)
-#803 := (iff #135 #135)
-#804 := [refl]: #803
-#806 := [quant-intro #804]: #805
-#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
-#807 := [mp #227 #806]: #802
-#514 := (not #802)
-#445 := (or #514 #451 #496)
-#504 := (>= #186 0::int)
-#452 := (or #451 #504)
-#456 := (or #514 #452)
-#429 := (iff #456 #445)
-#441 := (or #514 #453)
-#423 := (iff #441 #445)
-#428 := [rewrite]: #423
-#442 := (iff #456 #441)
-#454 := (iff #452 #453)
-#498 := (iff #504 #496)
-#487 := [rewrite]: #498
-#455 := [monotonicity #487]: #454
-#421 := [monotonicity #455]: #442
-#430 := [trans #421 #428]: #429
-#439 := [quant-inst]: #456
-#431 := [mp #439 #430]: #445
-#963 := [unit-resolution #431 #807]: #453
-#964 := [unit-resolution #963 #962]: #496
-#488 := (not #496)
-#490 := (or #494 #488)
-#69 := (= #10 #13)
-#94 := (or #69 #88)
-#796 := (forall (vars (?x2 int)) (:pat #795) #94)
-#99 := (forall (vars (?x2 int)) #94)
-#799 := (iff #99 #796)
-#797 := (iff #94 #94)
-#798 := [refl]: #797
-#800 := [quant-intro #798]: #799
-#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
-#801 := [mp #224 #800]: #796
-#530 := (not #796)
-#492 := (or #530 #494 #488)
-#505 := (not #504)
-#507 := (= #186 #506)
-#500 := (or #507 #505)
-#473 := (or #530 #500)
-#478 := (iff #473 #492)
-#475 := (or #530 #490)
-#477 := (iff #475 #492)
-#467 := [rewrite]: #477
-#466 := (iff #473 #475)
-#491 := (iff #500 #490)
-#489 := (iff #505 #488)
-#481 := [monotonicity #487]: #489
-#495 := (iff #507 #494)
-#497 := [rewrite]: #495
-#482 := [monotonicity #497 #481]: #491
-#476 := [monotonicity #482]: #466
-#444 := [trans #476 #467]: #478
-#474 := [quant-inst]: #473
-#446 := [mp #474 #444]: #492
-#965 := [unit-resolution #446 #801]: #490
-#966 := [unit-resolution #965 #964]: #494
-#967 := (not #494)
-#968 := (or #967 #438)
-#969 := [th-lemma]: #968
-#970 := [unit-resolution #969 #966]: #438
-#972 := (not #438)
-#973 := (or #971 #407 #972)
-#974 := [th-lemma]: #973
-#975 := [unit-resolution #974 #970 #954]: #971
-#977 := (or #976 #502)
-#978 := [th-lemma]: #977
-#979 := [unit-resolution #978 #975]: #976
-#553 := (>= #37 0::int)
-#546 := (not #553)
-#545 := (* -1::int #40)
-#549 := (+ #38 #545)
-#551 := (= #549 0::int)
-#984 := (not #551)
-#524 := (>= #549 0::int)
-#980 := (not #524)
-#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
-#981 := (or #980 #201 #407 #972)
-#982 := [th-lemma]: #981
-#983 := [unit-resolution #982 #205 #970 #954]: #980
-#985 := (or #984 #524)
-#986 := [th-lemma]: #985
-#987 := [unit-resolution #986 #983]: #984
-#548 := (or #551 #546)
-#531 := (or #530 #551 #546)
-#403 := (>= #38 0::int)
-#562 := (not #403)
-#558 := (= #38 #40)
-#563 := (or #558 #562)
-#534 := (or #530 #563)
-#537 := (iff #534 #531)
-#539 := (or #530 #548)
-#533 := (iff #539 #531)
-#536 := [rewrite]: #533
-#532 := (iff #534 #539)
-#538 := (iff #563 #548)
-#547 := (iff #562 #546)
-#541 := (iff #403 #553)
-#544 := [rewrite]: #541
-#543 := [monotonicity #544]: #547
-#552 := (iff #558 #551)
-#550 := [rewrite]: #552
-#528 := [monotonicity #550 #543]: #538
-#540 := [monotonicity #528]: #532
-#523 := [trans #540 #536]: #537
-#535 := [quant-inst]: #534
-#525 := [mp #535 #523]: #531
-#988 := [unit-resolution #525 #801]: #548
-#989 := [unit-resolution #988 #987]: #546
-#511 := (or #527 #553)
-#515 := (or #514 #527 #553)
-#509 := (or #527 #403)
-#516 := (or #514 #509)
-#522 := (iff #516 #515)
-#518 := (or #514 #511)
-#521 := (iff #518 #515)
-#510 := [rewrite]: #521
-#519 := (iff #516 #518)
-#512 := (iff #509 #511)
-#513 := [monotonicity #544]: #512
-#520 := [monotonicity #513]: #519
-#499 := [trans #520 #510]: #522
-#517 := [quant-inst]: #516
-#501 := [mp #517 #499]: #515
-#990 := [unit-resolution #501 #807]: #511
-[unit-resolution #990 #989 #979]: false
-unsat
-22877b17eafaba69b1f8a961a616fea28ae70d56 1 0
-unsat
-b5839159097bbd4e601a5681d1ca3493ec994a7c 1 0
-unsat
-90e1074350b5dcaae149781bcaa5d643b2ca9f48 1 0
-unsat
-08c7117fe974f5767051ed5aa61a27ce3084eb1d 1 0
-unsat
-858012417c9d327d8997f2a5dcb3da095ec65d34 1 0
-unsat
-84b2eee4890eaadb3638c7e522fb3237b3d476b0 1 0
-unsat
-8867717d9736308a2c27df0665a6e391b0562076 1 0
-unsat
-cd79c9a0488ab597d08dd9a0d6ac0f3647003bd6 1 0
-unsat
-395dd6c10b2a432137f9e3401cba8ec4dd64911b 1 0
-unsat
-17e3cc9534e04d86f095ec1a92c77d46d7dbb8e5 1 0
-unsat
-e046ea79beacf4bc3567b3b7f755232369d0c185 1 0
-unsat
-8ce4235464829d4be72e682f0c72bc5e3c6902d0 1 0
-unsat
-656a40b977d7716264443900d6bdb4d3d117d52f 1 0
-unsat
-ec27a57e58719625ff71dd4d68ed53a3851efb5c 1 0
-unsat
-2c3c366b8488ca0991cc767c94cdb78b18db9d5f 1 0
-unsat
-5894f6f19250b12885e38f54eae81f143b58fa01 1 0
-unsat
-e150815d9eb1ec168805b5501d7f4b2e378dd883 1 0
-unsat
-396d6254e993f414335de9378150e486d3cfcd4e 1 0
-unsat
-96014c61f582a811aff25ad7fa62b575b830fa8b 1 0
-unsat
-10580b87c0d062c9854e79d16047a53d045ccfac 1 0
-unsat
-87b5f388df1f43cc02ac0fa0d6944eb8cd8f8f50 1 0
-unsat
-92a5e2bb68f74b9e7dd3a9ef79ea641e9700d563 1 0
-unsat
-152e0f0f0a04b399b057beae92ae0455408b224f 1 0
-unsat
-41925af4711748a6e411453f2465920a1c6ffb8e 1 0
-unsat
-757462716f4a2619a1410bdca3faa2d058042c10 1 0
-unsat
-abdeeb4668a63f19473d6da94232379344d99fea 43 0
-#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)
-#309 := (not #225)
-#20 := (:var 0 bv[2])
-#21 := (uf_1 #20)
-#638 := (pattern #21)
-#54 := (<= #21 0::int)
-#55 := (not #54)
-#639 := (forall (vars (?x1 bv[2])) (:pat #638) #55)
-#58 := (forall (vars (?x1 bv[2])) #55)
-#642 := (iff #58 #639)
-#640 := (iff #55 #55)
-#641 := [refl]: #640
-#643 := [quant-intro #641]: #642
-#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
-#644 := [mp #111 #643]: #639
-#302 := (not #639)
-#313 := (or #302 #309)
-#314 := [quant-inst]: #313
-#635 := [unit-resolution #314 #644]: #309
-#7 := (= #5 0::int)
-#47 := [asserted]: #7
-#637 := (not #7)
-#627 := (or #637 #225)
-#287 := [th-lemma]: #627
-[unit-resolution #287 #47 #635]: false
-unsat
-585c02dc1784e4298147af8e1f7a14d1e20f4938 1 0
-unsat
-af0e29f90d51c2b97a1ecaa16facf1cd8b6c5ba3 50 0
-#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
-dda7f93ea68b6650d60fb96e3a60e68637d12660 105 0
-#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
-bab035487a4c595c2090c8097591bd8874c90db9 181 0
-#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
-4e1c8dc2fbb6a09931090ee5acf8d0e6f34352b4 62 0
-#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
-87c5323638926f09820cf502a43fcd61cba03c0c 115 0
-#2 := false
-decl up_2 :: (-> T2 bool)
-decl uf_3 :: T2
-#10 := uf_3
-#17 := (up_2 uf_3)
-#78 := (not #17)
-decl uf_1 :: (-> T1 T1)
-decl uf_4 :: T1
-#14 := uf_4
-#15 := (uf_1 uf_4)
-#46 := (= uf_4 #15)
-#79 := (not #46)
-#145 := [hypothesis]: #79
-#4 := (:var 0 T1)
-#5 := (uf_1 #4)
-#563 := (pattern #5)
-#37 := (= #4 #5)
-#564 := (forall (vars (?x1 T1)) (:pat #563) #37)
-#40 := (forall (vars (?x1 T1)) #37)
-#567 := (iff #40 #564)
-#565 := (iff #37 #37)
-#566 := [refl]: #565
-#568 := [quant-intro #566]: #567
-#72 := (~ #40 #40)
-#70 := (~ #37 #37)
-#71 := [refl]: #70
-#73 := [nnf-pos #71]: #72
-#6 := (= #5 #4)
-#7 := (forall (vars (?x1 T1)) #6)
-#41 := (iff #7 #40)
-#38 := (iff #6 #37)
-#39 := [rewrite]: #38
-#42 := [quant-intro #39]: #41
-#36 := [asserted]: #7
-#45 := [mp #36 #42]: #40
-#74 := [mp~ #45 #73]: #40
-#569 := [mp #74 #568]: #564
-#146 := (not #564)
-#233 := (or #146 #46)
-#147 := [quant-inst]: #233
-#232 := [unit-resolution #147 #569 #145]: false
-#234 := [lemma #232]: #46
-#66 := (or #78 #79)
-#54 := (and #17 #46)
-#59 := (not #54)
-#85 := (iff #59 #66)
-#67 := (not #66)
-#80 := (not #67)
-#83 := (iff #80 #66)
-#84 := [rewrite]: #83
-#81 := (iff #59 #80)
-#68 := (iff #54 #67)
-#69 := [rewrite]: #68
-#82 := [monotonicity #69]: #81
-#86 := [trans #82 #84]: #85
-#1 := true
-#18 := (iff #17 true)
-#16 := (= #15 uf_4)
-#19 := (and #16 #18)
-#20 := (not #19)
-#60 := (iff #20 #59)
-#57 := (iff #19 #54)
-#51 := (and #46 #17)
-#55 := (iff #51 #54)
-#56 := [rewrite]: #55
-#52 := (iff #19 #51)
-#49 := (iff #18 #17)
-#50 := [rewrite]: #49
-#47 := (iff #16 #46)
-#48 := [rewrite]: #47
-#53 := [monotonicity #48 #50]: #52
-#58 := [trans #53 #56]: #57
-#61 := [monotonicity #58]: #60
-#44 := [asserted]: #20
-#64 := [mp #44 #61]: #59
-#87 := [mp #64 #86]: #66
-#561 := [unit-resolution #87 #234]: #78
-#8 := (:var 0 T2)
-#9 := (up_2 #8)
-#570 := (pattern #9)
-#11 := (= #8 uf_3)
-#12 := (iff #9 #11)
-#571 := (forall (vars (?x2 T2)) (:pat #570) #12)
-#13 := (forall (vars (?x2 T2)) #12)
-#574 := (iff #13 #571)
-#572 := (iff #12 #12)
-#573 := [refl]: #572
-#575 := [quant-intro #573]: #574
-#65 := (~ #13 #13)
-#75 := (~ #12 #12)
-#76 := [refl]: #75
-#62 := [nnf-pos #76]: #65
-#43 := [asserted]: #13
-#77 := [mp~ #43 #62]: #13
-#576 := [mp #77 #575]: #571
-#555 := (not #571)
-#557 := (or #555 #17)
-#225 := (= uf_3 uf_3)
-#236 := (iff #17 #225)
-#212 := (or #555 #236)
-#551 := (iff #212 #557)
-#224 := (iff #557 #557)
-#558 := [rewrite]: #224
-#239 := (iff #236 #17)
-#238 := (iff #236 #18)
-#237 := (iff #225 true)
-#165 := [rewrite]: #237
-#235 := [monotonicity #165]: #238
-#218 := [trans #235 #50]: #239
-#223 := [monotonicity #218]: #551
-#559 := [trans #223 #558]: #551
-#344 := [quant-inst]: #212
-#560 := [mp #344 #559]: #557
-[unit-resolution #560 #576 #561]: false
-unsat
-352491b756faec7ffa24a6d9cce95d2879223e60 464 0
-#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)
-#351 := (uf_3 uf_5 #43)
-#267 := (uf_2 #351 #266)
-#791 := (= #267 #51)
-#789 := (= #51 #267)
-#752 := (= #50 #266)
-#521 := (uf_1 uf_5 uf_4)
-#522 := (uf_3 uf_5 #44)
-#615 := (uf_2 #522 #521)
-#750 := (= #615 #266)
-#612 := (= #266 #615)
-#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)
-#682 := (pattern #11)
-#7 := (uf_2 #5 #6)
-#8 := (uf_1 #4 #7)
-#681 := (pattern #8)
-#12 := (= #8 #11)
-#683 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3)) (:pat #681 #682) #12)
-#13 := (forall (vars (?x1 T1) (?x2 T2) (?x3 T3)) #12)
-#686 := (iff #13 #683)
-#684 := (iff #12 #12)
-#685 := [refl]: #684
-#687 := [quant-intro #685]: #686
-#195 := (~ #13 #13)
-#193 := (~ #12 #12)
-#194 := [refl]: #193
-#196 := [nnf-pos #194]: #195
-#69 := [asserted]: #13
-#197 := [mp~ #69 #196]: #13
-#688 := [mp #197 #687]: #683
-#355 := (not #683)
-#605 := (or #355 #612)
-#597 := [quant-inst]: #605
-#274 := [unit-resolution #597 #688]: #612
-#751 := [symm #274]: #750
-#748 := (= #50 #615)
-#579 := (= uf_4 #521)
-#14 := (:var 0 T1)
-#16 := (uf_1 #14 uf_4)
-#689 := (pattern #16)
-#71 := (= uf_4 #16)
-#690 := (forall (vars (?x4 T1)) (:pat #689) #71)
-#74 := (forall (vars (?x4 T1)) #71)
-#693 := (iff #74 #690)
-#691 := (iff #71 #71)
-#692 := [refl]: #691
-#694 := [quant-intro #692]: #693
-#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
-#695 := [mp #200 #694]: #690
-#583 := (not #690)
-#584 := (or #583 #579)
-#581 := [quant-inst]: #584
-#275 := [unit-resolution #581 #695]: #579
-#746 := (= #49 #522)
-decl uf_7 :: (-> T2 int)
-#668 := (uf_7 #44)
-#596 := (+ 1::int #668)
-#606 := (uf_6 #596)
-#742 := (= #606 #522)
-#609 := (= #522 #606)
-#20 := (:var 0 T2)
-#22 := (uf_7 #20)
-#697 := (pattern #22)
-#21 := (uf_3 uf_5 #20)
-#696 := (pattern #21)
-#78 := (+ 1::int #22)
-#82 := (uf_6 #78)
-#85 := (= #21 #82)
-#698 := (forall (vars (?x5 T2)) (:pat #696 #697) #85)
-#88 := (forall (vars (?x5 T2)) #85)
-#701 := (iff #88 #698)
-#699 := (iff #85 #85)
-#700 := [refl]: #699
-#702 := [quant-intro #700]: #701
-#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
-#703 := [mp #203 #702]: #698
-#607 := (not #698)
-#600 := (or #607 #609)
-#601 := [quant-inst]: #600
-#278 := [unit-resolution #601 #703]: #609
-#743 := [symm #278]: #742
-#744 := (= #49 #606)
-#526 := (uf_7 #606)
-#325 := (uf_6 #526)
-#327 := (= #325 #606)
-#28 := (uf_6 #22)
-#92 := (= #20 #28)
-#704 := (forall (vars (?x6 T2)) (:pat #697) #92)
-#96 := (forall (vars (?x6 T2)) #92)
-#705 := (iff #96 #704)
-#707 := (iff #704 #704)
-#708 := [rewrite]: #707
-#706 := [rewrite]: #705
-#709 := [trans #706 #708]: #705
-#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
-#710 := [mp #206 #709]: #704
-#368 := (not #704)
-#309 := (or #368 #327)
-#326 := (= #606 #325)
-#311 := (or #368 #326)
-#310 := (iff #311 #309)
-#301 := (iff #309 #309)
-#303 := [rewrite]: #301
-#316 := (iff #326 #327)
-#328 := [rewrite]: #316
-#313 := [monotonicity #328]: #310
-#304 := [trans #313 #303]: #310
-#312 := [quant-inst]: #311
-#307 := [mp #312 #304]: #309
-#279 := [unit-resolution #307 #710]: #327
-#740 := (= #49 #325)
-#738 := (= 2::int #526)
-#736 := (= #526 2::int)
-#568 := -1::int
-#533 := (* -1::int #668)
-#501 := (+ #526 #533)
-#481 := (<= #501 1::int)
-#527 := (= #501 1::int)
-#467 := (>= #668 -1::int)
-#592 := (>= #668 1::int)
-#378 := (= #668 1::int)
-#32 := (:var 0 int)
-#34 := (uf_6 #32)
-#711 := (pattern #34)
-#118 := (>= #32 0::int)
-#119 := (not #118)
-#35 := (uf_7 #34)
-#100 := (= #32 #35)
-#125 := (or #100 #119)
-#712 := (forall (vars (?x7 int)) (:pat #711) #125)
-#130 := (forall (vars (?x7 int)) #125)
-#715 := (iff #130 #712)
-#713 := (iff #125 #125)
-#714 := [refl]: #713
-#716 := [quant-intro #714]: #715
-#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
-#717 := [mp #209 #716]: #712
-#314 := (not #712)
-#365 := (or #314 #378)
-#667 := (>= 1::int 0::int)
-#665 := (not #667)
-#654 := (= 1::int #668)
-#655 := (or #654 #665)
-#366 := (or #314 #655)
-#645 := (iff #366 #365)
-#642 := (iff #365 #365)
-#646 := [rewrite]: #642
-#363 := (iff #655 #378)
-#374 := (or #378 false)
-#649 := (iff #374 #378)
-#653 := [rewrite]: #649
-#648 := (iff #655 #374)
-#651 := (iff #665 false)
-#1 := true
-#342 := (not true)
-#677 := (iff #342 false)
-#678 := [rewrite]: #677
-#273 := (iff #665 #342)
-#379 := (iff #667 true)
-#380 := [rewrite]: #379
-#650 := [monotonicity #380]: #273
-#373 := [trans #650 #678]: #651
-#362 := (iff #654 #378)
-#377 := [rewrite]: #362
-#652 := [monotonicity #377 #373]: #648
-#364 := [trans #652 #653]: #363
-#359 := [monotonicity #364]: #645
-#643 := [trans #359 #646]: #645
-#644 := [quant-inst]: #366
-#647 := [mp #644 #643]: #365
-#280 := [unit-resolution #647 #717]: #378
-#276 := (not #378)
-#281 := (or #276 #592)
-#268 := [th-lemma]: #281
-#270 := [unit-resolution #268 #280]: #592
-#271 := (not #592)
-#269 := (or #271 #467)
-#272 := [th-lemma]: #269
-#724 := [unit-resolution #272 #270]: #467
-#502 := (not #467)
-#486 := (or #314 #502 #527)
-#525 := (>= #596 0::int)
-#471 := (not #525)
-#507 := (= #596 #526)
-#531 := (or #507 #471)
-#487 := (or #314 #531)
-#494 := (iff #487 #486)
-#503 := (or #502 #527)
-#489 := (or #314 #503)
-#492 := (iff #489 #486)
-#493 := [rewrite]: #492
-#490 := (iff #487 #489)
-#480 := (iff #531 #503)
-#512 := (or #527 #502)
-#524 := (iff #512 #503)
-#479 := [rewrite]: #524
-#513 := (iff #531 #512)
-#509 := (iff #471 #502)
-#498 := (iff #525 #467)
-#500 := [rewrite]: #498
-#511 := [monotonicity #500]: #509
-#532 := (iff #507 #527)
-#508 := [rewrite]: #532
-#523 := [monotonicity #508 #511]: #513
-#485 := [trans #523 #479]: #480
-#491 := [monotonicity #485]: #490
-#495 := [trans #491 #493]: #494
-#488 := [quant-inst]: #487
-#496 := [mp #488 #495]: #486
-#725 := [unit-resolution #496 #717 #724]: #527
-#726 := (not #527)
-#727 := (or #726 #481)
-#728 := [th-lemma]: #727
-#729 := [unit-resolution #728 #725]: #481
-#497 := (>= #501 1::int)
-#730 := (or #726 #497)
-#731 := [th-lemma]: #730
-#732 := [unit-resolution #731 #725]: #497
-#591 := (<= #668 1::int)
-#733 := (or #276 #591)
-#734 := [th-lemma]: #733
-#735 := [unit-resolution #734 #280]: #591
-#737 := [th-lemma #270 #735 #732 #729]: #736
-#739 := [symm #737]: #738
-#741 := [monotonicity #739]: #740
-#745 := [trans #741 #279]: #744
-#747 := [trans #745 #743]: #746
-#749 := [monotonicity #747 #275]: #748
-#753 := [trans #749 #751]: #752
-#786 := (= #44 #351)
-#354 := (uf_7 #43)
-#616 := (+ 1::int #354)
-#603 := (uf_6 #616)
-#782 := (= #603 #351)
-#594 := (= #351 #603)
-#608 := (or #607 #594)
-#604 := [quant-inst]: #608
-#754 := [unit-resolution #604 #703]: #594
-#783 := [symm #754]: #782
-#784 := (= #44 #603)
-#585 := (uf_7 #603)
-#384 := (uf_6 #585)
-#376 := (= #384 #603)
-#369 := (or #368 #376)
-#385 := (= #603 #384)
-#360 := (or #368 #385)
-#371 := (iff #360 #369)
-#372 := (iff #369 #369)
-#338 := [rewrite]: #372
-#386 := (iff #385 #376)
-#367 := [rewrite]: #386
-#361 := [monotonicity #367]: #371
-#340 := [trans #361 #338]: #371
-#370 := [quant-inst]: #360
-#341 := [mp #370 #340]: #369
-#755 := [unit-resolution #341 #710]: #376
-#780 := (= #44 #384)
-#778 := (= 1::int #585)
-#776 := (= #585 1::int)
-#569 := (* -1::int #585)
-#570 := (+ #354 #569)
-#552 := (<= #570 -1::int)
-#571 := (= #570 -1::int)
-#574 := (>= #354 -1::int)
-#587 := (>= #354 0::int)
-#331 := (= #354 0::int)
-#656 := (or #314 #331)
-#353 := (>= 0::int 0::int)
-#344 := (not #353)
-#358 := (= 0::int #354)
-#337 := (or #358 #344)
-#318 := (or #314 #337)
-#320 := (iff #318 #656)
-#658 := (iff #656 #656)
-#659 := [rewrite]: #658
-#330 := (iff #337 #331)
-#680 := (or #331 false)
-#334 := (iff #680 #331)
-#671 := [rewrite]: #334
-#670 := (iff #337 #680)
-#679 := (iff #344 false)
-#343 := (iff #344 #342)
-#462 := (iff #353 true)
-#669 := [rewrite]: #462
-#676 := [monotonicity #669]: #343
-#674 := [trans #676 #678]: #679
-#673 := (iff #358 #331)
-#675 := [rewrite]: #673
-#329 := [monotonicity #675 #674]: #670
-#672 := [trans #329 #671]: #330
-#321 := [monotonicity #672]: #320
-#660 := [trans #321 #659]: #320
-#319 := [quant-inst]: #318
-#661 := [mp #319 #660]: #656
-#756 := [unit-resolution #661 #717]: #331
-#757 := (not #331)
-#758 := (or #757 #587)
-#759 := [th-lemma]: #758
-#760 := [unit-resolution #759 #756]: #587
-#761 := (not #587)
-#762 := (or #761 #574)
-#763 := [th-lemma]: #762
-#764 := [unit-resolution #763 #760]: #574
-#577 := (not #574)
-#560 := (or #314 #571 #577)
-#580 := (>= #616 0::int)
-#582 := (not #580)
-#565 := (= #616 #585)
-#566 := (or #565 #582)
-#561 := (or #314 #566)
-#547 := (iff #561 #560)
-#556 := (or #571 #577)
-#563 := (or #314 #556)
-#550 := (iff #563 #560)
-#546 := [rewrite]: #550
-#558 := (iff #561 #563)
-#557 := (iff #566 #556)
-#567 := (iff #582 #577)
-#575 := (iff #580 #574)
-#576 := [rewrite]: #575
-#578 := [monotonicity #576]: #567
-#572 := (iff #565 #571)
-#573 := [rewrite]: #572
-#559 := [monotonicity #573 #578]: #557
-#564 := [monotonicity #559]: #558
-#548 := [trans #564 #546]: #547
-#562 := [quant-inst]: #561
-#551 := [mp #562 #548]: #560
-#765 := [unit-resolution #551 #717 #764]: #571
-#766 := (not #571)
-#767 := (or #766 #552)
-#768 := [th-lemma]: #767
-#769 := [unit-resolution #768 #765]: #552
-#553 := (>= #570 -1::int)
-#770 := (or #766 #553)
-#771 := [th-lemma]: #770
-#772 := [unit-resolution #771 #765]: #553
-#586 := (<= #354 0::int)
-#773 := (or #757 #586)
-#774 := [th-lemma]: #773
-#775 := [unit-resolution #774 #756]: #586
-#777 := [th-lemma #760 #775 #772 #769]: #776
-#779 := [symm #777]: #778
-#781 := [monotonicity #779]: #780
-#785 := [trans #781 #755]: #784
-#787 := [trans #785 #783]: #786
-#790 := [monotonicity #787 #753]: #789
-#792 := [symm #790]: #791
-#352 := (= #47 #267)
-#356 := (or #355 #352)
-#357 := [quant-inst]: #356
-#788 := [unit-resolution #357 #688]: #352
-#793 := [trans #788 #792]: #52
-#53 := (not #52)
-#177 := [asserted]: #53
-[unit-resolution #177 #793]: false
-unsat
-ca467a37d809de06757809cab1cd30e08586674f 21 0
-#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
-c5b3c6b4f593e27f97db06f2c64fc61d8f9bebaa 366 0
-#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)
-#476 := (uf_3 #38)
-#403 := (= #476 #38)
-#531 := (= #38 #476)
-#620 := (uf_2 #38)
-#142 := -10::int
-#513 := (+ -10::int #620)
-#472 := (uf_1 #513)
-#503 := (uf_3 #472)
-#505 := (= #476 #503)
-#22 := 10::int
-#507 := (>= #620 10::int)
-#514 := (ite #507 #505 #531)
-#4 := (:var 0 T1)
-#21 := (uf_3 #4)
-#707 := (pattern #21)
-#5 := (uf_2 #4)
-#686 := (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)
-#708 := (forall (vars (?x4 T1)) (:pat #686 #707) #190)
-#193 := (forall (vars (?x4 T1)) #190)
-#711 := (iff #193 #708)
-#709 := (iff #190 #190)
-#710 := [refl]: #709
-#712 := [quant-intro #710]: #711
-#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
-#713 := [mp #212 #712]: #708
-#336 := (not #708)
-#518 := (or #336 #514)
-#528 := [quant-inst]: #518
-#477 := [unit-resolution #528 #713]: #514
-#529 := (not #507)
-#498 := (<= #620 6::int)
-#610 := (= #620 6::int)
-#10 := (:var 0 int)
-#12 := (uf_1 #10)
-#694 := (pattern #12)
-#9 := 0::int
-#82 := (>= #10 0::int)
-#83 := (not #82)
-#13 := (uf_2 #12)
-#64 := (= #10 #13)
-#89 := (or #64 #83)
-#695 := (forall (vars (?x2 int)) (:pat #694) #89)
-#94 := (forall (vars (?x2 int)) #89)
-#698 := (iff #94 #695)
-#696 := (iff #89 #89)
-#697 := [refl]: #696
-#699 := [quant-intro #697]: #698
-#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
-#700 := [mp #201 #699]: #695
-#673 := (not #695)
-#591 := (or #673 #610)
-#526 := (>= 6::int 0::int)
-#527 := (not #526)
-#617 := (= 6::int #620)
-#621 := (or #617 #527)
-#592 := (or #673 #621)
-#595 := (iff #592 #591)
-#597 := (iff #591 #591)
-#593 := [rewrite]: #597
-#600 := (iff #621 #610)
-#614 := (or #610 false)
-#605 := (iff #614 #610)
-#606 := [rewrite]: #605
-#603 := (iff #621 #614)
-#613 := (iff #527 false)
-#1 := true
-#663 := (not true)
-#666 := (iff #663 false)
-#667 := [rewrite]: #666
-#611 := (iff #527 #663)
-#599 := (iff #526 true)
-#601 := [rewrite]: #599
-#612 := [monotonicity #601]: #611
-#609 := [trans #612 #667]: #613
-#608 := (iff #617 #610)
-#602 := [rewrite]: #608
-#604 := [monotonicity #602 #609]: #603
-#607 := [trans #604 #606]: #600
-#596 := [monotonicity #607]: #595
-#598 := [trans #596 #593]: #595
-#594 := [quant-inst]: #592
-#584 := [mp #594 #598]: #591
-#478 := [unit-resolution #584 #700]: #610
-#453 := (not #610)
-#454 := (or #453 #498)
-#455 := [th-lemma]: #454
-#456 := [unit-resolution #455 #478]: #498
-#458 := (not #498)
-#459 := (or #458 #529)
-#460 := [th-lemma]: #459
-#302 := [unit-resolution #460 #456]: #529
-#508 := (not #514)
-#490 := (or #508 #507 #531)
-#491 := [def-axiom]: #490
-#461 := [unit-resolution #491 #302 #477]: #531
-#404 := [symm #461]: #403
-#405 := (= #36 #476)
-#649 := (uf_2 #35)
-#582 := (+ -10::int #649)
-#553 := (uf_1 #582)
-#556 := (uf_3 #553)
-#401 := (= #556 #476)
-#417 := (= #553 #38)
-#415 := (= #582 6::int)
-#335 := (uf_2 #31)
-#647 := -1::int
-#502 := (* -1::int #335)
-#463 := (+ #33 #502)
-#464 := (<= #463 0::int)
-#486 := (= #33 #335)
-#445 := (= #32 #31)
-#574 := (= #31 #32)
-#575 := (+ -10::int #335)
-#576 := (uf_1 #575)
-#577 := (uf_3 #576)
-#578 := (= #32 #577)
-#579 := (>= #335 10::int)
-#580 := (ite #579 #578 #574)
-#572 := (or #336 #580)
-#583 := [quant-inst]: #572
-#457 := [unit-resolution #583 #713]: #580
-#562 := (not #579)
-#554 := (<= #335 4::int)
-#324 := (= #335 4::int)
-#659 := (or #673 #324)
-#678 := (>= 4::int 0::int)
-#680 := (not #678)
-#677 := (= 4::int #335)
-#319 := (or #677 #680)
-#660 := (or #673 #319)
-#382 := (iff #660 #659)
-#384 := (iff #659 #659)
-#385 := [rewrite]: #384
-#672 := (iff #319 #324)
-#305 := (or #324 false)
-#310 := (iff #305 #324)
-#311 := [rewrite]: #310
-#669 := (iff #319 #305)
-#662 := (iff #680 false)
-#664 := (iff #680 #663)
-#325 := (iff #678 true)
-#326 := [rewrite]: #325
-#665 := [monotonicity #326]: #664
-#668 := [trans #665 #667]: #662
-#661 := (iff #677 #324)
-#323 := [rewrite]: #661
-#671 := [monotonicity #323 #668]: #669
-#670 := [trans #671 #311]: #672
-#383 := [monotonicity #670]: #382
-#277 := [trans #383 #385]: #382
-#367 := [quant-inst]: #660
-#655 := [mp #367 #277]: #659
-#462 := [unit-resolution #655 #700]: #324
-#441 := (not #324)
-#444 := (or #441 #554)
-#448 := [th-lemma]: #444
-#450 := [unit-resolution #448 #462]: #554
-#451 := (not #554)
-#449 := (or #451 #562)
-#452 := [th-lemma]: #449
-#440 := [unit-resolution #452 #450]: #562
-#561 := (not #580)
-#566 := (or #561 #579 #574)
-#567 := [def-axiom]: #566
-#443 := [unit-resolution #567 #440 #457]: #574
-#446 := [symm #443]: #445
-#442 := [monotonicity #446]: #486
-#447 := (not #486)
-#437 := (or #447 #464)
-#427 := [th-lemma]: #437
-#429 := [unit-resolution #427 #442]: #464
-#471 := (>= #463 0::int)
-#430 := (or #447 #471)
-#433 := [th-lemma]: #430
-#434 := [unit-resolution #433 #442]: #471
-#560 := (>= #335 4::int)
-#438 := (or #441 #560)
-#431 := [th-lemma]: #438
-#439 := [unit-resolution #431 #462]: #560
-#651 := (* -1::int #649)
-#648 := (+ #34 #651)
-#625 := (<= #648 0::int)
-#652 := (= #648 0::int)
-#643 := (>= #33 0::int)
-#435 := (not #471)
-#432 := (not #560)
-#436 := (or #643 #432 #435)
-#422 := [th-lemma]: #436
-#424 := [unit-resolution #422 #439 #434]: #643
-#644 := (not #643)
-#489 := (or #644 #652)
-#628 := (or #673 #644 #652)
-#370 := (>= #34 0::int)
-#371 := (not #370)
-#650 := (= #34 #649)
-#364 := (or #650 #371)
-#629 := (or #673 #364)
-#469 := (iff #629 #628)
-#636 := (or #673 #489)
-#466 := (iff #636 #628)
-#468 := [rewrite]: #466
-#630 := (iff #629 #636)
-#633 := (iff #364 #489)
-#646 := (or #652 #644)
-#631 := (iff #646 #489)
-#632 := [rewrite]: #631
-#487 := (iff #364 #646)
-#645 := (iff #371 #644)
-#638 := (iff #370 #643)
-#639 := [rewrite]: #638
-#640 := [monotonicity #639]: #645
-#641 := (iff #650 #652)
-#642 := [rewrite]: #641
-#488 := [monotonicity #642 #640]: #487
-#634 := [trans #488 #632]: #633
-#637 := [monotonicity #634]: #630
-#622 := [trans #637 #468]: #469
-#635 := [quant-inst]: #629
-#623 := [mp #635 #622]: #628
-#425 := [unit-resolution #623 #700]: #489
-#423 := [unit-resolution #425 #424]: #652
-#426 := (not #652)
-#408 := (or #426 #625)
-#410 := [th-lemma]: #408
-#411 := [unit-resolution #410 #423]: #625
-#626 := (>= #648 0::int)
-#412 := (or #426 #626)
-#413 := [th-lemma]: #412
-#414 := [unit-resolution #413 #423]: #626
-#416 := [th-lemma #414 #411 #439 #450 #434 #429]: #415
-#418 := [monotonicity #416]: #417
-#402 := [monotonicity #418]: #401
-#557 := (= #36 #556)
-#581 := (= #35 #36)
-#558 := (>= #649 10::int)
-#559 := (ite #558 #557 #581)
-#533 := (or #336 #559)
-#534 := [quant-inst]: #533
-#419 := [unit-resolution #534 #713]: #559
-#420 := (not #625)
-#409 := (or #558 #420 #432 #435)
-#421 := [th-lemma]: #409
-#398 := [unit-resolution #421 #411 #439 #434]: #558
-#428 := (not #558)
-#535 := (not #559)
-#539 := (or #535 #428 #557)
-#540 := [def-axiom]: #539
-#400 := [unit-resolution #540 #398 #419]: #557
-#406 := [trans #400 #402]: #405
-#399 := [trans #406 #404]: #39
-#40 := (not #39)
-#182 := [asserted]: #40
-[unit-resolution #182 #399]: false
-unsat
-9d577a545efebaa46a634487a3e922a7cddbb866 408 0
-#2 := false
-#22 := 0::int
-#8 := 2::int
-decl uf_6 :: (-> T3 T4 int)
-decl uf_9 :: T4
-#50 := uf_9
-decl uf_8 :: T3
-#49 := uf_8
-#51 := (uf_6 uf_8 uf_9)
-#624 := (mod #51 2::int)
-#172 := -1::int
-#640 := (* -1::int #624)
-decl uf_7 :: (-> T2 T4 T4)
-decl uf_5 :: T2
-#13 := uf_5
-#54 := (uf_7 uf_5 uf_9)
-#55 := (uf_6 uf_8 #54)
-#56 := (mod #55 2::int)
-#620 := (+ #56 #640)
-#608 := (>= #620 0::int)
-#566 := (= #620 0::int)
-#35 := (:var 0 T4)
-#38 := (uf_7 uf_5 #35)
-#34 := (:var 1 T3)
-#39 := (uf_6 #34 #38)
-#811 := (pattern #39)
-#40 := (mod #39 2::int)
-#173 := (* -1::int #40)
-#36 := (uf_6 #34 #35)
-#37 := (mod #36 2::int)
-#174 := (+ #37 #173)
-#175 := (= #174 0::int)
-#812 := (forall (vars (?x6 T3) (?x7 T4)) (:pat #811) #175)
-#178 := (forall (vars (?x6 T3) (?x7 T4)) #175)
-#815 := (iff #178 #812)
-#813 := (iff #175 #175)
-#814 := [refl]: #813
-#816 := [quant-intro #814]: #815
-#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
-#817 := [mp #304 #816]: #812
-#622 := (not #812)
-#628 := (or #622 #566)
-#756 := (* -1::int #56)
-#625 := (+ #624 #756)
-#632 := (= #625 0::int)
-#596 := (or #622 #632)
-#562 := (iff #596 #628)
-#595 := (iff #628 #628)
-#597 := [rewrite]: #595
-#626 := (iff #632 #566)
-#633 := (+ #756 #624)
-#638 := (= #633 0::int)
-#621 := (iff #638 #566)
-#602 := [rewrite]: #621
-#639 := (iff #632 #638)
-#634 := (= #625 #633)
-#637 := [rewrite]: #634
-#635 := [monotonicity #637]: #639
-#627 := [trans #635 #602]: #626
-#593 := [monotonicity #627]: #562
-#604 := [trans #593 #597]: #562
-#603 := [quant-inst]: #596
-#606 := [mp #603 #604]: #628
-#528 := [unit-resolution #606 #817]: #566
-#521 := (not #566)
-#464 := (or #521 #608)
-#456 := [th-lemma]: #464
-#465 := [unit-resolution #456 #528]: #608
-decl uf_10 :: int
-#52 := uf_10
-#57 := (mod uf_10 2::int)
-#243 := (* -1::int #57)
-#244 := (+ #56 #243)
-#447 := (>= #244 0::int)
-#387 := (not #447)
-#245 := (= #244 0::int)
-#248 := (not #245)
-#218 := (* -1::int #55)
-#219 := (+ uf_10 #218)
-#222 := (div #219 2::int)
-#251 := (* -1::int #222)
-decl uf_2 :: T2
-#4 := uf_2
-#59 := (uf_7 uf_2 uf_9)
-#60 := (uf_6 uf_8 #59)
-#252 := (+ #60 #251)
-#253 := (= #252 0::int)
-#448 := (<= #252 0::int)
-#605 := (+ uf_10 #55)
-#613 := (mod #605 2::int)
-#672 := (>= #613 2::int)
-#662 := (not #672)
-#1 := true
-#81 := [true-axiom]: true
-#520 := (or false #662)
-#523 := [th-lemma]: #520
-#524 := [unit-resolution #523 #81]: #662
-#701 := (* -1::int #613)
-#204 := -2::int
-#691 := (* -2::int #222)
-#702 := (+ #691 #701)
-#703 := (+ #218 #702)
-#699 := (+ uf_10 #703)
-#694 := (<= #699 0::int)
-#692 := (= #699 0::int)
-#545 := (or false #692)
-#546 := [th-lemma]: #545
-#548 := [unit-resolution #546 #81]: #692
-#549 := (not #692)
-#497 := (or #549 #694)
-#482 := [th-lemma]: #497
-#483 := [unit-resolution #482 #548]: #694
-#536 := (not #448)
-#395 := [hypothesis]: #536
-#555 := (* -1::int uf_10)
-#573 := (+ #51 #555)
-#543 := (<= #573 0::int)
-#53 := (= #51 uf_10)
-#256 := (not #253)
-#259 := (or #248 #256)
-#502 := 1::int
-#731 := (div uf_10 2::int)
-#515 := (* -1::int #731)
-#513 := (+ #640 #515)
-#618 := (div #51 2::int)
-#514 := (* -1::int #618)
-#516 := (+ #514 #513)
-#498 := (+ #243 #516)
-#500 := (+ #56 #498)
-#501 := (+ uf_10 #500)
-#503 := (>= #501 1::int)
-#486 := (not #503)
-#361 := (<= #244 0::int)
-#453 := (not #259)
-#517 := [hypothesis]: #453
-#440 := (or #259 #245)
-#451 := [def-axiom]: #440
-#519 := [unit-resolution #451 #517]: #245
-#478 := (or #248 #361)
-#470 := [th-lemma]: #478
-#479 := [unit-resolution #470 #519]: #361
-#449 := (>= #252 0::int)
-#452 := (or #259 #253)
-#380 := [def-axiom]: #452
-#480 := [unit-resolution #380 #517]: #253
-#471 := (or #256 #449)
-#481 := [th-lemma]: #471
-#462 := [unit-resolution #481 #480]: #449
-#487 := (not #361)
-#485 := (not #449)
-#476 := (or #486 #485 #487)
-#607 := (<= #620 0::int)
-#529 := (or #521 #607)
-#522 := [th-lemma]: #529
-#525 := [unit-resolution #522 #528]: #607
-#723 := (* -2::int #731)
-#724 := (+ #243 #723)
-#718 := (+ uf_10 #724)
-#720 := (<= #718 0::int)
-#722 := (= #718 0::int)
-#526 := (or false #722)
-#512 := [th-lemma]: #526
-#504 := [unit-resolution #512 #81]: #722
-#505 := (not #722)
-#506 := (or #505 #720)
-#507 := [th-lemma]: #506
-#508 := [unit-resolution #507 #504]: #720
-#509 := [hypothesis]: #361
-#583 := (* -2::int #618)
-#584 := (+ #583 #640)
-#585 := (+ #51 #584)
-#587 := (<= #585 0::int)
-#582 := (= #585 0::int)
-#510 := (or false #582)
-#499 := [th-lemma]: #510
-#511 := [unit-resolution #499 #81]: #582
-#488 := (not #582)
-#490 := (or #488 #587)
-#491 := [th-lemma]: #490
-#492 := [unit-resolution #491 #511]: #587
-#493 := [hypothesis]: #503
-#649 := (* -2::int #60)
-#644 := (+ #218 #649)
-#650 := (+ #51 #644)
-#636 := (>= #650 0::int)
-#623 := (= #650 0::int)
-#43 := (uf_7 uf_2 #35)
-#44 := (uf_6 #34 #43)
-#818 := (pattern #44)
-#205 := (* -2::int #44)
-#203 := (* -1::int #39)
-#206 := (+ #203 #205)
-#207 := (+ #36 #206)
-#208 := (= #207 0::int)
-#819 := (forall (vars (?x8 T3) (?x9 T4)) (:pat #811 #818) #208)
-#211 := (forall (vars (?x8 T3) (?x9 T4)) #208)
-#822 := (iff #211 #819)
-#820 := (iff #208 #208)
-#821 := [refl]: #820
-#823 := [quant-intro #821]: #822
-#279 := (~ #211 #211)
-#305 := (~ #208 #208)
-#306 := [refl]: #305
-#280 := [nnf-pos #306]: #279
-#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
-#824 := [mp #307 #823]: #819
-#518 := (not #819)
-#629 := (or #518 #623)
-#630 := [quant-inst]: #629
-#531 := [unit-resolution #630 #824]: #623
-#534 := (not #623)
-#494 := (or #534 #636)
-#495 := [th-lemma]: #494
-#496 := [unit-resolution #495 #531]: #636
-#489 := [hypothesis]: #449
-#484 := [th-lemma #483 #489 #496 #493 #492 #509 #508 #525 #524]: false
-#477 := [lemma #484]: #476
-#463 := [unit-resolution #477 #462 #479]: #486
-#727 := (>= #718 0::int)
-#466 := (or #505 #727)
-#457 := [th-lemma]: #466
-#467 := [unit-resolution #457 #504]: #727
-#434 := (or #248 #447)
-#436 := [th-lemma]: #434
-#437 := [unit-resolution #436 #519]: #447
-#544 := (>= #573 0::int)
-#445 := (not #544)
-#428 := (or #256 #448)
-#441 := [th-lemma]: #428
-#442 := [unit-resolution #441 #480]: #448
-#532 := (or #543 #536)
-#695 := (>= #699 0::int)
-#550 := (or #549 #695)
-#393 := [th-lemma]: #550
-#551 := [unit-resolution #393 #548]: #695
-#547 := (not #543)
-#552 := [hypothesis]: #547
-#631 := (<= #650 0::int)
-#538 := (or #534 #631)
-#540 := [th-lemma]: #538
-#541 := [unit-resolution #540 #531]: #631
-#539 := [hypothesis]: #448
-#666 := (>= #613 0::int)
-#542 := (or false #666)
-#530 := [th-lemma]: #542
-#533 := [unit-resolution #530 #81]: #666
-#535 := [th-lemma #533 #539 #541 #552 #551]: false
-#537 := [lemma #535]: #532
-#443 := [unit-resolution #537 #442]: #543
-#429 := (or #547 #445)
-#764 := (not #53)
-#771 := (or #764 #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
-#433 := (not #262)
-#438 := (or #764 #259 #433)
-#439 := [def-axiom]: #438
-#772 := [unit-resolution #439 #267]: #771
-#444 := [unit-resolution #772 #517]: #764
-#435 := (or #53 #547 #445)
-#446 := [th-lemma]: #435
-#431 := [unit-resolution #446 #444]: #429
-#432 := [unit-resolution #431 #443]: #445
-#588 := (>= #585 0::int)
-#411 := (or #488 #588)
-#413 := [th-lemma]: #411
-#418 := [unit-resolution #413 #511]: #588
-#419 := [th-lemma #418 #432 #437 #467 #465 #463]: false
-#420 := [lemma #419]: #259
-#427 := (or #53 #453)
-#768 := (or #53 #453 #433)
-#770 := [def-axiom]: #768
-#557 := [unit-resolution #770 #267]: #427
-#406 := [unit-resolution #557 #420]: #53
-#377 := (or #764 #543)
-#381 := [th-lemma]: #377
-#382 := [unit-resolution #381 #406]: #543
-#385 := [th-lemma #496 #382 #395 #483 #524]: false
-#386 := [lemma #385]: #448
-#390 := (or #253 #536)
-#408 := [hypothesis]: #485
-#409 := (or #764 #544)
-#397 := [th-lemma]: #409
-#399 := [unit-resolution #397 #406]: #544
-#400 := [th-lemma #399 #408 #533 #551 #541]: false
-#403 := [lemma #400]: #449
-#392 := (or #253 #536 #485)
-#394 := [th-lemma]: #392
-#657 := [unit-resolution #394 #403]: #390
-#658 := [unit-resolution #657 #386]: #253
-#450 := (or #453 #248 #256)
-#454 := [def-axiom]: #450
-#762 := [unit-resolution #454 #420]: #259
-#664 := [unit-resolution #762 #658]: #248
-#372 := (or #245 #387)
-#560 := (+ #57 #640)
-#610 := (>= #560 0::int)
-#742 := (= #57 #624)
-#424 := (= #624 #57)
-#405 := [monotonicity #406]: #424
-#407 := [symm #405]: #742
-#705 := (not #742)
-#706 := (or #705 #610)
-#568 := [th-lemma]: #706
-#569 := [unit-resolution #568 #407]: #610
-#398 := [hypothesis]: #487
-#404 := [th-lemma #525 #398 #569]: false
-#378 := [lemma #404]: #361
-#379 := (or #245 #487 #387)
-#388 := [th-lemma]: #379
-#369 := [unit-resolution #388 #378]: #372
-#370 := [unit-resolution #369 #664]: #387
-#708 := (<= #560 0::int)
-#373 := (or #705 #708)
-#374 := [th-lemma]: #373
-#375 := [unit-resolution #374 #407]: #708
-[th-lemma #375 #370 #465]: false
-unsat
-af6e260cca3c1cafcab25bb9a90bb548b2b7ec6b 50 0
-#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)
-#910 := (pattern #104)
-#911 := (forall (vars (?x12 int)) (:pat #910) #104)
-#294 := (forall (vars (?x12 int)) #104)
-#914 := (iff #294 #911)
-#912 := (iff #104 #104)
-#913 := [refl]: #912
-#915 := [quant-intro #913]: #914
-#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
-#916 := [mp #363 #915]: #911
-#418 := (not #911)
-#503 := (or #418 #113)
-#504 := [quant-inst]: #503
-[unit-resolution #504 #916 #297]: false
-unsat
-679f514494fa97481f8fb2124de829ed6e4d2b68 506 0
-#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
-#513 := (uf_2 uf_19 uf_7)
-#644 := (uf_13 #513)
-#564 := (= #644 #106)
-#858 := (= #106 #644)
-#79 := (:var 0 T1)
-#82 := (uf_2 #79 uf_7)
-#930 := (pattern #82)
-#80 := (uf_18 #79)
-#929 := (pattern #80)
-#83 := (uf_13 #82)
-#81 := (uf_17 #80)
-#84 := (= #81 #83)
-#931 := (forall (vars (?x16 T1)) (:pat #929 #930) #84)
-#85 := (forall (vars (?x16 T1)) #84)
-#934 := (iff #85 #931)
-#932 := (iff #84 #84)
-#933 := [refl]: #932
-#935 := [quant-intro #933]: #934
-#347 := (~ #85 #85)
-#384 := (~ #84 #84)
-#385 := [refl]: #384
-#348 := [nnf-pos #385]: #347
-#238 := [asserted]: #85
-#386 := [mp~ #238 #348]: #85
-#936 := [mp #386 #935]: #931
-#861 := (not #931)
-#856 := (or #861 #858)
-#862 := [quant-inst]: #856
-#579 := [unit-resolution #862 #936]: #858
-#565 := [symm #579]: #564
-#553 := (= #103 #644)
-decl uf_1 :: (-> T2 T3)
-#834 := (uf_1 #513)
-#831 := (= #834 #644)
-#835 := (= #644 #834)
-#5 := (:var 0 T2)
-#66 := (uf_13 #5)
-#906 := (pattern #66)
-#8 := (uf_1 #5)
-#905 := (pattern #8)
-#222 := (= #8 #66)
-#907 := (forall (vars (?x13 T2)) (:pat #905 #906) #222)
-#226 := (forall (vars (?x13 T2)) #222)
-#910 := (iff #226 #907)
-#908 := (iff #222 #222)
-#909 := [refl]: #908
-#911 := [quant-intro #909]: #910
-#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
-#912 := [mp #377 #911]: #907
-#526 := (not #907)
-#547 := (or #526 #835)
-#548 := (or #526 #831)
-#827 := (iff #548 #547)
-#824 := (iff #547 #547)
-#828 := [rewrite]: #824
-#545 := (iff #831 #835)
-#546 := [rewrite]: #545
-#541 := [monotonicity #546]: #827
-#825 := [trans #541 #828]: #827
-#826 := [quant-inst]: #548
-#829 := [mp #826 #825]: #547
-#578 := [unit-resolution #829 #912]: #835
-#563 := [symm #578]: #831
-#542 := (= #103 #834)
-decl uf_3 :: (-> int T3)
-decl uf_4 :: (-> T3 int)
-#30 := (uf_1 uf_7)
-#698 := (uf_4 #30)
-#11 := 1::int
-#127 := (uf_3 1::int)
-#130 := (uf_4 #127)
-#701 := (+ #130 #698)
-#704 := (uf_3 #701)
-#779 := (= #704 #834)
-#4 := (:var 1 T1)
-#6 := (uf_2 #4 #5)
-#863 := (pattern #6)
-#9 := (uf_4 #8)
-#133 := (+ #9 #130)
-#136 := (uf_3 #133)
-#7 := (uf_1 #6)
-#139 := (= #7 #136)
-#864 := (forall (vars (?x1 T1) (?x2 T2)) (:pat #863) #139)
-#142 := (forall (vars (?x1 T1) (?x2 T2)) #139)
-#867 := (iff #142 #864)
-#865 := (iff #139 #139)
-#866 := [refl]: #865
-#868 := [quant-intro #866]: #867
-#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
-#869 := [mp #363 #868]: #864
-#790 := (not #864)
-#786 := (or #790 #779)
-#699 := (+ #698 #130)
-#692 := (uf_3 #699)
-#700 := (= #834 #692)
-#791 := (or #790 #700)
-#781 := (iff #791 #786)
-#783 := (iff #786 #786)
-#777 := [rewrite]: #783
-#788 := (iff #700 #779)
-#798 := (= #834 #704)
-#776 := (iff #798 #779)
-#778 := [rewrite]: #776
-#785 := (iff #700 #798)
-#797 := (= #692 #704)
-#702 := (= #699 #701)
-#703 := [rewrite]: #702
-#794 := [monotonicity #703]: #797
-#787 := [monotonicity #794]: #785
-#789 := [trans #787 #778]: #788
-#782 := [monotonicity #789]: #781
-#784 := [trans #782 #777]: #781
-#780 := [quant-inst]: #791
-#768 := [mp #780 #784]: #786
-#577 := [unit-resolution #768 #869]: #779
-#550 := (= #103 #704)
-#572 := (= #127 #704)
-#582 := (= #704 #127)
-#598 := (= #701 1::int)
-#774 := (<= #698 0::int)
-#773 := (= #698 0::int)
-#31 := (uf_3 0::int)
-#852 := (uf_4 #31)
-#854 := (= #852 0::int)
-#72 := (:var 0 int)
-#92 := (uf_3 #72)
-#945 := (pattern #92)
-#266 := (>= #72 0::int)
-#267 := (not #266)
-#93 := (uf_4 #92)
-#248 := (= #72 #93)
-#273 := (or #248 #267)
-#946 := (forall (vars (?x18 int)) (:pat #945) #273)
-#278 := (forall (vars (?x18 int)) #273)
-#949 := (iff #278 #946)
-#947 := (iff #273 #273)
-#948 := [refl]: #947
-#950 := [quant-intro #948]: #949
-#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
-#951 := [mp #392 #950]: #946
-#487 := (not #946)
-#488 := (or #487 #854)
-#859 := (>= 0::int 0::int)
-#860 := (not #859)
-#511 := (= 0::int #852)
-#516 := (or #511 #860)
-#849 := (or #487 #516)
-#850 := (iff #849 #488)
-#837 := (iff #488 #488)
-#544 := [rewrite]: #837
-#846 := (iff #516 #854)
-#843 := (or #854 false)
-#845 := (iff #843 #854)
-#482 := [rewrite]: #845
-#844 := (iff #516 #843)
-#841 := (iff #860 false)
-#1 := true
-#500 := (not true)
-#503 := (iff #500 false)
-#840 := [rewrite]: #503
-#501 := (iff #860 #500)
-#496 := (iff #859 true)
-#838 := [rewrite]: #496
-#502 := [monotonicity #838]: #501
-#842 := [trans #502 #840]: #841
-#853 := (iff #511 #854)
-#512 := [rewrite]: #853
-#839 := [monotonicity #512 #842]: #844
-#848 := [trans #839 #482]: #846
-#836 := [monotonicity #848]: #850
-#559 := [trans #836 #544]: #850
-#847 := [quant-inst]: #849
-#560 := [mp #847 #559]: #488
-#622 := [unit-resolution #560 #951]: #854
-#589 := (= #698 #852)
-#32 := (= #30 #31)
-#159 := [asserted]: #32
-#590 := [monotonicity #159]: #589
-#591 := [trans #590 #622]: #773
-#592 := (not #773)
-#593 := (or #592 #774)
-#594 := [th-lemma]: #593
-#595 := [unit-resolution #594 #591]: #774
-#770 := (>= #698 0::int)
-#596 := (or #592 #770)
-#597 := [th-lemma]: #596
-#586 := [unit-resolution #597 #591]: #770
-#680 := (<= #130 1::int)
-#605 := (= #130 1::int)
-#708 := (or #487 #605)
-#746 := (>= 1::int 0::int)
-#732 := (not #746)
-#710 := (= 1::int #130)
-#711 := (or #710 #732)
-#689 := (or #487 #711)
-#714 := (iff #689 #708)
-#715 := (iff #708 #708)
-#683 := [rewrite]: #715
-#707 := (iff #711 #605)
-#724 := (or #605 false)
-#722 := (iff #724 #605)
-#727 := [rewrite]: #722
-#725 := (iff #711 #724)
-#720 := (iff #732 false)
-#723 := (iff #732 #500)
-#717 := (iff #746 true)
-#718 := [rewrite]: #717
-#719 := [monotonicity #718]: #723
-#721 := [trans #719 #840]: #720
-#712 := (iff #710 #605)
-#716 := [rewrite]: #712
-#726 := [monotonicity #716 #721]: #725
-#653 := [trans #726 #727]: #707
-#709 := [monotonicity #653]: #714
-#690 := [trans #709 #683]: #714
-#713 := [quant-inst]: #689
-#649 := [mp #713 #690]: #708
-#616 := [unit-resolution #649 #951]: #605
-#609 := (not #605)
-#612 := (or #609 #680)
-#613 := [th-lemma]: #612
-#599 := [unit-resolution #613 #616]: #680
-#682 := (>= #130 1::int)
-#601 := (or #609 #682)
-#602 := [th-lemma]: #601
-#600 := [unit-resolution #602 #616]: #682
-#575 := [th-lemma #600 #599 #586 #595]: #598
-#583 := [monotonicity #575]: #582
-#574 := [symm #583]: #572
-#568 := (= #103 #127)
-decl uf_5 :: (-> T4 T3)
-decl uf_8 :: T4
-#33 := uf_8
-#34 := (uf_5 uf_8)
-#810 := (uf_4 #34)
-#812 := (+ #130 #810)
-#814 := (uf_3 #812)
-#571 := (= #814 #127)
-#576 := (= #127 #814)
-#587 := (= 1::int #812)
-#603 := (= #812 1::int)
-#771 := (<= #810 0::int)
-#769 := (= #810 0::int)
-#619 := (= #810 #852)
-#35 := (= #34 #31)
-#162 := (= #31 #34)
-#163 := (iff #35 #162)
-#164 := [rewrite]: #163
-#160 := [asserted]: #35
-#167 := [mp #160 #164]: #162
-#623 := [symm #167]: #35
-#624 := [monotonicity #623]: #619
-#614 := [trans #624 #622]: #769
-#604 := (not #769)
-#606 := (or #604 #771)
-#607 := [th-lemma]: #606
-#610 := [unit-resolution #607 #614]: #771
-#772 := (>= #810 0::int)
-#611 := (or #604 #772)
-#615 := [th-lemma]: #611
-#608 := [unit-resolution #615 #614]: #772
-#585 := [th-lemma #600 #599 #608 #610]: #603
-#588 := [symm #585]: #587
-#584 := [monotonicity #588]: #576
-#573 := [symm #584]: #571
-#567 := (= #103 #814)
-decl uf_6 :: (-> int T4 T4)
-#539 := (uf_6 3::int uf_8)
-#818 := (uf_5 #539)
-#646 := (= #818 #814)
-#802 := (= #814 #818)
-#20 := (:var 0 T4)
-#19 := (:var 1 int)
-#21 := (uf_6 #19 #20)
-#870 := (pattern #21)
-#23 := (uf_5 #20)
-#24 := (uf_4 #23)
-#146 := (+ #24 #130)
-#150 := (uf_3 #146)
-#22 := (uf_5 #21)
-#153 := (= #22 #150)
-#871 := (forall (vars (?x3 int) (?x4 T4)) (:pat #870) #153)
-#156 := (forall (vars (?x3 int) (?x4 T4)) #153)
-#874 := (iff #156 #871)
-#872 := (iff #153 #153)
-#873 := [refl]: #872
-#875 := [quant-intro #873]: #874
-#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
-#876 := [mp #366 #875]: #871
-#687 := (not #871)
-#688 := (or #687 #802)
-#811 := (+ #810 #130)
-#805 := (uf_3 #811)
-#806 := (= #818 #805)
-#647 := (or #687 #806)
-#697 := (iff #647 #688)
-#793 := (iff #688 #688)
-#796 := [rewrite]: #793
-#804 := (iff #806 #802)
-#803 := (iff #646 #802)
-#801 := [rewrite]: #803
-#799 := (iff #806 #646)
-#643 := (= #805 #814)
-#813 := (= #811 #812)
-#807 := [rewrite]: #813
-#645 := [monotonicity #807]: #643
-#800 := [monotonicity #645]: #799
-#686 := [trans #800 #801]: #804
-#792 := [monotonicity #686]: #697
-#681 := [trans #792 #796]: #697
-#795 := [quant-inst]: #647
-#696 := [mp #795 #681]: #688
-#626 := [unit-resolution #696 #876]: #802
-#570 := [symm #626]: #646
-#557 := (= #103 #818)
-decl uf_14 :: (-> T4 T3)
-#536 := (uf_14 #539)
-#820 := (= #536 #818)
-#69 := (uf_14 #20)
-#914 := (pattern #69)
-#913 := (pattern #23)
-#230 := (= #23 #69)
-#915 := (forall (vars (?x14 T4)) (:pat #913 #914) #230)
-#234 := (forall (vars (?x14 T4)) #230)
-#918 := (iff #234 #915)
-#916 := (iff #230 #230)
-#917 := [refl]: #916
-#919 := [quant-intro #917]: #918
-#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
-#920 := [mp #380 #919]: #915
-#540 := (not #915)
-#821 := (or #540 #820)
-#819 := (= #818 #536)
-#822 := (or #540 #819)
-#823 := (iff #822 #821)
-#665 := (iff #821 #821)
-#666 := [rewrite]: #665
-#815 := (iff #819 #820)
-#816 := [rewrite]: #815
-#664 := [monotonicity #816]: #823
-#808 := [trans #664 #666]: #823
-#817 := [quant-inst]: #822
-#809 := [mp #817 #808]: #821
-#628 := [unit-resolution #809 #920]: #820
-#857 := (= #103 #536)
-#75 := (uf_6 #72 uf_8)
-#922 := (pattern #75)
-#73 := (uf_16 #72)
-#921 := (pattern #73)
-#76 := (uf_14 #75)
-#74 := (uf_15 #73)
-#77 := (= #74 #76)
-#923 := (forall (vars (?x15 int)) (:pat #921 #922) #77)
-#78 := (forall (vars (?x15 int)) #77)
-#926 := (iff #78 #923)
-#924 := (iff #77 #77)
-#925 := [refl]: #924
-#927 := [quant-intro #925]: #926
-#345 := (~ #78 #78)
-#381 := (~ #77 #77)
-#382 := [refl]: #381
-#346 := [nnf-pos #382]: #345
-#237 := [asserted]: #78
-#383 := [mp~ #237 #346]: #78
-#928 := [mp #383 #927]: #923
-#851 := (not #923)
-#524 := (or #851 #857)
-#525 := [quant-inst]: #524
-#580 := [unit-resolution #525 #928]: #857
-#566 := [trans #580 #628]: #557
-#558 := [trans #566 #570]: #567
-#549 := [trans #558 #573]: #568
-#551 := [trans #549 #574]: #550
-#552 := [trans #551 #577]: #542
-#543 := [trans #552 #563]: #553
-#554 := [trans #543 #565]: #107
-#108 := (not #107)
-#325 := [asserted]: #108
-[unit-resolution #325 #554]: false
-unsat
--- a/src/HOL/SMT/Examples/SMT_Examples.thy Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,587 +0,0 @@
-(* Title: HOL/SMT/SMT_Examples.thy
- Author: Sascha Boehme, TU Muenchen
-*)
-
-header {* Examples for the 'smt' tactic. *}
-
-theory SMT_Examples
-imports SMT
-begin
-
-declare [[smt_solver=z3, z3_proofs=true]]
-
-declare [[smt_certificates="$ISABELLE_SMT/Examples/SMT_Examples.certs"]]
-
-text {*
-To avoid re-generation of certificates,
-the following option is set to "false":
-*}
-
-declare [[smt_fixed=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)"
- 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" by smt
-
-lemma "P=P=P=P=P=P=P=P=P=P" 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 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 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 by smt
-
-lemma "\<forall>x::int. P x \<longrightarrow> (\<forall>y::int. P x \<or> P y)"
- by smt
-
-lemma
- assumes "(\<forall>x y. P x y = x)"
- shows "(\<exists>y. P x y) = P x c"
- using assms 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 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 by smt
-
-
-section {* Arithmetic *}
-
-subsection {* Linear arithmetic over integers and reals *}
-
-lemma "(3::int) = 3" by smt
-
-lemma "(3::real) = 3" by smt
-
-lemma "(3 :: int) + 1 = 4" by smt
-
-lemma "x + (y + z) = y + (z + (x::int))" by smt
-
-lemma "max (3::int) 8 > 5" by smt
-
-lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt
-
-lemma "P ((2::int) < 3) = P True" by smt
-
-lemma "x + 3 \<ge> 4 \<or> x < (1::int)" by smt
-
-lemma
- assumes "x \<ge> (3::int)" and "y = x + 4"
- shows "y - x > 0"
- using assms by smt
-
-lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt
-
-lemma
- fixes x :: real
- assumes "3 * x + 7 * a < 4" and "3 < 2 * x"
- shows "a < 0"
- using assms by smt
-
-lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)" by smt
-
-lemma "distinct [x < (3::int), 3 \<le> x]" by smt
-
-lemma
- assumes "a > (0::int)"
- shows "distinct [a, a * 2, a - a]"
- using assms 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))"
- by smt
-
-text{*
-The following example was taken from HOL/ex/PresburgerEx.thy, where it says:
-
- This following theorem proves that all solutions to the
- recurrence relation $x_{i+2} = |x_{i+1}| - x_i$ are periodic with
- period 9. The example was brought to our attention by John
- Harrison. It does does not require Presburger arithmetic but merely
- quantifier-free linear arithmetic and holds for the rationals as well.
-
- 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. 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)"
- by smt
-
-
-lemma "let P = 2 * x + 1 > x + (x::real) in P \<or> False \<or> P" by smt
-
-lemma "x + (let y = x mod 2 in 2 * y + 1) \<ge> x + (1::int)" by smt
-
-lemma "x + (let y = x mod 2 in y + y) < x + (3::int)" by smt
-
-lemma
- assumes "x \<noteq> (0::real)"
- shows "x + x \<noteq> (let P = (abs x > 1) in if P \<or> \<not>P then 4 else 2) * x"
- using assms by smt
-
-lemma
- assumes "(n + m) mod 2 = 0" and "n mod 4 = 3"
- shows "n mod 2 = 1 & m mod 2 = (1::int)"
- using assms by smt
-
-
-subsection {* Linear arithmetic with quantifiers *}
-
-lemma "~ (\<exists>x::int. False)" by smt
-
-lemma "~ (\<exists>x::real. False)" by smt
-
-lemma "\<exists>x::int. 0 < x"
- using [[z3_proofs=false]] (* no Z3 proof *)
- by smt
-
-lemma "\<exists>x::real. 0 < x"
- using [[z3_proofs=false]] (* no Z3 proof *)
- by smt
-
-lemma "\<forall>x::int. \<exists>y. y > x"
- using [[z3_proofs=false]] (* no Z3 proof *)
- by smt
-
-lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt
-
-lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0" by smt
-
-lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)" by smt
-
-lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)" by smt
-
-lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2" by smt
-
-lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x" by smt
-
-lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True" by smt
-
-lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)" by smt
-
-lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt
-
-lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y" by smt
-
-lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x" by smt
-
-lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0" by smt
-
-lemma "\<forall>x::int. trigger [pat x] (x < a \<longrightarrow> 2 * x < 2 * a)" by smt
-
-
-subsection {* Non-linear arithmetic over integers and reals *}
-
-lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
- using [[z3_proofs=false]] -- {* Isabelle's arithmetic decision procedures
- are too weak to automatically prove @{thm zero_less_mult_pos}. *}
- by smt
-
-lemma "(a::int) * (x + 1 + y) = a * x + a * (y + 1)" by smt
-
-lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)" 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)"
- by smt
-
-
-subsection {* Linear arithmetic for natural numbers *}
-
-lemma "2 * (x::nat) ~= 1" 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
- "let x = (1::nat) + y in
- let P = (if x > 0 then True else False) in
- False \<or> P = (x - 1 = y) \<or> (\<not>P \<longrightarrow> False)"
- by smt
-
-lemma "distinct [a + (1::nat), a * 2 + 3, a - a]" by smt
-
-lemma "int (nat \<bar>x::int\<bar>) = \<bar>x\<bar>" 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)" by (smt prime_nat_def)
-
-
-section {* Bitvectors *}
-
-locale z3_bv_test
-begin
-
-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" by smt
-
-lemma "(27 :: 4 word) = 11" by smt
-
-lemma "23 < (27::8 word)" by smt
-
-lemma "27 + 11 = (6::5 word)" by smt
-
-lemma "7 * 3 = (21::8 word)" by smt
-
-lemma "11 - 27 = (-16::8 word)" by smt
-
-lemma "- -11 = (11::5 word)" by smt
-
-lemma "-40 + 1 = (-39::7 word)" by smt
-
-lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by smt
-
-lemma "x = (5 :: 4 word) \<Longrightarrow> 4 * x = 4" by smt
-
-
-subsection {* Bit-level logic *}
-
-lemma "0b110 AND 0b101 = (0b100 :: 32 word)" by smt
-
-lemma "0b110 OR 0b011 = (0b111 :: 8 word)" by smt
-
-lemma "0xF0 XOR 0xFF = (0x0F :: 8 word)" by smt
-
-lemma "NOT (0xF0 :: 16 word) = 0xFF0F" by smt
-
-lemma "word_cat (27::4 word) (27::8 word) = (2843::12 word)" by smt
-
-lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)"
- by smt
-
-lemma "slice 1 (0b10110 :: 4 word) = (0b11 :: 2 word)" by smt
-
-lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by smt
-
-lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt
-
-lemma "bv_lshr 0b10011 2 = (0b100::8 word)" by smt
-
-lemma "bv_ashr 0b10011 2 = (0b100::8 word)" by smt
-
-lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt
-
-lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by smt
-
-lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" by smt
-
-lemma "w < 256 \<Longrightarrow> (w :: 16 word) AND 0x00FF = w" by smt
-
-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]]
- by smt
-
-lemma "P (0 \<le> (a :: 4 word)) = P True"
- using [[smt_solver=z3, z3_proofs=false]]
- 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
-
-
-section {* Higher-order problems and recursion *}
-
-lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> (f (i1 := v1, i2 := v2)) i = f i" by smt
-
-lemma "(f g (x::'a::type) = (g x \<and> True)) \<or> (f g x = True) \<or> (g x = True)"
- by smt
-
-lemma "id 3 = 3 \<and> id True = True" by (smt 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 map.simps)
-
-lemma "(ALL x. P x) | ~ All P" 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 dec_10.simps)
-
-axiomatization
- eval_dioph :: "int list \<Rightarrow> nat list \<Rightarrow> int"
- where
- eval_dioph_mod:
- "eval_dioph ks xs mod int n = eval_dioph ks (map (\<lambda>x. x mod n) xs) mod int n"
- and
- eval_dioph_div_mult:
- "eval_dioph ks (map (\<lambda>x. x div n) xs) * int n +
- eval_dioph ks (map (\<lambda>x. x mod n) xs) = eval_dioph ks xs"
-lemma
- "(eval_dioph ks xs = l) =
- (eval_dioph ks (map (\<lambda>x. x mod 2) xs) mod 2 = l mod 2 \<and>
- eval_dioph ks (map (\<lambda>x. x div 2) xs) =
- (l - eval_dioph ks (map (\<lambda>x. x mod 2) xs)) div 2)"
- by (smt eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
-
-
-section {* Monomorphization examples *}
-
-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 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 g1 g2 g3 list.size)
-
-end
--- a/src/HOL/SMT/ROOT.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1 +0,0 @@
-use_thys ["SMT"];
--- a/src/HOL/SMT/SMT.thy Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,79 +0,0 @@
-(* Title: HOL/SMT/SMT.thy
- Author: Sascha Boehme, TU Muenchen
-*)
-
-header {* Bindings to several SMT solvers *}
-
-theory SMT
-imports SMT_Base Z3
-uses
- "Tools/cvc3_solver.ML"
- "Tools/yices_solver.ML"
-begin
-
-setup {* CVC3_Solver.setup #> Yices_Solver.setup *}
-
-
-
-section {* Setup *}
-
-text {*
-Without further ado, the SMT solvers CVC3 and Z3 are provided
-remotely via an SMT server. For faster responses, the solver
-environment variables CVC3_SOLVER, YICES_SOLVER, and Z3_SOLVER
-need to point to the respective SMT solver executable.
-*}
-
-
-
-section {* Available configuration options *}
-
-text {* Choose the SMT solver to be applied (one of cvc3, yices, or z3): *}
-
-declare [[ smt_solver = z3 ]]
-
-text {* Restrict the runtime of an SMT solver (in seconds): *}
-
-declare [[ smt_timeout = 20 ]]
-
-
-subsection {* Z3-specific options *}
-
-text {* Pass extra command-line arguments to Z3 to control its behaviour: *}
-
-declare [[ z3_options = "" ]]
-
-text {* Enable proof reconstruction for Z3: *}
-
-declare [[ z3_proofs = false ]]
-
-text {* Enable or disable tracing of the theorems used for proving a
-proposition: *}
-
-declare [[ z3_trace_assms = false ]]
-
-
-subsection {* Certificates *}
-
-text {* To avoid invocation of an SMT solver for the same problem
-again and again, cache certificates in a file (the filename must
-be given by an absolute path, an empty string disables the usage
-of certificates): *}
-
-declare [[ smt_certificates = "" ]]
-
-text {* Allows or disallows the addition of new certificates to
-the current certificates file (when set to @{text false}, only
-existing certificates are used and no SMT solver is invoked): *}
-
-declare [[ smt_fixed = false ]]
-
-
-subsection {* Special configuration options *}
-
-text {* Trace the problem file, the result of the SMT solver and
-further information: *}
-
-declare [[ smt_trace = false ]]
-
-end
--- a/src/HOL/SMT/SMT_Base.thy Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,130 +0,0 @@
-(* Title: HOL/SMT/SMT_Base.thy
- Author: Sascha Boehme, TU Muenchen
-*)
-
-header {* SMT-specific definitions and basic tools *}
-
-theory SMT_Base
-imports Real "~~/src/HOL/Word/Word"
-uses
- "~~/src/Tools/cache_io.ML"
- ("Tools/smt_additional_facts.ML")
- ("Tools/smt_monomorph.ML")
- ("Tools/smt_normalize.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 :: "'a \<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)"
-
-
-
-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"
-
-definition array_ext where "array_ext a b = (SOME x. a = b \<or> a x \<noteq> b x)"
-
-lemma fun_upd_eq: "(f = f (x := y)) = (f x = y)"
-proof
- assume "f = f(x:=y)"
- hence "f x = (f(x:=y)) x" by simp
- thus "f x = y" by simp
-qed (auto simp add: ext)
-
-lemmas array_rules =
- ext fun_upd_apply fun_upd_same fun_upd_other fun_upd_upd fun_upd_eq apply_def
-
-
-
-section {* First-order logic *}
-
-text {*
-Some SMT solver formats require a strict separation between formulas and terms.
-During normalization, all uninterpreted constants are treated as function
-symbols, and atoms (with uninterpreted head symbol) are turned into terms by
-equating them with true using the following term-level equation symbol:
-*}
-
-definition term_eq :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infix "term'_eq" 50)
- where "(x term_eq y) = (x = y)"
-
-
-
-section {* Setup *}
-
-use "Tools/smt_additional_facts.ML"
-use "Tools/smt_monomorph.ML"
-use "Tools/smt_normalize.ML"
-use "Tools/smt_translate.ML"
-use "Tools/smt_solver.ML"
-use "Tools/smtlib_interface.ML"
-
-setup {* SMT_Solver.setup *}
-
-end
--- a/src/HOL/SMT/Tools/cvc3_solver.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,48 +0,0 @@
-(* Title: HOL/SMT/Tools/cvc3_solver.ML
- Author: Sascha Boehme, TU Muenchen
-
-Interface of the SMT solver CVC3.
-*)
-
-signature CVC3_SOLVER =
-sig
- val setup: theory -> theory
-end
-
-structure CVC3_Solver: CVC3_SOLVER =
-struct
-
-val solver_name = "cvc3"
-val env_var = "CVC3_SOLVER"
-
-val options = ["-lang", "smtlib", "-output-lang", "presentation"]
-
-val is_sat = String.isPrefix "Satisfiable."
-val is_unsat = String.isPrefix "Unsatisfiable."
-val is_unknown = String.isPrefix "Unknown."
-
-fun raise_cex real = raise SMT_Solver.SMT_COUNTEREXAMPLE (real, [])
-
-fun core_oracle (output, _) =
- let
- val empty_line = (fn "" => true | _ => false)
- val split_first = (fn [] => ("", []) | l :: ls => (l, ls))
- val (l, _) = split_first (dropwhile empty_line output)
- in
- if is_unsat l then @{cprop False}
- else if is_sat l then raise_cex true
- else if is_unknown l then raise_cex false
- else raise SMT_Solver.SMT (solver_name ^ " failed")
- end
-
-fun smtlib_solver oracle _ = {
- command = {env_var=env_var, remote_name=SOME solver_name},
- arguments = options,
- interface = SMTLIB_Interface.interface,
- reconstruct = pair o oracle }
-
-val setup =
- Thm.add_oracle (Binding.name solver_name, core_oracle) #-> (fn (_, oracle) =>
- SMT_Solver.add_solver (solver_name, smtlib_solver oracle))
-
-end
--- a/src/HOL/SMT/Tools/smt_additional_facts.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,45 +0,0 @@
-(* Title: HOL/SMT/Tools/smt_additional_facts.ML
- Author: Sascha Boehme, TU Muenchen
-
-Include additional facts.
-*)
-
-signature SMT_ADDITIONAL_FACTS =
-sig
- val add_facts: thm list -> thm list
-end
-
-structure SMT_Additional_Facts: SMT_ADDITIONAL_FACTS =
-struct
-
-infix 2 ??
-fun (ex ?? f) thms = if exists (ex o Thm.prop_of) thms then f thms else thms
-
-
-
-(* pairs *)
-
-val pair_rules = [@{thm fst_conv}, @{thm snd_conv}, @{thm pair_collapse}]
-
-val pair_type = (fn Type (@{type_name "*"}, _) => true | _ => false)
-val exists_pair_type = Term.exists_type (Term.exists_subtype pair_type)
-
-val add_pair_rules = exists_pair_type ?? append pair_rules
-
-
-
-(* function update *)
-
-val fun_upd_rules = [@{thm fun_upd_same}, @{thm fun_upd_apply}]
-
-val is_fun_upd = (fn Const (@{const_name fun_upd}, _) => true | _ => false)
-val exists_fun_upd = Term.exists_subterm is_fun_upd
-
-val add_fun_upd_rules = exists_fun_upd ?? append fun_upd_rules
-
-
-(* include additional facts *)
-
-val add_facts = add_pair_rules #> add_fun_upd_rules
-
-end
--- a/src/HOL/SMT/Tools/smt_monomorph.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,201 +0,0 @@
-(* Title: HOL/SMT/Tools/smt_monomorph.ML
- Author: Sascha Boehme, TU Muenchen
-
-Monomorphization of theorems, i.e., computation of all (necessary) instances.
-*)
-
-signature SMT_MONOMORPH =
-sig
- val monomorph: thm list -> Proof.context -> thm list * Proof.context
-end
-
-structure SMT_Monomorph: SMT_MONOMORPH =
-struct
-
-val typ_has_tvars = Term.exists_subtype (fn TVar _ => true | _ => false)
-
-val ignored = member (op =) [
- @{const_name All}, @{const_name Ex}, @{const_name Let}, @{const_name If},
- @{const_name "op ="}, @{const_name zero_class.zero},
- @{const_name one_class.one}, @{const_name number_of}]
-
-fun is_const f (n, T) = not (ignored n) andalso f T
-fun add_const_if f g (Const c) = if is_const f c then g c else I
- | add_const_if _ _ _ = I
-
-fun collect_consts_if f g thm =
- Term.fold_aterms (add_const_if f g) (Thm.prop_of thm)
-
-fun add_consts f =
- collect_consts_if f (fn (n, T) => Symtab.map_entry n (insert (op =) T))
-
-val insert_const = OrdList.insert (prod_ord fast_string_ord Term_Ord.typ_ord)
-fun tvar_consts_of thm = collect_consts_if typ_has_tvars insert_const thm []
-
-
-fun incr_indexes thms =
- let fun inc thm idx = (Thm.incr_indexes idx thm, Thm.maxidx_of thm + idx + 1)
- in fst (fold_map inc thms 0) end
-
-
-(* Compute all substitutions from the types "Ts" to all relevant
- types in "grounds", with respect to the given substitution. *)
-fun new_substitutions thy grounds (n, T) subst =
- if not (typ_has_tvars T) then [subst]
- else
- Symtab.lookup_list grounds n
- |> map_filter (try (fn U => Sign.typ_match thy (T, U) subst))
- |> cons subst
-
-
-(* Instantiate a set of constants with a substitution. Also collect
- all new ground instances for the next round of specialization. *)
-fun apply_subst grounds consts subst =
- let
- fun is_new_ground (n, T) = not (typ_has_tvars T) andalso
- not (member (op =) (Symtab.lookup_list grounds n) T)
-
- fun apply_const (n, T) new_grounds =
- let val c = (n, Envir.subst_type subst T)
- in
- new_grounds
- |> is_new_ground c ? Symtab.insert_list (op =) c
- |> pair c
- end
- in fold_map apply_const consts #>> pair subst end
-
-
-(* Compute new substitutions for the theorem "thm", based on
- previously found substitutions.
- Also collect new grounds, i.e., instantiated constants
- (without schematic types) which do not occur in any of the
- previous rounds. Note that thus no schematic type variables are
- shared among theorems. *)
-fun specialize thy all_grounds new_grounds (thm, scs) =
- let
- fun spec (subst, consts) next_grounds =
- [subst]
- |> fold (maps o new_substitutions thy new_grounds) consts
- |> rpair next_grounds
- |-> fold_map (apply_subst all_grounds consts)
- in
- fold_map spec scs #>> (fn scss =>
- (thm, fold (fold (insert (eq_snd (op =)))) scss []))
- end
-
-
-(* Compute all necessary substitutions.
- Instead of operating on the propositions of the theorems, the
- computation uses only the constants occurring with schematic type
- variables in the propositions. To ease comparisons, such sets of
- costants are always kept in their initial order. *)
-fun incremental_monomorph thy limit all_grounds new_grounds ths =
- let
- val all_grounds' = Symtab.merge_list (op =) (all_grounds, new_grounds)
- val spec = specialize thy all_grounds' new_grounds
- val (ths', new_grounds') = fold_map spec ths Symtab.empty
- in
- if Symtab.is_empty new_grounds' then ths'
- else if limit > 0
- then incremental_monomorph thy (limit-1) all_grounds' new_grounds' ths'
- else (warning "SMT: monomorphization limit reached"; ths')
- end
-
-
-fun filter_most_specific thy =
- let
- fun typ_match (_, T) (_, U) = Sign.typ_match thy (T, U)
-
- fun is_trivial subst = Vartab.is_empty subst orelse
- forall (fn (v, (S, T)) => TVar (v, S) = T) (Vartab.dest subst)
-
- fun match general specific =
- (case try (fold2 typ_match general specific) Vartab.empty of
- NONE => false
- | SOME subst => not (is_trivial subst))
-
- fun most_specific _ [] = []
- | most_specific css ((ss, cs) :: scs) =
- let val substs = most_specific (cs :: css) scs
- in
- if exists (match cs) css orelse exists (match cs o snd) scs
- then substs else ss :: substs
- end
-
- in most_specific [] end
-
-
-fun instantiate thy Tenv =
- let
- fun replace (v, (_, T)) (U as TVar (u, _)) = if u = v then T else U
- | replace _ T = T
-
- fun complete (vT as (v, _)) subst =
- subst
- |> not (Vartab.defined subst v) ? Vartab.update vT
- |> Vartab.map (apsnd (Term.map_atyps (replace vT)))
-
- fun cert (ix, (S, T)) = pairself (Thm.ctyp_of thy) (TVar (ix, S), T)
-
- fun inst thm subst =
- let val cTs = Vartab.fold (cons o cert) (fold complete Tenv subst) []
- in Thm.instantiate (cTs, []) thm end
-
- in uncurry (map o inst) end
-
-
-fun mono_all ctxt _ [] monos = (monos, ctxt)
- | mono_all ctxt limit polys monos =
- let
- fun invent_types thm ctxt =
- let val (vs, Ss) = split_list (Term.add_tvars (Thm.prop_of thm) [])
- in
- ctxt
- |> Variable.invent_types Ss
- |>> map2 (fn v => fn (n, S) => (v, (S, TFree (n, S)))) vs
- end
- val (Tenvs, ctxt') = fold_map invent_types polys ctxt
-
- val thy = ProofContext.theory_of ctxt'
-
- val ths = polys
- |> map (fn thm => (thm, [(Vartab.empty, tvar_consts_of thm)]))
-
- (* all constant names occurring with schematic types *)
- val ns = fold (fold (fold (insert (op =) o fst) o snd) o snd) ths []
-
- (* all known instances with non-schematic types *)
- val grounds =
- Symtab.make (map (rpair []) ns)
- |> fold (add_consts (K true)) monos
- |> fold (add_consts (not o typ_has_tvars)) polys
- in
- polys
- |> map (fn thm => (thm, [(Vartab.empty, tvar_consts_of thm)]))
- |> incremental_monomorph thy limit Symtab.empty grounds
- |> map (apsnd (filter_most_specific thy))
- |> flat o map2 (instantiate thy) Tenvs
- |> append monos
- |> rpair ctxt'
- end
-
-
-val monomorph_limit = 10
-
-
-(* Instantiate all polymorphic constants (i.e., constants occurring
- both with ground types and type variables) with all (necessary)
- ground types; thereby create copies of theorems containing those
- constants.
- To prevent non-termination, there is an upper limit for the
- number of recursions involved in the fixpoint construction.
- The initial set of theorems must not contain any schematic term
- variables, and the final list of theorems does not contain any
- schematic type variables anymore. *)
-fun monomorph thms ctxt =
- thms
- |> List.partition (Term.exists_type typ_has_tvars o Thm.prop_of)
- |>> incr_indexes
- |-> mono_all ctxt monomorph_limit
-
-end
--- a/src/HOL/SMT/Tools/smt_normalize.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,470 +0,0 @@
-(* Title: HOL/SMT/Tools/smt_normalize.ML
- Author: Sascha Boehme, TU Muenchen
-
-Normalization steps on theorems required by SMT solvers:
- * unfold trivial let expressions,
- * simplify trivial distincts (those with less than three elements),
- * rewrite bool case expressions as if expressions,
- * normalize numerals (e.g. replace negative numerals by negated positive
- numerals),
- * embed natural numbers into integers,
- * add extra rules specifying types and constants which occur frequently,
- * fully translate into object logic, add universal closure,
- * lift lambda terms,
- * make applications explicit for functions with varying number of arguments.
-*)
-
-signature SMT_NORMALIZE =
-sig
- val normalize: thm list -> Proof.context -> thm list * Proof.context
-end
-
-structure SMT_Normalize: SMT_NORMALIZE =
-struct
-
-infix 2 ??
-fun (test ?? f) x = if test x then f x else x
-
-fun if_conv c cv1 cv2 ct = (if c (Thm.term_of ct) then cv1 else cv2) ct
-fun if_true_conv c cv = if_conv c cv Conv.all_conv
-
-
-
-(* simplification of trivial distincts (distinct should have at least
- three elements in the argument list) *)
-
-local
- fun is_trivial_distinct (Const (@{const_name distinct}, _) $ t) =
- length (HOLogic.dest_list t) <= 2
- | is_trivial_distinct _ = false
-
- val thms = @{lemma
- "distinct [] == True"
- "distinct [x] == True"
- "distinct [x, y] == (x ~= y)"
- by simp_all}
- fun distinct_conv _ =
- if_true_conv is_trivial_distinct (More_Conv.rewrs_conv thms)
-in
-fun trivial_distinct ctxt =
- map ((Term.exists_subterm is_trivial_distinct o Thm.prop_of) ??
- Conv.fconv_rule (More_Conv.top_conv distinct_conv ctxt))
-end
-
-
-
-(* rewrite bool case expressions as if expressions *)
-
-local
- val is_bool_case = (fn
- Const (@{const_name "bool.bool_case"}, _) $ _ $ _ $ _ => true
- | _ => false)
-
- val thms = @{lemma
- "(case P of True => x | False => y) == (if P then x else y)"
- "(case P of False => y | True => x) == (if P then x else y)"
- by (rule eq_reflection, simp)+}
- val unfold_conv = if_true_conv is_bool_case (More_Conv.rewrs_conv thms)
-in
-fun rewrite_bool_cases ctxt =
- map ((Term.exists_subterm is_bool_case o Thm.prop_of) ??
- Conv.fconv_rule (More_Conv.top_conv (K unfold_conv) ctxt))
-end
-
-
-
-(* normalization of numerals: rewriting of negative integer numerals into
- positive numerals, Numeral0 into 0, Numeral1 into 1 *)
-
-local
- fun is_number_sort ctxt T =
- Sign.of_sort (ProofContext.theory_of ctxt) (T, @{sort number_ring})
-
- fun is_strange_number ctxt (t as Const (@{const_name number_of}, _) $ _) =
- (case try HOLogic.dest_number t of
- SOME (T, i) => is_number_sort ctxt T andalso i < 2
- | NONE => false)
- | is_strange_number _ _ = false
-
- val pos_numeral_ss = HOL_ss
- addsimps [@{thm Int.number_of_minus}, @{thm Int.number_of_Min}]
- addsimps [@{thm Int.number_of_Pls}, @{thm Int.numeral_1_eq_1}]
- addsimps @{thms Int.pred_bin_simps}
- addsimps @{thms Int.normalize_bin_simps}
- addsimps @{lemma
- "Int.Min = - Int.Bit1 Int.Pls"
- "Int.Bit0 (- Int.Pls) = - Int.Pls"
- "Int.Bit0 (- k) = - Int.Bit0 k"
- "Int.Bit1 (- k) = - Int.Bit1 (Int.pred k)"
- by simp_all (simp add: pred_def)}
-
- fun pos_conv ctxt = if_conv (is_strange_number ctxt)
- (Simplifier.rewrite (Simplifier.context ctxt pos_numeral_ss))
- Conv.no_conv
-in
-fun normalize_numerals ctxt =
- map ((Term.exists_subterm (is_strange_number ctxt) o Thm.prop_of) ??
- Conv.fconv_rule (More_Conv.top_sweep_conv pos_conv ctxt))
-end
-
-
-
-(* embedding of standard natural number operations into integer operations *)
-
-local
- val nat_embedding = @{lemma
- "nat (int n) = n"
- "i >= 0 --> int (nat i) = i"
- "i < 0 --> int (nat i) = 0"
- by simp_all}
-
- val nat_rewriting = @{lemma
- "0 = nat 0"
- "1 = nat 1"
- "number_of i = nat (number_of i)"
- "int (nat 0) = 0"
- "int (nat 1) = 1"
- "a < b = (int a < int b)"
- "a <= b = (int a <= int b)"
- "Suc a = nat (int a + 1)"
- "a + b = nat (int a + int b)"
- "a - b = nat (int a - int b)"
- "a * b = nat (int a * int b)"
- "a div b = nat (int a div int b)"
- "a mod b = nat (int a mod int b)"
- "min a b = nat (min (int a) (int b))"
- "max a b = nat (max (int a) (int b))"
- "int (nat (int a + int b)) = int a + int b"
- "int (nat (int a * int b)) = int a * int b"
- "int (nat (int a div int b)) = int a div int b"
- "int (nat (int a mod int b)) = int a mod int b"
- "int (nat (min (int a) (int b))) = min (int a) (int b)"
- "int (nat (max (int a) (int b))) = max (int a) (int b)"
- by (simp add: nat_mult_distrib nat_div_distrib nat_mod_distrib
- int_mult[symmetric] zdiv_int[symmetric] zmod_int[symmetric])+}
-
- fun on_positive num f x =
- (case try HOLogic.dest_number (Thm.term_of num) of
- SOME (_, i) => if i >= 0 then SOME (f x) else NONE
- | NONE => NONE)
-
- val cancel_int_nat_ss = HOL_ss
- addsimps [@{thm Nat_Numeral.nat_number_of}]
- addsimps [@{thm Nat_Numeral.int_nat_number_of}]
- addsimps @{thms neg_simps}
-
- fun cancel_int_nat_simproc _ ss ct =
- let
- val num = Thm.dest_arg (Thm.dest_arg ct)
- val goal = Thm.mk_binop @{cterm "op == :: int => _"} ct num
- val simpset = Simplifier.inherit_context ss cancel_int_nat_ss
- fun tac _ = Simplifier.simp_tac simpset 1
- in on_positive num (Goal.prove_internal [] goal) tac end
-
- val nat_ss = HOL_ss
- addsimps nat_rewriting
- addsimprocs [Simplifier.make_simproc {
- name = "cancel_int_nat_num", lhss = [@{cpat "int (nat _)"}],
- proc = cancel_int_nat_simproc, identifier = [] }]
-
- fun conv ctxt = Simplifier.rewrite (Simplifier.context ctxt nat_ss)
-
- val uses_nat_type = Term.exists_type (Term.exists_subtype (equal @{typ nat}))
- val uses_nat_int =
- Term.exists_subterm (member (op aconv) [@{term int}, @{term nat}])
-in
-fun nat_as_int ctxt =
- map ((uses_nat_type o Thm.prop_of) ?? Conv.fconv_rule (conv ctxt)) #>
- exists (uses_nat_int o Thm.prop_of) ?? append nat_embedding
-end
-
-
-
-(* unfold definitions of specific constants *)
-
-local
- fun mk_entry (t as Const (n, _)) thm = ((n, t), thm)
- | mk_entry t _ = raise TERM ("mk_entry", [t])
- fun prepare_def thm =
- (case Thm.prop_of thm of
- Const (@{const_name "=="}, _) $ t $ _ => mk_entry (Term.head_of t) thm
- | t => raise TERM ("prepare_def", [t]))
-
- val defs = map prepare_def [
- @{thm abs_if[where 'a = int, THEN eq_reflection]},
- @{thm abs_if[where 'a = real, THEN eq_reflection]},
- @{thm min_def[where 'a = int, THEN eq_reflection]},
- @{thm min_def[where 'a = real, THEN eq_reflection]},
- @{thm max_def[where 'a = int, THEN eq_reflection]},
- @{thm max_def[where 'a = real, THEN eq_reflection]},
- @{thm Ex1_def}, @{thm Ball_def}, @{thm Bex_def}]
-
- fun matches thy ((t as Const (n, _)), (m, p)) =
- n = m andalso Pattern.matches thy (p, t)
- | matches _ _ = false
-
- fun lookup_def thy = AList.lookup (matches thy) defs
- fun lookup_def_head thy = lookup_def thy o Term.head_of
-
- fun occurs_def thy = Term.exists_subterm (is_some o lookup_def thy)
-
- fun unfold_def_conv ctxt ct =
- (case lookup_def_head (ProofContext.theory_of ctxt) (Thm.term_of ct) of
- SOME thm => Conv.rewr_conv thm
- | NONE => Conv.all_conv) ct
-in
-fun unfold_defs ctxt =
- (occurs_def (ProofContext.theory_of ctxt) o Thm.prop_of) ??
- Conv.fconv_rule (More_Conv.top_conv unfold_def_conv ctxt)
-end
-
-
-
-(* further normalizations: beta/eta, universal closure, atomize *)
-
-local
- val all1 = @{lemma "All P == ALL x. P x" by (rule reflexive)}
- val all2 = @{lemma "All == (%P. ALL x. P x)" by (rule reflexive)}
- val ex1 = @{lemma "Ex P == EX x. P x" by (rule reflexive)}
- val ex2 = @{lemma "Ex == (%P. EX x. P x)" by (rule reflexive)}
- val let1 = @{lemma "Let c P == let x = c in P x" by (rule reflexive)}
- val let2 = @{lemma "Let c == (%P. let x = c in P x)" by (rule reflexive)}
- val let3 = @{lemma "Let == (%c P. let x = c in P x)" by (rule reflexive)}
-
- fun all_abs_conv cv ctxt =
- Conv.abs_conv (all_abs_conv cv o snd) ctxt else_conv cv ctxt
- fun keep_conv ctxt = More_Conv.binder_conv norm_conv ctxt
- and unfold_conv rule ctxt =
- Conv.rewr_conv rule then_conv all_abs_conv keep_conv ctxt
- and unfold_let_conv rule ctxt =
- Conv.rewr_conv rule then_conv
- all_abs_conv (fn cx => Conv.combination_conv
- (Conv.arg_conv (norm_conv cx)) (Conv.abs_conv (norm_conv o snd) cx)) ctxt
- and norm_conv ctxt ct =
- (case Thm.term_of ct of
- Const (@{const_name All}, _) $ Abs _ => keep_conv
- | Const (@{const_name All}, _) $ _ => unfold_conv all1
- | Const (@{const_name All}, _) => unfold_conv all2
- | Const (@{const_name Ex}, _) $ Abs _ => keep_conv
- | Const (@{const_name Ex}, _) $ _ => unfold_conv ex1
- | Const (@{const_name Ex}, _) => unfold_conv ex2
- | Const (@{const_name Let}, _) $ _ $ Abs _ => keep_conv
- | Const (@{const_name Let}, _) $ _ $ _ => unfold_let_conv let1
- | Const (@{const_name Let}, _) $ _ => unfold_let_conv let2
- | Const (@{const_name Let}, _) => unfold_let_conv let3
- | Abs _ => Conv.abs_conv (norm_conv o snd)
- | _ $ _ => Conv.comb_conv o norm_conv
- | _ => K Conv.all_conv) ctxt ct
-
- fun is_normed t =
- (case t of
- Const (@{const_name All}, _) $ Abs (_, _, u) => is_normed u
- | Const (@{const_name All}, _) $ _ => false
- | Const (@{const_name All}, _) => false
- | Const (@{const_name Ex}, _) $ Abs (_, _, u) => is_normed u
- | Const (@{const_name Ex}, _) $ _ => false
- | Const (@{const_name Ex}, _) => false
- | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>
- is_normed u1 andalso is_normed u2
- | Const (@{const_name Let}, _) $ _ $ _ => false
- | Const (@{const_name Let}, _) $ _ => false
- | Const (@{const_name Let}, _) => false
- | Abs (_, _, u) => is_normed u
- | u1 $ u2 => is_normed u1 andalso is_normed u2
- | _ => true)
-in
-fun norm_binder_conv ctxt = if_conv is_normed Conv.all_conv (norm_conv ctxt)
-end
-
-fun norm_def ctxt thm =
- (case Thm.prop_of thm of
- @{term Trueprop} $ (Const (@{const_name "op ="}, _) $ _ $ Abs _) =>
- norm_def ctxt (thm RS @{thm fun_cong})
- | Const (@{const_name "=="}, _) $ _ $ Abs _ =>
- norm_def ctxt (thm RS @{thm meta_eq_to_obj_eq})
- | _ => thm)
-
-fun atomize_conv ctxt ct =
- (case Thm.term_of ct of
- @{term "op ==>"} $ _ $ _ =>
- Conv.binop_conv (atomize_conv ctxt) then_conv
- Conv.rewr_conv @{thm atomize_imp}
- | Const (@{const_name "=="}, _) $ _ $ _ =>
- Conv.binop_conv (atomize_conv ctxt) then_conv
- Conv.rewr_conv @{thm atomize_eq}
- | Const (@{const_name all}, _) $ Abs _ =>
- More_Conv.binder_conv atomize_conv ctxt then_conv
- Conv.rewr_conv @{thm atomize_all}
- | _ => Conv.all_conv) ct
-
-fun normalize_rule ctxt =
- Conv.fconv_rule (
- (* reduce lambda abstractions, except at known binders: *)
- Thm.beta_conversion true then_conv
- Thm.eta_conversion then_conv
- norm_binder_conv ctxt) #>
- norm_def ctxt #>
- Drule.forall_intr_vars #>
- Conv.fconv_rule (atomize_conv ctxt)
-
-
-
-(* lift lambda terms into additional rules *)
-
-local
- val meta_eq = @{cpat "op =="}
- val meta_eqT = hd (Thm.dest_ctyp (Thm.ctyp_of_term meta_eq))
- 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 cert ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
-
- 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 apply cv thm =
- let val thm' = Thm.combination thm (Thm.reflexive cv)
- in Thm.transitive thm' (Thm.beta_conversion false (Thm.rhs_of thm')) end
- fun apply_def cvs eq = Thm.symmetric (fold apply cvs eq)
-
- fun replace_lambda cvs ct (cx as (ctxt, defs)) =
- let
- val cvs' = used_vars cvs ct
- val ct' = fold_rev Thm.cabs cvs' ct
- in
- (case Termtab.lookup defs (Thm.term_of ct') of
- SOME eq => (apply_def cvs' eq, cx)
- | NONE =>
- let
- val {T, ...} = Thm.rep_cterm ct' and n = Name.uu
- val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
- val cu = mk_meta_eq (cert ctxt (Free (n', T))) ct'
- val (eq, ctxt'') = yield_singleton Assumption.add_assumes cu ctxt'
- val defs' = Termtab.update (Thm.term_of ct', eq) defs
- in (apply_def cvs' eq, (ctxt'', 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 (ctxt, defs) =
- let
- val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
- val (cv, cu) = Thm.dest_abs (SOME n) ct
- in (ctxt', defs) |> f (cv :: cvs) cu |>> Thm.abstract_rule n cv end
-
- fun traverse cvs ct =
- (case Thm.term_of ct of
- Const (@{const_name All}, _) $ Abs _ => in_arg (in_abs traverse cvs)
- | Const (@{const_name Ex}, _) $ Abs _ => in_arg (in_abs traverse cvs)
- | Const (@{const_name Let}, _) $ _ $ Abs _ =>
- in_comb (in_arg (traverse cvs)) (in_abs traverse cvs)
- | Abs _ => at_lambda cvs
- | _ $ _ => in_comb (traverse cvs) (traverse cvs)
- | _ => none) ct
-
- and at_lambda cvs ct =
- in_abs traverse cvs ct #-> (fn thm =>
- replace_lambda cvs (Thm.rhs_of thm) #>> Thm.transitive thm)
-
- fun has_free_lambdas t =
- (case t of
- Const (@{const_name All}, _) $ Abs (_, _, u) => has_free_lambdas u
- | Const (@{const_name Ex}, _) $ Abs (_, _, u) => has_free_lambdas u
- | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>
- has_free_lambdas u1 orelse has_free_lambdas u2
- | Abs _ => true
- | u1 $ u2 => has_free_lambdas u1 orelse has_free_lambdas u2
- | _ => false)
-
- fun lift_lm f thm cx =
- if not (has_free_lambdas (Thm.prop_of thm)) then (thm, cx)
- else cx |> f (Thm.cprop_of thm) |>> (fn thm' => Thm.equal_elim thm' thm)
-in
-fun lift_lambdas thms ctxt =
- let
- val cx = (ctxt, Termtab.empty)
- val (thms', (ctxt', defs)) = fold_map (lift_lm (traverse [])) thms cx
- val eqs = Termtab.fold (cons o normalize_rule ctxt' o snd) defs []
- in (eqs @ thms', ctxt') end
-end
-
-
-
-(* make application explicit for functions with varying number of arguments *)
-
-local
- val const = prefix "c" and free = prefix "f"
- fun min i (e as (_, j)) = if i <> j then (true, Int.min (i, j)) else e
- fun add t i = Symtab.map_default (t, (false, i)) (min i)
- fun traverse t =
- (case Term.strip_comb t of
- (Const (n, _), ts) => add (const n) (length ts) #> fold traverse ts
- | (Free (n, _), ts) => add (free n) (length ts) #> fold traverse ts
- | (Abs (_, _, u), ts) => fold traverse (u :: ts)
- | (_, ts) => fold traverse ts)
- val prune = (fn (n, (true, i)) => Symtab.update (n, i) | _ => I)
- fun prune_tab tab = Symtab.fold prune tab Symtab.empty
-
- fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
- fun nary_conv conv1 conv2 ct =
- (Conv.combination_conv (nary_conv conv1 conv2) conv2 else_conv conv1) ct
- fun abs_conv conv tb = Conv.abs_conv (fn (cv, cx) =>
- let val n = fst (Term.dest_Free (Thm.term_of cv))
- in conv (Symtab.update (free n, 0) tb) cx end)
- val apply_rule = @{lemma "f x == apply f x" by (simp add: apply_def)}
-in
-fun explicit_application ctxt thms =
- let
- fun sub_conv tb ctxt ct =
- (case Term.strip_comb (Thm.term_of ct) of
- (Const (n, _), ts) => app_conv tb (const n) (length ts) ctxt
- | (Free (n, _), ts) => app_conv tb (free n) (length ts) ctxt
- | (Abs _, _) => nary_conv (abs_conv sub_conv tb ctxt) (sub_conv tb ctxt)
- | (_, _) => nary_conv Conv.all_conv (sub_conv tb ctxt)) ct
- and app_conv tb n i ctxt =
- (case Symtab.lookup tb n of
- NONE => nary_conv Conv.all_conv (sub_conv tb ctxt)
- | SOME j => apply_conv tb ctxt (i - j))
- and apply_conv tb ctxt i ct = (
- if i = 0 then nary_conv Conv.all_conv (sub_conv tb ctxt)
- else
- Conv.rewr_conv apply_rule then_conv
- binop_conv (apply_conv tb ctxt (i-1)) (sub_conv tb ctxt)) ct
-
- fun needs_exp_app tab = Term.exists_subterm (fn
- Bound _ $ _ => true
- | Const (n, _) => Symtab.defined tab (const n)
- | Free (n, _) => Symtab.defined tab (free n)
- | _ => false)
-
- fun rewrite tab ctxt thm =
- if not (needs_exp_app tab (Thm.prop_of thm)) then thm
- else Conv.fconv_rule (sub_conv tab ctxt) thm
-
- val tab = prune_tab (fold (traverse o Thm.prop_of) thms Symtab.empty)
- in map (rewrite tab ctxt) thms end
-end
-
-
-
-(* combined normalization *)
-
-fun normalize thms ctxt =
- thms
- |> trivial_distinct ctxt
- |> rewrite_bool_cases ctxt
- |> normalize_numerals ctxt
- |> nat_as_int ctxt
- |> map (unfold_defs ctxt #> normalize_rule ctxt)
- |> rpair ctxt
- |-> SMT_Monomorph.monomorph
- |-> lift_lambdas
- |-> (fn thms' => `(fn ctxt' => explicit_application ctxt' thms'))
-
-end
--- a/src/HOL/SMT/Tools/smt_solver.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,342 +0,0 @@
-(* Title: HOL/SMT/Tools/smt_solver.ML
- Author: Sascha Boehme, TU Muenchen
-
-SMT solvers registry and SMT tactic.
-*)
-
-signature SMT_SOLVER =
-sig
- exception SMT of string
- exception SMT_COUNTEREXAMPLE of bool * term list
-
- type solver_config = {
- command: {env_var: string, remote_name: string option},
- arguments: string list,
- interface: string list -> SMT_Translate.config,
- reconstruct: (string list * SMT_Translate.recon) -> Proof.context ->
- thm * Proof.context }
-
- (*options*)
- val timeout: int Config.T
- val with_timeout: Proof.context -> ('a -> 'b) -> 'a -> 'b
- val trace: bool Config.T
- val trace_msg: Proof.context -> ('a -> string) -> 'a -> unit
-
- (*certificates*)
- val fixed_certificates: bool Config.T
- val select_certificates: string -> Context.generic -> Context.generic
-
- (*solvers*)
- type solver = Proof.context -> thm list -> thm
- type solver_info = Context.generic -> Pretty.T list
- val add_solver: string * (Proof.context -> solver_config) -> theory ->
- theory
- val all_solver_names_of: theory -> string list
- val add_solver_info: string * solver_info -> theory -> theory
- val solver_name_of: Context.generic -> string
- val select_solver: string -> Context.generic -> Context.generic
- val solver_of: Context.generic -> solver
-
- (*tactic*)
- val smt_tac': bool -> Proof.context -> thm list -> int -> Tactical.tactic
- val smt_tac: Proof.context -> thm list -> int -> Tactical.tactic
-
- (*setup*)
- val setup: theory -> theory
- val print_setup: Context.generic -> unit
-end
-
-structure SMT_Solver: SMT_SOLVER =
-struct
-
-exception SMT of string
-exception SMT_COUNTEREXAMPLE of bool * term list
-
-
-type solver_config = {
- command: {env_var: string, remote_name: string option},
- arguments: string list,
- interface: string list -> SMT_Translate.config,
- reconstruct: (string list * SMT_Translate.recon) -> Proof.context ->
- thm * Proof.context }
-
-
-
-(* SMT options *)
-
-val (timeout, setup_timeout) = Attrib.config_int "smt_timeout" (K 30)
-
-fun with_timeout ctxt f x =
- TimeLimit.timeLimit (Time.fromSeconds (Config.get ctxt timeout)) f x
- handle TimeLimit.TimeOut => raise SMT "timeout"
-
-val (trace, setup_trace) = Attrib.config_bool "smt_trace" (K false)
-
-fun trace_msg ctxt f x =
- if Config.get ctxt trace then tracing (f x) else ()
-
-
-
-(* SMT certificates *)
-
-val (fixed_certificates, setup_fixed_certificates) =
- Attrib.config_bool "smt_fixed" (K false)
-
-structure Certificates = Generic_Data
-(
- type T = Cache_IO.cache option
- val empty = NONE
- val extend = I
- fun merge (s, _) = s
-)
-
-fun select_certificates name = Certificates.put (
- if name = "" then NONE
- else SOME (Cache_IO.make (Path.explode name)))
-
-
-
-(* interface to external solvers *)
-
-local
-
-fun choose {env_var, remote_name} =
- let
- val local_solver = getenv env_var
- val remote_solver = the_default "" remote_name
- val remote_url = getenv "REMOTE_SMT_URL"
- in
- if local_solver <> ""
- then
- (tracing ("Invoking local SMT solver " ^ quote local_solver ^ " ...");
- [local_solver])
- else if remote_solver <> ""
- then
- (tracing ("Invoking remote SMT solver " ^ quote remote_solver ^ " at " ^
- quote remote_url ^ " ...");
- [getenv "REMOTE_SMT", remote_solver])
- else error ("Undefined Isabelle environment variable: " ^ quote env_var)
- end
-
-fun make_cmd solver args problem_path proof_path = space_implode " " (
- map File.shell_quote (solver @ args) @
- [File.shell_path problem_path, "2>&1", ">", File.shell_path proof_path])
-
-fun run ctxt cmd args input =
- (case Certificates.get (Context.Proof ctxt) of
- NONE => Cache_IO.run (make_cmd (choose cmd) args) input
- | SOME certs =>
- (case Cache_IO.lookup certs input of
- (NONE, key) =>
- if Config.get ctxt fixed_certificates
- then error ("Bad certificates cache: missing certificate")
- else Cache_IO.run_and_cache certs key (make_cmd (choose cmd) args)
- input
- | (SOME output, _) =>
- (tracing ("Using cached certificate from " ^
- File.shell_path (Cache_IO.cache_path_of certs) ^ " ...");
- output)))
-
-in
-
-fun run_solver ctxt cmd args input =
- let
- fun pretty tag ls = Pretty.string_of (Pretty.big_list tag
- (map Pretty.str ls))
-
- val _ = trace_msg ctxt (pretty "SMT problem:" o split_lines) input
-
- val (res, err) = with_timeout ctxt (run ctxt cmd args) input
- val _ = trace_msg ctxt (pretty "SMT solver:") err
-
- val ls = rev (dropwhile (equal "") (rev res))
- val _ = trace_msg ctxt (pretty "SMT result:") ls
- in ls end
-
-end
-
-fun trace_recon_data ctxt {typs, terms, ...} =
- let
- fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p]
- fun pretty_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T)
- fun pretty_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t)
- in
- trace_msg ctxt (fn () => Pretty.string_of (Pretty.big_list "SMT names:" [
- Pretty.big_list "sorts:" (map pretty_typ (Symtab.dest typs)),
- Pretty.big_list "functions:" (map pretty_term (Symtab.dest terms))])) ()
- end
-
-fun invoke translate_config command arguments thms ctxt =
- thms
- |> SMT_Translate.translate translate_config ctxt
- ||> tap (trace_recon_data ctxt)
- |>> run_solver ctxt command arguments
- |> rpair ctxt
-
-fun discharge_definitions thm =
- if Thm.nprems_of thm = 0 then thm
- else discharge_definitions (@{thm reflexive} RS thm)
-
-fun gen_solver name solver ctxt prems =
- let
- val {command, arguments, interface, reconstruct} = solver ctxt
- val comments = ("solver: " ^ name) ::
- ("timeout: " ^ string_of_int (Config.get ctxt timeout)) ::
- "arguments:" :: arguments
- in
- SMT_Additional_Facts.add_facts prems
- |> rpair ctxt
- |-> SMT_Normalize.normalize
- |-> invoke (interface comments) command arguments
- |-> reconstruct
- |-> (fn thm => fn ctxt' => thm
- |> singleton (ProofContext.export ctxt' ctxt)
- |> discharge_definitions)
- end
-
-
-
-(* solver store *)
-
-type solver = Proof.context -> thm list -> thm
-type solver_info = Context.generic -> Pretty.T list
-
-structure Solvers = Theory_Data
-(
- type T = ((Proof.context -> solver_config) * solver_info) Symtab.table
- val empty = Symtab.empty
- val extend = I
- fun merge data = Symtab.merge (K true) data
- handle Symtab.DUP name => error ("Duplicate SMT solver: " ^ quote name)
-)
-
-val no_solver = "(none)"
-val add_solver = Solvers.map o Symtab.update_new o apsnd (rpair (K []))
-val all_solver_names_of = Symtab.keys o Solvers.get
-val lookup_solver = Symtab.lookup o Solvers.get
-fun add_solver_info (n, i) = Solvers.map (Symtab.map_entry n (apsnd (K i)))
-
-
-
-(* selected solver *)
-
-structure Selected_Solver = Generic_Data
-(
- type T = string
- val empty = no_solver
- val extend = I
- fun merge (s, _) = s
-)
-
-val solver_name_of = Selected_Solver.get
-
-fun select_solver name context =
- if is_none (lookup_solver (Context.theory_of context) name)
- then error ("SMT solver not registered: " ^ quote name)
- else Selected_Solver.map (K name) context
-
-fun raw_solver_of context name =
- (case lookup_solver (Context.theory_of context) name of
- NONE => error "No SMT solver selected"
- | SOME (s, _) => s)
-
-fun solver_of context =
- let val name = solver_name_of context
- in gen_solver name (raw_solver_of context name) end
-
-
-
-(* SMT tactic *)
-
-local
- fun pretty_cex ctxt (real, ex) =
- let
- val msg = if real then "SMT: counterexample found"
- else "SMT: potential counterexample found"
- in
- if null ex then msg ^ "."
- else Pretty.string_of (Pretty.big_list (msg ^ ":")
- (map (Syntax.pretty_term ctxt) ex))
- end
-
- fun fail_tac f msg st = (f msg; Tactical.no_tac st)
-
- fun SAFE pass_exns tac ctxt i st =
- if pass_exns then tac ctxt i st
- else (tac ctxt i st
- handle SMT msg => fail_tac (trace_msg ctxt (prefix "SMT: ")) msg st
- | SMT_COUNTEREXAMPLE ce => fail_tac tracing (pretty_cex ctxt ce) st)
-
- fun smt_solver rules ctxt = solver_of (Context.Proof ctxt) ctxt rules
-
- val has_topsort = Term.exists_type (Term.exists_subtype (fn
- TFree (_, []) => true
- | TVar (_, []) => true
- | _ => false))
-in
-fun smt_tac' pass_exns ctxt rules =
- Tactic.rtac @{thm ccontr} THEN'
- SUBPROOF (fn {context, prems, ...} =>
- let val thms = rules @ prems
- in
- if exists (has_topsort o Thm.prop_of) thms
- then fail_tac (trace_msg context I)
- "SMT: proof state contains the universal sort {}"
- else SAFE pass_exns (Tactic.rtac o smt_solver thms) context 1
- end) ctxt
-
-val smt_tac = smt_tac' false
-end
-
-val smt_method =
- Scan.optional Attrib.thms [] >>
- (fn thms => fn ctxt => METHOD (fn facts =>
- HEADGOAL (smt_tac ctxt (thms @ facts))))
-
-
-
-(* setup *)
-
-val setup =
- Attrib.setup (Binding.name "smt_solver")
- (Scan.lift (OuterParse.$$$ "=" |-- Args.name) >>
- (Thm.declaration_attribute o K o select_solver))
- "SMT solver configuration" #>
- setup_timeout #>
- setup_trace #>
- setup_fixed_certificates #>
- Attrib.setup (Binding.name "smt_certificates")
- (Scan.lift (OuterParse.$$$ "=" |-- Args.name) >>
- (Thm.declaration_attribute o K o select_certificates))
- "SMT certificates" #>
- Method.setup (Binding.name "smt") smt_method
- "Applies an SMT solver to the current goal."
-
-
-fun print_setup gen =
- let
- val t = string_of_int (Config.get_generic gen timeout)
- val names = sort_strings (all_solver_names_of (Context.theory_of gen))
- val ns = if null names then [no_solver] else names
- val take_info = (fn (_, []) => NONE | info => SOME info)
- val infos =
- Context.theory_of gen
- |> Symtab.dest o Solvers.get
- |> map_filter (fn (n, (_, info)) => take_info (n, info gen))
- |> sort (prod_ord string_ord (K EQUAL))
- |> map (fn (n, ps) => Pretty.big_list (n ^ ":") ps)
- in
- Pretty.writeln (Pretty.big_list "SMT setup:" [
- Pretty.str ("Current SMT solver: " ^ solver_name_of gen),
- Pretty.str_list "Available SMT solvers: " "" ns,
- Pretty.str ("Current timeout: " ^ t ^ " seconds"),
- 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/smt_translate.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,343 +0,0 @@
-(* Title: HOL/SMT/Tools/smt_translate.ML
- Author: Sascha Boehme, TU Muenchen
-
-Translate theorems into an SMT intermediate format and serialize them.
-*)
-
-signature SMT_TRANSLATE =
-sig
- (* intermediate term structure *)
- datatype squant = SForall | SExists
- datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
- datatype sterm =
- SVar of int |
- SApp of string * sterm list |
- SLet of string * sterm * sterm |
- SQua of squant * string list * sterm spattern list * sterm
-
- (* configuration options *)
- type prefixes = {sort_prefix: string, func_prefix: string}
- type strict = {
- is_builtin_conn: string * typ -> bool,
- is_builtin_pred: string * typ -> bool,
- is_builtin_distinct: bool}
- type builtins = {
- builtin_typ: typ -> string option,
- builtin_num: typ -> int -> string option,
- builtin_fun: string * typ -> term list -> (string * term list) option }
- datatype smt_theory = Integer | Real | Bitvector
- type sign = {
- theories: smt_theory list,
- sorts: string list,
- funcs: (string * (string list * string)) list }
- type config = {
- prefixes: prefixes,
- strict: strict option,
- builtins: builtins,
- serialize: sign -> sterm list -> string }
- type recon = {
- typs: typ Symtab.table,
- terms: term Symtab.table,
- unfolds: thm list,
- assms: thm list option }
-
- val translate: config -> Proof.context -> thm list -> string * recon
-end
-
-structure SMT_Translate: SMT_TRANSLATE =
-struct
-
-(* intermediate term structure *)
-
-datatype squant = SForall | SExists
-
-datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
-
-datatype sterm =
- SVar of int |
- SApp of string * sterm list |
- SLet of string * sterm * sterm |
- SQua of squant * string list * sterm spattern list * sterm
-
-
-
-(* configuration options *)
-
-type prefixes = {sort_prefix: string, func_prefix: string}
-
-type strict = {
- is_builtin_conn: string * typ -> bool,
- is_builtin_pred: string * typ -> bool,
- is_builtin_distinct: bool}
-
-type builtins = {
- builtin_typ: typ -> string option,
- builtin_num: typ -> int -> string option,
- builtin_fun: string * typ -> term list -> (string * term list) option }
-
-datatype smt_theory = Integer | Real | Bitvector
-
-type sign = {
- theories: smt_theory list,
- sorts: string list,
- funcs: (string * (string list * string)) list }
-
-type config = {
- prefixes: prefixes,
- strict: strict option,
- builtins: builtins,
- serialize: sign -> sterm list -> string }
-
-type recon = {
- typs: typ Symtab.table,
- terms: term Symtab.table,
- unfolds: thm list,
- assms: thm list option }
-
-
-
-(* utility functions *)
-
-val dest_funT =
- let
- fun dest Ts 0 T = (rev Ts, T)
- | dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U
- | dest _ _ T = raise TYPE ("dest_funT", [T], [])
- in dest [] end
-
-val quantifier = (fn
- @{const_name All} => SOME SForall
- | @{const_name Ex} => SOME SExists
- | _ => NONE)
-
-fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) =
- if q = qname then group_quant qname (T :: Ts) u else (Ts, t)
- | group_quant _ Ts t = (Ts, t)
-
-fun dest_pat ts (Const (@{const_name pat}, _) $ t) = SPat (rev (t :: ts))
- | dest_pat ts (Const (@{const_name nopat}, _) $ t) = SNoPat (rev (t :: ts))
- | dest_pat ts (Const (@{const_name andpat}, _) $ p $ t) = dest_pat (t::ts) p
- | dest_pat _ t = raise TERM ("dest_pat", [t])
-
-fun dest_trigger (@{term trigger} $ tl $ t) =
- (map (dest_pat []) (HOLogic.dest_list tl), t)
- | dest_trigger t = ([], t)
-
-fun dest_quant qn T t = quantifier qn |> Option.map (fn q =>
- let
- val (Ts, u) = group_quant qn [T] t
- val (ps, b) = dest_trigger u
- in (q, rev Ts, ps, b) end)
-
-fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
- | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
-
-fun prop_of thm = HOLogic.dest_Trueprop (Thm.prop_of thm)
-
-
-
-(* enforce a strict separation between formulas and terms *)
-
-val term_eq_rewr = @{lemma "x term_eq y == x = y" by (simp add: term_eq_def)}
-
-val term_bool = @{lemma "~(True term_eq False)" by (simp add: term_eq_def)}
-val term_bool' = Simplifier.rewrite_rule [term_eq_rewr] term_bool
-
-
-val needs_rewrite = Thm.prop_of #> Term.exists_subterm (fn
- Const (@{const_name Let}, _) => true
- | @{term "op = :: bool => _"} $ _ $ @{term True} => true
- | Const (@{const_name If}, _) $ _ $ @{term True} $ @{term False} => true
- | _ => false)
-
-val rewrite_rules = [
- Let_def,
- @{lemma "P = True == P" by (rule eq_reflection) simp},
- @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
-
-fun rewrite ctxt = Simplifier.full_rewrite
- (Simplifier.context ctxt empty_ss addsimps rewrite_rules)
-
-fun normalize ctxt thm =
- if needs_rewrite thm then Conv.fconv_rule (rewrite ctxt) thm else thm
-
-val unfold_rules = term_eq_rewr :: rewrite_rules
-
-
-val revert_types =
- let
- fun revert @{typ prop} = @{typ bool}
- | revert (Type (n, Ts)) = Type (n, map revert Ts)
- | revert T = T
- in Term.map_types revert end
-
-
-fun strictify {is_builtin_conn, is_builtin_pred, is_builtin_distinct} ctxt =
- let
-
- fun is_builtin_conn' (@{const_name True}, _) = false
- | is_builtin_conn' (@{const_name False}, _) = false
- | is_builtin_conn' c = is_builtin_conn c
-
- val propT = @{typ prop} and boolT = @{typ bool}
- val as_propT = (fn @{typ bool} => propT | T => T)
- fun mapTs f g = Term.strip_type #> (fn (Ts, T) => map f Ts ---> g T)
- fun conn (n, T) = (n, mapTs as_propT as_propT T)
- fun pred (n, T) = (n, mapTs I as_propT T)
-
- val term_eq = @{term "op = :: bool => _"} |> Term.dest_Const |> pred
- fun as_term t = Const term_eq $ t $ @{term True}
-
- val if_term = Const (@{const_name If}, [propT, boolT, boolT] ---> boolT)
- fun wrap_in_if t = if_term $ t $ @{term True} $ @{term False}
-
- fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t))
-
- fun in_term t =
- (case Term.strip_comb t of
- (c as Const (@{const_name If}, _), [t1, t2, t3]) =>
- c $ in_form t1 $ in_term t2 $ in_term t3
- | (h as Const c, ts) =>
- if is_builtin_conn' (conn c) orelse is_builtin_pred (pred c)
- then wrap_in_if (in_form t)
- else Term.list_comb (h, map in_term ts)
- | (h as Free _, ts) => Term.list_comb (h, map in_term ts)
- | _ => t)
-
- and in_pat ((c as Const (@{const_name pat}, _)) $ t) = c $ in_term t
- | in_pat ((c as Const (@{const_name nopat}, _)) $ t) = c $ in_term t
- | in_pat ((c as Const (@{const_name andpat}, _)) $ p $ t) =
- c $ in_pat p $ in_term t
- | in_pat t = raise TERM ("in_pat", [t])
-
- and in_pats p = in_list @{typ pattern} in_pat p
-
- and in_trig ((c as @{term trigger}) $ p $ t) = c $ in_pats p $ in_form t
- | in_trig t = in_form t
-
- and in_form t =
- (case Term.strip_comb t of
- (q as Const (qn, _), [Abs (n, T, t')]) =>
- if is_some (quantifier qn) then q $ Abs (n, T, in_trig t')
- else as_term (in_term t)
- | (Const (c as (@{const_name distinct}, T)), [t']) =>
- if is_builtin_distinct then Const (pred c) $ in_list T in_term t'
- else as_term (in_term t)
- | (Const c, ts) =>
- if is_builtin_conn (conn c)
- then Term.list_comb (Const (conn c), map in_form ts)
- else if is_builtin_pred (pred c)
- then Term.list_comb (Const (pred c), map in_term ts)
- else as_term (in_term t)
- | _ => as_term (in_term t))
- in
- map (normalize ctxt) #> (fn thms => ((unfold_rules, term_bool' :: thms),
- map (in_form o prop_of) (term_bool :: thms)))
- end
-
-
-
-(* translation from Isabelle terms into SMT intermediate terms *)
-
-val empty_context = (1, Typtab.empty, 1, Termtab.empty, [])
-
-fun make_sign (_, typs, _, terms, thys) = {
- theories = thys,
- sorts = Typtab.fold (cons o snd) typs [],
- funcs = Termtab.fold (cons o snd) terms [] }
-
-fun make_recon (unfolds, assms) (_, typs, _, terms, _) = {
- typs = Symtab.make (map swap (Typtab.dest typs)),
- terms = Symtab.make (map (fn (t, (n, _)) => (n, t)) (Termtab.dest terms)),
- unfolds = unfolds,
- assms = SOME assms }
-
-fun string_of_index pre i = pre ^ string_of_int i
-
-fun add_theory T (Tidx, typs, idx, terms, thys) =
- let
- fun add @{typ int} = insert (op =) Integer
- | add @{typ real} = insert (op =) Real
- | add (Type (@{type_name word}, _)) = insert (op =) Bitvector
- | add (Type (_, Ts)) = fold add Ts
- | add _ = I
- in (Tidx, typs, idx, terms, add T thys) end
-
-fun fresh_typ sort_prefix T (cx as (Tidx, typs, idx, terms, thys)) =
- (case Typtab.lookup typs T of
- SOME s => (s, cx)
- | NONE =>
- let
- val s = string_of_index sort_prefix Tidx
- val typs' = Typtab.update (T, s) typs
- in (s, (Tidx+1, typs', idx, terms, thys)) end)
-
-fun fresh_fun func_prefix t ss (cx as (Tidx, typs, idx, terms, thys)) =
- (case Termtab.lookup terms t of
- SOME (f, _) => (f, cx)
- | NONE =>
- let
- val f = string_of_index func_prefix idx
- val terms' = Termtab.update (revert_types t, (f, ss)) terms
- in (f, (Tidx, typs, idx+1, terms', thys)) end)
-
-fun relaxed thms = (([], thms), map prop_of thms)
-
-fun with_context f (ths, ts) =
- let val (us, context) = fold_map f ts empty_context
- in ((make_sign context, us), make_recon ths context) end
-
-
-fun translate {prefixes, strict, builtins, serialize} ctxt =
- let
- val {sort_prefix, func_prefix} = prefixes
- val {builtin_typ, builtin_num, builtin_fun} = builtins
-
- fun transT T = add_theory T #>
- (case builtin_typ T of
- SOME n => pair n
- | NONE => fresh_typ sort_prefix T)
-
- fun app n ts = SApp (n, ts)
-
- fun trans t =
- (case Term.strip_comb t of
- (Const (qn, _), [Abs (_, T, t1)]) =>
- (case dest_quant qn T t1 of
- SOME (q, Ts, ps, b) =>
- fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
- trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', b'))
- | NONE => raise TERM ("intermediate", [t]))
- | (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) =>
- transT T ##>> trans t1 ##>> trans t2 #>>
- (fn ((U, u1), u2) => SLet (U, u1, u2))
- | (h as Const (c as (@{const_name distinct}, T)), [t1]) =>
- (case builtin_fun c (HOLogic.dest_list t1) of
- SOME (n, ts) => add_theory T #> fold_map trans ts #>> app n
- | NONE => transs h T [t1])
- | (h as Const (c as (_, T)), ts) =>
- (case try HOLogic.dest_number t of
- SOME (T, i) =>
- (case builtin_num T i of
- SOME n => add_theory T #> pair (SApp (n, []))
- | NONE => transs t T [])
- | NONE =>
- (case builtin_fun c ts of
- SOME (n, ts') => add_theory T #> fold_map trans ts' #>> app n
- | NONE => transs h T ts))
- | (h as Free (_, T), ts) => transs h T ts
- | (Bound i, []) => pair (SVar i)
- | _ => raise TERM ("intermediate", [t]))
-
- and transs t T ts =
- let val (Us, U) = dest_funT (length ts) T
- in
- fold_map transT Us ##>> transT U #-> (fn Up =>
- fresh_fun func_prefix t Up ##>> fold_map trans ts #>> SApp)
- end
- in
- (if is_some strict then strictify (the strict) ctxt else relaxed) #>
- with_context trans #>> uncurry serialize
- end
-
-end
--- a/src/HOL/SMT/Tools/smtlib_interface.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,214 +0,0 @@
-(* Title: HOL/SMT/Tools/smtlib_interface.ML
- Author: Sascha Boehme, TU Muenchen
-
-Interface to SMT solvers based on the SMT-LIB format.
-*)
-
-signature SMTLIB_INTERFACE =
-sig
- val interface: string list -> SMT_Translate.config
-end
-
-structure SMTLIB_Interface: SMTLIB_INTERFACE =
-struct
-
-structure T = SMT_Translate
-
-fun dest_binT T =
- (case T of
- Type (@{type_name "Numeral_Type.num0"}, _) => 0
- | Type (@{type_name "Numeral_Type.num1"}, _) => 1
- | Type (@{type_name "Numeral_Type.bit0"}, [T]) => 2 * dest_binT T
- | Type (@{type_name "Numeral_Type.bit1"}, [T]) => 1 + 2 * dest_binT T
- | _ => raise TYPE ("dest_binT", [T], []))
-
-fun dest_wordT (Type (@{type_name word}, [T])) = dest_binT T
- | dest_wordT T = raise TYPE ("dest_wordT", [T], [])
-
-
-
-(* builtins *)
-
-fun index1 n i = n ^ "[" ^ string_of_int i ^ "]"
-fun index2 n i j = n ^ "[" ^ string_of_int i ^ ":" ^ string_of_int j ^ "]"
-
-fun builtin_typ @{typ int} = SOME "Int"
- | builtin_typ @{typ real} = SOME "Real"
- | builtin_typ (Type (@{type_name word}, [T])) =
- Option.map (index1 "BitVec") (try dest_binT T)
- | builtin_typ _ = NONE
-
-fun builtin_num @{typ int} i = SOME (string_of_int i)
- | builtin_num @{typ real} i = SOME (string_of_int i ^ ".0")
- | builtin_num (Type (@{type_name word}, [T])) i =
- Option.map (index1 ("bv" ^ string_of_int i)) (try dest_binT T)
- | builtin_num _ _ = NONE
-
-val is_propT = (fn @{typ prop} => true | _ => false)
-fun is_connT T = Term.strip_type T |> (fn (Us, U) => forall is_propT (U :: Us))
-fun is_predT T = is_propT (Term.body_type T)
-
-fun just c ts = SOME (c, ts)
-
-val is_arith_type = member (op =) [@{typ int}, @{typ real}] o Term.domain_type
-
-fun fixed_bvT (Ts, T) x =
- if forall (can dest_wordT) (T :: Ts) then SOME x else NONE
-
-fun if_fixed_bvT' T = fixed_bvT ([], Term.domain_type T)
-fun if_fixed_bvT T = curry (fixed_bvT ([], Term.domain_type T))
-fun if_full_fixed_bvT T = curry (fixed_bvT (Term.strip_type T))
-
-fun dest_word_funT (Type ("fun", [T, U])) = (dest_wordT T, dest_wordT U)
- | dest_word_funT T = raise TYPE ("dest_word_funT", [T], [])
-fun dest_nat (@{term nat} $ n :: ts) = (snd (HOLogic.dest_number n), ts)
- | dest_nat ts = raise TERM ("dest_nat", ts)
-fun dest_nat_word_funT (T, ts) =
- (dest_word_funT (Term.range_type T), dest_nat ts)
-
-fun bv_extend n T ts =
- (case try dest_word_funT T of
- SOME (i, j) => if j-i >= 0 then SOME (index1 n (j-i), ts) else NONE
- | _ => NONE)
-
-fun bv_rotate n T ts =
- try dest_nat ts
- |> Option.map (fn (i, ts') => (index1 n i, ts'))
-
-fun bv_extract n T ts =
- try dest_nat_word_funT (T, ts)
- |> Option.map (fn ((_, i), (lb, ts')) => (index2 n (i + lb - 1) lb, ts'))
-
-
-fun conn @{const_name True} = SOME "true"
- | conn @{const_name False} = SOME "false"
- | conn @{const_name Not} = SOME "not"
- | conn @{const_name "op &"} = SOME "and"
- | conn @{const_name "op |"} = SOME "or"
- | conn @{const_name "op -->"} = SOME "implies"
- | conn @{const_name "op ="} = SOME "iff"
- | conn @{const_name If} = SOME "if_then_else"
- | conn _ = NONE
-
-fun pred @{const_name distinct} _ = SOME "distinct"
- | pred @{const_name "op ="} _ = SOME "="
- | pred @{const_name term_eq} _ = SOME "="
- | pred @{const_name less} T =
- if is_arith_type T then SOME "<"
- else if_fixed_bvT' T "bvult"
- | pred @{const_name less_eq} T =
- if is_arith_type T then SOME "<="
- else if_fixed_bvT' T "bvule"
- | pred @{const_name word_sless} T = if_fixed_bvT' T "bvslt"
- | pred @{const_name word_sle} T = if_fixed_bvT' T "bvsle"
- | pred _ _ = NONE
-
-fun func @{const_name If} _ = just "ite"
- | func @{const_name uminus} T =
- if is_arith_type T then just "~"
- else if_fixed_bvT T "bvneg"
- | func @{const_name plus} T =
- if is_arith_type T then just "+"
- else if_fixed_bvT T "bvadd"
- | func @{const_name minus} T =
- if is_arith_type T then just "-"
- else if_fixed_bvT T "bvsub"
- | func @{const_name times} T =
- if is_arith_type T then just "*"
- else if_fixed_bvT T "bvmul"
- | func @{const_name bitNOT} T = if_fixed_bvT T "bvnot"
- | func @{const_name bitAND} T = if_fixed_bvT T "bvand"
- | func @{const_name bitOR} T = if_fixed_bvT T "bvor"
- | func @{const_name bitXOR} T = if_fixed_bvT T "bvxor"
- | func @{const_name div} T = if_fixed_bvT T "bvudiv"
- | func @{const_name mod} T = if_fixed_bvT T "bvurem"
- | func @{const_name sdiv} T = if_fixed_bvT T "bvsdiv"
- | func @{const_name smod} T = if_fixed_bvT T "bvsmod"
- | func @{const_name srem} T = if_fixed_bvT T "bvsrem"
- | func @{const_name word_cat} T = if_full_fixed_bvT T "concat"
- | func @{const_name bv_shl} T = if_full_fixed_bvT T "bvshl"
- | func @{const_name bv_lshr} T = if_full_fixed_bvT T "bvlshr"
- | func @{const_name bv_ashr} T = if_full_fixed_bvT T "bvashr"
- | func @{const_name slice} T = bv_extract "extract" T
- | func @{const_name ucast} T = bv_extend "zero_extend" T
- | func @{const_name scast} T = bv_extend "sign_extend" T
- | func @{const_name word_rotl} T = bv_rotate "rotate_left" T
- | func @{const_name word_rotr} T = bv_rotate "rotate_right" T
- | func _ _ = K NONE
-
-fun is_builtin_conn (n, T) = is_connT T andalso is_some (conn n)
-fun is_builtin_pred (n, T) = is_predT T andalso is_some (pred n T)
-
-fun builtin_fun (n, T) ts =
- if is_connT T then conn n |> Option.map (rpair ts)
- else if is_predT T then pred n T |> Option.map (rpair ts)
- else func n T ts
-
-
-
-(* serialization *)
-
-val add = Buffer.add
-fun sep f = add " " #> f
-fun enclose l r f = sep (add l #> f #> add r)
-val par = enclose "(" ")"
-fun app n f = (fn [] => sep (add n) | xs => par (add n #> fold f xs))
-fun line f = f #> add "\n"
-
-fun var i = add "?v" #> add (string_of_int i)
-
-fun sterm l (T.SVar i) = sep (var (l - i - 1))
- | sterm l (T.SApp (n, ts)) = app n (sterm l) ts
- | sterm _ (T.SLet _) = raise Fail "SMT-LIB: unsupported let expression"
- | sterm l (T.SQua (q, ss, ps, t)) =
- let
- val quant = add o (fn T.SForall => "forall" | T.SExists => "exists")
- val vs = map_index (apfst (Integer.add l)) ss
- fun var_decl (i, s) = par (var i #> sep (add s))
- val sub = sterm (l + length ss)
- fun pat kind ts = sep (add kind #> enclose "{" " }" (fold sub ts))
- fun pats (T.SPat ts) = pat ":pat" ts
- | pats (T.SNoPat ts) = pat ":nopat" ts
- in par (quant q #> fold var_decl vs #> sub t #> fold pats ps) end
-
-fun choose_logic theories =
- if member (op =) theories T.Bitvector then "QF_AUFBV"
- else if member (op =) theories T.Real then "AUFLIRA"
- else "AUFLIA"
-
-fun serialize comments {theories, sorts, funcs} ts =
- Buffer.empty
- |> line (add "(benchmark Isabelle")
- |> line (add ":status unknown")
- |> line (add ":logic " #> add (choose_logic theories))
- |> length sorts > 0 ?
- line (add ":extrasorts" #> par (fold (sep o add) sorts))
- |> length funcs > 0 ? (
- line (add ":extrafuns" #> add " (") #>
- fold (fn (f, (ss, s)) =>
- line (sep (app f (sep o add) (ss @ [s])))) funcs #>
- line (add ")"))
- |> fold (fn t => line (add ":assumption" #> sterm 0 t)) ts
- |> line (add ":formula true)")
- |> fold (fn str => line (add "; " #> add str)) comments
- |> Buffer.content
-
-
-
-(* interface *)
-
-fun interface comments = {
- prefixes = {
- sort_prefix = "S",
- func_prefix = "f"},
- strict = SOME {
- is_builtin_conn = is_builtin_conn,
- is_builtin_pred = is_builtin_pred,
- is_builtin_distinct = true},
- builtins = {
- builtin_typ = builtin_typ,
- builtin_num = builtin_num,
- builtin_fun = builtin_fun},
- serialize = serialize comments}
-
-end
--- a/src/HOL/SMT/Tools/yices_solver.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,44 +0,0 @@
-(* Title: HOL/SMT/Tools/yices_solver.ML
- Author: Sascha Boehme, TU Muenchen
-
-Interface of the SMT solver Yices.
-*)
-
-signature YICES_SOLVER =
-sig
- val setup: theory -> theory
-end
-
-structure Yices_Solver: YICES_SOLVER =
-struct
-
-val solver_name = "yices"
-val env_var = "YICES_SOLVER"
-
-val options = ["--smtlib"]
-
-fun raise_cex real = raise SMT_Solver.SMT_COUNTEREXAMPLE (real, [])
-
-fun core_oracle (output, _) =
- let
- val empty_line = (fn "" => true | _ => false)
- val split_first = (fn [] => ("", []) | l :: ls => (l, ls))
- val (l, _) = split_first (dropwhile empty_line output)
- in
- if String.isPrefix "unsat" l then @{cprop False}
- else if String.isPrefix "sat" l then raise_cex true
- else if String.isPrefix "unknown" l then raise_cex false
- else raise SMT_Solver.SMT (solver_name ^ " failed")
- end
-
-fun smtlib_solver oracle _ = {
- command = {env_var=env_var, remote_name=NONE},
- arguments = options,
- interface = SMTLIB_Interface.interface,
- reconstruct = pair o oracle }
-
-val setup =
- Thm.add_oracle (Binding.name solver_name, core_oracle) #-> (fn (_, oracle) =>
- SMT_Solver.add_solver (solver_name, smtlib_solver oracle))
-
-end
--- a/src/HOL/SMT/Tools/z3_interface.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,35 +0,0 @@
-(* Title: HOL/SMT/Tools/z3_interface.ML
- Author: Sascha Boehme, TU Muenchen
-
-Interface to Z3 based on a relaxed version of SMT-LIB.
-*)
-
-signature Z3_INTERFACE =
-sig
- val interface: string list -> SMT_Translate.config
-end
-
-structure Z3_Interface: Z3_INTERFACE =
-struct
-
-fun z3_builtin_fun bf c ts =
- (case Const c of
- @{term "op / :: real => _"} => SOME ("/", ts)
- | _ => bf c ts)
-
-fun interface comments =
- let
- val {prefixes, strict, builtins, serialize} =
- SMTLIB_Interface.interface comments
- val {builtin_typ, builtin_num, builtin_fun} = builtins
- in
- {prefixes = prefixes,
- strict = strict,
- builtins = {
- builtin_typ = builtin_typ,
- builtin_num = builtin_num,
- builtin_fun = z3_builtin_fun builtin_fun},
- serialize = serialize}
- end
-
-end
--- a/src/HOL/SMT/Tools/z3_model.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,146 +0,0 @@
-(* Title: HOL/SMT/Tools/z3_model.ML
- Author: Sascha Boehme and Philipp Meyer, TU Muenchen
-
-Parser for counterexamples generated by Z3.
-*)
-
-signature Z3_MODEL =
-sig
- val parse_counterex: SMT_Translate.recon -> string list -> term list
-end
-
-structure Z3_Model: Z3_MODEL =
-struct
-
-(* counterexample expressions *)
-
-datatype expr = True | False | Number of int * int option | Value of int |
- Array of array
-and array = Fresh of expr | Store of (array * expr) * expr
-
-
-(* parsing *)
-
-val space = Scan.many Symbol.is_ascii_blank
-fun in_parens p = Scan.$$ "(" |-- p --| Scan.$$ ")"
-fun in_braces p = (space -- Scan.$$ "{") |-- p --| (space -- Scan.$$ "}")
-
-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 ($$ "-" >> K (fn i => ~i)) I :|--
- (fn sign => nat_num >> sign)
-
-val is_char = Symbol.is_ascii_letter orf Symbol.is_ascii_digit orf
- member (op =) (explode "_+*-/%~=<>$&|?!.@^#")
-val name = Scan.many1 is_char >> implode
-
-fun array_expr st = st |>
- in_parens (space |-- (
- Scan.this_string "const" |-- expr >> Fresh ||
- Scan.this_string "store" -- space |-- array_expr -- expr -- expr >> Store))
-
-and expr st = st |> (space |-- (
- Scan.this_string "true" >> K True ||
- Scan.this_string "false" >> K False ||
- int_num -- Scan.option (Scan.$$ "/" |-- int_num) >> Number ||
- Scan.this_string "val!" |-- nat_num >> Value ||
- array_expr >> Array))
-
-val mapping = space -- Scan.this_string "->"
-val value = mapping |-- expr
-
-val args_case = Scan.repeat expr -- value
-val else_case = space -- Scan.this_string "else" |-- value >>
- pair ([] : expr list)
-
-val func =
- let fun cases st = (else_case >> single || args_case ::: cases) st
- in in_braces cases end
-
-val cex = space |-- Scan.repeat (space |-- name --| mapping --
- (func || expr >> (single o pair [])))
-
-fun read_cex ls =
- explode (cat_lines ls)
- |> try (fst o Scan.finite Symbol.stopper cex)
- |> the_default []
-
-
-(* translation into terms *)
-
-fun lookup_term tab (name, e) = Option.map (rpair e) (Symtab.lookup tab name)
-
-fun with_name_context tab f xs =
- let
- val ns = Symtab.fold (Term.add_free_names o snd) tab []
- val nctxt = Name.make_context ns
- in fst (fold_map f xs (Inttab.empty, nctxt)) end
-
-fun fresh_term T (tab, nctxt) =
- let val (n, nctxt') = yield_singleton Name.variants "" nctxt
- in (Free (n, T), (tab, nctxt')) end
-
-fun term_of_value T i (cx as (tab, _)) =
- (case Inttab.lookup tab i of
- SOME t => (t, cx)
- | NONE =>
- let val (t, (tab', nctxt')) = fresh_term T cx
- in (t, (Inttab.update (i, t) tab', nctxt')) end)
-
-fun trans_expr _ True = pair @{term True}
- | trans_expr _ False = pair @{term False}
- | trans_expr T (Number (i, NONE)) = pair (HOLogic.mk_number T i)
- | trans_expr T (Number (i, SOME j)) =
- pair (Const (@{const_name divide}, [T, T] ---> T) $
- HOLogic.mk_number T i $ HOLogic.mk_number T j)
- | trans_expr T (Value i) = term_of_value T i
- | trans_expr T (Array a) = trans_array T a
-
-and trans_array T a =
- let val dT = Term.domain_type T and rT = Term.range_type T
- in
- (case a of
- Fresh e => trans_expr rT e #>> (fn t => Abs ("x", dT, t))
- | Store ((a', e1), e2) =>
- trans_array T a' ##>> trans_expr dT e1 ##>> trans_expr rT e2 #>>
- (fn ((m, k), v) =>
- Const (@{const_name fun_upd}, [T, dT, rT] ---> T) $ m $ k $ v))
- end
-
-fun trans_pat i T f x =
- f (Term.domain_type T) ##>> trans (i-1) (Term.range_type T) x #>>
- (fn (u, (us, t)) => (u :: us, t))
-
-and trans i T ([], v) =
- if i > 0 then trans_pat i T fresh_term ([], v)
- else trans_expr T v #>> pair []
- | trans i T (p :: ps, v) = trans_pat i T (fn U => trans_expr U p) (ps, v)
-
-fun mk_eq' t us u = HOLogic.mk_eq (Term.list_comb (t, us), u)
-fun mk_eq (Const (@{const_name apply}, _)) (u' :: us', u) = mk_eq' u' us' u
- | mk_eq t (us, u) = mk_eq' t us u
-
-fun translate (t, cs) =
- let val T = Term.fastype_of t
- in
- (case (can HOLogic.dest_number t, cs) of
- (true, [c]) => trans 0 T c #>> (fn (_, u) => [mk_eq u ([], t)])
- | (_, (es, _) :: _) => fold_map (trans (length es) T) cs #>> map (mk_eq t)
- | _ => raise TERM ("translate: no cases", [t]))
- end
-
-
-(* overall procedure *)
-
-fun parse_counterex ({terms, ...} : SMT_Translate.recon) ls =
- read_cex ls
- |> map_filter (lookup_term terms)
- |> with_name_context terms translate
- |> flat
-
-end
--- a/src/HOL/SMT/Tools/z3_proof_literals.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,346 +0,0 @@
-(* Title: HOL/SMT/Tools/z3_proof_literals.ML
- Author: Sascha Boehme, TU Muenchen
-
-Proof tools related to conjunctions and disjunctions.
-*)
-
-signature Z3_PROOF_LITERALS =
-sig
- (* literal table *)
- type littab = thm Termtab.table
- val make_littab: thm list -> littab
- val insert_lit: thm -> littab -> littab
- val delete_lit: thm -> littab -> littab
- val lookup_lit: littab -> term -> thm option
- val get_first_lit: (term -> bool) -> littab -> thm option
-
- (* rules *)
- val true_thm: thm
- val rewrite_true: thm
-
- (* properties *)
- val is_conj: term -> bool
- val is_disj: term -> bool
- val exists_lit: bool -> (term -> bool) -> term -> bool
-
- (* proof tools *)
- val explode: bool -> bool -> bool -> term list -> thm -> thm list
- val join: bool -> littab -> term -> thm
- val prove_conj_disj_eq: cterm -> thm
-end
-
-structure Z3_Proof_Literals: Z3_PROOF_LITERALS =
-struct
-
-structure T = Z3_Proof_Tools
-
-
-
-(** literal table **)
-
-type littab = thm Termtab.table
-
-fun make_littab thms = fold (Termtab.update o `T.prop_of) thms Termtab.empty
-
-fun insert_lit thm = Termtab.update (`T.prop_of thm)
-fun delete_lit thm = Termtab.delete (T.prop_of thm)
-fun lookup_lit lits = Termtab.lookup lits
-fun get_first_lit f =
- Termtab.get_first (fn (t, thm) => if f t then SOME thm else NONE)
-
-
-
-(** rules **)
-
-val true_thm = @{lemma "~False" by simp}
-val rewrite_true = @{lemma "True == ~ False" by simp}
-
-
-
-(** properties and term operations **)
-
-val is_neg = (fn @{term Not} $ _ => true | _ => false)
-fun is_neg' f = (fn @{term Not} $ t => f t | _ => false)
-val is_dneg = is_neg' is_neg
-val is_conj = (fn @{term "op &"} $ _ $ _ => true | _ => false)
-val is_disj = (fn @{term "op |"} $ _ $ _ => true | _ => false)
-
-fun dest_disj_term' f = (fn
- @{term Not} $ (@{term "op |"} $ t $ u) => SOME (f t, f u)
- | _ => NONE)
-
-val dest_conj_term = (fn @{term "op &"} $ t $ u => SOME (t, u) | _ => NONE)
-val dest_disj_term =
- dest_disj_term' (fn @{term Not} $ t => t | t => @{term Not} $ t)
-
-fun exists_lit is_conj P =
- let
- val dest = if is_conj then dest_conj_term else dest_disj_term
- fun exists t = P t orelse
- (case dest t of
- SOME (t1, t2) => exists t1 orelse exists t2
- | NONE => false)
- in exists end
-
-
-
-(** proof tools **)
-
-(* explosion of conjunctions and disjunctions *)
-
-local
- fun destc ct = Thm.dest_binop (Thm.dest_arg ct)
- val dest_conj1 = T.precompose2 destc @{thm conjunct1}
- val dest_conj2 = T.precompose2 destc @{thm conjunct2}
- fun dest_conj_rules t =
- dest_conj_term t |> Option.map (K (dest_conj1, dest_conj2))
-
- fun destd f ct = f (Thm.dest_binop (Thm.dest_arg (Thm.dest_arg ct)))
- val dn1 = apfst Thm.dest_arg and dn2 = apsnd Thm.dest_arg
- val dest_disj1 = T.precompose2 (destd I) @{lemma "~(P | Q) ==> ~P" by fast}
- val dest_disj2 = T.precompose2 (destd dn1) @{lemma "~(~P | Q) ==> P" by fast}
- val dest_disj3 = T.precompose2 (destd I) @{lemma "~(P | Q) ==> ~Q" by fast}
- val dest_disj4 = T.precompose2 (destd dn2) @{lemma "~(P | ~Q) ==> Q" by fast}
-
- fun dest_disj_rules t =
- (case dest_disj_term' is_neg t of
- SOME (true, true) => SOME (dest_disj2, dest_disj4)
- | SOME (true, false) => SOME (dest_disj2, dest_disj3)
- | SOME (false, true) => SOME (dest_disj1, dest_disj4)
- | SOME (false, false) => SOME (dest_disj1, dest_disj3)
- | NONE => NONE)
-
- fun destn ct = [Thm.dest_arg (Thm.dest_arg (Thm.dest_arg ct))]
- val dneg_rule = T.precompose destn @{thm notnotD}
-in
-
-(* explode a term into literals and collect all rules to be able to deduce
- particular literals afterwards *)
-fun explode_term is_conj =
- let
- val dest = if is_conj then dest_conj_term else dest_disj_term
- val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
-
- fun add (t, rs) = Termtab.map_default (t, rs)
- (fn rs' => if length rs' < length rs then rs' else rs)
-
- fun explode1 rules t =
- (case dest t of
- SOME (t1, t2) =>
- let val (rule1, rule2) = the (dest_rules t)
- in
- explode1 (rule1 :: rules) t1 #>
- explode1 (rule2 :: rules) t2 #>
- add (t, rev rules)
- end
- | NONE => add (t, rev rules))
-
- fun explode0 (@{term Not} $ (@{term Not} $ t)) =
- Termtab.make [(t, [dneg_rule])]
- | explode0 t = explode1 [] t Termtab.empty
-
- in explode0 end
-
-(* extract a literal by applying previously collected rules *)
-fun extract_lit thm rules = fold T.compose rules thm
-
-
-(* explode a theorem into its literals *)
-fun explode is_conj full keep_intermediate stop_lits =
- let
- val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
- val tab = fold (Termtab.update o rpair ()) stop_lits Termtab.empty
-
- fun explode1 thm =
- if Termtab.defined tab (T.prop_of thm) then cons thm
- else
- (case dest_rules (T.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) (T.prop_of thm)
- then explode1 (T.compose dest_rule thm)
- else cons (T.compose dest_rule thm)
-
- fun explode0 thm =
- if not is_conj andalso is_dneg (T.prop_of thm)
- then [T.compose dneg_rule thm]
- else explode1 thm []
-
- in explode0 end
-
-end
-
-
-
-(* joining of literals to conjunctions or disjunctions *)
-
-local
- fun on_cprem i f thm = f (Thm.cprem_of thm i)
- fun on_cprop f thm = f (Thm.cprop_of thm)
- fun precomp2 f g thm = (on_cprem 1 f thm, on_cprem 2 g thm, f, g, thm)
- fun comp2 (cv1, cv2, f, g, rule) thm1 thm2 =
- Thm.instantiate ([], [(cv1, on_cprop f thm1), (cv2, on_cprop g thm2)]) rule
- |> T.discharge thm1 |> T.discharge thm2
-
- fun d1 ct = Thm.dest_arg ct and d2 ct = Thm.dest_arg (Thm.dest_arg ct)
-
- val conj_rule = precomp2 d1 d1 @{thm conjI}
- fun comp_conj ((_, thm1), (_, thm2)) = comp2 conj_rule thm1 thm2
-
- val disj1 = precomp2 d2 d2 @{lemma "~P ==> ~Q ==> ~(P | Q)" by fast}
- val disj2 = precomp2 d2 d1 @{lemma "~P ==> Q ==> ~(P | ~Q)" by fast}
- val disj3 = precomp2 d1 d2 @{lemma "P ==> ~Q ==> ~(~P | Q)" by fast}
- val disj4 = precomp2 d1 d1 @{lemma "P ==> Q ==> ~(~P | ~Q)" by fast}
-
- fun comp_disj ((false, thm1), (false, thm2)) = comp2 disj1 thm1 thm2
- | comp_disj ((false, thm1), (true, thm2)) = comp2 disj2 thm1 thm2
- | comp_disj ((true, thm1), (false, thm2)) = comp2 disj3 thm1 thm2
- | comp_disj ((true, thm1), (true, thm2)) = comp2 disj4 thm1 thm2
-
- fun dest_conj (@{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 = T.precompose (single o d2 o d1) @{thm notnotD}
- val dnegI = T.precompose (single o d1) @{lemma "P ==> ~~P" by fast}
- fun as_dneg f t = f (@{term Not} $ (@{term Not} $ t))
-
- fun dni f = apsnd f o Thm.dest_binop o f o d1
- val negIffE = T.precompose2 (dni d1) @{lemma "~(P = (~Q)) ==> Q = P" by fast}
- val negIffI = T.precompose2 (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 join is_conj littab t =
- let
- val comp = if is_conj then comp_conj else comp_disj
- val dest = if is_conj then dest_conj else dest_disj
-
- val lookup = lookup_lit littab
-
- fun lookup_rule t =
- (case t of
- @{term Not} $ (@{term Not} $ t) => (T.compose dnegI, lookup t)
- | @{term Not} $ (@{term "op = :: bool => _"} $ t $ (@{term Not} $ u)) =>
- (T.compose negIffI, lookup (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 (@{term Not} $ (eq $ u $ t))) end
- | _ =>
- (case as_dneg lookup t of
- NONE => (T.compose negIffE, as_negIff lookup t)
- | x => (T.compose dnegE, x)))
-
- fun join1 (s, t) =
- (case lookup t of
- SOME lit => (s, lit)
- | NONE =>
- (case lookup_rule t of
- (rewrite, SOME lit) => (s, rewrite lit)
- | (_, NONE) => (s, comp (pairself join1 (dest t)))))
-
- in snd (join1 (if is_conj then (false, t) else (true, t))) end
-
-end
-
-
-
-(* proving equality of conjunctions or disjunctions *)
-
-fun iff_intro thm1 thm2 = thm2 COMP (thm1 COMP @{thm iffI})
-
-local
- val cp1 = @{lemma "(~P) = (~Q) ==> P = Q" by simp}
- val cp2 = @{lemma "(~P) = Q ==> P = (~Q)" by 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
- val contra_rule = @{lemma "P ==> ~P ==> False" by (rule notE)}
- fun contra_left conj thm =
- let
- val rules = explode_term conj (T.prop_of thm)
- fun contra_lits (t, rs) =
- (case t of
- @{term Not} $ u => Termtab.lookup rules u |> Option.map (pair rs)
- | _ => NONE)
- in
- (case Termtab.lookup rules @{term False} of
- SOME rs => extract_lit thm rs
- | NONE =>
- the (Termtab.get_first contra_lits rules)
- |> pairself (extract_lit thm)
- |> (fn (nlit, plit) => nlit COMP (plit COMP contra_rule)))
- end
-
- val falseE_v = Thm.dest_arg (Thm.dest_arg (Thm.cprop_of @{thm FalseE}))
- fun contra_right ct = Thm.instantiate ([], [(falseE_v, ct)]) @{thm FalseE}
-in
-fun contradict conj ct =
- iff_intro (T.under_assumption (contra_left conj) ct) (contra_right ct)
-end
-
-
-local
- fun prove_eq l r (cl, cr) =
- let
- fun explode' is_conj = explode is_conj true (l <> r) []
- fun make_tab is_conj thm = make_littab (true_thm :: explode' is_conj thm)
- fun prove is_conj ct tab = join is_conj tab (Thm.term_of ct)
-
- val thm1 = T.under_assumption (prove r cr o make_tab l) cl
- val thm2 = T.under_assumption (prove l cl o make_tab r) cr
- in iff_intro thm1 thm2 end
-
- datatype conj_disj = CONJ | DISJ | NCON | NDIS
- fun kind_of t =
- if is_conj t then SOME CONJ
- else if is_disj t then SOME DISJ
- else if is_neg' is_conj t then SOME NCON
- else if is_neg' is_disj t then SOME NDIS
- else NONE
-in
-
-fun prove_conj_disj_eq ct =
- let val cp as (cl, cr) = Thm.dest_binop (Thm.dest_arg ct)
- in
- (case (kind_of (Thm.term_of cl), Thm.term_of cr) of
- (SOME CONJ, @{term False}) => contradict true cl
- | (SOME DISJ, @{term "~False"}) => contrapos2 (contradict false o fst) cp
- | (kl, _) =>
- (case (kl, kind_of (Thm.term_of cr)) of
- (SOME CONJ, SOME CONJ) => prove_eq true true cp
- | (SOME CONJ, SOME NDIS) => prove_eq true false cp
- | (SOME CONJ, _) => prove_eq true true cp
- | (SOME DISJ, SOME DISJ) => contrapos1 (prove_eq false false) cp
- | (SOME DISJ, SOME NCON) => contrapos2 (prove_eq false true) cp
- | (SOME DISJ, _) => contrapos1 (prove_eq false false) cp
- | (SOME NCON, SOME NCON) => contrapos1 (prove_eq true true) cp
- | (SOME NCON, SOME DISJ) => contrapos3 (prove_eq true false) cp
- | (SOME NCON, NONE) => contrapos3 (prove_eq true false) cp
- | (SOME NDIS, SOME NDIS) => prove_eq false false cp
- | (SOME NDIS, SOME CONJ) => prove_eq false true cp
- | (SOME NDIS, NONE) => prove_eq false true cp
- | _ => raise CTERM ("prove_conj_disj_eq", [ct])))
- end
-
-end
-
-end
--- a/src/HOL/SMT/Tools/z3_proof_parser.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,499 +0,0 @@
-(* Title: HOL/SMT/Tools/z3_proof_parser.ML
- Author: Sascha Boehme, TU Muenchen
-
-Parser for Z3 proofs.
-*)
-
-signature Z3_PROOF_PARSER =
-sig
- (* proof rules *)
- 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 string_of_rule: rule -> string
-
- (* proof parser *)
- datatype proof_step = Proof_Step of {
- rule: rule,
- prems: int list,
- prop: cterm }
- val parse: Proof.context -> typ Symtab.table -> term Symtab.table ->
- string list ->
- int * (proof_step Inttab.table * string list * Proof.context)
-end
-
-structure Z3_Proof_Parser: Z3_PROOF_PARSER =
-struct
-
-(** proof rules **)
-
-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)]
-
-fun string_of_rule r =
- let fun eq_rule (s, r') = if r = r' then SOME s else NONE
- in the (Symtab.get_first eq_rule rule_names) end
-
-
-
-(** certified terms and variables **)
-
-val (var_prefix, decl_prefix) = ("v", "sk") (* must be distinct *)
-
-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
-
-fun ctyp_of (ct, _) = Thm.ctyp_of_term ct
-fun instT' t = instT (ctyp_of t)
-
-fun certify ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
-
-val maxidx_of = #maxidx o Thm.rep_cterm
-
-fun mk_inst ctxt vars =
- let
- val max = fold (Integer.max o fst) vars 0
- val ns = fst (Variable.variant_fixes (replicate (max + 1) var_prefix) ctxt)
- fun mk (i, v) = (v, certify ctxt (Free (nth ns i, #T (Thm.rep_cterm v))))
- in map mk vars end
-
-fun close ctxt (ct, vars) =
- let
- val inst = mk_inst ctxt vars
- val mk_prop = Thm.capply @{cterm Trueprop}
- val names = fold (Term.add_free_names o Thm.term_of o snd) inst []
- in (mk_prop (Thm.instantiate_cterm ([], inst) ct), names) end
-
-
-fun mk_bound thy (i, T) =
- let val ct = Thm.cterm_of thy (Var ((Name.uu, 0), T))
- in (ct, [(i, ct)]) end
-
-local
- fun mk_quant thy q T (ct, vars) =
- let
- val cv =
- (case AList.lookup (op =) vars 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 (Thm.capply cq (Thm.cabs cv ct), map_filter dec vars) end
-
- val forall = mk_inst_pair (destT1 o destT1) @{cpat All}
- val exists = mk_inst_pair (destT1 o destT1) @{cpat Ex}
-in
-fun mk_forall thy = fold_rev (mk_quant thy forall)
-fun mk_exists thy = fold_rev (mk_quant thy exists)
-end
-
-
-local
- fun equal_var cv (_, cu) = (cv aconvc cu)
-
- fun apply (ct2, vars2) (ct1, vars1) =
- let
- val incr = Thm.incr_indexes_cterm (maxidx_of ct1 + maxidx_of ct2 + 2)
-
- fun part (v as (i, cv)) =
- (case AList.lookup (op =) vars1 i of
- SOME cu => apfst (if cu aconvc cv then I else cons (cv, cu))
- | NONE =>
- if not (exists (equal_var cv) vars1) then apsnd (cons v)
- else
- let val cv' = incr cv
- in apfst (cons (cv, cv')) #> apsnd (cons (i, cv')) end)
-
- val (ct2', vars2') =
- if null vars1 then (ct2, vars2)
- else fold part vars2 ([], [])
- |>> (fn inst => Thm.instantiate_cterm ([], inst) ct2)
-
- in (Thm.capply ct1 ct2', vars1 @ vars2') end
-in
-fun mk_fun ct ts = fold apply ts (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
-
-
-val mk_true = mk_fun @{cterm "~False"} []
-val mk_false = mk_fun @{cterm "False"} []
-fun mk_not t = mk_fun @{cterm Not} [t]
-val mk_imp = 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 e) es]
-
-
-(* arithmetic *)
-
-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 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_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 => _"}
-
-
-(* arrays *)
-
-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 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 array)
- in mk_fun (instTs cTs update) [array, index, value] end
-
-
-(* bitvectors *)
-
-fun mk_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 mk_wordT size = Type (@{type_name "word"}, [mk_binT size])
-
-fun mk_bv_num thy (num, size) =
- mk_fun (Numeral.mk_cnumber (Thm.ctyp_of thy (mk_wordT size)) num) []
-
-
-
-(** proof parser **)
-
-datatype proof_step = Proof_Step of {
- rule: rule,
- prems: int list,
- prop: cterm }
-
-
-(* parser context *)
-
-fun make_context ctxt typs terms =
- let
- val ctxt' =
- ctxt
- |> Symtab.fold (Variable.declare_typ o snd) typs
- |> Symtab.fold (Variable.declare_term o snd) terms
-
- fun cert @{term True} = @{cterm "~False"}
- | cert t = certify ctxt' t
- in (typs, Symtab.map cert terms, Inttab.empty, Inttab.empty, [], ctxt') end
-
-fun fresh_name n (typs, terms, exprs, steps, vars, ctxt) =
- let val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
- in (n', (typs, terms, exprs, steps, vars, ctxt')) end
-
-fun theory_of (_, _, _, _, _, ctxt) = ProofContext.theory_of ctxt
-
-fun typ_of_sort n (cx as (typs, _, _, _, _, _)) =
- (case Symtab.lookup typs n of
- SOME T => (T, cx)
- | NONE => cx
- |> fresh_name ("'" ^ n) |>> TFree o rpair @{sort type}
- |> (fn (T, (typs, terms, exprs, steps, vars, ctxt)) =>
- (T, (Symtab.update (n, T) typs, terms, exprs, steps, vars, ctxt))))
-
-fun add_decl (n, T) (cx as (_, terms, _, _, _, _)) =
- (case Symtab.lookup terms n of
- SOME _ => cx
- | NONE => cx |> fresh_name (decl_prefix ^ n)
- |> (fn (m, (typs, terms, exprs, steps, vars, ctxt)) =>
- let val upd = Symtab.update (n, certify ctxt (Free (m, T)))
- in (typs, upd terms, exprs, steps, vars, ctxt) end))
-
-datatype sym = Sym of string * sym list
-
-fun mk_app _ (Sym ("true", _), _) = SOME mk_true
- | mk_app _ (Sym ("false", _), _) = SOME mk_false
- | mk_app _ (Sym ("=", _), [t, u]) = SOME (mk_eq t u)
- | mk_app _ (Sym ("distinct", _), ts) = SOME (mk_distinct ts)
- | mk_app _ (Sym ("ite", _), [s, t, u]) = SOME (mk_if s t u)
- | mk_app _ (Sym ("and", _), ts) = SOME (mk_nary @{cterm "op &"} mk_true ts)
- | mk_app _ (Sym ("or", _), ts) = SOME (mk_nary @{cterm "op |"} mk_false ts)
- | mk_app _ (Sym ("iff", _), [t, u]) = SOME (mk_iff t u)
- | mk_app _ (Sym ("xor", _), [t, u]) = SOME (mk_not (mk_iff t u))
- | mk_app _ (Sym ("not", _), [t]) = SOME (mk_not t)
- | mk_app _ (Sym ("implies", _), [t, u]) = SOME (mk_imp t u)
- | mk_app _ (Sym ("~", _), [t, u]) = SOME (mk_iff t u)
- | mk_app _ (Sym ("<", _), [t, u]) = SOME (mk_lt t u)
- | mk_app _ (Sym ("<=", _), [t, u]) = SOME (mk_le t u)
- | mk_app _ (Sym (">", _), [t, u]) = SOME (mk_lt u t)
- | mk_app _ (Sym (">=", _), [t, u]) = SOME (mk_le u t)
- | mk_app _ (Sym ("+", _), [t, u]) = SOME (mk_add t u)
- | mk_app _ (Sym ("-", _), [t, u]) = SOME (mk_sub t u)
- | mk_app _ (Sym ("-", _), [t]) = SOME (mk_uminus t)
- | mk_app _ (Sym ("*", _), [t, u]) = SOME (mk_mul t u)
- | mk_app _ (Sym ("/", _), [t, u]) = SOME (mk_real_div t u)
- | mk_app _ (Sym ("div", _), [t, u]) = SOME (mk_int_div t u)
- | mk_app _ (Sym ("mod", _), [t, u]) = SOME (mk_mod t u)
- | mk_app _ (Sym ("select", _), [m, k]) = SOME (mk_access m k)
- | mk_app _ (Sym ("store", _), [m, k, v]) = SOME (mk_update m k v)
- | mk_app _ (Sym ("pattern", _), _) = SOME mk_true
- | mk_app (_, terms, _, _, _, _) (Sym (n, _), ts) =
- Symtab.lookup terms n |> Option.map (fn ct => mk_fun ct ts)
-
-fun add_expr k t (typs, terms, exprs, steps, vars, ctxt) =
- (typs, terms, Inttab.update (k, t) exprs, steps, vars, ctxt)
-
-fun lookup_expr (_, _, exprs, _, _, _) = Inttab.lookup exprs
-
-fun add_proof_step k ((r, prems), prop) cx =
- let
- val (typs, terms, exprs, steps, vars, ctxt) = cx
- val (ct, vs) = close ctxt prop
- val step = Proof_Step {rule=r, prems=prems, prop=ct}
- val vars' = union (op =) vs vars
- in (typs, terms, exprs, Inttab.update (k, step) steps, vars', ctxt) end
-
-fun finish (_, _, _, steps, vars, ctxt) = (steps, vars, ctxt)
-
-
-(* core parser *)
-
-fun parse_exn line_no msg = raise SMT_Solver.SMT ("Z3 proof parser (line " ^
- string_of_int line_no ^ "): " ^ msg)
-
-fun scan_exn msg ((line_no, _), _) = parse_exn line_no msg
-
-fun with_info f cx =
- (case f ((NONE, 1), cx) of
- ((SOME root, _), cx') => (root, cx')
- | ((_, line_no), _) => parse_exn line_no "bad proof")
-
-fun parse_line _ _ (st as ((SOME _, _), _)) = st
- | parse_line scan line ((_, line_no), cx) =
- let val st = ((line_no, cx), explode line)
- in
- (case Scan.catch (Scan.finite' Symbol.stopper (Scan.option scan)) st of
- (SOME r, ((_, cx'), _)) => ((r, line_no+1), cx')
- | (NONE, _) => parse_exn line_no ("bad proof line: " ^ quote line))
- end
-
-fun with_context f x ((line_no, cx), st) =
- let val (y, cx') = f x cx
- in (y, ((line_no, cx'), st)) end
-
-
-fun lookup_context f x (st as ((_, cx), _)) = (f cx x, st)
-
-
-(* parser combinators and parsers for basic entities *)
-
-fun $$ s = Scan.lift (Scan.$$ s)
-fun this s = Scan.lift (Scan.this_string s)
-fun blank st = Scan.lift (Scan.many1 Symbol.is_ascii_blank) st
-fun sep scan = blank |-- scan
-fun seps scan = Scan.repeat (sep scan)
-fun seps1 scan = Scan.repeat1 (sep scan)
-fun seps_by scan_sep scan = scan ::: Scan.repeat (scan_sep |-- scan)
-
-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)
-
-fun mk_num ds = fold (fn d => fn i => i * 10 + d) ds 0
-val nat_num = Scan.lift (Scan.repeat1 (Scan.some digit)) >> mk_num
-val int_num = Scan.optional ($$ "-" >> K (fn i => ~i)) I :|--
- (fn sign => nat_num >> sign)
-
-val is_char = Symbol.is_ascii_letter orf Symbol.is_ascii_digit orf
- member (op =) (explode "_+*-/%~=<>$&|?!.@^#")
-val name = Scan.lift (Scan.many1 is_char) >> implode
-
-fun sym st = (name -- Scan.optional (bra (seps_by ($$ ":") sym)) [] >> Sym) st
-
-fun id st = ($$ "#" |-- nat_num) st
-
-
-(* parsers for various parts of Z3 proofs *)
-
-fun sort st = Scan.first [
- this "bool" >> K @{typ bool},
- this "int" >> K @{typ int},
- this "real" >> K @{typ real},
- this "bv" |-- bra nat_num >> mk_wordT,
- this "array" |-- bra (sort --| $$ ":" -- sort) >> (op -->),
- par (this "->" |-- seps1 sort) >> ((op --->) o split_last),
- name :|-- with_context typ_of_sort] st
-
-fun bound st = (par (this ":var" |-- sep nat_num -- sep sort) :|--
- lookup_context (mk_bound o theory_of)) st
-
-fun number st = st |> (
- int_num -- Scan.option ($$ "/" |-- int_num) --| this "::" :|--
- (fn num as (n, _) =>
- this "int" >> K (mk_int_num n) ||
- this "real" >> K (mk_real_frac_num num)))
-
-fun bv_number st = (this "bv" |-- bra (nat_num --| $$ ":" -- nat_num) :|--
- lookup_context (mk_bv_num o theory_of)) st
-
-fun appl (app as (Sym (n, _), _)) = lookup_context mk_app app :|-- (fn
- SOME app' => Scan.succeed app'
- | NONE => scan_exn ("unknown function: " ^ quote n))
-
-fun constant st = ((sym >> rpair []) :|-- appl) st
-
-fun expr_id st = (id :|-- (fn i => lookup_context lookup_expr i :|-- (fn
- SOME e => Scan.succeed e
- | NONE => scan_exn ("unknown term id: " ^ quote (string_of_int i))))) st
-
-fun arg st = Scan.first [expr_id, number, bv_number, constant] st
-
-fun application st = par ((sym -- Scan.repeat1 (sep arg)) :|-- appl) st
-
-fun variables st = par (this "vars" |-- seps1 (par (name |-- sep sort))) st
-
-fun patterns st = seps (par ((this ":pat" || this ":nopat") |-- seps1 id)) st
-
-fun quant_kind st = st |> (
- this "forall" >> K (mk_forall o theory_of) ||
- this "exists" >> K (mk_exists o theory_of))
-
-fun quantifier st =
- (par (quant_kind -- sep variables --| patterns -- sep arg) :|--
- lookup_context (fn cx => fn ((mk_q, Ts), body) => mk_q cx Ts body)) st
-
-fun expr k =
- Scan.first [bound, quantifier, application, number, bv_number, constant] :|--
- with_context (pair NONE oo add_expr k)
-
-fun rule_name st = ((name >> `(Symtab.lookup rule_names)) :|-- (fn
- (SOME r, _) => Scan.succeed r
- | (NONE, n) => scan_exn ("unknown proof rule: " ^ quote n))) st
-
-fun rule f k =
- bra (rule_name -- seps id) --| $$ ":" -- sep arg #->
- with_context (pair (f k) oo add_proof_step k)
-
-fun decl st = (this "decl" |-- sep name --| sep (this "::") -- sep sort :|--
- with_context (pair NONE oo add_decl)) st
-
-fun def st = (id --| sep (this ":=")) st
-
-fun node st = st |> (
- decl ||
- def :|-- (fn k => sep (expr k) || sep (rule (K NONE) k)) ||
- rule SOME ~1)
-
-
-(* overall parser *)
-
-(* Currently, terms are parsed bottom-up (i.e., along with parsing the proof
- text line by line), but proofs are reconstructed top-down (i.e. by an
- in-order top-down traversal of the proof tree/graph). The latter approach
- was taken because some proof texts comprise irrelevant proof steps which
- will thus not be reconstructed. This approach might also be beneficial
- for constructing terms, but it would also increase the complexity of the
- (otherwise rather modular) code. *)
-
-fun parse ctxt typs terms proof_text =
- make_context ctxt typs terms
- |> with_info (fold (parse_line node) proof_text)
- ||> finish
-
-end
--- a/src/HOL/SMT/Tools/z3_proof_reconstruction.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,821 +0,0 @@
-(* Title: HOL/SMT/Tools/z3_proof_reconstruction.ML
- Author: Sascha Boehme, TU Muenchen
-
-Proof reconstruction for proofs found by Z3.
-*)
-
-signature Z3_PROOF_RECONSTRUCTION =
-sig
- val trace_assms: bool Config.T
- val reconstruct: string list * SMT_Translate.recon -> Proof.context ->
- thm * Proof.context
- val setup: theory -> theory
-end
-
-structure Z3_Proof_Reconstruction: Z3_PROOF_RECONSTRUCTION =
-struct
-
-structure P = Z3_Proof_Parser
-structure T = Z3_Proof_Tools
-structure L = Z3_Proof_Literals
-
-fun z3_exn msg = raise SMT_Solver.SMT ("Z3 proof reconstruction: " ^ msg)
-
-
-
-(** net of schematic rules **)
-
-val z3_ruleN = "z3_rule"
-
-local
- val description = "declaration of Z3 proof rules"
-
- val eq = Thm.eq_thm
-
- structure Z3_Rules = Generic_Data
- (
- type T = thm Net.net
- val empty = Net.empty
- val extend = I
- val merge = Net.merge eq
- )
-
- val prep = `Thm.prop_of o Simplifier.rewrite_rule [L.rewrite_true]
-
- fun ins thm net = Net.insert_term eq (prep thm) net handle Net.INSERT => net
- fun del thm net = Net.delete_term eq (prep thm) net handle Net.DELETE => net
-
- val add = Thm.declaration_attribute (Z3_Rules.map o ins)
- val del = Thm.declaration_attribute (Z3_Rules.map o del)
-in
-
-fun get_schematic_rules ctxt = Net.content (Z3_Rules.get (Context.Proof ctxt))
-
-fun by_schematic_rule ctxt ct =
- the (T.net_instance (Z3_Rules.get (Context.Proof ctxt)) ct)
-
-val z3_rules_setup =
- Attrib.setup (Binding.name z3_ruleN) (Attrib.add_del add del) description #>
- PureThy.add_thms_dynamic (Binding.name z3_ruleN, Net.content o Z3_Rules.get)
-
-end
-
-
-
-(** proof tools **)
-
-fun named ctxt name prover ct =
- let val _ = SMT_Solver.trace_msg ctxt I ("Z3: trying " ^ name ^ " ...")
- in prover ct end
-
-fun NAMED ctxt name tac i st =
- let val _ = SMT_Solver.trace_msg ctxt I ("Z3: trying " ^ name ^ " ...")
- in tac i st end
-
-fun pretty_goal ctxt thms t =
- [Pretty.block [Pretty.str "proposition: ", Syntax.pretty_term ctxt t]]
- |> not (null thms) ? cons (Pretty.big_list "assumptions:"
- (map (Display.pretty_thm ctxt) thms))
-
-fun try_apply ctxt thms =
- let
- fun try_apply_err ct = Pretty.string_of (Pretty.chunks [
- Pretty.big_list ("Z3 found a proof," ^
- " but proof reconstruction failed at the following subgoal:")
- (pretty_goal ctxt thms (Thm.term_of ct)),
- Pretty.str ("Adding a rule to the lemma group " ^ quote z3_ruleN ^
- " might solve this problem.")])
-
- fun apply [] ct = error (try_apply_err ct)
- | apply (prover :: provers) ct =
- (case try prover ct of
- SOME thm => (SMT_Solver.trace_msg ctxt I "Z3: succeeded"; thm)
- | NONE => apply provers ct)
-
- in apply o cons (named ctxt "schematic rules" (by_schematic_rule ctxt)) end
-
-
-
-(** theorems and proofs **)
-
-(* theorem incarnations *)
-
-datatype theorem =
- Thm of thm | (* theorem without special features *)
- MetaEq of thm | (* meta equality "t == s" *)
- Literals of thm * L.littab
- (* "P1 & ... & Pn" and table of all literals P1, ..., Pn *)
-
-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 = mk_meta_eq (thm_of p)
-
-fun literals_of (Literals (_, lits)) = lits
- | literals_of p = L.make_littab [thm_of p]
-
-
-(* proof representation *)
-
-datatype proof = Unproved of P.proof_step | Proved of theorem
-
-
-
-(** core proof rules **)
-
-(* assumption *)
-
-val (trace_assms, trace_assms_setup) =
- Attrib.config_bool "z3_trace_assms" (K false)
-
-local
- val remove_trigger = @{lemma "trigger t p == p"
- by (rule eq_reflection, rule trigger_def)}
-
- val prep_rules = [@{thm Let_def}, remove_trigger, L.rewrite_true]
-
- fun rewrite_conv ctxt eqs = Simplifier.full_rewrite
- (Simplifier.context ctxt Simplifier.empty_ss addsimps eqs)
-
- fun rewrites ctxt eqs = map (Conv.fconv_rule (rewrite_conv ctxt eqs))
-
- fun trace ctxt thm =
- if Config.get ctxt trace_assms
- then tracing (Display.string_of_thm ctxt thm)
- else ()
-
- fun lookup_assm ctxt assms ct =
- (case T.net_instance assms ct of
- SOME thm => (trace ctxt thm; thm)
- | _ => z3_exn ("not asserted: " ^
- quote (Syntax.string_of_term ctxt (Thm.term_of ct))))
-in
-fun prepare_assms ctxt unfolds assms =
- let
- val unfolds' = rewrites ctxt [L.rewrite_true] unfolds
- val assms' = rewrites ctxt (union Thm.eq_thm unfolds' prep_rules) assms
- in (unfolds', T.thm_net_of assms') end
-
-fun asserted _ NONE ct = Thm (Thm.assume ct)
- | asserted ctxt (SOME (unfolds, assms)) ct =
- let val revert_conv = rewrite_conv ctxt unfolds
- in Thm (T.with_conv revert_conv (lookup_assm ctxt assms) ct) end
-end
-
-
-
-(* P = Q ==> P ==> Q or P --> Q ==> P ==> Q *)
-local
- val meta_iffD1 = @{lemma "P == Q ==> P ==> (Q::bool)" by simp}
- val meta_iffD1_c = T.precompose2 Thm.dest_binop meta_iffD1
-
- val iffD1_c = T.precompose2 (Thm.dest_binop o Thm.dest_arg) @{thm iffD1}
- val mp_c = T.precompose2 (Thm.dest_binop o Thm.dest_arg) @{thm mp}
-in
-fun mp (MetaEq thm) p = Thm (Thm.implies_elim (T.compose meta_iffD1_c thm) p)
- | mp p_q p =
- let
- val pq = thm_of p_q
- val thm = T.compose iffD1_c pq handle THM _ => T.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 is_sublit conj t = L.exists_lit conj (fn u => u aconv t)
-
- fun derive conj t lits idx ptab =
- let
- val lit = the (L.get_first_lit (is_sublit conj t) lits)
- val ls = L.explode conj false false [t] lit
- val lits' = fold L.insert_lit ls (L.delete_lit lit lits)
-
- fun upd (Proved thm) = Proved (Literals (thm_of thm, lits'))
- | upd p = p
- in (the (L.lookup_lit lits' t), Inttab.map_entry idx upd ptab) end
-
- fun lit_elim conj (p, idx) ct ptab =
- let val lits = literals_of p
- in
- (case L.lookup_lit lits (T.term_of ct) of
- SOME lit => (Thm lit, ptab)
- | NONE => apfst Thm (derive conj (T.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 = L.explode 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 = T.precompose dest_ccontr @{thm ccontr}
-in
-fun lemma thm ct =
- let
- val cu = Thm.capply @{cterm Not} (Thm.dest_arg ct)
- val hyps = map_filter (try HOLogic.dest_Trueprop) (#hyps (Thm.rep_thm thm))
- in Thm (T.compose ccontr (T.under_assumption (intro hyps thm) cu)) end
-end
-
-
-
-(* \/{P1, ..., Pn, Q1, ..., Qn}, ~P1, ..., ~Pn ==> \/{Q1, ..., Qn} *)
-local
- val explode_disj = L.explode false true false
- val join_disj = L.join false
- fun unit thm thms th =
- let val t = @{term Not} $ T.prop_of thm and ts = map T.prop_of thms
- in join_disj (L.make_littab (thms @ explode_disj ts th)) t end
-
- fun dest_arg2 ct = Thm.dest_arg (Thm.dest_arg ct)
- fun dest ct = pairself dest_arg2 (Thm.dest_binop ct)
- val contrapos = T.precompose2 dest @{lemma "(~P ==> ~Q) ==> Q ==> P" by fast}
-in
-fun unit_resolution thm thms ct =
- Thm.capply @{cterm Not} (Thm.dest_arg ct)
- |> T.under_assumption (unit thm thms)
- |> Thm o T.discharge thm o T.compose contrapos
-end
-
-
-
-(* P ==> P == True or P ==> P == False *)
-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 & *)
-fun distributivity ctxt = Thm o try_apply ctxt [] [
- named ctxt "fast" (T.by_tac (Classical.best_tac HOL_cs))]
- (* FIXME: not very well tested *)
-
-
-
-(* 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 lits = L.true_thm :: L.explode conj1 true (conj1 <> conj2) [] thm
- in L.join conj2 (L.make_littab lits) (Thm.term_of ct2) end
-
- fun prove rule (ct1, conj1) (ct2, conj2) =
- T.under_assumption (prove' conj1 conj2 ct2) ct1 COMP rule
-
- fun prove_def_axiom ct =
- let val (ct1, ct2) = Thm.dest_binop (Thm.dest_arg 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 T.with_conv (dis_conv T.unfold_distinct_conv) prv 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 T.with_conv (dis_conv T.unfold_distinct_conv) prv ct end
- | _ => raise CTERM ("prove_def_axiom", [ct]))
- end
-
- val rewr_if =
- @{lemma "(if P then Q1 else Q2) = ((P --> Q1) & (~P --> Q2))" by simp}
-in
-fun def_axiom ctxt = Thm o try_apply ctxt [] [
- named ctxt "conj/disj/distinct" prove_def_axiom,
- T.by_abstraction ctxt [] (fn ctxt' =>
- named ctxt' "simp+fast" (T.by_tac (
- Simplifier.simp_tac (HOL_ss addsimps [rewr_if])
- THEN_ALL_NEW Classical.best_tac HOL_cs)))]
-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 = T.match_instantiate Thm.dest_arg
-
- fun apply_rule ct =
- (case get_first (try (inst_rule ct)) intro_rules of
- SOME thm => thm
- | NONE => raise CTERM ("intro_def", [ct]))
-in
-fun intro_def ct = T.make_hyp_def (apply_rule ct) #>> Thm
-
-fun apply_def thm =
- get_first (try (fn rule => MetaEq (thm COMP rule))) apply_rules
- |> the_default (Thm thm)
-end
-
-
-
-(* negation normal form *)
-
-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 vars qs p ct =
- T.as_meta_eq ct
- |> T.by_tac (nnf_quant_tac (T.varify vars (meta_eq_of p)) qs)
-
- fun prove_nnf ctxt = try_apply ctxt [] [
- named ctxt "conj/disj" L.prove_conj_disj_eq]
-in
-fun nnf ctxt vars ps ct =
- (case T.term_of ct of
- _ $ (l as Const _ $ Abs _) $ (r as Const _ $ Abs _) =>
- if l aconv r
- then MetaEq (Thm.reflexive (Thm.dest_arg (Thm.dest_arg ct)))
- else MetaEq (nnf_quant vars quant_rules1 (hd ps) ct)
- | _ $ (@{term Not} $ (Const _ $ Abs _)) $ (Const _ $ Abs _) =>
- MetaEq (nnf_quant vars quant_rules2 (hd ps) ct)
- | _ =>
- let
- val nnf_rewr_conv = Conv.arg_conv (Conv.arg_conv
- (T.unfold_eqs ctxt (map (Thm.symmetric o meta_eq_of) ps)))
- in Thm (T.with_conv nnf_rewr_conv (prove_nnf ctxt) ct) end)
-end
-
-
-
-(** equality proof rules **)
-
-(* |- t = t *)
-fun refl ct = MetaEq (Thm.reflexive (Thm.dest_arg (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 trans1 = @{lemma "s == t ==> t = u ==> s == u" by simp}
- val trans2 = @{lemma "s = t ==> t == u ==> s == u" by simp}
- val trans3 = @{lemma "s = t ==> t = u ==> s == u" by simp}
-in
-fun trans (MetaEq thm1) (MetaEq thm2) = MetaEq (Thm.transitive thm1 thm2)
- | trans (MetaEq thm) q = MetaEq (thm_of q COMP (thm COMP trans1))
- | trans p (MetaEq thm) = MetaEq (thm COMP (thm_of p COMP trans2))
- | trans p q = MetaEq (thm_of q COMP (thm_of p COMP trans3))
-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 L.is_conj (prove_eq_exn f)
- | @{term "op |"} => prove_nary L.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 lookup = AList.lookup (op aconv) (map (`Thm.prop_of o meta_eq_of) eqs)
- val cp = Thm.dest_binop (Thm.dest_arg ct)
- in MetaEq (prove_eq_exn lookup cp handle MONO => mono lookup cp) end
-end
-
-
-
-(* |- f a b = f b a (where f is equality) *)
-local
- val rule = @{lemma "a = b == b = a" by (atomize(full)) (rule eq_commute)}
-in
-fun commutativity ct = MetaEq (T.match_instantiate I (T.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) ==> (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}]
-in
-fun quant_intro vars p ct =
- let
- val thm = meta_eq_of p
- val rules' = T.varify vars thm :: rules
- val cu = T.as_meta_eq ct
- in MetaEq (T.by_tac (REPEAT_ALL_NEW (Tactic.match_tac rules')) cu) end
-end
-
-
-
-(* |- ((ALL x. P x) | Q) = (ALL x. P x | Q) *)
-fun pull_quant ctxt = Thm o try_apply ctxt [] [
- named ctxt "fast" (T.by_tac (Classical.fast_tac HOL_cs))]
- (* FIXME: not very well tested *)
-
-
-
-(* |- (ALL x. P x & Q x) = ((ALL x. P x) & (ALL x. Q x)) *)
-fun push_quant ctxt = Thm o try_apply ctxt [] [
- named ctxt "fast" (T.by_tac (Classical.fast_tac HOL_cs))]
- (* FIXME: not very well tested *)
-
-
-
-(* |- (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}
-
- fun elim_unused_conv ctxt =
- Conv.params_conv ~1 (K (Conv.arg_conv (Conv.arg1_conv
- (More_Conv.rewrs_conv [elim_all, elim_ex])))) ctxt
-
- fun elim_unused_tac ctxt =
- REPEAT_ALL_NEW (
- Tactic.match_tac [@{thm refl}, @{thm iff_allI}, @{thm iff_exI}]
- ORELSE' CONVERSION (elim_unused_conv ctxt))
-in
-fun elim_unused_vars ctxt = Thm o T.by_tac (elim_unused_tac ctxt)
-end
-
-
-
-(* |- (ALL x1 ... xn. ~(x1 = t1 & ... xn = tn) | P x1 ... xn) = P t1 ... tn *)
-fun dest_eq_res ctxt = Thm o try_apply ctxt [] [
- named ctxt "fast" (T.by_tac (Classical.fast_tac HOL_cs))]
- (* FIXME: not very well tested *)
-
-
-
-(* |- ~(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 T.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 pair2 (a, b) (c, d) = [(a, c), (b, d)]
- 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 ([], (pair2 (dest f sk') (p, c))) sk')
- |> Conv.fconv_rule (Thm.beta_conversion true)
-
- fun kind (Const (@{const_name Ex}, _) $ _) = (sk_ex_rule, I, I)
- | kind (@{term Not} $ (Const (@{const_name All}, _) $ _)) =
- (sk_all_rule, Thm.dest_arg, Thm.capply @{cterm Not})
- | kind t = raise TERM ("skolemize", [t])
-
- fun dest_abs_type (Abs (_, T, _)) = T
- | dest_abs_type t = raise TERM ("dest_abs_type", [t])
-
- fun bodies_of thy lhs rhs =
- let
- val (rule, dest, make) = kind (Thm.term_of lhs)
-
- fun dest_body idx cbs ct =
- let
- val cb = Thm.dest_arg (dest ct)
- val T = dest_abs_type (Thm.term_of cb)
- val cv = Thm.cterm_of thy (Var (("x", idx), T))
- val cu = make (Drule.beta_conv cb cv)
- val cbs' = (cv, cb) :: cbs
- in
- (snd (Thm.first_order_match (cu, rhs)), rev cbs')
- handle Pattern.MATCH => dest_body (idx+1) cbs' cu
- end
- in (rule, dest_body 1 [] lhs) end
-
- fun transitive f thm = Thm.transitive thm (f (Thm.rhs_of thm))
-
- fun sk_step (rule, elim) (cv, mct, cb) ((is, thm), ctxt) =
- (case mct of
- SOME ct =>
- ctxt
- |> T.make_hyp_def (inst_sk rule (Thm.instantiate_cterm ([], is) cb) ct)
- |>> pair ((cv, ct) :: is) o Thm.transitive thm
- | NONE => ((is, transitive (Conv.rewr_conv elim) thm), ctxt))
-in
-fun skolemize ct ctxt =
- let
- val (lhs, rhs) = Thm.dest_binop (Thm.dest_arg ct)
- val (rule, (ctab, cbs)) = bodies_of (ProofContext.theory_of ctxt) lhs rhs
- fun lookup_var (cv, cb) = (cv, AList.lookup (op aconvc) ctab cv, cb)
- in
- (([], Thm.reflexive lhs), ctxt)
- |> fold (sk_step rule) (map lookup_var cbs)
- |>> MetaEq o snd
- end
-end
-
-
-
-(** theory proof rules **)
-
-(* theory lemmas: linear arithmetic, arrays *)
-
-fun th_lemma ctxt simpset thms = Thm o try_apply ctxt thms [
- T.by_abstraction ctxt thms (fn ctxt' => T.by_tac (
- NAMED ctxt' "arith" (Arith_Data.arith_tac ctxt')
- ORELSE' NAMED ctxt' "simp+arith" (Simplifier.simp_tac simpset THEN_ALL_NEW
- Arith_Data.arith_tac ctxt')))]
-
-
-
-(* 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_Simps = Named_Thms
-(
- val name = "z3_simp"
- val description = "simplification rules for Z3 proof reconstruction"
-)
-
-local
- fun spec_meta_eq_of thm =
- (case try (fn th => th RS @{thm spec}) thm of
- SOME thm' => spec_meta_eq_of thm'
- | NONE => mk_meta_eq thm)
-
- fun prep (Thm thm) = spec_meta_eq_of thm
- | prep (MetaEq thm) = thm
- | prep (Literals (thm, _)) = spec_meta_eq_of thm
-
- fun unfold_conv ctxt ths =
- Conv.arg_conv (Conv.binop_conv (T.unfold_eqs ctxt (map prep ths)))
-
- fun with_conv _ [] prv = prv
- | with_conv ctxt ths prv = T.with_conv (unfold_conv ctxt ths) prv
-
- val unfold_conv =
- Conv.arg_conv (Conv.binop_conv (Conv.try_conv T.unfold_distinct_conv))
- val prove_conj_disj_eq = T.with_conv unfold_conv L.prove_conj_disj_eq
-in
-
-fun rewrite ctxt simpset ths = Thm o with_conv ctxt ths (try_apply ctxt [] [
- named ctxt "conj/disj/distinct" prove_conj_disj_eq,
- T.by_abstraction ctxt [] (fn ctxt' => T.by_tac (
- NAMED ctxt' "simp" (Simplifier.simp_tac simpset)
- THEN_ALL_NEW (
- NAMED ctxt' "fast" (Classical.fast_tac HOL_cs)
- ORELSE' NAMED ctxt' "arith" (Arith_Data.arith_tac ctxt'))))])
-
-end
-
-
-
-(** proof reconstruction **)
-
-(* tracing and checking *)
-
-local
- fun count_rules ptab =
- let
- fun count (_, Unproved _) (solved, total) = (solved, total + 1)
- | count (_, Proved _) (solved, total) = (solved + 1, total + 1)
- in Inttab.fold count ptab (0, 0) end
-
- fun header idx r (solved, total) =
- "Z3: #" ^ string_of_int idx ^ ": " ^ P.string_of_rule r ^ " (goal " ^
- string_of_int (solved + 1) ^ " of " ^ string_of_int total ^ ")"
-
- fun check ctxt idx r ps ct p =
- let val thm = thm_of p |> tap (Thm.join_proofs o single)
- in
- if (Thm.cprop_of thm) aconvc ct then ()
- else z3_exn (Pretty.string_of (Pretty.big_list ("proof step failed: " ^
- quote (P.string_of_rule r) ^ " (#" ^ string_of_int idx ^ ")")
- (pretty_goal ctxt (map (thm_of o fst) ps) (Thm.prop_of thm) @
- [Pretty.block [Pretty.str "expected: ",
- Syntax.pretty_term ctxt (Thm.term_of ct)]])))
- end
-in
-fun trace_rule idx prove r ps ct (cxp as (ctxt, ptab)) =
- let
- val _ = SMT_Solver.trace_msg ctxt (header idx r o count_rules) ptab
- val result as (p, cxp' as (ctxt', _)) = prove r ps ct cxp
- val _ = if not (Config.get ctxt' SMT_Solver.trace) then ()
- else check ctxt' idx r ps ct p
- in result end
-end
-
-
-(* overall reconstruction procedure *)
-
-fun not_supported r =
- raise Fail ("Z3: proof rule not implemented: " ^ quote (P.string_of_rule r))
-
-fun prove ctxt unfolds assms vars =
- let
- val assms' = Option.map (prepare_assms ctxt unfolds) assms
- val simpset = T.make_simpset ctxt (Z3_Simps.get ctxt)
-
- fun step r ps ct (cxp as (cx, ptab)) =
- (case (r, ps) of
- (* core rules *)
- (P.TrueAxiom, _) => (Thm L.true_thm, cxp)
- | (P.Asserted, _) => (asserted cx assms' ct, cxp)
- | (P.Goal, _) => (asserted cx assms' ct, cxp)
- | (P.ModusPonens, [(p, _), (q, _)]) => (mp q (thm_of p), cxp)
- | (P.ModusPonensOeq, [(p, _), (q, _)]) => (mp q (thm_of p), cxp)
- | (P.AndElim, [(p, i)]) => and_elim (p, i) ct ptab ||> pair cx
- | (P.NotOrElim, [(p, i)]) => not_or_elim (p, i) ct ptab ||> pair cx
- | (P.Hypothesis, _) => (Thm (Thm.assume ct), cxp)
- | (P.Lemma, [(p, _)]) => (lemma (thm_of p) ct, cxp)
- | (P.UnitResolution, (p, _) :: ps) =>
- (unit_resolution (thm_of p) (map (thm_of o fst) ps) ct, cxp)
- | (P.IffTrue, [(p, _)]) => (iff_true (thm_of p), cxp)
- | (P.IffFalse, [(p, _)]) => (iff_false (thm_of p), cxp)
- | (P.Distributivity, _) => (distributivity cx ct, cxp)
- | (P.DefAxiom, _) => (def_axiom cx ct, cxp)
- | (P.IntroDef, _) => intro_def ct cx ||> rpair ptab
- | (P.ApplyDef, [(p, _)]) => (apply_def (thm_of p), cxp)
- | (P.IffOeq, [(p, _)]) => (p, cxp)
- | (P.NnfPos, _) => (nnf cx vars (map fst ps) ct, cxp)
- | (P.NnfNeg, _) => (nnf cx vars (map fst ps) ct, cxp)
-
- (* equality rules *)
- | (P.Reflexivity, _) => (refl ct, cxp)
- | (P.Symmetry, [(p, _)]) => (symm p, cxp)
- | (P.Transitivity, [(p, _), (q, _)]) => (trans p q, cxp)
- | (P.Monotonicity, _) => (monotonicity (map fst ps) ct, cxp)
- | (P.Commutativity, _) => (commutativity ct, cxp)
-
- (* quantifier rules *)
- | (P.QuantIntro, [(p, _)]) => (quant_intro vars p ct, cxp)
- | (P.PullQuant, _) => (pull_quant cx ct, cxp)
- | (P.PushQuant, _) => (push_quant cx ct, cxp)
- | (P.ElimUnusedVars, _) => (elim_unused_vars cx ct, cxp)
- | (P.DestEqRes, _) => (dest_eq_res cx ct, cxp)
- | (P.QuantInst, _) => (quant_inst ct, cxp)
- | (P.Skolemize, _) => skolemize ct cx ||> rpair ptab
-
- (* theory rules *)
- | (P.ThLemma, _) =>
- (th_lemma cx simpset (map (thm_of o fst) ps) ct, cxp)
- | (P.Rewrite, _) => (rewrite cx simpset [] ct, cxp)
- | (P.RewriteStar, ps) =>
- (rewrite cx simpset (map fst ps) ct, cxp)
-
- | (P.NnfStar, _) => not_supported r
- | (P.CnfStar, _) => not_supported r
- | (P.TransitivityStar, _) => not_supported r
- | (P.PullQuantStar, _) => not_supported r
-
- | _ => raise Fail ("Z3: proof rule " ^ quote (P.string_of_rule r) ^
- " has an unexpected number of arguments."))
-
- fun conclude idx rule prop (ps, cxp) =
- trace_rule idx step rule ps prop cxp
- |-> (fn p => apsnd (Inttab.update (idx, Proved p)) #> pair p)
-
- fun lookup idx (cxp as (cx, ptab)) =
- (case Inttab.lookup ptab idx of
- SOME (Unproved (P.Proof_Step {rule, prems, prop})) =>
- fold_map lookup prems cxp
- |>> map2 rpair prems
- |> conclude idx rule prop
- | SOME (Proved p) => (p, cxp)
- | NONE => z3_exn ("unknown proof id: " ^ quote (string_of_int idx)))
-
- fun result (p, (cx, _)) = (thm_of p, cx)
- in
- (fn (idx, ptab) => result (lookup idx (ctxt, Inttab.map Unproved ptab)))
- end
-
-fun reconstruct (output, {typs, terms, unfolds, assms}) ctxt =
- P.parse ctxt typs terms output
- |> (fn (idx, (ptab, vars, cx)) => prove cx unfolds assms vars (idx, ptab))
-
-val setup = trace_assms_setup #> z3_rules_setup #> Z3_Simps.setup
-
-end
--- a/src/HOL/SMT/Tools/z3_proof_tools.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,364 +0,0 @@
-(* Title: HOL/SMT/Tools/z3_proof_tools.ML
- Author: Sascha Boehme, TU Muenchen
-
-Helper functions required for Z3 proof reconstruction.
-*)
-
-signature Z3_PROOF_TOOLS =
-sig
- (* accessing and modifying terms *)
- val term_of: cterm -> term
- val prop_of: thm -> term
- val mk_prop: cterm -> cterm
- val as_meta_eq: cterm -> cterm
-
- (* theorem nets *)
- val thm_net_of: thm list -> thm Net.net
- val net_instance: thm Net.net -> cterm -> thm option
-
- (* proof combinators *)
- val under_assumption: (thm -> thm) -> cterm -> thm
- val with_conv: conv -> (cterm -> thm) -> cterm -> thm
- val discharge: thm -> thm -> thm
- val varify: string list -> thm -> thm
- val unfold_eqs: Proof.context -> thm list -> conv
- val match_instantiate: (cterm -> cterm) -> cterm -> thm -> thm
- val by_tac: (int -> tactic) -> cterm -> thm
- val make_hyp_def: thm -> Proof.context -> thm * Proof.context
- val by_abstraction: Proof.context -> thm list -> (Proof.context -> cterm ->
- thm) -> cterm -> thm
-
- (* a faster COMP *)
- type compose_data
- val precompose: (cterm -> cterm list) -> thm -> compose_data
- val precompose2: (cterm -> cterm * cterm) -> thm -> compose_data
- val compose: compose_data -> thm -> thm
-
- (* unfolding of 'distinct' *)
- val unfold_distinct_conv: conv
-
- (* simpset *)
- val make_simpset: Proof.context -> thm list -> simpset
-end
-
-structure Z3_Proof_Tools: Z3_PROOF_TOOLS =
-struct
-
-
-
-(* accessing terms *)
-
-val dest_prop = (fn @{term Trueprop} $ t => t | t => t)
-
-fun term_of ct = dest_prop (Thm.term_of ct)
-fun prop_of thm = dest_prop (Thm.prop_of thm)
-
-val mk_prop = Thm.capply @{cterm Trueprop}
-
-val (eqT, eq) = `(hd o Thm.dest_ctyp o Thm.ctyp_of_term) @{cpat "op =="}
-fun mk_meta_eq_cterm ct cu =
- let val inst = ([(eqT, Thm.ctyp_of_term ct)], [])
- in Thm.mk_binop (Thm.instantiate_cterm inst eq) ct cu end
-
-fun as_meta_eq ct = uncurry mk_meta_eq_cterm (Thm.dest_binop (Thm.dest_arg ct))
-
-
-
-(* theorem nets *)
-
-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 maybe_instantiate ct thm =
- try Thm.first_order_match (Thm.cprop_of thm, ct)
- |> Option.map (fn inst => Thm.instantiate inst thm)
-
-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
-
-
-
-(* proof combinators *)
-
-fun under_assumption f ct =
- let val ct' = 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 discharge p pq = Thm.implies_elim pq p
-
-fun varify vars = Drule.generalize ([], vars)
-
-fun unfold_eqs _ [] = Conv.all_conv
- | unfold_eqs ctxt eqs =
- More_Conv.top_sweep_conv (K (More_Conv.rewrs_conv eqs)) ctxt
-
-fun match_instantiate f ct thm =
- Thm.instantiate (Thm.match (f (Thm.cprop_of thm), ct)) thm
-
-fun by_tac tac ct = Goal.norm_result (Goal.prove_internal [] ct (K (tac 1)))
-
-(* |- c x == t x ==> P (c x) ~~> c == t |- P (c x) *)
-fun make_hyp_def thm ctxt =
- let
- val (lhs, rhs) = Thm.dest_binop (Thm.cprem_of thm 1)
- val (cf, cvs) = Drule.strip_comb lhs
- val eq = mk_meta_eq_cterm 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
- yield_singleton Assumption.add_assumes eq ctxt
- |>> Thm.implies_elim thm o fold apply cvs
- end
-
-
-
-(* abstraction *)
-
-local
-
-fun typ_of ct = #T (Thm.rep_cterm ct)
-fun certify ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
-
-fun abs_context ctxt = (ctxt, Termtab.empty, 1, false)
-
-fun context_of (ctxt, _, _, _) = ctxt
-
-fun replace (cv, ct) = Thm.forall_elim ct o Thm.forall_intr cv
-
-fun abs_instantiate (_, tab, _, beta_norm) =
- fold replace (map snd (Termtab.dest tab)) #>
- beta_norm ? Conv.fconv_rule (Thm.beta_conversion true)
-
-fun generalize cvs =
- let
- val no_name = ""
-
- fun dest (Free (n, _)) = n
- | dest _ = no_name
-
- fun gen vs (t as Free (n, _)) =
- let val i = find_index (equal n) vs
- in
- if i >= 0 then insert (op aconvc) (nth cvs i) #> pair (Bound i)
- else pair t
- end
- | gen vs (t $ u) = gen vs t ##>> gen vs u #>> (op $)
- | gen vs (Abs (n, T, t)) =
- gen (no_name :: vs) t #>> (fn u => Abs (n, T, u))
- | gen _ t = pair t
-
- in (fn ct => gen (map (dest o Thm.term_of) cvs) (Thm.term_of ct) []) end
-
-fun fresh_abstraction cvs ct (cx as (ctxt, tab, idx, beta_norm)) =
- let val (t, cvs') = generalize cvs ct
- in
- (case Termtab.lookup tab t of
- SOME (cv, _) => (cv, cx)
- | NONE =>
- let
- val (n, ctxt') = yield_singleton Variable.variant_fixes "x" ctxt
- val cv = certify ctxt (Free (n, map typ_of cvs' ---> typ_of ct))
- val cv' = Drule.list_comb (cv, cvs')
- val e = (t, (cv, fold_rev Thm.cabs cvs' ct))
- val beta_norm' = beta_norm orelse not (null cvs')
- in (cv', (ctxt', Termtab.update e tab, idx + 1, beta_norm')) end)
- end
-
-fun abs_arg f cvs ct =
- let val (cf, cu) = Thm.dest_comb ct
- in f cvs cu #>> Thm.capply cf end
-
-fun abs_comb f g cvs ct =
- let val (cf, cu) = Thm.dest_comb ct
- in f cvs cf ##>> g cvs cu #>> uncurry Thm.capply end
-
-fun abs_list f g cvs ct =
- (case Thm.term_of ct of
- Const (@{const_name Nil}, _) => pair ct
- | Const (@{const_name Cons}, _) $ _ $ _ =>
- abs_comb (abs_arg f) (abs_list f g) cvs ct
- | _ => g cvs ct)
-
-fun abs_abs f cvs ct =
- let val (cv, cu) = Thm.dest_abs NONE ct
- in f (cv :: cvs) cu #>> Thm.cabs cv end
-
-val is_atomic = (fn _ $ _ => false | Abs _ => false | _ => true)
-val is_arithT = (fn @{typ int} => true | @{typ real} => true | _ => false)
-fun is_number t =
- (case try HOLogic.dest_number t of
- SOME (T, _) => is_arithT T
- | NONE => false)
-
-val abstract =
- let (* FIXME: provide an option to avoid abstraction of If/distinct/All/Ex *)
- fun abstr1 cvs ct = abs_arg abstr cvs ct
- and abstr2 cvs ct = abs_comb abstr1 abstr cvs ct
- and abstr3 cvs ct = abs_comb abstr2 abstr cvs ct
- and abstr_abs cvs ct = abs_arg (abs_abs abstr) cvs ct
-
- and abstr cvs ct =
- (case Thm.term_of ct of
- @{term Trueprop} $ _ => abstr1 cvs ct
- | @{term "op ==>"} $ _ $ _ => abstr2 cvs ct
- | @{term True} => pair ct
- | @{term False} => pair ct
- | @{term Not} $ _ => abstr1 cvs ct
- | @{term "op &"} $ _ $ _ => abstr2 cvs ct
- | @{term "op |"} $ _ $ _ => abstr2 cvs ct
- | @{term "op -->"} $ _ $ _ => abstr2 cvs ct
- | Const (@{const_name "op ="}, _) $ _ $ _ => abstr2 cvs ct
- | Const (@{const_name distinct}, _) $ _ =>
- abs_arg (abs_list abstr fresh_abstraction) cvs ct
- | Const (@{const_name If}, _) $ _ $ _ $ _ => abstr3 cvs ct
- | Const (@{const_name All}, _) $ _ => abstr_abs cvs ct
- | Const (@{const_name Ex}, _) $ _ => abstr_abs cvs ct
- | @{term "uminus :: int => _"} $ _ => abstr1 cvs ct
- | @{term "uminus :: real => _"} $ _ => abstr1 cvs ct
- | @{term "op + :: int => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op + :: real => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op - :: int => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op - :: real => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op * :: int => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op * :: real => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op div :: int => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op mod :: int => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op / :: real => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op < :: int => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op < :: real => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op <= :: int => _"} $ _ $ _ => abstr2 cvs ct
- | @{term "op <= :: real => _"} $ _ $ _ => abstr2 cvs ct
- | Const (@{const_name apply}, _) $ _ $ _ => abstr2 cvs ct
- | Const (@{const_name fun_upd}, _) $ _ $ _ $ _ => abstr3 cvs ct
- | t =>
- if is_atomic t orelse is_number t then pair ct
- else fresh_abstraction cvs ct)
- in abstr [] end
-
-fun with_prems thms f ct =
- fold_rev (Thm.mk_binop @{cterm "op ==>"} o Thm.cprop_of) thms ct
- |> f
- |> fold (fn prem => fn th => Thm.implies_elim th prem) thms
-
-in
-
-fun by_abstraction ctxt thms prove = with_prems thms (fn ct =>
- let val (cu, cx) = abstract ct (abs_context ctxt)
- in abs_instantiate cx (prove (context_of cx) cu) end)
-
-end
-
-
-
-(* a faster COMP *)
-
-type compose_data = cterm list * (cterm -> cterm list) * thm
-
-fun list2 (x, y) = [x, y]
-
-fun precompose f rule = (f (Thm.cprem_of rule 1), f, rule)
-fun precompose2 f rule = precompose (list2 o f) rule
-
-fun compose (cvs, f, rule) thm =
- discharge thm (Thm.instantiate ([], cvs ~~ f (Thm.cprop_of thm)) rule)
-
-
-
-(* unfolding of 'distinct' *)
-
-local
- val set1 = @{lemma "x ~: set [] == ~False" by simp}
- val set2 = @{lemma "x ~: set [x] == False" by simp}
- val set3 = @{lemma "x ~: set [y] == x ~= y" by simp}
- val set4 = @{lemma "x ~: set (x # ys) == False" by simp}
- val set5 = @{lemma "x ~: set (y # ys) == x ~= y & x ~: set ys" by simp}
-
- fun set_conv ct =
- (More_Conv.rewrs_conv [set1, set2, set3, set4] else_conv
- (Conv.rewr_conv set5 then_conv Conv.arg_conv set_conv)) ct
-
- val dist1 = @{lemma "distinct [] == ~False" by simp}
- val dist2 = @{lemma "distinct [x] == ~False" by simp}
- val dist3 = @{lemma "distinct (x # xs) == x ~: set xs & distinct xs"
- by simp}
-
- fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
-in
-fun unfold_distinct_conv ct =
- (More_Conv.rewrs_conv [dist1, dist2] else_conv
- (Conv.rewr_conv dist3 then_conv binop_conv set_conv unfold_distinct_conv)) ct
-end
-
-
-
-(* simpset *)
-
-local
- val antisym_le1 = mk_meta_eq @{thm order_class.antisym_conv}
- val antisym_le2 = mk_meta_eq @{thm linorder_class.antisym_conv2}
- val antisym_less1 = mk_meta_eq @{thm linorder_class.antisym_conv1}
- val antisym_less2 = mk_meta_eq @{thm linorder_class.antisym_conv3}
-
- fun eq_prop t thm = HOLogic.mk_Trueprop t aconv Thm.prop_of thm
- fun dest_binop ((c as Const _) $ t $ u) = (c, t, u)
- | dest_binop t = raise TERM ("dest_binop", [t])
-
- fun prove_antisym_le ss t =
- let
- val (le, r, s) = dest_binop t
- val less = Const (@{const_name less}, Term.fastype_of le)
- val prems = Simplifier.prems_of_ss ss
- in
- (case find_first (eq_prop (le $ s $ r)) prems of
- NONE =>
- find_first (eq_prop (HOLogic.mk_not (less $ r $ s))) prems
- |> Option.map (fn thm => thm RS antisym_less1)
- | SOME thm => SOME (thm RS antisym_le1))
- end
- handle THM _ => NONE
-
- fun prove_antisym_less ss t =
- let
- val (less, r, s) = dest_binop (HOLogic.dest_not t)
- val le = Const (@{const_name less_eq}, Term.fastype_of less)
- val prems = prems_of_ss ss
- in
- (case find_first (eq_prop (le $ r $ s)) prems of
- NONE =>
- find_first (eq_prop (HOLogic.mk_not (less $ s $ r))) prems
- |> Option.map (fn thm => thm RS antisym_less2)
- | SOME thm => SOME (thm RS antisym_le2))
- end
- handle THM _ => NONE
-in
-
-fun make_simpset ctxt rules = Simplifier.context ctxt (HOL_ss
- addsimps @{thms field_simps}
- addsimps [@{thm times_divide_eq_right}, @{thm times_divide_eq_left}]
- 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}
- addsimps @{thms array_rules}
- 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),
- Simplifier.simproc @{theory} "antisym_le" ["(x::'a::order) <= y"]
- (K prove_antisym_le),
- Simplifier.simproc @{theory} "antisym_less" ["~ (x::'a::linorder) < y"]
- (K prove_antisym_less)]
- addsimps rules)
-
-end
-
-end
--- a/src/HOL/SMT/Tools/z3_solver.ML Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,80 +0,0 @@
-(* Title: HOL/SMT/Tools/z3_solver.ML
- Author: Sascha Boehme, TU Muenchen
-
-Interface of the SMT solver Z3.
-*)
-
-signature Z3_SOLVER =
-sig
- val proofs: bool Config.T
- val options: string Config.T
- val setup: theory -> theory
-end
-
-structure Z3_Solver: Z3_SOLVER =
-struct
-
-val solver_name = "z3"
-val env_var = "Z3_SOLVER"
-
-val (proofs, proofs_setup) = Attrib.config_bool "z3_proofs" (K false)
-val (options, options_setup) = Attrib.config_string "z3_options" (K "")
-
-fun add xs ys = ys @ xs
-
-fun explode_options s = String.tokens (Symbol.is_ascii_blank o str) s
-
-fun get_options ctxt =
- ["MODEL=true", "PRE_SIMPLIFY_EXPR=false", "CONTEXT_SIMPLIFIER=false"]
- |> Config.get ctxt proofs ? add ["DISPLAY_PROOF=true", "PROOF_MODE=2"]
- |> add (explode_options (Config.get ctxt options))
-
-fun pretty_config context = [
- Pretty.str ("With proofs: " ^
- (if Config.get_generic context proofs then "true" else "false")),
- Pretty.str ("Options: " ^
- space_implode " " (get_options (Context.proof_of context))) ]
-
-fun cmdline_options ctxt =
- get_options ctxt
- |> add ["-smt"]
-
-fun raise_cex real recon ls =
- let val cex = Z3_Model.parse_counterex recon ls
- in raise SMT_Solver.SMT_COUNTEREXAMPLE (real, cex) end
-
-fun if_unsat f (output, recon) =
- let
- fun jnk l =
- String.isPrefix "WARNING" l orelse
- String.isPrefix "ERROR" l orelse
- forall Symbol.is_ascii_blank (Symbol.explode l)
- val (ls, l) = the_default ([], "") (try split_last (filter_out jnk output))
- in
- if String.isPrefix "unsat" l then f (ls, recon)
- else if String.isPrefix "sat" l then raise_cex true recon ls
- else if String.isPrefix "unknown" l then raise_cex false recon ls
- else raise SMT_Solver.SMT (solver_name ^ " failed")
- end
-
-val core_oracle = if_unsat (K @{cprop False})
-
-val prover = if_unsat Z3_Proof_Reconstruction.reconstruct
-
-fun solver oracle ctxt =
- let val with_proof = Config.get ctxt proofs
- in
- {command = {env_var=env_var, remote_name=SOME solver_name},
- arguments = cmdline_options ctxt,
- interface = Z3_Interface.interface,
- reconstruct = if with_proof then prover else pair o oracle}
- end
-
-val setup =
- proofs_setup #>
- options_setup #>
- Thm.add_oracle (Binding.name solver_name, core_oracle) #-> (fn (_, oracle) =>
- SMT_Solver.add_solver (solver_name, solver oracle)) #>
- SMT_Solver.add_solver_info (solver_name, pretty_config)
-
-end
--- a/src/HOL/SMT/Z3.thy Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,89 +0,0 @@
-(* 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 "~~/src/HOL/Decision_Procs/Dense_Linear_Order"
-uses
- "Tools/z3_proof_parser.ML"
- "Tools/z3_proof_tools.ML"
- "Tools/z3_proof_literals.ML"
- "Tools/z3_proof_reconstruction.ML"
- "Tools/z3_model.ML"
- "Tools/z3_interface.ML"
- "Tools/z3_solver.ML"
-begin
-
-setup {*
- Z3_Proof_Reconstruction.setup #>
- Z3_Solver.setup #>
- Arith_Data.add_tactic "Ferrante-Rackoff" (K FerranteRackoff.dlo_tac)
-*}
-
-lemmas [z3_rule] =
- refl eq_commute conj_commute disj_commute simp_thms nnf_simps
- ring_distribs field_simps times_divide_eq_right times_divide_eq_left
- if_True if_False not_not
-
-lemma [z3_rule]:
- "(P \<longrightarrow> Q) = (Q \<or> \<not>P)"
- "(\<not>P \<longrightarrow> Q) = (P \<or> Q)"
- "(\<not>P \<longrightarrow> Q) = (Q \<or> P)"
- by auto
-
-lemma [z3_rule]:
- "((P = Q) \<longrightarrow> R) = (R | (Q = (\<not>P)))"
- by auto
-
-lemma [z3_rule]:
- "((\<not>P) = P) = False"
- "(P = (\<not>P)) = False"
- "(P \<noteq> Q) = (Q = (\<not>P))"
- "(P = Q) = ((\<not>P \<or> Q) \<and> (P \<or> \<not>Q))"
- "(P \<noteq> Q) = ((\<not>P \<or> \<not>Q) \<and> (P \<or> Q))"
- by auto
-
-lemma [z3_rule]:
- "(if P then P else \<not>P) = True"
- "(if \<not>P then \<not>P else P) = True"
- "(if P then True else False) = P"
- "(if P then False else True) = (\<not>P)"
- "(if \<not>P then x else y) = (if P then y else x)"
- by auto
-
-lemma [z3_rule]:
- "P = Q \<or> P \<or> Q"
- "P = Q \<or> \<not>P \<or> \<not>Q"
- "(\<not>P) = Q \<or> \<not>P \<or> Q"
- "(\<not>P) = Q \<or> P \<or> \<not>Q"
- "P = (\<not>Q) \<or> \<not>P \<or> Q"
- "P = (\<not>Q) \<or> P \<or> \<not>Q"
- "P \<noteq> Q \<or> P \<or> \<not>Q"
- "P \<noteq> Q \<or> \<not>P \<or> Q"
- "P \<noteq> (\<not>Q) \<or> P \<or> Q"
- "(\<not>P) \<noteq> Q \<or> P \<or> Q"
- "P \<or> Q \<or> P \<noteq> (\<not>Q)"
- "P \<or> Q \<or> (\<not>P) \<noteq> Q"
- "P \<or> \<not>Q \<or> P \<noteq> Q"
- "\<not>P \<or> Q \<or> P \<noteq> Q"
- by auto
-
-lemma [z3_rule]:
- "0 + (x::int) = x"
- "x + 0 = x"
- "0 * x = 0"
- "1 * x = x"
- "x + y = y + x"
- by auto
-
-lemma [z3_rule]:
- "0 + (x::real) = x"
- "x + 0 = x"
- "0 * x = 0"
- "1 * x = x"
- "x + y = y + x"
- by auto
-
-end
--- a/src/HOL/SMT/etc/settings Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,14 +0,0 @@
-ISABELLE_SMT="$COMPONENT"
-
-RUN_SMT_SOLVER="$ISABELLE_SMT/lib/scripts/run_smt_solver"
-REMOTE_SMT="$ISABELLE_SMT/lib/scripts/remote_smt"
-
-REMOTE_SMT_URL="http://smt.in.tum.de/smt"
-
-#
-# Paths to local SMT solvers:
-#
-# CVC_SOLVER=PATH
-# YICES_SOLVER=PATH
-# Z3_SOLVER=PATH
-
--- a/src/HOL/SMT/lib/scripts/remote_smt Wed May 12 23:54:01 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,31 +0,0 @@
-#!/usr/bin/env perl
-#
-# Author: Sascha Boehme, TU Muenchen
-#
-# Invoke remote SMT solvers.
-
-use strict;
-use warnings;
-use LWP;
-
-
-# arguments
-
-my $solver = $ARGV[0];
-my @options = @ARGV[1 .. ($#ARGV - 1)];
-my $problem_file = $ARGV[-1];
-
-
-# call solver
-
-my $agent = LWP::UserAgent->new;
-$agent->agent("SMT-Request");
-$agent->timeout(180);
-my $response = $agent->post($ENV{"REMOTE_SMT_URL"}, [
- "Solver" => $solver,
- "Options" => join(" ", @options),
- "Problem" => [$problem_file] ],
- "Content_Type" => "form-data");
-if (not $response->is_success) { die "HTTP-Error: " . $response->message; }
-else { print $response->content; }
-
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,587 @@
+(* Title: HOL/SMT/SMT_Examples.thy
+ Author: Sascha Boehme, TU Muenchen
+*)
+
+header {* Examples for the 'smt' tactic. *}
+
+theory SMT_Examples
+imports SMT
+begin
+
+declare [[smt_solver=z3, z3_proofs=true]]
+
+declare [[smt_certificates="$ISABELLE_SMT/Examples/SMT_Examples.certs"]]
+
+text {*
+To avoid re-generation of certificates,
+the following option is set to "false":
+*}
+
+declare [[smt_fixed=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)"
+ 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" by smt
+
+lemma "P=P=P=P=P=P=P=P=P=P" 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 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 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 by smt
+
+lemma "\<forall>x::int. P x \<longrightarrow> (\<forall>y::int. P x \<or> P y)"
+ by smt
+
+lemma
+ assumes "(\<forall>x y. P x y = x)"
+ shows "(\<exists>y. P x y) = P x c"
+ using assms 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 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 by smt
+
+
+section {* Arithmetic *}
+
+subsection {* Linear arithmetic over integers and reals *}
+
+lemma "(3::int) = 3" by smt
+
+lemma "(3::real) = 3" by smt
+
+lemma "(3 :: int) + 1 = 4" by smt
+
+lemma "x + (y + z) = y + (z + (x::int))" by smt
+
+lemma "max (3::int) 8 > 5" by smt
+
+lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt
+
+lemma "P ((2::int) < 3) = P True" by smt
+
+lemma "x + 3 \<ge> 4 \<or> x < (1::int)" by smt
+
+lemma
+ assumes "x \<ge> (3::int)" and "y = x + 4"
+ shows "y - x > 0"
+ using assms by smt
+
+lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt
+
+lemma
+ fixes x :: real
+ assumes "3 * x + 7 * a < 4" and "3 < 2 * x"
+ shows "a < 0"
+ using assms by smt
+
+lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)" by smt
+
+lemma "distinct [x < (3::int), 3 \<le> x]" by smt
+
+lemma
+ assumes "a > (0::int)"
+ shows "distinct [a, a * 2, a - a]"
+ using assms 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))"
+ by smt
+
+text{*
+The following example was taken from HOL/ex/PresburgerEx.thy, where it says:
+
+ This following theorem proves that all solutions to the
+ recurrence relation $x_{i+2} = |x_{i+1}| - x_i$ are periodic with
+ period 9. The example was brought to our attention by John
+ Harrison. It does does not require Presburger arithmetic but merely
+ quantifier-free linear arithmetic and holds for the rationals as well.
+
+ 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. 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)"
+ by smt
+
+
+lemma "let P = 2 * x + 1 > x + (x::real) in P \<or> False \<or> P" by smt
+
+lemma "x + (let y = x mod 2 in 2 * y + 1) \<ge> x + (1::int)" by smt
+
+lemma "x + (let y = x mod 2 in y + y) < x + (3::int)" by smt
+
+lemma
+ assumes "x \<noteq> (0::real)"
+ shows "x + x \<noteq> (let P = (abs x > 1) in if P \<or> \<not>P then 4 else 2) * x"
+ using assms by smt
+
+lemma
+ assumes "(n + m) mod 2 = 0" and "n mod 4 = 3"
+ shows "n mod 2 = 1 & m mod 2 = (1::int)"
+ using assms by smt
+
+
+subsection {* Linear arithmetic with quantifiers *}
+
+lemma "~ (\<exists>x::int. False)" by smt
+
+lemma "~ (\<exists>x::real. False)" by smt
+
+lemma "\<exists>x::int. 0 < x"
+ using [[z3_proofs=false]] (* no Z3 proof *)
+ by smt
+
+lemma "\<exists>x::real. 0 < x"
+ using [[z3_proofs=false]] (* no Z3 proof *)
+ by smt
+
+lemma "\<forall>x::int. \<exists>y. y > x"
+ using [[z3_proofs=false]] (* no Z3 proof *)
+ by smt
+
+lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt
+
+lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0" by smt
+
+lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)" by smt
+
+lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)" by smt
+
+lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2" by smt
+
+lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x" by smt
+
+lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True" by smt
+
+lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)" by smt
+
+lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt
+
+lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y" by smt
+
+lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x" by smt
+
+lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0" by smt
+
+lemma "\<forall>x::int. trigger [pat x] (x < a \<longrightarrow> 2 * x < 2 * a)" by smt
+
+
+subsection {* Non-linear arithmetic over integers and reals *}
+
+lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
+ using [[z3_proofs=false]] -- {* Isabelle's arithmetic decision procedures
+ are too weak to automatically prove @{thm zero_less_mult_pos}. *}
+ by smt
+
+lemma "(a::int) * (x + 1 + y) = a * x + a * (y + 1)" by smt
+
+lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)" 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)"
+ by smt
+
+
+subsection {* Linear arithmetic for natural numbers *}
+
+lemma "2 * (x::nat) ~= 1" 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
+ "let x = (1::nat) + y in
+ let P = (if x > 0 then True else False) in
+ False \<or> P = (x - 1 = y) \<or> (\<not>P \<longrightarrow> False)"
+ by smt
+
+lemma "distinct [a + (1::nat), a * 2 + 3, a - a]" by smt
+
+lemma "int (nat \<bar>x::int\<bar>) = \<bar>x\<bar>" 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)" by (smt prime_nat_def)
+
+
+section {* Bitvectors *}
+
+locale z3_bv_test
+begin
+
+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" by smt
+
+lemma "(27 :: 4 word) = 11" by smt
+
+lemma "23 < (27::8 word)" by smt
+
+lemma "27 + 11 = (6::5 word)" by smt
+
+lemma "7 * 3 = (21::8 word)" by smt
+
+lemma "11 - 27 = (-16::8 word)" by smt
+
+lemma "- -11 = (11::5 word)" by smt
+
+lemma "-40 + 1 = (-39::7 word)" by smt
+
+lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by smt
+
+lemma "x = (5 :: 4 word) \<Longrightarrow> 4 * x = 4" by smt
+
+
+subsection {* Bit-level logic *}
+
+lemma "0b110 AND 0b101 = (0b100 :: 32 word)" by smt
+
+lemma "0b110 OR 0b011 = (0b111 :: 8 word)" by smt
+
+lemma "0xF0 XOR 0xFF = (0x0F :: 8 word)" by smt
+
+lemma "NOT (0xF0 :: 16 word) = 0xFF0F" by smt
+
+lemma "word_cat (27::4 word) (27::8 word) = (2843::12 word)" by smt
+
+lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)"
+ by smt
+
+lemma "slice 1 (0b10110 :: 4 word) = (0b11 :: 2 word)" by smt
+
+lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by smt
+
+lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt
+
+lemma "bv_lshr 0b10011 2 = (0b100::8 word)" by smt
+
+lemma "bv_ashr 0b10011 2 = (0b100::8 word)" by smt
+
+lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt
+
+lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by smt
+
+lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" by smt
+
+lemma "w < 256 \<Longrightarrow> (w :: 16 word) AND 0x00FF = w" by smt
+
+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]]
+ by smt
+
+lemma "P (0 \<le> (a :: 4 word)) = P True"
+ using [[smt_solver=z3, z3_proofs=false]]
+ 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
+
+
+section {* Higher-order problems and recursion *}
+
+lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> (f (i1 := v1, i2 := v2)) i = f i" by smt
+
+lemma "(f g (x::'a::type) = (g x \<and> True)) \<or> (f g x = True) \<or> (g x = True)"
+ by smt
+
+lemma "id 3 = 3 \<and> id True = True" by (smt 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 map.simps)
+
+lemma "(ALL x. P x) | ~ All P" 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 dec_10.simps)
+
+axiomatization
+ eval_dioph :: "int list \<Rightarrow> nat list \<Rightarrow> int"
+ where
+ eval_dioph_mod:
+ "eval_dioph ks xs mod int n = eval_dioph ks (map (\<lambda>x. x mod n) xs) mod int n"
+ and
+ eval_dioph_div_mult:
+ "eval_dioph ks (map (\<lambda>x. x div n) xs) * int n +
+ eval_dioph ks (map (\<lambda>x. x mod n) xs) = eval_dioph ks xs"
+lemma
+ "(eval_dioph ks xs = l) =
+ (eval_dioph ks (map (\<lambda>x. x mod 2) xs) mod 2 = l mod 2 \<and>
+ eval_dioph ks (map (\<lambda>x. x div 2) xs) =
+ (l - eval_dioph ks (map (\<lambda>x. x mod 2) xs)) div 2)"
+ by (smt eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
+
+
+section {* Monomorphization examples *}
+
+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 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 g1 g2 g3 list.size)
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/cvc3_solver.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,48 @@
+(* Title: HOL/Tools/SMT/cvc3_solver.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Interface of the SMT solver CVC3.
+*)
+
+signature CVC3_SOLVER =
+sig
+ val setup: theory -> theory
+end
+
+structure CVC3_Solver: CVC3_SOLVER =
+struct
+
+val solver_name = "cvc3"
+val env_var = "CVC3_SOLVER"
+
+val options = ["-lang", "smtlib", "-output-lang", "presentation"]
+
+val is_sat = String.isPrefix "Satisfiable."
+val is_unsat = String.isPrefix "Unsatisfiable."
+val is_unknown = String.isPrefix "Unknown."
+
+fun raise_cex real = raise SMT_Solver.SMT_COUNTEREXAMPLE (real, [])
+
+fun core_oracle (output, _) =
+ let
+ val empty_line = (fn "" => true | _ => false)
+ val split_first = (fn [] => ("", []) | l :: ls => (l, ls))
+ val (l, _) = split_first (dropwhile empty_line output)
+ in
+ if is_unsat l then @{cprop False}
+ else if is_sat l then raise_cex true
+ else if is_unknown l then raise_cex false
+ else raise SMT_Solver.SMT (solver_name ^ " failed")
+ end
+
+fun smtlib_solver oracle _ = {
+ command = {env_var=env_var, remote_name=SOME solver_name},
+ arguments = options,
+ interface = SMTLIB_Interface.interface,
+ reconstruct = pair o oracle }
+
+val setup =
+ Thm.add_oracle (Binding.name solver_name, core_oracle) #-> (fn (_, oracle) =>
+ SMT_Solver.add_solver (solver_name, smtlib_solver oracle))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/etc/settings Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,13 @@
+ISABELLE_SMT="$COMPONENT"
+
+REMOTE_SMT="$ISABELLE_SMT/lib/scripts/remote_smt"
+
+REMOTE_SMT_URL="http://smt.in.tum.de/smt"
+
+#
+# Paths to local SMT solvers:
+#
+# CVC_SOLVER=PATH
+# YICES_SOLVER=PATH
+# Z3_SOLVER=PATH
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/lib/scripts/remote_smt Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,31 @@
+#!/usr/bin/env perl
+#
+# Author: Sascha Boehme, TU Muenchen
+#
+# Invoke remote SMT solvers.
+
+use strict;
+use warnings;
+use LWP;
+
+
+# arguments
+
+my $solver = $ARGV[0];
+my @options = @ARGV[1 .. ($#ARGV - 1)];
+my $problem_file = $ARGV[-1];
+
+
+# call solver
+
+my $agent = LWP::UserAgent->new;
+$agent->agent("SMT-Request");
+$agent->timeout(180);
+my $response = $agent->post($ENV{"REMOTE_SMT_URL"}, [
+ "Solver" => $solver,
+ "Options" => join(" ", @options),
+ "Problem" => [$problem_file] ],
+ "Content_Type" => "form-data");
+if (not $response->is_success) { die "HTTP-Error: " . $response->message; }
+else { print $response->content; }
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_monomorph.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,201 @@
+(* Title: HOL/Tools/SMT/smt_monomorph.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Monomorphization of theorems, i.e., computation of all (necessary) instances.
+*)
+
+signature SMT_MONOMORPH =
+sig
+ val monomorph: thm list -> Proof.context -> thm list * Proof.context
+end
+
+structure SMT_Monomorph: SMT_MONOMORPH =
+struct
+
+val typ_has_tvars = Term.exists_subtype (fn TVar _ => true | _ => false)
+
+val ignored = member (op =) [
+ @{const_name All}, @{const_name Ex}, @{const_name Let}, @{const_name If},
+ @{const_name "op ="}, @{const_name zero_class.zero},
+ @{const_name one_class.one}, @{const_name number_of}]
+
+fun is_const f (n, T) = not (ignored n) andalso f T
+fun add_const_if f g (Const c) = if is_const f c then g c else I
+ | add_const_if _ _ _ = I
+
+fun collect_consts_if f g thm =
+ Term.fold_aterms (add_const_if f g) (Thm.prop_of thm)
+
+fun add_consts f =
+ collect_consts_if f (fn (n, T) => Symtab.map_entry n (insert (op =) T))
+
+val insert_const = OrdList.insert (prod_ord fast_string_ord Term_Ord.typ_ord)
+fun tvar_consts_of thm = collect_consts_if typ_has_tvars insert_const thm []
+
+
+fun incr_indexes thms =
+ let fun inc thm idx = (Thm.incr_indexes idx thm, Thm.maxidx_of thm + idx + 1)
+ in fst (fold_map inc thms 0) end
+
+
+(* Compute all substitutions from the types "Ts" to all relevant
+ types in "grounds", with respect to the given substitution. *)
+fun new_substitutions thy grounds (n, T) subst =
+ if not (typ_has_tvars T) then [subst]
+ else
+ Symtab.lookup_list grounds n
+ |> map_filter (try (fn U => Sign.typ_match thy (T, U) subst))
+ |> cons subst
+
+
+(* Instantiate a set of constants with a substitution. Also collect
+ all new ground instances for the next round of specialization. *)
+fun apply_subst grounds consts subst =
+ let
+ fun is_new_ground (n, T) = not (typ_has_tvars T) andalso
+ not (member (op =) (Symtab.lookup_list grounds n) T)
+
+ fun apply_const (n, T) new_grounds =
+ let val c = (n, Envir.subst_type subst T)
+ in
+ new_grounds
+ |> is_new_ground c ? Symtab.insert_list (op =) c
+ |> pair c
+ end
+ in fold_map apply_const consts #>> pair subst end
+
+
+(* Compute new substitutions for the theorem "thm", based on
+ previously found substitutions.
+ Also collect new grounds, i.e., instantiated constants
+ (without schematic types) which do not occur in any of the
+ previous rounds. Note that thus no schematic type variables are
+ shared among theorems. *)
+fun specialize thy all_grounds new_grounds (thm, scs) =
+ let
+ fun spec (subst, consts) next_grounds =
+ [subst]
+ |> fold (maps o new_substitutions thy new_grounds) consts
+ |> rpair next_grounds
+ |-> fold_map (apply_subst all_grounds consts)
+ in
+ fold_map spec scs #>> (fn scss =>
+ (thm, fold (fold (insert (eq_snd (op =)))) scss []))
+ end
+
+
+(* Compute all necessary substitutions.
+ Instead of operating on the propositions of the theorems, the
+ computation uses only the constants occurring with schematic type
+ variables in the propositions. To ease comparisons, such sets of
+ costants are always kept in their initial order. *)
+fun incremental_monomorph thy limit all_grounds new_grounds ths =
+ let
+ val all_grounds' = Symtab.merge_list (op =) (all_grounds, new_grounds)
+ val spec = specialize thy all_grounds' new_grounds
+ val (ths', new_grounds') = fold_map spec ths Symtab.empty
+ in
+ if Symtab.is_empty new_grounds' then ths'
+ else if limit > 0
+ then incremental_monomorph thy (limit-1) all_grounds' new_grounds' ths'
+ else (warning "SMT: monomorphization limit reached"; ths')
+ end
+
+
+fun filter_most_specific thy =
+ let
+ fun typ_match (_, T) (_, U) = Sign.typ_match thy (T, U)
+
+ fun is_trivial subst = Vartab.is_empty subst orelse
+ forall (fn (v, (S, T)) => TVar (v, S) = T) (Vartab.dest subst)
+
+ fun match general specific =
+ (case try (fold2 typ_match general specific) Vartab.empty of
+ NONE => false
+ | SOME subst => not (is_trivial subst))
+
+ fun most_specific _ [] = []
+ | most_specific css ((ss, cs) :: scs) =
+ let val substs = most_specific (cs :: css) scs
+ in
+ if exists (match cs) css orelse exists (match cs o snd) scs
+ then substs else ss :: substs
+ end
+
+ in most_specific [] end
+
+
+fun instantiate thy Tenv =
+ let
+ fun replace (v, (_, T)) (U as TVar (u, _)) = if u = v then T else U
+ | replace _ T = T
+
+ fun complete (vT as (v, _)) subst =
+ subst
+ |> not (Vartab.defined subst v) ? Vartab.update vT
+ |> Vartab.map (apsnd (Term.map_atyps (replace vT)))
+
+ fun cert (ix, (S, T)) = pairself (Thm.ctyp_of thy) (TVar (ix, S), T)
+
+ fun inst thm subst =
+ let val cTs = Vartab.fold (cons o cert) (fold complete Tenv subst) []
+ in Thm.instantiate (cTs, []) thm end
+
+ in uncurry (map o inst) end
+
+
+fun mono_all ctxt _ [] monos = (monos, ctxt)
+ | mono_all ctxt limit polys monos =
+ let
+ fun invent_types thm ctxt =
+ let val (vs, Ss) = split_list (Term.add_tvars (Thm.prop_of thm) [])
+ in
+ ctxt
+ |> Variable.invent_types Ss
+ |>> map2 (fn v => fn (n, S) => (v, (S, TFree (n, S)))) vs
+ end
+ val (Tenvs, ctxt') = fold_map invent_types polys ctxt
+
+ val thy = ProofContext.theory_of ctxt'
+
+ val ths = polys
+ |> map (fn thm => (thm, [(Vartab.empty, tvar_consts_of thm)]))
+
+ (* all constant names occurring with schematic types *)
+ val ns = fold (fold (fold (insert (op =) o fst) o snd) o snd) ths []
+
+ (* all known instances with non-schematic types *)
+ val grounds =
+ Symtab.make (map (rpair []) ns)
+ |> fold (add_consts (K true)) monos
+ |> fold (add_consts (not o typ_has_tvars)) polys
+ in
+ polys
+ |> map (fn thm => (thm, [(Vartab.empty, tvar_consts_of thm)]))
+ |> incremental_monomorph thy limit Symtab.empty grounds
+ |> map (apsnd (filter_most_specific thy))
+ |> flat o map2 (instantiate thy) Tenvs
+ |> append monos
+ |> rpair ctxt'
+ end
+
+
+val monomorph_limit = 10
+
+
+(* Instantiate all polymorphic constants (i.e., constants occurring
+ both with ground types and type variables) with all (necessary)
+ ground types; thereby create copies of theorems containing those
+ constants.
+ To prevent non-termination, there is an upper limit for the
+ number of recursions involved in the fixpoint construction.
+ The initial set of theorems must not contain any schematic term
+ variables, and the final list of theorems does not contain any
+ schematic type variables anymore. *)
+fun monomorph thms ctxt =
+ thms
+ |> List.partition (Term.exists_type typ_has_tvars o Thm.prop_of)
+ |>> incr_indexes
+ |-> mono_all ctxt monomorph_limit
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_normalize.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,448 @@
+(* Title: HOL/Tools/SMT/smt_normalize.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Normalization steps on theorems required by SMT solvers:
+ * simplify trivial distincts (those with less than three elements),
+ * rewrite bool case expressions as if expressions,
+ * normalize numerals (e.g. replace negative numerals by negated positive
+ numerals),
+ * embed natural numbers into integers,
+ * add extra rules specifying types and constants which occur frequently,
+ * fully translate into object logic, add universal closure,
+ * lift lambda terms,
+ * make applications explicit for functions with varying number of arguments.
+*)
+
+signature SMT_NORMALIZE =
+sig
+ type extra_norm = thm list -> Proof.context -> thm list * Proof.context
+ val normalize: extra_norm -> thm list -> Proof.context ->
+ thm list * Proof.context
+ val eta_expand_conv: (Proof.context -> conv) -> Proof.context -> conv
+end
+
+structure SMT_Normalize: SMT_NORMALIZE =
+struct
+
+infix 2 ??
+fun (test ?? f) x = if test x then f x else x
+
+fun if_conv c cv1 cv2 ct = (if c (Thm.term_of ct) then cv1 else cv2) ct
+fun if_true_conv c cv = if_conv c cv Conv.all_conv
+
+
+
+(* simplification of trivial distincts (distinct should have at least
+ three elements in the argument list) *)
+
+local
+ fun is_trivial_distinct (Const (@{const_name distinct}, _) $ t) =
+ length (HOLogic.dest_list t) <= 2
+ | is_trivial_distinct _ = false
+
+ val thms = @{lemma
+ "distinct [] == True"
+ "distinct [x] == True"
+ "distinct [x, y] == (x ~= y)"
+ by simp_all}
+ fun distinct_conv _ =
+ if_true_conv is_trivial_distinct (More_Conv.rewrs_conv thms)
+in
+fun trivial_distinct ctxt =
+ map ((Term.exists_subterm is_trivial_distinct o Thm.prop_of) ??
+ Conv.fconv_rule (More_Conv.top_conv distinct_conv ctxt))
+end
+
+
+
+(* rewrite bool case expressions as if expressions *)
+
+local
+ val is_bool_case = (fn
+ Const (@{const_name "bool.bool_case"}, _) $ _ $ _ $ _ => true
+ | _ => false)
+
+ val thms = @{lemma
+ "(case P of True => x | False => y) == (if P then x else y)"
+ "(case P of False => y | True => x) == (if P then x else y)"
+ by (rule eq_reflection, simp)+}
+ val unfold_conv = if_true_conv is_bool_case (More_Conv.rewrs_conv thms)
+in
+fun rewrite_bool_cases ctxt =
+ map ((Term.exists_subterm is_bool_case o Thm.prop_of) ??
+ Conv.fconv_rule (More_Conv.top_conv (K unfold_conv) ctxt))
+end
+
+
+
+(* normalization of numerals: rewriting of negative integer numerals into
+ positive numerals, Numeral0 into 0, Numeral1 into 1 *)
+
+local
+ fun is_number_sort ctxt T =
+ Sign.of_sort (ProofContext.theory_of ctxt) (T, @{sort number_ring})
+
+ fun is_strange_number ctxt (t as Const (@{const_name number_of}, _) $ _) =
+ (case try HOLogic.dest_number t of
+ SOME (T, i) => is_number_sort ctxt T andalso i < 2
+ | NONE => false)
+ | is_strange_number _ _ = false
+
+ val pos_numeral_ss = HOL_ss
+ addsimps [@{thm Int.number_of_minus}, @{thm Int.number_of_Min}]
+ addsimps [@{thm Int.number_of_Pls}, @{thm Int.numeral_1_eq_1}]
+ addsimps @{thms Int.pred_bin_simps}
+ addsimps @{thms Int.normalize_bin_simps}
+ addsimps @{lemma
+ "Int.Min = - Int.Bit1 Int.Pls"
+ "Int.Bit0 (- Int.Pls) = - Int.Pls"
+ "Int.Bit0 (- k) = - Int.Bit0 k"
+ "Int.Bit1 (- k) = - Int.Bit1 (Int.pred k)"
+ by simp_all (simp add: pred_def)}
+
+ fun pos_conv ctxt = if_conv (is_strange_number ctxt)
+ (Simplifier.rewrite (Simplifier.context ctxt pos_numeral_ss))
+ Conv.no_conv
+in
+fun normalize_numerals ctxt =
+ map ((Term.exists_subterm (is_strange_number ctxt) o Thm.prop_of) ??
+ Conv.fconv_rule (More_Conv.top_sweep_conv pos_conv ctxt))
+end
+
+
+
+(* embedding of standard natural number operations into integer operations *)
+
+local
+ val nat_embedding = @{lemma
+ "nat (int n) = n"
+ "i >= 0 --> int (nat i) = i"
+ "i < 0 --> int (nat i) = 0"
+ by simp_all}
+
+ val nat_rewriting = @{lemma
+ "0 = nat 0"
+ "1 = nat 1"
+ "number_of i = nat (number_of i)"
+ "int (nat 0) = 0"
+ "int (nat 1) = 1"
+ "a < b = (int a < int b)"
+ "a <= b = (int a <= int b)"
+ "Suc a = nat (int a + 1)"
+ "a + b = nat (int a + int b)"
+ "a - b = nat (int a - int b)"
+ "a * b = nat (int a * int b)"
+ "a div b = nat (int a div int b)"
+ "a mod b = nat (int a mod int b)"
+ "min a b = nat (min (int a) (int b))"
+ "max a b = nat (max (int a) (int b))"
+ "int (nat (int a + int b)) = int a + int b"
+ "int (nat (int a * int b)) = int a * int b"
+ "int (nat (int a div int b)) = int a div int b"
+ "int (nat (int a mod int b)) = int a mod int b"
+ "int (nat (min (int a) (int b))) = min (int a) (int b)"
+ "int (nat (max (int a) (int b))) = max (int a) (int b)"
+ by (simp_all add: nat_mult_distrib nat_div_distrib nat_mod_distrib
+ int_mult[symmetric] zdiv_int[symmetric] zmod_int[symmetric])}
+
+ fun on_positive num f x =
+ (case try HOLogic.dest_number (Thm.term_of num) of
+ SOME (_, i) => if i >= 0 then SOME (f x) else NONE
+ | NONE => NONE)
+
+ val cancel_int_nat_ss = HOL_ss
+ addsimps [@{thm Nat_Numeral.nat_number_of}]
+ addsimps [@{thm Nat_Numeral.int_nat_number_of}]
+ addsimps @{thms neg_simps}
+
+ fun cancel_int_nat_simproc _ ss ct =
+ let
+ val num = Thm.dest_arg (Thm.dest_arg ct)
+ val goal = Thm.mk_binop @{cterm "op == :: int => _"} ct num
+ val simpset = Simplifier.inherit_context ss cancel_int_nat_ss
+ fun tac _ = Simplifier.simp_tac simpset 1
+ in on_positive num (Goal.prove_internal [] goal) tac end
+
+ val nat_ss = HOL_ss
+ addsimps nat_rewriting
+ addsimprocs [Simplifier.make_simproc {
+ name = "cancel_int_nat_num", lhss = [@{cpat "int (nat _)"}],
+ proc = cancel_int_nat_simproc, identifier = [] }]
+
+ fun conv ctxt = Simplifier.rewrite (Simplifier.context ctxt nat_ss)
+
+ val uses_nat_type = Term.exists_type (Term.exists_subtype (equal @{typ nat}))
+ val uses_nat_int =
+ Term.exists_subterm (member (op aconv) [@{term int}, @{term nat}])
+in
+fun nat_as_int ctxt =
+ map ((uses_nat_type o Thm.prop_of) ?? Conv.fconv_rule (conv ctxt)) #>
+ exists (uses_nat_int o Thm.prop_of) ?? append nat_embedding
+end
+
+
+
+(* further normalizations: beta/eta, universal closure, atomize *)
+
+val eta_expand_eq = @{lemma "f == (%x. f x)" by (rule reflexive)}
+
+fun eta_expand_conv cv ctxt =
+ Conv.rewr_conv eta_expand_eq then_conv Conv.abs_conv (cv o snd) ctxt
+
+local
+ val eta_conv = eta_expand_conv
+
+ fun keep_conv ctxt = More_Conv.binder_conv norm_conv ctxt
+ and eta_binder_conv ctxt = Conv.arg_conv (eta_conv norm_conv ctxt)
+ and keep_let_conv ctxt = Conv.combination_conv
+ (Conv.arg_conv (norm_conv ctxt)) (Conv.abs_conv (norm_conv o snd) ctxt)
+ and unfold_let_conv ctxt = Conv.combination_conv
+ (Conv.arg_conv (norm_conv ctxt)) (eta_conv norm_conv ctxt)
+ and unfold_conv thm ctxt = Conv.rewr_conv thm then_conv keep_conv ctxt
+ and unfold_ex1_conv ctxt = unfold_conv @{thm Ex1_def} ctxt
+ and unfold_ball_conv ctxt = unfold_conv @{thm Ball_def} ctxt
+ and unfold_bex_conv ctxt = unfold_conv @{thm Bex_def} ctxt
+ and norm_conv ctxt ct =
+ (case Thm.term_of ct of
+ Const (@{const_name All}, _) $ Abs _ => keep_conv
+ | Const (@{const_name All}, _) $ _ => eta_binder_conv
+ | Const (@{const_name All}, _) => eta_conv eta_binder_conv
+ | Const (@{const_name Ex}, _) $ Abs _ => keep_conv
+ | Const (@{const_name Ex}, _) $ _ => eta_binder_conv
+ | Const (@{const_name Ex}, _) => eta_conv eta_binder_conv
+ | Const (@{const_name Let}, _) $ _ $ Abs _ => keep_let_conv
+ | Const (@{const_name Let}, _) $ _ $ _ => unfold_let_conv
+ | Const (@{const_name Let}, _) $ _ => eta_conv unfold_let_conv
+ | Const (@{const_name Let}, _) => eta_conv (eta_conv unfold_let_conv)
+ | Const (@{const_name Ex1}, _) $ _ => unfold_ex1_conv
+ | Const (@{const_name Ex1}, _) => eta_conv unfold_ex1_conv
+ | Const (@{const_name Ball}, _) $ _ $ _ => unfold_ball_conv
+ | Const (@{const_name Ball}, _) $ _ => eta_conv unfold_ball_conv
+ | Const (@{const_name Ball}, _) => eta_conv (eta_conv unfold_ball_conv)
+ | Const (@{const_name Bex}, _) $ _ $ _ => unfold_bex_conv
+ | Const (@{const_name Bex}, _) $ _ => eta_conv unfold_bex_conv
+ | Const (@{const_name Bex}, _) => eta_conv (eta_conv unfold_bex_conv)
+ | Abs _ => Conv.abs_conv (norm_conv o snd)
+ | _ $ _ => Conv.comb_conv o norm_conv
+ | _ => K Conv.all_conv) ctxt ct
+
+ fun is_normed t =
+ (case t of
+ Const (@{const_name All}, _) $ Abs (_, _, u) => is_normed u
+ | Const (@{const_name All}, _) $ _ => false
+ | Const (@{const_name All}, _) => false
+ | Const (@{const_name Ex}, _) $ Abs (_, _, u) => is_normed u
+ | Const (@{const_name Ex}, _) $ _ => false
+ | Const (@{const_name Ex}, _) => false
+ | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>
+ is_normed u1 andalso is_normed u2
+ | Const (@{const_name Let}, _) $ _ $ _ => false
+ | Const (@{const_name Let}, _) $ _ => false
+ | Const (@{const_name Let}, _) => false
+ | Const (@{const_name Ex1}, _) => false
+ | Const (@{const_name Ball}, _) => false
+ | Const (@{const_name Bex}, _) => false
+ | Abs (_, _, u) => is_normed u
+ | u1 $ u2 => is_normed u1 andalso is_normed u2
+ | _ => true)
+in
+fun norm_binder_conv ctxt = if_conv is_normed Conv.all_conv (norm_conv ctxt)
+end
+
+fun norm_def ctxt thm =
+ (case Thm.prop_of thm of
+ @{term Trueprop} $ (Const (@{const_name "op ="}, _) $ _ $ Abs _) =>
+ norm_def ctxt (thm RS @{thm fun_cong})
+ | Const (@{const_name "=="}, _) $ _ $ Abs _ =>
+ norm_def ctxt (thm RS @{thm meta_eq_to_obj_eq})
+ | _ => thm)
+
+fun atomize_conv ctxt ct =
+ (case Thm.term_of ct of
+ @{term "op ==>"} $ _ $ _ =>
+ Conv.binop_conv (atomize_conv ctxt) then_conv
+ Conv.rewr_conv @{thm atomize_imp}
+ | Const (@{const_name "=="}, _) $ _ $ _ =>
+ Conv.binop_conv (atomize_conv ctxt) then_conv
+ Conv.rewr_conv @{thm atomize_eq}
+ | Const (@{const_name all}, _) $ Abs _ =>
+ More_Conv.binder_conv atomize_conv ctxt then_conv
+ Conv.rewr_conv @{thm atomize_all}
+ | _ => Conv.all_conv) ct
+
+fun normalize_rule ctxt =
+ Conv.fconv_rule (
+ (* reduce lambda abstractions, except at known binders: *)
+ Thm.beta_conversion true then_conv
+ Thm.eta_conversion then_conv
+ norm_binder_conv ctxt) #>
+ norm_def ctxt #>
+ Drule.forall_intr_vars #>
+ Conv.fconv_rule (atomize_conv ctxt)
+
+
+
+(* lift lambda terms into additional rules *)
+
+local
+ val meta_eq = @{cpat "op =="}
+ val meta_eqT = hd (Thm.dest_ctyp (Thm.ctyp_of_term meta_eq))
+ 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 cert ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
+
+ 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 apply cv thm =
+ let val thm' = Thm.combination thm (Thm.reflexive cv)
+ in Thm.transitive thm' (Thm.beta_conversion false (Thm.rhs_of thm')) end
+ fun apply_def cvs eq = Thm.symmetric (fold apply cvs eq)
+
+ fun replace_lambda cvs ct (cx as (ctxt, defs)) =
+ let
+ val cvs' = used_vars cvs ct
+ val ct' = fold_rev Thm.cabs cvs' ct
+ in
+ (case Termtab.lookup defs (Thm.term_of ct') of
+ SOME eq => (apply_def cvs' eq, cx)
+ | NONE =>
+ let
+ val {T, ...} = Thm.rep_cterm ct' and n = Name.uu
+ val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
+ val cu = mk_meta_eq (cert ctxt (Free (n', T))) ct'
+ val (eq, ctxt'') = yield_singleton Assumption.add_assumes cu ctxt'
+ val defs' = Termtab.update (Thm.term_of ct', eq) defs
+ in (apply_def cvs' eq, (ctxt'', 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 (ctxt, defs) =
+ let
+ val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
+ val (cv, cu) = Thm.dest_abs (SOME n) ct
+ in (ctxt', defs) |> f (cv :: cvs) cu |>> Thm.abstract_rule n cv end
+
+ fun traverse cvs ct =
+ (case Thm.term_of ct of
+ Const (@{const_name All}, _) $ Abs _ => in_arg (in_abs traverse cvs)
+ | Const (@{const_name Ex}, _) $ Abs _ => in_arg (in_abs traverse cvs)
+ | Const (@{const_name Let}, _) $ _ $ Abs _ =>
+ in_comb (in_arg (traverse cvs)) (in_abs traverse cvs)
+ | Abs _ => at_lambda cvs
+ | _ $ _ => in_comb (traverse cvs) (traverse cvs)
+ | _ => none) ct
+
+ and at_lambda cvs ct =
+ in_abs traverse cvs ct #-> (fn thm =>
+ replace_lambda cvs (Thm.rhs_of thm) #>> Thm.transitive thm)
+
+ fun has_free_lambdas t =
+ (case t of
+ Const (@{const_name All}, _) $ Abs (_, _, u) => has_free_lambdas u
+ | Const (@{const_name Ex}, _) $ Abs (_, _, u) => has_free_lambdas u
+ | Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) =>
+ has_free_lambdas u1 orelse has_free_lambdas u2
+ | Abs _ => true
+ | u1 $ u2 => has_free_lambdas u1 orelse has_free_lambdas u2
+ | _ => false)
+
+ fun lift_lm f thm cx =
+ if not (has_free_lambdas (Thm.prop_of thm)) then (thm, cx)
+ else cx |> f (Thm.cprop_of thm) |>> (fn thm' => Thm.equal_elim thm' thm)
+in
+fun lift_lambdas thms ctxt =
+ let
+ val cx = (ctxt, Termtab.empty)
+ val (thms', (ctxt', defs)) = fold_map (lift_lm (traverse [])) thms cx
+ val eqs = Termtab.fold (cons o normalize_rule ctxt' o snd) defs []
+ in (eqs @ thms', ctxt') end
+end
+
+
+
+(* make application explicit for functions with varying number of arguments *)
+
+local
+ val const = prefix "c" and free = prefix "f"
+ fun min i (e as (_, j)) = if i <> j then (true, Int.min (i, j)) else e
+ fun add t i = Symtab.map_default (t, (false, i)) (min i)
+ fun traverse t =
+ (case Term.strip_comb t of
+ (Const (n, _), ts) => add (const n) (length ts) #> fold traverse ts
+ | (Free (n, _), ts) => add (free n) (length ts) #> fold traverse ts
+ | (Abs (_, _, u), ts) => fold traverse (u :: ts)
+ | (_, ts) => fold traverse ts)
+ val prune = (fn (n, (true, i)) => Symtab.update (n, i) | _ => I)
+ fun prune_tab tab = Symtab.fold prune tab Symtab.empty
+
+ fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
+ fun nary_conv conv1 conv2 ct =
+ (Conv.combination_conv (nary_conv conv1 conv2) conv2 else_conv conv1) ct
+ fun abs_conv conv tb = Conv.abs_conv (fn (cv, cx) =>
+ let val n = fst (Term.dest_Free (Thm.term_of cv))
+ in conv (Symtab.update (free n, 0) tb) cx end)
+ val apply_rule = @{lemma "f x == apply f x" by (simp add: apply_def)}
+in
+fun explicit_application ctxt thms =
+ let
+ fun sub_conv tb ctxt ct =
+ (case Term.strip_comb (Thm.term_of ct) of
+ (Const (n, _), ts) => app_conv tb (const n) (length ts) ctxt
+ | (Free (n, _), ts) => app_conv tb (free n) (length ts) ctxt
+ | (Abs _, _) => nary_conv (abs_conv sub_conv tb ctxt) (sub_conv tb ctxt)
+ | (_, _) => nary_conv Conv.all_conv (sub_conv tb ctxt)) ct
+ and app_conv tb n i ctxt =
+ (case Symtab.lookup tb n of
+ NONE => nary_conv Conv.all_conv (sub_conv tb ctxt)
+ | SOME j => apply_conv tb ctxt (i - j))
+ and apply_conv tb ctxt i ct = (
+ if i = 0 then nary_conv Conv.all_conv (sub_conv tb ctxt)
+ else
+ Conv.rewr_conv apply_rule then_conv
+ binop_conv (apply_conv tb ctxt (i-1)) (sub_conv tb ctxt)) ct
+
+ fun needs_exp_app tab = Term.exists_subterm (fn
+ Bound _ $ _ => true
+ | Const (n, _) => Symtab.defined tab (const n)
+ | Free (n, _) => Symtab.defined tab (free n)
+ | _ => false)
+
+ fun rewrite tab ctxt thm =
+ if not (needs_exp_app tab (Thm.prop_of thm)) then thm
+ else Conv.fconv_rule (sub_conv tab ctxt) thm
+
+ val tab = prune_tab (fold (traverse o Thm.prop_of) thms Symtab.empty)
+ in map (rewrite tab ctxt) thms end
+end
+
+
+
+(* combined normalization *)
+
+type extra_norm = thm list -> Proof.context -> thm list * Proof.context
+
+fun with_context f thms ctxt = (f ctxt thms, ctxt)
+
+fun normalize extra_norm thms ctxt =
+ thms
+ |> trivial_distinct ctxt
+ |> rewrite_bool_cases ctxt
+ |> normalize_numerals ctxt
+ |> nat_as_int ctxt
+ |> rpair ctxt
+ |-> extra_norm
+ |-> with_context (fn cx => map (normalize_rule cx))
+ |-> SMT_Monomorph.monomorph
+ |-> lift_lambdas
+ |-> with_context explicit_application
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_solver.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,360 @@
+(* Title: HOL/Tools/SMT/smt_solver.ML
+ Author: Sascha Boehme, TU Muenchen
+
+SMT solvers registry and SMT tactic.
+*)
+
+signature SMT_SOLVER =
+sig
+ exception SMT of string
+ exception SMT_COUNTEREXAMPLE of bool * term list
+
+ type interface = {
+ extra_norm: SMT_Normalize.extra_norm,
+ translate: SMT_Translate.config }
+ type solver_config = {
+ command: {env_var: string, remote_name: string option},
+ arguments: string list,
+ interface: interface,
+ reconstruct: (string list * SMT_Translate.recon) -> Proof.context ->
+ thm * Proof.context }
+
+ (*options*)
+ val timeout: int Config.T
+ val with_timeout: Proof.context -> ('a -> 'b) -> 'a -> 'b
+ val trace: bool Config.T
+ val trace_msg: Proof.context -> ('a -> string) -> 'a -> unit
+
+ (*certificates*)
+ val fixed_certificates: bool Config.T
+ val select_certificates: string -> Context.generic -> Context.generic
+
+ (*solvers*)
+ type solver = Proof.context -> thm list -> thm
+ type solver_info = Context.generic -> Pretty.T list
+ val add_solver: string * (Proof.context -> solver_config) -> theory ->
+ theory
+ val all_solver_names_of: theory -> string list
+ val add_solver_info: string * solver_info -> theory -> theory
+ val solver_name_of: Context.generic -> string
+ val select_solver: string -> Context.generic -> Context.generic
+ val solver_of: Context.generic -> solver
+
+ (*tactic*)
+ val smt_tac': bool -> Proof.context -> thm list -> int -> Tactical.tactic
+ val smt_tac: Proof.context -> thm list -> int -> Tactical.tactic
+
+ (*setup*)
+ val setup: theory -> theory
+ val print_setup: Context.generic -> unit
+end
+
+structure SMT_Solver: SMT_SOLVER =
+struct
+
+exception SMT of string
+exception SMT_COUNTEREXAMPLE of bool * term list
+
+
+type interface = {
+ extra_norm: SMT_Normalize.extra_norm,
+ translate: SMT_Translate.config }
+
+type solver_config = {
+ command: {env_var: string, remote_name: string option},
+ arguments: string list,
+ interface: interface,
+ reconstruct: (string list * SMT_Translate.recon) -> Proof.context ->
+ thm * Proof.context }
+
+
+
+(* SMT options *)
+
+val (timeout, setup_timeout) = Attrib.config_int "smt_timeout" (K 30)
+
+fun with_timeout ctxt f x =
+ TimeLimit.timeLimit (Time.fromSeconds (Config.get ctxt timeout)) f x
+ handle TimeLimit.TimeOut => raise SMT "timeout"
+
+val (trace, setup_trace) = Attrib.config_bool "smt_trace" (K false)
+
+fun trace_msg ctxt f x =
+ if Config.get ctxt trace then tracing (f x) else ()
+
+
+
+(* SMT certificates *)
+
+val (fixed_certificates, setup_fixed_certificates) =
+ Attrib.config_bool "smt_fixed" (K false)
+
+structure Certificates = Generic_Data
+(
+ type T = Cache_IO.cache option
+ val empty = NONE
+ val extend = I
+ fun merge (s, _) = s
+)
+
+val get_certificates_path =
+ Option.map (Cache_IO.cache_path_of) o Certificates.get
+
+fun select_certificates name = Certificates.put (
+ if name = "" then NONE
+ else SOME (Cache_IO.make (Path.explode name)))
+
+
+
+(* interface to external solvers *)
+
+local
+
+fun choose {env_var, remote_name} =
+ let
+ val local_solver = getenv env_var
+ val remote_solver = the_default "" remote_name
+ val remote_url = getenv "REMOTE_SMT_URL"
+ in
+ if local_solver <> ""
+ then
+ (tracing ("Invoking local SMT solver " ^ quote local_solver ^ " ...");
+ [local_solver])
+ else if remote_solver <> ""
+ then
+ (tracing ("Invoking remote SMT solver " ^ quote remote_solver ^ " at " ^
+ quote remote_url ^ " ...");
+ [getenv "REMOTE_SMT", remote_solver])
+ else error ("Undefined Isabelle environment variable: " ^ quote env_var)
+ end
+
+fun make_cmd solver args problem_path proof_path = space_implode " " (
+ map File.shell_quote (solver @ args) @
+ [File.shell_path problem_path, "2>&1", ">", File.shell_path proof_path])
+
+fun run ctxt cmd args input =
+ (case Certificates.get (Context.Proof ctxt) of
+ NONE => Cache_IO.run (make_cmd (choose cmd) args) input
+ | SOME certs =>
+ (case Cache_IO.lookup certs input of
+ (NONE, key) =>
+ if Config.get ctxt fixed_certificates
+ then error ("Bad certificates cache: missing certificate")
+ else Cache_IO.run_and_cache certs key (make_cmd (choose cmd) args)
+ input
+ | (SOME output, _) =>
+ (tracing ("Using cached certificate from " ^
+ File.shell_path (Cache_IO.cache_path_of certs) ^ " ...");
+ output)))
+
+in
+
+fun run_solver ctxt cmd args input =
+ let
+ fun pretty tag ls = Pretty.string_of (Pretty.big_list tag
+ (map Pretty.str ls))
+
+ val _ = trace_msg ctxt (pretty "SMT problem:" o split_lines) input
+
+ val (res, err) = with_timeout ctxt (run ctxt cmd args) input
+ val _ = trace_msg ctxt (pretty "SMT solver:") err
+
+ val ls = rev (dropwhile (equal "") (rev res))
+ val _ = trace_msg ctxt (pretty "SMT result:") ls
+ in ls end
+
+end
+
+fun trace_recon_data ctxt {typs, terms, ...} =
+ let
+ fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p]
+ fun pretty_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T)
+ fun pretty_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t)
+ in
+ trace_msg ctxt (fn () => Pretty.string_of (Pretty.big_list "SMT names:" [
+ Pretty.big_list "sorts:" (map pretty_typ (Symtab.dest typs)),
+ Pretty.big_list "functions:" (map pretty_term (Symtab.dest terms))])) ()
+ end
+
+fun invoke translate_config comments command arguments thms ctxt =
+ thms
+ |> SMT_Translate.translate translate_config ctxt comments
+ ||> tap (trace_recon_data ctxt)
+ |>> run_solver ctxt command arguments
+ |> rpair ctxt
+
+fun discharge_definitions thm =
+ if Thm.nprems_of thm = 0 then thm
+ else discharge_definitions (@{thm reflexive} RS thm)
+
+fun gen_solver name solver ctxt prems =
+ let
+ val {command, arguments, interface, reconstruct} = solver ctxt
+ val comments = ("solver: " ^ name) ::
+ ("timeout: " ^ string_of_int (Config.get ctxt timeout)) ::
+ "arguments:" :: arguments
+ val {extra_norm, translate} = interface
+ in
+ (prems, ctxt)
+ |-> SMT_Normalize.normalize extra_norm
+ |-> invoke translate comments command arguments
+ |-> reconstruct
+ |-> (fn thm => fn ctxt' => thm
+ |> singleton (ProofContext.export ctxt' ctxt)
+ |> discharge_definitions)
+ end
+
+
+
+(* solver store *)
+
+type solver = Proof.context -> thm list -> thm
+type solver_info = Context.generic -> Pretty.T list
+
+structure Solvers = Theory_Data
+(
+ type T = ((Proof.context -> solver_config) * solver_info) Symtab.table
+ val empty = Symtab.empty
+ val extend = I
+ fun merge data = Symtab.merge (K true) data
+ handle Symtab.DUP name => error ("Duplicate SMT solver: " ^ quote name)
+)
+
+val no_solver = "(none)"
+val add_solver = Solvers.map o Symtab.update_new o apsnd (rpair (K []))
+val all_solver_names_of = Symtab.keys o Solvers.get
+val lookup_solver = Symtab.lookup o Solvers.get
+fun add_solver_info (n, i) = Solvers.map (Symtab.map_entry n (apsnd (K i)))
+
+
+
+(* selected solver *)
+
+structure Selected_Solver = Generic_Data
+(
+ type T = string
+ val empty = no_solver
+ val extend = I
+ fun merge (s, _) = s
+)
+
+val solver_name_of = Selected_Solver.get
+
+fun select_solver name context =
+ if is_none (lookup_solver (Context.theory_of context) name)
+ then error ("SMT solver not registered: " ^ quote name)
+ else Selected_Solver.map (K name) context
+
+fun raw_solver_of context name =
+ (case lookup_solver (Context.theory_of context) name of
+ NONE => error "No SMT solver selected"
+ | SOME (s, _) => s)
+
+fun solver_of context =
+ let val name = solver_name_of context
+ in gen_solver name (raw_solver_of context name) end
+
+
+
+(* SMT tactic *)
+
+local
+ fun pretty_cex ctxt (real, ex) =
+ let
+ val msg = if real then "SMT: counterexample found"
+ else "SMT: potential counterexample found"
+ in
+ if null ex then msg ^ "."
+ else Pretty.string_of (Pretty.big_list (msg ^ ":")
+ (map (Syntax.pretty_term ctxt) ex))
+ end
+
+ fun fail_tac f msg st = (f msg; Tactical.no_tac st)
+
+ fun SAFE pass_exns tac ctxt i st =
+ if pass_exns then tac ctxt i st
+ else (tac ctxt i st
+ handle SMT msg => fail_tac (trace_msg ctxt (prefix "SMT: ")) msg st
+ | SMT_COUNTEREXAMPLE ce => fail_tac tracing (pretty_cex ctxt ce) st)
+
+ fun smt_solver rules ctxt = solver_of (Context.Proof ctxt) ctxt rules
+
+ val has_topsort = Term.exists_type (Term.exists_subtype (fn
+ TFree (_, []) => true
+ | TVar (_, []) => true
+ | _ => false))
+in
+fun smt_tac' pass_exns ctxt rules =
+ Tactic.rtac @{thm ccontr} THEN'
+ SUBPROOF (fn {context, prems, ...} =>
+ let val thms = rules @ prems
+ in
+ if exists (has_topsort o Thm.prop_of) thms
+ then fail_tac (trace_msg context I)
+ "SMT: proof state contains the universal sort {}"
+ else SAFE pass_exns (Tactic.rtac o smt_solver thms) context 1
+ end) ctxt
+
+val smt_tac = smt_tac' false
+end
+
+val smt_method =
+ Scan.optional Attrib.thms [] >>
+ (fn thms => fn ctxt => METHOD (fn facts =>
+ HEADGOAL (smt_tac ctxt (thms @ facts))))
+
+
+
+(* setup *)
+
+val setup =
+ Attrib.setup (Binding.name "smt_solver")
+ (Scan.lift (OuterParse.$$$ "=" |-- Args.name) >>
+ (Thm.declaration_attribute o K o select_solver))
+ "SMT solver configuration" #>
+ setup_timeout #>
+ setup_trace #>
+ setup_fixed_certificates #>
+ Attrib.setup (Binding.name "smt_certificates")
+ (Scan.lift (OuterParse.$$$ "=" |-- Args.name) >>
+ (Thm.declaration_attribute o K o select_certificates))
+ "SMT certificates" #>
+ Method.setup (Binding.name "smt") smt_method
+ "Applies an SMT solver to the current goal."
+
+
+fun print_setup gen =
+ let
+ val t = string_of_int (Config.get_generic gen timeout)
+ val names = sort_strings (all_solver_names_of (Context.theory_of gen))
+ val ns = if null names then [no_solver] else names
+ val take_info = (fn (_, []) => NONE | info => SOME info)
+ val infos =
+ Context.theory_of gen
+ |> Symtab.dest o Solvers.get
+ |> map_filter (fn (n, (_, info)) => take_info (n, info gen))
+ |> sort (prod_ord string_ord (K EQUAL))
+ |> map (fn (n, ps) => Pretty.big_list (n ^ ":") ps)
+ val certs_filename =
+ (case get_certificates_path gen of
+ SOME path => Path.implode path
+ | NONE => "(disabled)")
+ val fixed = if Config.get_generic gen fixed_certificates then "true"
+ else "false"
+ in
+ Pretty.writeln (Pretty.big_list "SMT setup:" [
+ Pretty.str ("Current SMT solver: " ^ solver_name_of gen),
+ Pretty.str_list "Available SMT solvers: " "" ns,
+ Pretty.str ("Current timeout: " ^ t ^ " seconds"),
+ Pretty.str ("Certificates cache: " ^ certs_filename),
+ Pretty.str ("Fixed certificates: " ^ fixed),
+ 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
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_translate.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,344 @@
+(* Title: HOL/Tools/SMT/smt_translate.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Translate theorems into an SMT intermediate format and serialize them.
+*)
+
+signature SMT_TRANSLATE =
+sig
+ (* intermediate term structure *)
+ datatype squant = SForall | SExists
+ datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
+ datatype sterm =
+ SVar of int |
+ SApp of string * sterm list |
+ SLet of string * sterm * sterm |
+ SQua of squant * string list * sterm spattern list * sterm
+
+ (* configuration options *)
+ type prefixes = {sort_prefix: string, func_prefix: string}
+ type strict = {
+ is_builtin_conn: string * typ -> bool,
+ is_builtin_pred: string * typ -> bool,
+ is_builtin_distinct: bool}
+ type builtins = {
+ builtin_typ: typ -> string option,
+ builtin_num: typ -> int -> string option,
+ builtin_fun: string * typ -> term list -> (string * term list) option }
+ datatype smt_theory = Integer | Real | Bitvector
+ type sign = {
+ theories: smt_theory list,
+ sorts: string list,
+ funcs: (string * (string list * string)) list }
+ type config = {
+ prefixes: prefixes,
+ strict: strict option,
+ builtins: builtins,
+ serialize: string list -> sign -> sterm list -> string }
+ type recon = {
+ typs: typ Symtab.table,
+ terms: term Symtab.table,
+ unfolds: thm list,
+ assms: thm list option }
+
+ val translate: config -> Proof.context -> string list -> thm list ->
+ string * recon
+end
+
+structure SMT_Translate: SMT_TRANSLATE =
+struct
+
+(* intermediate term structure *)
+
+datatype squant = SForall | SExists
+
+datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
+
+datatype sterm =
+ SVar of int |
+ SApp of string * sterm list |
+ SLet of string * sterm * sterm |
+ SQua of squant * string list * sterm spattern list * sterm
+
+
+
+(* configuration options *)
+
+type prefixes = {sort_prefix: string, func_prefix: string}
+
+type strict = {
+ is_builtin_conn: string * typ -> bool,
+ is_builtin_pred: string * typ -> bool,
+ is_builtin_distinct: bool}
+
+type builtins = {
+ builtin_typ: typ -> string option,
+ builtin_num: typ -> int -> string option,
+ builtin_fun: string * typ -> term list -> (string * term list) option }
+
+datatype smt_theory = Integer | Real | Bitvector
+
+type sign = {
+ theories: smt_theory list,
+ sorts: string list,
+ funcs: (string * (string list * string)) list }
+
+type config = {
+ prefixes: prefixes,
+ strict: strict option,
+ builtins: builtins,
+ serialize: string list -> sign -> sterm list -> string }
+
+type recon = {
+ typs: typ Symtab.table,
+ terms: term Symtab.table,
+ unfolds: thm list,
+ assms: thm list option }
+
+
+
+(* utility functions *)
+
+val dest_funT =
+ let
+ fun dest Ts 0 T = (rev Ts, T)
+ | dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U
+ | dest _ _ T = raise TYPE ("dest_funT", [T], [])
+ in dest [] end
+
+val quantifier = (fn
+ @{const_name All} => SOME SForall
+ | @{const_name Ex} => SOME SExists
+ | _ => NONE)
+
+fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) =
+ if q = qname then group_quant qname (T :: Ts) u else (Ts, t)
+ | group_quant _ Ts t = (Ts, t)
+
+fun dest_pat ts (Const (@{const_name pat}, _) $ t) = SPat (rev (t :: ts))
+ | dest_pat ts (Const (@{const_name nopat}, _) $ t) = SNoPat (rev (t :: ts))
+ | dest_pat ts (Const (@{const_name andpat}, _) $ p $ t) = dest_pat (t::ts) p
+ | dest_pat _ t = raise TERM ("dest_pat", [t])
+
+fun dest_trigger (@{term trigger} $ tl $ t) =
+ (map (dest_pat []) (HOLogic.dest_list tl), t)
+ | dest_trigger t = ([], t)
+
+fun dest_quant qn T t = quantifier qn |> Option.map (fn q =>
+ let
+ val (Ts, u) = group_quant qn [T] t
+ val (ps, b) = dest_trigger u
+ in (q, rev Ts, ps, b) end)
+
+fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
+ | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
+
+fun prop_of thm = HOLogic.dest_Trueprop (Thm.prop_of thm)
+
+
+
+(* enforce a strict separation between formulas and terms *)
+
+val term_eq_rewr = @{lemma "x term_eq y == x = y" by (simp add: term_eq_def)}
+
+val term_bool = @{lemma "~(True term_eq False)" by (simp add: term_eq_def)}
+val term_bool' = Simplifier.rewrite_rule [term_eq_rewr] term_bool
+
+
+val needs_rewrite = Thm.prop_of #> Term.exists_subterm (fn
+ Const (@{const_name Let}, _) => true
+ | @{term "op = :: bool => _"} $ _ $ @{term True} => true
+ | Const (@{const_name If}, _) $ _ $ @{term True} $ @{term False} => true
+ | _ => false)
+
+val rewrite_rules = [
+ Let_def,
+ @{lemma "P = True == P" by (rule eq_reflection) simp},
+ @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
+
+fun rewrite ctxt = Simplifier.full_rewrite
+ (Simplifier.context ctxt empty_ss addsimps rewrite_rules)
+
+fun normalize ctxt thm =
+ if needs_rewrite thm then Conv.fconv_rule (rewrite ctxt) thm else thm
+
+val unfold_rules = term_eq_rewr :: rewrite_rules
+
+
+val revert_types =
+ let
+ fun revert @{typ prop} = @{typ bool}
+ | revert (Type (n, Ts)) = Type (n, map revert Ts)
+ | revert T = T
+ in Term.map_types revert end
+
+
+fun strictify {is_builtin_conn, is_builtin_pred, is_builtin_distinct} ctxt =
+ let
+
+ fun is_builtin_conn' (@{const_name True}, _) = false
+ | is_builtin_conn' (@{const_name False}, _) = false
+ | is_builtin_conn' c = is_builtin_conn c
+
+ val propT = @{typ prop} and boolT = @{typ bool}
+ val as_propT = (fn @{typ bool} => propT | T => T)
+ fun mapTs f g = Term.strip_type #> (fn (Ts, T) => map f Ts ---> g T)
+ fun conn (n, T) = (n, mapTs as_propT as_propT T)
+ fun pred (n, T) = (n, mapTs I as_propT T)
+
+ val term_eq = @{term "op = :: bool => _"} |> Term.dest_Const |> pred
+ fun as_term t = Const term_eq $ t $ @{term True}
+
+ val if_term = Const (@{const_name If}, [propT, boolT, boolT] ---> boolT)
+ fun wrap_in_if t = if_term $ t $ @{term True} $ @{term False}
+
+ fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t))
+
+ fun in_term t =
+ (case Term.strip_comb t of
+ (c as Const (@{const_name If}, _), [t1, t2, t3]) =>
+ c $ in_form t1 $ in_term t2 $ in_term t3
+ | (h as Const c, ts) =>
+ if is_builtin_conn' (conn c) orelse is_builtin_pred (pred c)
+ then wrap_in_if (in_form t)
+ else Term.list_comb (h, map in_term ts)
+ | (h as Free _, ts) => Term.list_comb (h, map in_term ts)
+ | _ => t)
+
+ and in_pat ((c as Const (@{const_name pat}, _)) $ t) = c $ in_term t
+ | in_pat ((c as Const (@{const_name nopat}, _)) $ t) = c $ in_term t
+ | in_pat ((c as Const (@{const_name andpat}, _)) $ p $ t) =
+ c $ in_pat p $ in_term t
+ | in_pat t = raise TERM ("in_pat", [t])
+
+ and in_pats p = in_list @{typ pattern} in_pat p
+
+ and in_trig ((c as @{term trigger}) $ p $ t) = c $ in_pats p $ in_form t
+ | in_trig t = in_form t
+
+ and in_form t =
+ (case Term.strip_comb t of
+ (q as Const (qn, _), [Abs (n, T, t')]) =>
+ if is_some (quantifier qn) then q $ Abs (n, T, in_trig t')
+ else as_term (in_term t)
+ | (Const (c as (@{const_name distinct}, T)), [t']) =>
+ if is_builtin_distinct then Const (pred c) $ in_list T in_term t'
+ else as_term (in_term t)
+ | (Const c, ts) =>
+ if is_builtin_conn (conn c)
+ then Term.list_comb (Const (conn c), map in_form ts)
+ else if is_builtin_pred (pred c)
+ then Term.list_comb (Const (pred c), map in_term ts)
+ else as_term (in_term t)
+ | _ => as_term (in_term t))
+ in
+ map (normalize ctxt) #> (fn thms => ((unfold_rules, term_bool' :: thms),
+ map (in_form o prop_of) (term_bool :: thms)))
+ end
+
+
+
+(* translation from Isabelle terms into SMT intermediate terms *)
+
+val empty_context = (1, Typtab.empty, 1, Termtab.empty, [])
+
+fun make_sign (_, typs, _, terms, thys) = {
+ theories = thys,
+ sorts = Typtab.fold (cons o snd) typs [],
+ funcs = Termtab.fold (cons o snd) terms [] }
+
+fun make_recon (unfolds, assms) (_, typs, _, terms, _) = {
+ typs = Symtab.make (map swap (Typtab.dest typs)),
+ terms = Symtab.make (map (fn (t, (n, _)) => (n, t)) (Termtab.dest terms)),
+ unfolds = unfolds,
+ assms = SOME assms }
+
+fun string_of_index pre i = pre ^ string_of_int i
+
+fun add_theory T (Tidx, typs, idx, terms, thys) =
+ let
+ fun add @{typ int} = insert (op =) Integer
+ | add @{typ real} = insert (op =) Real
+ | add (Type (@{type_name word}, _)) = insert (op =) Bitvector
+ | add (Type (_, Ts)) = fold add Ts
+ | add _ = I
+ in (Tidx, typs, idx, terms, add T thys) end
+
+fun fresh_typ sort_prefix T (cx as (Tidx, typs, idx, terms, thys)) =
+ (case Typtab.lookup typs T of
+ SOME s => (s, cx)
+ | NONE =>
+ let
+ val s = string_of_index sort_prefix Tidx
+ val typs' = Typtab.update (T, s) typs
+ in (s, (Tidx+1, typs', idx, terms, thys)) end)
+
+fun fresh_fun func_prefix t ss (cx as (Tidx, typs, idx, terms, thys)) =
+ (case Termtab.lookup terms t of
+ SOME (f, _) => (f, cx)
+ | NONE =>
+ let
+ val f = string_of_index func_prefix idx
+ val terms' = Termtab.update (revert_types t, (f, ss)) terms
+ in (f, (Tidx, typs, idx+1, terms', thys)) end)
+
+fun relaxed thms = (([], thms), map prop_of thms)
+
+fun with_context f (ths, ts) =
+ let val (us, context) = fold_map f ts empty_context
+ in ((make_sign context, us), make_recon ths context) end
+
+
+fun translate {prefixes, strict, builtins, serialize} ctxt comments =
+ let
+ val {sort_prefix, func_prefix} = prefixes
+ val {builtin_typ, builtin_num, builtin_fun} = builtins
+
+ fun transT T = add_theory T #>
+ (case builtin_typ T of
+ SOME n => pair n
+ | NONE => fresh_typ sort_prefix T)
+
+ fun app n ts = SApp (n, ts)
+
+ fun trans t =
+ (case Term.strip_comb t of
+ (Const (qn, _), [Abs (_, T, t1)]) =>
+ (case dest_quant qn T t1 of
+ SOME (q, Ts, ps, b) =>
+ fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
+ trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', b'))
+ | NONE => raise TERM ("intermediate", [t]))
+ | (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) =>
+ transT T ##>> trans t1 ##>> trans t2 #>>
+ (fn ((U, u1), u2) => SLet (U, u1, u2))
+ | (h as Const (c as (@{const_name distinct}, T)), [t1]) =>
+ (case builtin_fun c (HOLogic.dest_list t1) of
+ SOME (n, ts) => add_theory T #> fold_map trans ts #>> app n
+ | NONE => transs h T [t1])
+ | (h as Const (c as (_, T)), ts) =>
+ (case try HOLogic.dest_number t of
+ SOME (T, i) =>
+ (case builtin_num T i of
+ SOME n => add_theory T #> pair (SApp (n, []))
+ | NONE => transs t T [])
+ | NONE =>
+ (case builtin_fun c ts of
+ SOME (n, ts') => add_theory T #> fold_map trans ts' #>> app n
+ | NONE => transs h T ts))
+ | (h as Free (_, T), ts) => transs h T ts
+ | (Bound i, []) => pair (SVar i)
+ | _ => raise TERM ("intermediate", [t]))
+
+ and transs t T ts =
+ let val (Us, U) = dest_funT (length ts) T
+ in
+ fold_map transT Us ##>> transT U #-> (fn Up =>
+ fresh_fun func_prefix t Up ##>> fold_map trans ts #>> SApp)
+ end
+ in
+ (if is_some strict then strictify (the strict) ctxt else relaxed) #>
+ with_context trans #>> uncurry (serialize comments)
+ end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smtlib_interface.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,287 @@
+(* Title: HOL/Tools/SMT/smtlib_interface.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Interface to SMT solvers based on the SMT-LIB format.
+*)
+
+signature SMTLIB_INTERFACE =
+sig
+ val interface: SMT_Solver.interface
+end
+
+structure SMTLIB_Interface: SMTLIB_INTERFACE =
+struct
+
+structure N = SMT_Normalize
+structure T = SMT_Translate
+
+
+
+(** facts about uninterpreted constants **)
+
+infix 2 ??
+fun (ex ?? f) thms = if exists (ex o Thm.prop_of) thms then f thms else thms
+
+
+(* pairs *)
+
+val pair_rules = [@{thm fst_conv}, @{thm snd_conv}, @{thm pair_collapse}]
+
+val pair_type = (fn Type (@{type_name "*"}, _) => true | _ => false)
+val exists_pair_type = Term.exists_type (Term.exists_subtype pair_type)
+
+val add_pair_rules = exists_pair_type ?? append pair_rules
+
+
+(* function update *)
+
+val fun_upd_rules = [@{thm fun_upd_same}, @{thm fun_upd_apply}]
+
+val is_fun_upd = (fn Const (@{const_name fun_upd}, _) => true | _ => false)
+val exists_fun_upd = Term.exists_subterm is_fun_upd
+
+val add_fun_upd_rules = exists_fun_upd ?? append fun_upd_rules
+
+
+(* abs/min/max *)
+
+val exists_abs_min_max = Term.exists_subterm (fn
+ Const (@{const_name abs}, _) => true
+ | Const (@{const_name min}, _) => true
+ | Const (@{const_name max}, _) => true
+ | _ => false)
+
+val unfold_abs_conv = Conv.rewr_conv @{thm abs_if[THEN eq_reflection]}
+val unfold_min_conv = Conv.rewr_conv @{thm min_def[THEN eq_reflection]}
+val unfold_max_conv = Conv.rewr_conv @{thm max_def[THEN eq_reflection]}
+
+fun expand_conv cv = N.eta_expand_conv (K cv)
+fun expand2_conv cv = N.eta_expand_conv (N.eta_expand_conv (K cv))
+
+fun unfold_def_conv ctxt ct =
+ (case Thm.term_of ct of
+ Const (@{const_name abs}, _) $ _ => unfold_abs_conv
+ | Const (@{const_name abs}, _) => expand_conv unfold_abs_conv ctxt
+ | Const (@{const_name min}, _) $ _ $ _ => unfold_min_conv
+ | Const (@{const_name min}, _) $ _ => expand_conv unfold_min_conv ctxt
+ | Const (@{const_name min}, _) => expand2_conv unfold_min_conv ctxt
+ | Const (@{const_name max}, _) $ _ $ _ => unfold_max_conv
+ | Const (@{const_name max}, _) $ _ => expand_conv unfold_max_conv ctxt
+ | Const (@{const_name max}, _) => expand2_conv unfold_max_conv ctxt
+ | _ => Conv.all_conv) ct
+
+fun unfold_abs_min_max_defs ctxt thm =
+ if exists_abs_min_max (Thm.prop_of thm)
+ then Conv.fconv_rule (More_Conv.top_conv unfold_def_conv ctxt) thm
+ else thm
+
+
+(* include additional facts *)
+
+fun extra_norm thms ctxt =
+ thms
+ |> add_pair_rules
+ |> add_fun_upd_rules
+ |> map (unfold_abs_min_max_defs ctxt)
+ |> rpair ctxt
+
+
+
+(** builtins **)
+
+fun dest_binT T =
+ (case T of
+ Type (@{type_name "Numeral_Type.num0"}, _) => 0
+ | Type (@{type_name "Numeral_Type.num1"}, _) => 1
+ | Type (@{type_name "Numeral_Type.bit0"}, [T]) => 2 * dest_binT T
+ | Type (@{type_name "Numeral_Type.bit1"}, [T]) => 1 + 2 * dest_binT T
+ | _ => raise TYPE ("dest_binT", [T], []))
+
+fun dest_wordT (Type (@{type_name word}, [T])) = dest_binT T
+ | dest_wordT T = raise TYPE ("dest_wordT", [T], [])
+
+fun index1 n i = n ^ "[" ^ string_of_int i ^ "]"
+fun index2 n i j = n ^ "[" ^ string_of_int i ^ ":" ^ string_of_int j ^ "]"
+
+fun builtin_typ @{typ int} = SOME "Int"
+ | builtin_typ @{typ real} = SOME "Real"
+ | builtin_typ (Type (@{type_name word}, [T])) =
+ Option.map (index1 "BitVec") (try dest_binT T)
+ | builtin_typ _ = NONE
+
+fun builtin_num @{typ int} i = SOME (string_of_int i)
+ | builtin_num @{typ real} i = SOME (string_of_int i ^ ".0")
+ | builtin_num (Type (@{type_name word}, [T])) i =
+ Option.map (index1 ("bv" ^ string_of_int i)) (try dest_binT T)
+ | builtin_num _ _ = NONE
+
+val is_propT = (fn @{typ prop} => true | _ => false)
+fun is_connT T = Term.strip_type T |> (fn (Us, U) => forall is_propT (U :: Us))
+fun is_predT T = is_propT (Term.body_type T)
+
+fun just c ts = SOME (c, ts)
+
+val is_arith_type = member (op =) [@{typ int}, @{typ real}] o Term.domain_type
+
+fun fixed_bvT (Ts, T) x =
+ if forall (can dest_wordT) (T :: Ts) then SOME x else NONE
+
+fun if_fixed_bvT' T = fixed_bvT ([], Term.domain_type T)
+fun if_fixed_bvT T = curry (fixed_bvT ([], Term.domain_type T))
+fun if_full_fixed_bvT T = curry (fixed_bvT (Term.strip_type T))
+
+fun dest_word_funT (Type ("fun", [T, U])) = (dest_wordT T, dest_wordT U)
+ | dest_word_funT T = raise TYPE ("dest_word_funT", [T], [])
+fun dest_nat (@{term nat} $ n :: ts) = (snd (HOLogic.dest_number n), ts)
+ | dest_nat ts = raise TERM ("dest_nat", ts)
+fun dest_nat_word_funT (T, ts) =
+ (dest_word_funT (Term.range_type T), dest_nat ts)
+
+fun bv_extend n T ts =
+ (case try dest_word_funT T of
+ SOME (i, j) => if j-i >= 0 then SOME (index1 n (j-i), ts) else NONE
+ | _ => NONE)
+
+fun bv_rotate n T ts =
+ try dest_nat ts
+ |> Option.map (fn (i, ts') => (index1 n i, ts'))
+
+fun bv_extract n T ts =
+ try dest_nat_word_funT (T, ts)
+ |> Option.map (fn ((_, i), (lb, ts')) => (index2 n (i + lb - 1) lb, ts'))
+
+
+fun conn @{const_name True} = SOME "true"
+ | conn @{const_name False} = SOME "false"
+ | conn @{const_name Not} = SOME "not"
+ | conn @{const_name "op &"} = SOME "and"
+ | conn @{const_name "op |"} = SOME "or"
+ | conn @{const_name "op -->"} = SOME "implies"
+ | conn @{const_name "op ="} = SOME "iff"
+ | conn @{const_name If} = SOME "if_then_else"
+ | conn _ = NONE
+
+fun pred @{const_name distinct} _ = SOME "distinct"
+ | pred @{const_name "op ="} _ = SOME "="
+ | pred @{const_name term_eq} _ = SOME "="
+ | pred @{const_name less} T =
+ if is_arith_type T then SOME "<"
+ else if_fixed_bvT' T "bvult"
+ | pred @{const_name less_eq} T =
+ if is_arith_type T then SOME "<="
+ else if_fixed_bvT' T "bvule"
+ | pred @{const_name word_sless} T = if_fixed_bvT' T "bvslt"
+ | pred @{const_name word_sle} T = if_fixed_bvT' T "bvsle"
+ | pred _ _ = NONE
+
+fun func @{const_name If} _ = just "ite"
+ | func @{const_name uminus} T =
+ if is_arith_type T then just "~"
+ else if_fixed_bvT T "bvneg"
+ | func @{const_name plus} T =
+ if is_arith_type T then just "+"
+ else if_fixed_bvT T "bvadd"
+ | func @{const_name minus} T =
+ if is_arith_type T then just "-"
+ else if_fixed_bvT T "bvsub"
+ | func @{const_name times} T =
+ if is_arith_type T then just "*"
+ else if_fixed_bvT T "bvmul"
+ | func @{const_name bitNOT} T = if_fixed_bvT T "bvnot"
+ | func @{const_name bitAND} T = if_fixed_bvT T "bvand"
+ | func @{const_name bitOR} T = if_fixed_bvT T "bvor"
+ | func @{const_name bitXOR} T = if_fixed_bvT T "bvxor"
+ | func @{const_name div} T = if_fixed_bvT T "bvudiv"
+ | func @{const_name mod} T = if_fixed_bvT T "bvurem"
+ | func @{const_name sdiv} T = if_fixed_bvT T "bvsdiv"
+ | func @{const_name smod} T = if_fixed_bvT T "bvsmod"
+ | func @{const_name srem} T = if_fixed_bvT T "bvsrem"
+ | func @{const_name word_cat} T = if_full_fixed_bvT T "concat"
+ | func @{const_name bv_shl} T = if_full_fixed_bvT T "bvshl"
+ | func @{const_name bv_lshr} T = if_full_fixed_bvT T "bvlshr"
+ | func @{const_name bv_ashr} T = if_full_fixed_bvT T "bvashr"
+ | func @{const_name slice} T = bv_extract "extract" T
+ | func @{const_name ucast} T = bv_extend "zero_extend" T
+ | func @{const_name scast} T = bv_extend "sign_extend" T
+ | func @{const_name word_rotl} T = bv_rotate "rotate_left" T
+ | func @{const_name word_rotr} T = bv_rotate "rotate_right" T
+ | func _ _ = K NONE
+
+fun is_builtin_conn (n, T) = is_connT T andalso is_some (conn n)
+fun is_builtin_pred (n, T) = is_predT T andalso is_some (pred n T)
+
+fun builtin_fun (n, T) ts =
+ if is_connT T then conn n |> Option.map (rpair ts)
+ else if is_predT T then pred n T |> Option.map (rpair ts)
+ else func n T ts
+
+
+
+(** serialization **)
+
+val add = Buffer.add
+fun sep f = add " " #> f
+fun enclose l r f = sep (add l #> f #> add r)
+val par = enclose "(" ")"
+fun app n f = (fn [] => sep (add n) | xs => par (add n #> fold f xs))
+fun line f = f #> add "\n"
+
+fun var i = add "?v" #> add (string_of_int i)
+
+fun sterm l (T.SVar i) = sep (var (l - i - 1))
+ | sterm l (T.SApp (n, ts)) = app n (sterm l) ts
+ | sterm _ (T.SLet _) = raise Fail "SMT-LIB: unsupported let expression"
+ | sterm l (T.SQua (q, ss, ps, t)) =
+ let
+ val quant = add o (fn T.SForall => "forall" | T.SExists => "exists")
+ val vs = map_index (apfst (Integer.add l)) ss
+ fun var_decl (i, s) = par (var i #> sep (add s))
+ val sub = sterm (l + length ss)
+ fun pat kind ts = sep (add kind #> enclose "{" " }" (fold sub ts))
+ fun pats (T.SPat ts) = pat ":pat" ts
+ | pats (T.SNoPat ts) = pat ":nopat" ts
+ in par (quant q #> fold var_decl vs #> sub t #> fold pats ps) end
+
+fun choose_logic theories =
+ if member (op =) theories T.Bitvector then "QF_AUFBV"
+ else if member (op =) theories T.Real then "AUFLIRA"
+ else "AUFLIA"
+
+fun serialize comments {theories, sorts, funcs} ts =
+ Buffer.empty
+ |> line (add "(benchmark Isabelle")
+ |> line (add ":status unknown")
+ |> line (add ":logic " #> add (choose_logic theories))
+ |> length sorts > 0 ?
+ line (add ":extrasorts" #> par (fold (sep o add) sorts))
+ |> length funcs > 0 ? (
+ line (add ":extrafuns" #> add " (") #>
+ fold (fn (f, (ss, s)) =>
+ line (sep (app f (sep o add) (ss @ [s])))) funcs #>
+ line (add ")"))
+ |> fold (fn t => line (add ":assumption" #> sterm 0 t)) ts
+ |> line (add ":formula true)")
+ |> fold (fn str => line (add "; " #> add str)) comments
+ |> Buffer.content
+
+
+
+(** interface **)
+
+val interface = {
+ extra_norm = extra_norm,
+ translate = {
+ prefixes = {
+ sort_prefix = "S",
+ func_prefix = "f"},
+ strict = SOME {
+ is_builtin_conn = is_builtin_conn,
+ is_builtin_pred = is_builtin_pred,
+ is_builtin_distinct = true},
+ builtins = {
+ builtin_typ = builtin_typ,
+ builtin_num = builtin_num,
+ builtin_fun = builtin_fun},
+ serialize = serialize}}
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/yices_solver.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,44 @@
+(* Title: HOL/Tools/SMT/yices_solver.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Interface of the SMT solver Yices.
+*)
+
+signature YICES_SOLVER =
+sig
+ val setup: theory -> theory
+end
+
+structure Yices_Solver: YICES_SOLVER =
+struct
+
+val solver_name = "yices"
+val env_var = "YICES_SOLVER"
+
+val options = ["--smtlib"]
+
+fun raise_cex real = raise SMT_Solver.SMT_COUNTEREXAMPLE (real, [])
+
+fun core_oracle (output, _) =
+ let
+ val empty_line = (fn "" => true | _ => false)
+ val split_first = (fn [] => ("", []) | l :: ls => (l, ls))
+ val (l, _) = split_first (dropwhile empty_line output)
+ in
+ if String.isPrefix "unsat" l then @{cprop False}
+ else if String.isPrefix "sat" l then raise_cex true
+ else if String.isPrefix "unknown" l then raise_cex false
+ else raise SMT_Solver.SMT (solver_name ^ " failed")
+ end
+
+fun smtlib_solver oracle _ = {
+ command = {env_var=env_var, remote_name=NONE},
+ arguments = options,
+ interface = SMTLIB_Interface.interface,
+ reconstruct = pair o oracle }
+
+val setup =
+ Thm.add_oracle (Binding.name solver_name, core_oracle) #-> (fn (_, oracle) =>
+ SMT_Solver.add_solver (solver_name, smtlib_solver oracle))
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_interface.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,37 @@
+(* Title: HOL/Tools/SMT/z3_interface.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Interface to Z3 based on a relaxed version of SMT-LIB.
+*)
+
+signature Z3_INTERFACE =
+sig
+ val interface: SMT_Translate.config
+
+ val is_builtin: term -> bool
+end
+
+structure Z3_Interface: Z3_INTERFACE =
+struct
+
+fun z3_builtin_fun bf c ts =
+ (case Const c of
+ @{term "op / :: real => _"} => SOME ("/", ts)
+ | _ => bf c ts)
+
+
+val {prefixes, strict, builtins, serialize} = SMTLIB_Interface.interface
+val {builtin_typ, builtin_num, builtin_fun} = builtins
+
+val interface = {
+ extra_norm =
+ translate = {
+ prefixes = prefixes,
+ strict = strict,
+ builtins = {
+ builtin_typ = builtin_typ,
+ builtin_num = builtin_num,
+ builtin_fun = z3_builtin_fun builtin_fun},
+ serialize = serialize}}
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_model.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,146 @@
+(* Title: HOL/Tools/SMT/z3_model.ML
+ Author: Sascha Boehme and Philipp Meyer, TU Muenchen
+
+Parser for counterexamples generated by Z3.
+*)
+
+signature Z3_MODEL =
+sig
+ val parse_counterex: SMT_Translate.recon -> string list -> term list
+end
+
+structure Z3_Model: Z3_MODEL =
+struct
+
+(* counterexample expressions *)
+
+datatype expr = True | False | Number of int * int option | Value of int |
+ Array of array
+and array = Fresh of expr | Store of (array * expr) * expr
+
+
+(* parsing *)
+
+val space = Scan.many Symbol.is_ascii_blank
+fun in_parens p = Scan.$$ "(" |-- p --| Scan.$$ ")"
+fun in_braces p = (space -- Scan.$$ "{") |-- p --| (space -- Scan.$$ "}")
+
+val digit = (fn
+ "0" => SOME 0 | "1" => SOME 1 | "2" => SOME 2 | "3" => SOME 3 |
+ "4" => SOME 4 | "5" => SOME 5 | "6" => SOME 6 | "7" => SOME 7 |
+ "8" => SOME 8 | "9" => SOME 9 | _ => NONE)
+
+val nat_num = Scan.repeat1 (Scan.some digit) >>
+ (fn ds => fold (fn d => fn i => i * 10 + d) ds 0)
+val int_num = Scan.optional ($$ "-" >> 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
+
+fun array_expr st = st |>
+ in_parens (space |-- (
+ Scan.this_string "const" |-- expr >> Fresh ||
+ Scan.this_string "store" -- space |-- array_expr -- expr -- expr >> Store))
+
+and expr st = st |> (space |-- (
+ Scan.this_string "true" >> K True ||
+ Scan.this_string "false" >> K False ||
+ int_num -- Scan.option (Scan.$$ "/" |-- int_num) >> Number ||
+ Scan.this_string "val!" |-- nat_num >> Value ||
+ array_expr >> Array))
+
+val mapping = space -- Scan.this_string "->"
+val value = mapping |-- expr
+
+val args_case = Scan.repeat expr -- value
+val else_case = space -- Scan.this_string "else" |-- value >>
+ pair ([] : expr list)
+
+val func =
+ let fun cases st = (else_case >> single || args_case ::: cases) st
+ in in_braces cases end
+
+val cex = space |-- Scan.repeat (space |-- name --| mapping --
+ (func || expr >> (single o pair [])))
+
+fun read_cex ls =
+ explode (cat_lines ls)
+ |> try (fst o Scan.finite Symbol.stopper cex)
+ |> the_default []
+
+
+(* translation into terms *)
+
+fun lookup_term tab (name, e) = Option.map (rpair e) (Symtab.lookup tab name)
+
+fun with_name_context tab f xs =
+ let
+ val ns = Symtab.fold (Term.add_free_names o snd) tab []
+ val nctxt = Name.make_context ns
+ in fst (fold_map f xs (Inttab.empty, nctxt)) end
+
+fun fresh_term T (tab, nctxt) =
+ let val (n, nctxt') = yield_singleton Name.variants "" nctxt
+ in (Free (n, T), (tab, nctxt')) end
+
+fun term_of_value T i (cx as (tab, _)) =
+ (case Inttab.lookup tab i of
+ SOME t => (t, cx)
+ | NONE =>
+ let val (t, (tab', nctxt')) = fresh_term T cx
+ in (t, (Inttab.update (i, t) tab', nctxt')) end)
+
+fun trans_expr _ True = pair @{term True}
+ | trans_expr _ False = pair @{term False}
+ | trans_expr T (Number (i, NONE)) = pair (HOLogic.mk_number T i)
+ | trans_expr T (Number (i, SOME j)) =
+ pair (Const (@{const_name divide}, [T, T] ---> T) $
+ HOLogic.mk_number T i $ HOLogic.mk_number T j)
+ | trans_expr T (Value i) = term_of_value T i
+ | trans_expr T (Array a) = trans_array T a
+
+and trans_array T a =
+ let val dT = Term.domain_type T and rT = Term.range_type T
+ in
+ (case a of
+ Fresh e => trans_expr rT e #>> (fn t => Abs ("x", dT, t))
+ | Store ((a', e1), e2) =>
+ trans_array T a' ##>> trans_expr dT e1 ##>> trans_expr rT e2 #>>
+ (fn ((m, k), v) =>
+ Const (@{const_name fun_upd}, [T, dT, rT] ---> T) $ m $ k $ v))
+ end
+
+fun trans_pat i T f x =
+ f (Term.domain_type T) ##>> trans (i-1) (Term.range_type T) x #>>
+ (fn (u, (us, t)) => (u :: us, t))
+
+and trans i T ([], v) =
+ if i > 0 then trans_pat i T fresh_term ([], v)
+ else trans_expr T v #>> pair []
+ | trans i T (p :: ps, v) = trans_pat i T (fn U => trans_expr U p) (ps, v)
+
+fun mk_eq' t us u = HOLogic.mk_eq (Term.list_comb (t, us), u)
+fun mk_eq (Const (@{const_name apply}, _)) (u' :: us', u) = mk_eq' u' us' u
+ | mk_eq t (us, u) = mk_eq' t us u
+
+fun translate (t, cs) =
+ let val T = Term.fastype_of t
+ in
+ (case (can HOLogic.dest_number t, cs) of
+ (true, [c]) => trans 0 T c #>> (fn (_, u) => [mk_eq u ([], t)])
+ | (_, (es, _) :: _) => fold_map (trans (length es) T) cs #>> map (mk_eq t)
+ | _ => raise TERM ("translate: no cases", [t]))
+ end
+
+
+(* overall procedure *)
+
+fun parse_counterex ({terms, ...} : SMT_Translate.recon) ls =
+ read_cex ls
+ |> map_filter (lookup_term terms)
+ |> with_name_context terms translate
+ |> flat
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_proof_literals.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,346 @@
+(* Title: HOL/Tools/SMT/z3_proof_literals.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Proof tools related to conjunctions and disjunctions.
+*)
+
+signature Z3_PROOF_LITERALS =
+sig
+ (* literal table *)
+ type littab = thm Termtab.table
+ val make_littab: thm list -> littab
+ val insert_lit: thm -> littab -> littab
+ val delete_lit: thm -> littab -> littab
+ val lookup_lit: littab -> term -> thm option
+ val get_first_lit: (term -> bool) -> littab -> thm option
+
+ (* rules *)
+ val true_thm: thm
+ val rewrite_true: thm
+
+ (* properties *)
+ val is_conj: term -> bool
+ val is_disj: term -> bool
+ val exists_lit: bool -> (term -> bool) -> term -> bool
+
+ (* proof tools *)
+ val explode: bool -> bool -> bool -> term list -> thm -> thm list
+ val join: bool -> littab -> term -> thm
+ val prove_conj_disj_eq: cterm -> thm
+end
+
+structure Z3_Proof_Literals: Z3_PROOF_LITERALS =
+struct
+
+structure T = Z3_Proof_Tools
+
+
+
+(** literal table **)
+
+type littab = thm Termtab.table
+
+fun make_littab thms = fold (Termtab.update o `T.prop_of) thms Termtab.empty
+
+fun insert_lit thm = Termtab.update (`T.prop_of thm)
+fun delete_lit thm = Termtab.delete (T.prop_of thm)
+fun lookup_lit lits = Termtab.lookup lits
+fun get_first_lit f =
+ Termtab.get_first (fn (t, thm) => if f t then SOME thm else NONE)
+
+
+
+(** rules **)
+
+val true_thm = @{lemma "~False" by simp}
+val rewrite_true = @{lemma "True == ~ False" by simp}
+
+
+
+(** properties and term operations **)
+
+val is_neg = (fn @{term Not} $ _ => true | _ => false)
+fun is_neg' f = (fn @{term Not} $ t => f t | _ => false)
+val is_dneg = is_neg' is_neg
+val is_conj = (fn @{term "op &"} $ _ $ _ => true | _ => false)
+val is_disj = (fn @{term "op |"} $ _ $ _ => true | _ => false)
+
+fun dest_disj_term' f = (fn
+ @{term Not} $ (@{term "op |"} $ t $ u) => SOME (f t, f u)
+ | _ => NONE)
+
+val dest_conj_term = (fn @{term "op &"} $ t $ u => SOME (t, u) | _ => NONE)
+val dest_disj_term =
+ dest_disj_term' (fn @{term Not} $ t => t | t => @{term Not} $ t)
+
+fun exists_lit is_conj P =
+ let
+ val dest = if is_conj then dest_conj_term else dest_disj_term
+ fun exists t = P t orelse
+ (case dest t of
+ SOME (t1, t2) => exists t1 orelse exists t2
+ | NONE => false)
+ in exists end
+
+
+
+(** proof tools **)
+
+(* explosion of conjunctions and disjunctions *)
+
+local
+ fun destc ct = Thm.dest_binop (Thm.dest_arg ct)
+ val dest_conj1 = T.precompose2 destc @{thm conjunct1}
+ val dest_conj2 = T.precompose2 destc @{thm conjunct2}
+ fun dest_conj_rules t =
+ dest_conj_term t |> Option.map (K (dest_conj1, dest_conj2))
+
+ fun destd f ct = f (Thm.dest_binop (Thm.dest_arg (Thm.dest_arg ct)))
+ val dn1 = apfst Thm.dest_arg and dn2 = apsnd Thm.dest_arg
+ val dest_disj1 = T.precompose2 (destd I) @{lemma "~(P | Q) ==> ~P" by fast}
+ val dest_disj2 = T.precompose2 (destd dn1) @{lemma "~(~P | Q) ==> P" by fast}
+ val dest_disj3 = T.precompose2 (destd I) @{lemma "~(P | Q) ==> ~Q" by fast}
+ val dest_disj4 = T.precompose2 (destd dn2) @{lemma "~(P | ~Q) ==> Q" by fast}
+
+ fun dest_disj_rules t =
+ (case dest_disj_term' is_neg t of
+ SOME (true, true) => SOME (dest_disj2, dest_disj4)
+ | SOME (true, false) => SOME (dest_disj2, dest_disj3)
+ | SOME (false, true) => SOME (dest_disj1, dest_disj4)
+ | SOME (false, false) => SOME (dest_disj1, dest_disj3)
+ | NONE => NONE)
+
+ fun destn ct = [Thm.dest_arg (Thm.dest_arg (Thm.dest_arg ct))]
+ val dneg_rule = T.precompose destn @{thm notnotD}
+in
+
+(* explode a term into literals and collect all rules to be able to deduce
+ particular literals afterwards *)
+fun explode_term is_conj =
+ let
+ val dest = if is_conj then dest_conj_term else dest_disj_term
+ val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
+
+ fun add (t, rs) = Termtab.map_default (t, rs)
+ (fn rs' => if length rs' < length rs then rs' else rs)
+
+ fun explode1 rules t =
+ (case dest t of
+ SOME (t1, t2) =>
+ let val (rule1, rule2) = the (dest_rules t)
+ in
+ explode1 (rule1 :: rules) t1 #>
+ explode1 (rule2 :: rules) t2 #>
+ add (t, rev rules)
+ end
+ | NONE => add (t, rev rules))
+
+ fun explode0 (@{term Not} $ (@{term Not} $ t)) =
+ Termtab.make [(t, [dneg_rule])]
+ | explode0 t = explode1 [] t Termtab.empty
+
+ in explode0 end
+
+(* extract a literal by applying previously collected rules *)
+fun extract_lit thm rules = fold T.compose rules thm
+
+
+(* explode a theorem into its literals *)
+fun explode is_conj full keep_intermediate stop_lits =
+ let
+ val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
+ val tab = fold (Termtab.update o rpair ()) stop_lits Termtab.empty
+
+ fun explode1 thm =
+ if Termtab.defined tab (T.prop_of thm) then cons thm
+ else
+ (case dest_rules (T.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) (T.prop_of thm)
+ then explode1 (T.compose dest_rule thm)
+ else cons (T.compose dest_rule thm)
+
+ fun explode0 thm =
+ if not is_conj andalso is_dneg (T.prop_of thm)
+ then [T.compose dneg_rule thm]
+ else explode1 thm []
+
+ in explode0 end
+
+end
+
+
+
+(* joining of literals to conjunctions or disjunctions *)
+
+local
+ fun on_cprem i f thm = f (Thm.cprem_of thm i)
+ fun on_cprop f thm = f (Thm.cprop_of thm)
+ fun precomp2 f g thm = (on_cprem 1 f thm, on_cprem 2 g thm, f, g, thm)
+ fun comp2 (cv1, cv2, f, g, rule) thm1 thm2 =
+ Thm.instantiate ([], [(cv1, on_cprop f thm1), (cv2, on_cprop g thm2)]) rule
+ |> T.discharge thm1 |> T.discharge thm2
+
+ fun d1 ct = Thm.dest_arg ct and d2 ct = Thm.dest_arg (Thm.dest_arg ct)
+
+ val conj_rule = precomp2 d1 d1 @{thm conjI}
+ fun comp_conj ((_, thm1), (_, thm2)) = comp2 conj_rule thm1 thm2
+
+ val disj1 = precomp2 d2 d2 @{lemma "~P ==> ~Q ==> ~(P | Q)" by fast}
+ val disj2 = precomp2 d2 d1 @{lemma "~P ==> Q ==> ~(P | ~Q)" by fast}
+ val disj3 = precomp2 d1 d2 @{lemma "P ==> ~Q ==> ~(~P | Q)" by fast}
+ val disj4 = precomp2 d1 d1 @{lemma "P ==> Q ==> ~(~P | ~Q)" by fast}
+
+ fun comp_disj ((false, thm1), (false, thm2)) = comp2 disj1 thm1 thm2
+ | comp_disj ((false, thm1), (true, thm2)) = comp2 disj2 thm1 thm2
+ | comp_disj ((true, thm1), (false, thm2)) = comp2 disj3 thm1 thm2
+ | comp_disj ((true, thm1), (true, thm2)) = comp2 disj4 thm1 thm2
+
+ fun dest_conj (@{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 = T.precompose (single o d2 o d1) @{thm notnotD}
+ val dnegI = T.precompose (single o d1) @{lemma "P ==> ~~P" by fast}
+ fun as_dneg f t = f (@{term Not} $ (@{term Not} $ t))
+
+ fun dni f = apsnd f o Thm.dest_binop o f o d1
+ val negIffE = T.precompose2 (dni d1) @{lemma "~(P = (~Q)) ==> Q = P" by fast}
+ val negIffI = T.precompose2 (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 join is_conj littab t =
+ let
+ val comp = if is_conj then comp_conj else comp_disj
+ val dest = if is_conj then dest_conj else dest_disj
+
+ val lookup = lookup_lit littab
+
+ fun lookup_rule t =
+ (case t of
+ @{term Not} $ (@{term Not} $ t) => (T.compose dnegI, lookup t)
+ | @{term Not} $ (@{term "op = :: bool => _"} $ t $ (@{term Not} $ u)) =>
+ (T.compose negIffI, lookup (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 (@{term Not} $ (eq $ u $ t))) end
+ | _ =>
+ (case as_dneg lookup t of
+ NONE => (T.compose negIffE, as_negIff lookup t)
+ | x => (T.compose dnegE, x)))
+
+ fun join1 (s, t) =
+ (case lookup t of
+ SOME lit => (s, lit)
+ | NONE =>
+ (case lookup_rule t of
+ (rewrite, SOME lit) => (s, rewrite lit)
+ | (_, NONE) => (s, comp (pairself join1 (dest t)))))
+
+ in snd (join1 (if is_conj then (false, t) else (true, t))) end
+
+end
+
+
+
+(* proving equality of conjunctions or disjunctions *)
+
+fun iff_intro thm1 thm2 = thm2 COMP (thm1 COMP @{thm iffI})
+
+local
+ val cp1 = @{lemma "(~P) = (~Q) ==> P = Q" by simp}
+ val cp2 = @{lemma "(~P) = Q ==> P = (~Q)" by 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
+ val contra_rule = @{lemma "P ==> ~P ==> False" by (rule notE)}
+ fun contra_left conj thm =
+ let
+ val rules = explode_term conj (T.prop_of thm)
+ fun contra_lits (t, rs) =
+ (case t of
+ @{term Not} $ u => Termtab.lookup rules u |> Option.map (pair rs)
+ | _ => NONE)
+ in
+ (case Termtab.lookup rules @{term False} of
+ SOME rs => extract_lit thm rs
+ | NONE =>
+ the (Termtab.get_first contra_lits rules)
+ |> pairself (extract_lit thm)
+ |> (fn (nlit, plit) => nlit COMP (plit COMP contra_rule)))
+ end
+
+ val falseE_v = Thm.dest_arg (Thm.dest_arg (Thm.cprop_of @{thm FalseE}))
+ fun contra_right ct = Thm.instantiate ([], [(falseE_v, ct)]) @{thm FalseE}
+in
+fun contradict conj ct =
+ iff_intro (T.under_assumption (contra_left conj) ct) (contra_right ct)
+end
+
+
+local
+ fun prove_eq l r (cl, cr) =
+ let
+ fun explode' is_conj = explode is_conj true (l <> r) []
+ fun make_tab is_conj thm = make_littab (true_thm :: explode' is_conj thm)
+ fun prove is_conj ct tab = join is_conj tab (Thm.term_of ct)
+
+ val thm1 = T.under_assumption (prove r cr o make_tab l) cl
+ val thm2 = T.under_assumption (prove l cl o make_tab r) cr
+ in iff_intro thm1 thm2 end
+
+ datatype conj_disj = CONJ | DISJ | NCON | NDIS
+ fun kind_of t =
+ if is_conj t then SOME CONJ
+ else if is_disj t then SOME DISJ
+ else if is_neg' is_conj t then SOME NCON
+ else if is_neg' is_disj t then SOME NDIS
+ else NONE
+in
+
+fun prove_conj_disj_eq ct =
+ let val cp as (cl, cr) = Thm.dest_binop (Thm.dest_arg ct)
+ in
+ (case (kind_of (Thm.term_of cl), Thm.term_of cr) of
+ (SOME CONJ, @{term False}) => contradict true cl
+ | (SOME DISJ, @{term "~False"}) => contrapos2 (contradict false o fst) cp
+ | (kl, _) =>
+ (case (kl, kind_of (Thm.term_of cr)) of
+ (SOME CONJ, SOME CONJ) => prove_eq true true cp
+ | (SOME CONJ, SOME NDIS) => prove_eq true false cp
+ | (SOME CONJ, _) => prove_eq true true cp
+ | (SOME DISJ, SOME DISJ) => contrapos1 (prove_eq false false) cp
+ | (SOME DISJ, SOME NCON) => contrapos2 (prove_eq false true) cp
+ | (SOME DISJ, _) => contrapos1 (prove_eq false false) cp
+ | (SOME NCON, SOME NCON) => contrapos1 (prove_eq true true) cp
+ | (SOME NCON, SOME DISJ) => contrapos3 (prove_eq true false) cp
+ | (SOME NCON, NONE) => contrapos3 (prove_eq true false) cp
+ | (SOME NDIS, SOME NDIS) => prove_eq false false cp
+ | (SOME NDIS, SOME CONJ) => prove_eq false true cp
+ | (SOME NDIS, NONE) => prove_eq false true cp
+ | _ => raise CTERM ("prove_conj_disj_eq", [ct])))
+ end
+
+end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_proof_parser.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,499 @@
+(* Title: HOL/Tools/SMT/z3_proof_parser.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Parser for Z3 proofs.
+*)
+
+signature Z3_PROOF_PARSER =
+sig
+ (* proof rules *)
+ 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 string_of_rule: rule -> string
+
+ (* proof parser *)
+ datatype proof_step = Proof_Step of {
+ rule: rule,
+ prems: int list,
+ prop: cterm }
+ val parse: Proof.context -> typ Symtab.table -> term Symtab.table ->
+ string list ->
+ int * (proof_step Inttab.table * string list * Proof.context)
+end
+
+structure Z3_Proof_Parser: Z3_PROOF_PARSER =
+struct
+
+(** proof rules **)
+
+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)]
+
+fun string_of_rule r =
+ let fun eq_rule (s, r') = if r = r' then SOME s else NONE
+ in the (Symtab.get_first eq_rule rule_names) end
+
+
+
+(** certified terms and variables **)
+
+val (var_prefix, decl_prefix) = ("v", "sk") (* must be distinct *)
+
+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
+
+fun ctyp_of (ct, _) = Thm.ctyp_of_term ct
+fun instT' t = instT (ctyp_of t)
+
+fun certify ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
+
+val maxidx_of = #maxidx o Thm.rep_cterm
+
+fun mk_inst ctxt vars =
+ let
+ val max = fold (Integer.max o fst) vars 0
+ val ns = fst (Variable.variant_fixes (replicate (max + 1) var_prefix) ctxt)
+ fun mk (i, v) = (v, certify ctxt (Free (nth ns i, #T (Thm.rep_cterm v))))
+ in map mk vars end
+
+fun close ctxt (ct, vars) =
+ let
+ val inst = mk_inst ctxt vars
+ val mk_prop = Thm.capply @{cterm Trueprop}
+ val names = fold (Term.add_free_names o Thm.term_of o snd) inst []
+ in (mk_prop (Thm.instantiate_cterm ([], inst) ct), names) end
+
+
+fun mk_bound thy (i, T) =
+ let val ct = Thm.cterm_of thy (Var ((Name.uu, 0), T))
+ in (ct, [(i, ct)]) end
+
+local
+ fun mk_quant thy q T (ct, vars) =
+ let
+ val cv =
+ (case AList.lookup (op =) vars 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 (Thm.capply cq (Thm.cabs cv ct), map_filter dec vars) end
+
+ val forall = mk_inst_pair (destT1 o destT1) @{cpat All}
+ val exists = mk_inst_pair (destT1 o destT1) @{cpat Ex}
+in
+fun mk_forall thy = fold_rev (mk_quant thy forall)
+fun mk_exists thy = fold_rev (mk_quant thy exists)
+end
+
+
+local
+ fun equal_var cv (_, cu) = (cv aconvc cu)
+
+ fun apply (ct2, vars2) (ct1, vars1) =
+ let
+ val incr = Thm.incr_indexes_cterm (maxidx_of ct1 + maxidx_of ct2 + 2)
+
+ fun part (v as (i, cv)) =
+ (case AList.lookup (op =) vars1 i of
+ SOME cu => apfst (if cu aconvc cv then I else cons (cv, cu))
+ | NONE =>
+ if not (exists (equal_var cv) vars1) then apsnd (cons v)
+ else
+ let val cv' = incr cv
+ in apfst (cons (cv, cv')) #> apsnd (cons (i, cv')) end)
+
+ val (ct2', vars2') =
+ if null vars1 then (ct2, vars2)
+ else fold part vars2 ([], [])
+ |>> (fn inst => Thm.instantiate_cterm ([], inst) ct2)
+
+ in (Thm.capply ct1 ct2', vars1 @ vars2') end
+in
+fun mk_fun ct ts = fold apply ts (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
+
+
+val mk_true = mk_fun @{cterm "~False"} []
+val mk_false = mk_fun @{cterm "False"} []
+fun mk_not t = mk_fun @{cterm Not} [t]
+val mk_imp = 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 e) es]
+
+
+(* arithmetic *)
+
+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 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_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 => _"}
+
+
+(* arrays *)
+
+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 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 array)
+ in mk_fun (instTs cTs update) [array, index, value] end
+
+
+(* bitvectors *)
+
+fun mk_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 mk_wordT size = Type (@{type_name "word"}, [mk_binT size])
+
+fun mk_bv_num thy (num, size) =
+ mk_fun (Numeral.mk_cnumber (Thm.ctyp_of thy (mk_wordT size)) num) []
+
+
+
+(** proof parser **)
+
+datatype proof_step = Proof_Step of {
+ rule: rule,
+ prems: int list,
+ prop: cterm }
+
+
+(* parser context *)
+
+fun make_context ctxt typs terms =
+ let
+ val ctxt' =
+ ctxt
+ |> Symtab.fold (Variable.declare_typ o snd) typs
+ |> Symtab.fold (Variable.declare_term o snd) terms
+
+ fun cert @{term True} = @{cterm "~False"}
+ | cert t = certify ctxt' t
+ in (typs, Symtab.map cert terms, Inttab.empty, Inttab.empty, [], ctxt') end
+
+fun fresh_name n (typs, terms, exprs, steps, vars, ctxt) =
+ let val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
+ in (n', (typs, terms, exprs, steps, vars, ctxt')) end
+
+fun theory_of (_, _, _, _, _, ctxt) = ProofContext.theory_of ctxt
+
+fun typ_of_sort n (cx as (typs, _, _, _, _, _)) =
+ (case Symtab.lookup typs n of
+ SOME T => (T, cx)
+ | NONE => cx
+ |> fresh_name ("'" ^ n) |>> TFree o rpair @{sort type}
+ |> (fn (T, (typs, terms, exprs, steps, vars, ctxt)) =>
+ (T, (Symtab.update (n, T) typs, terms, exprs, steps, vars, ctxt))))
+
+fun add_decl (n, T) (cx as (_, terms, _, _, _, _)) =
+ (case Symtab.lookup terms n of
+ SOME _ => cx
+ | NONE => cx |> fresh_name (decl_prefix ^ n)
+ |> (fn (m, (typs, terms, exprs, steps, vars, ctxt)) =>
+ let val upd = Symtab.update (n, certify ctxt (Free (m, T)))
+ in (typs, upd terms, exprs, steps, vars, ctxt) end))
+
+datatype sym = Sym of string * sym list
+
+fun mk_app _ (Sym ("true", _), _) = SOME mk_true
+ | mk_app _ (Sym ("false", _), _) = SOME mk_false
+ | mk_app _ (Sym ("=", _), [t, u]) = SOME (mk_eq t u)
+ | mk_app _ (Sym ("distinct", _), ts) = SOME (mk_distinct ts)
+ | mk_app _ (Sym ("ite", _), [s, t, u]) = SOME (mk_if s t u)
+ | mk_app _ (Sym ("and", _), ts) = SOME (mk_nary @{cterm "op &"} mk_true ts)
+ | mk_app _ (Sym ("or", _), ts) = SOME (mk_nary @{cterm "op |"} mk_false ts)
+ | mk_app _ (Sym ("iff", _), [t, u]) = SOME (mk_iff t u)
+ | mk_app _ (Sym ("xor", _), [t, u]) = SOME (mk_not (mk_iff t u))
+ | mk_app _ (Sym ("not", _), [t]) = SOME (mk_not t)
+ | mk_app _ (Sym ("implies", _), [t, u]) = SOME (mk_imp t u)
+ | mk_app _ (Sym ("~", _), [t, u]) = SOME (mk_iff t u)
+ | mk_app _ (Sym ("<", _), [t, u]) = SOME (mk_lt t u)
+ | mk_app _ (Sym ("<=", _), [t, u]) = SOME (mk_le t u)
+ | mk_app _ (Sym (">", _), [t, u]) = SOME (mk_lt u t)
+ | mk_app _ (Sym (">=", _), [t, u]) = SOME (mk_le u t)
+ | mk_app _ (Sym ("+", _), [t, u]) = SOME (mk_add t u)
+ | mk_app _ (Sym ("-", _), [t, u]) = SOME (mk_sub t u)
+ | mk_app _ (Sym ("-", _), [t]) = SOME (mk_uminus t)
+ | mk_app _ (Sym ("*", _), [t, u]) = SOME (mk_mul t u)
+ | mk_app _ (Sym ("/", _), [t, u]) = SOME (mk_real_div t u)
+ | mk_app _ (Sym ("div", _), [t, u]) = SOME (mk_int_div t u)
+ | mk_app _ (Sym ("mod", _), [t, u]) = SOME (mk_mod t u)
+ | mk_app _ (Sym ("select", _), [m, k]) = SOME (mk_access m k)
+ | mk_app _ (Sym ("store", _), [m, k, v]) = SOME (mk_update m k v)
+ | mk_app _ (Sym ("pattern", _), _) = SOME mk_true
+ | mk_app (_, terms, _, _, _, _) (Sym (n, _), ts) =
+ Symtab.lookup terms n |> Option.map (fn ct => mk_fun ct ts)
+
+fun add_expr k t (typs, terms, exprs, steps, vars, ctxt) =
+ (typs, terms, Inttab.update (k, t) exprs, steps, vars, ctxt)
+
+fun lookup_expr (_, _, exprs, _, _, _) = Inttab.lookup exprs
+
+fun add_proof_step k ((r, prems), prop) cx =
+ let
+ val (typs, terms, exprs, steps, vars, ctxt) = cx
+ val (ct, vs) = close ctxt prop
+ val step = Proof_Step {rule=r, prems=prems, prop=ct}
+ val vars' = union (op =) vs vars
+ in (typs, terms, exprs, Inttab.update (k, step) steps, vars', ctxt) end
+
+fun finish (_, _, _, steps, vars, ctxt) = (steps, vars, ctxt)
+
+
+(* core parser *)
+
+fun parse_exn line_no msg = raise SMT_Solver.SMT ("Z3 proof parser (line " ^
+ string_of_int line_no ^ "): " ^ msg)
+
+fun scan_exn msg ((line_no, _), _) = parse_exn line_no msg
+
+fun with_info f cx =
+ (case f ((NONE, 1), cx) of
+ ((SOME root, _), cx') => (root, cx')
+ | ((_, line_no), _) => parse_exn line_no "bad proof")
+
+fun parse_line _ _ (st as ((SOME _, _), _)) = st
+ | parse_line scan line ((_, line_no), cx) =
+ let val st = ((line_no, cx), explode line)
+ in
+ (case Scan.catch (Scan.finite' Symbol.stopper (Scan.option scan)) st of
+ (SOME r, ((_, cx'), _)) => ((r, line_no+1), cx')
+ | (NONE, _) => parse_exn line_no ("bad proof line: " ^ quote line))
+ end
+
+fun with_context f x ((line_no, cx), st) =
+ let val (y, cx') = f x cx
+ in (y, ((line_no, cx'), st)) end
+
+
+fun lookup_context f x (st as ((_, cx), _)) = (f cx x, st)
+
+
+(* parser combinators and parsers for basic entities *)
+
+fun $$ s = Scan.lift (Scan.$$ s)
+fun this s = Scan.lift (Scan.this_string s)
+fun blank st = Scan.lift (Scan.many1 Symbol.is_ascii_blank) st
+fun sep scan = blank |-- scan
+fun seps scan = Scan.repeat (sep scan)
+fun seps1 scan = Scan.repeat1 (sep scan)
+fun seps_by scan_sep scan = scan ::: Scan.repeat (scan_sep |-- scan)
+
+fun par scan = $$ "(" |-- scan --| $$ ")"
+fun bra scan = $$ "[" |-- scan --| $$ "]"
+
+val digit = (fn
+ "0" => SOME 0 | "1" => SOME 1 | "2" => SOME 2 | "3" => SOME 3 |
+ "4" => SOME 4 | "5" => SOME 5 | "6" => SOME 6 | "7" => SOME 7 |
+ "8" => SOME 8 | "9" => SOME 9 | _ => NONE)
+
+fun mk_num ds = fold (fn d => fn i => i * 10 + d) ds 0
+val nat_num = Scan.lift (Scan.repeat1 (Scan.some digit)) >> mk_num
+val int_num = Scan.optional ($$ "-" >> K (fn i => ~i)) I :|--
+ (fn sign => nat_num >> sign)
+
+val is_char = Symbol.is_ascii_letter orf Symbol.is_ascii_digit orf
+ member (op =) (explode "_+*-/%~=<>$&|?!.@^#")
+val name = Scan.lift (Scan.many1 is_char) >> implode
+
+fun sym st = (name -- Scan.optional (bra (seps_by ($$ ":") sym)) [] >> Sym) st
+
+fun id st = ($$ "#" |-- nat_num) st
+
+
+(* parsers for various parts of Z3 proofs *)
+
+fun sort st = Scan.first [
+ this "bool" >> K @{typ bool},
+ this "int" >> K @{typ int},
+ this "real" >> K @{typ real},
+ this "bv" |-- bra nat_num >> mk_wordT,
+ this "array" |-- bra (sort --| $$ ":" -- sort) >> (op -->),
+ par (this "->" |-- seps1 sort) >> ((op --->) o split_last),
+ name :|-- with_context typ_of_sort] st
+
+fun bound st = (par (this ":var" |-- sep nat_num -- sep sort) :|--
+ lookup_context (mk_bound o theory_of)) st
+
+fun number st = st |> (
+ int_num -- Scan.option ($$ "/" |-- int_num) --| this "::" :|--
+ (fn num as (n, _) =>
+ this "int" >> K (mk_int_num n) ||
+ this "real" >> K (mk_real_frac_num num)))
+
+fun bv_number st = (this "bv" |-- bra (nat_num --| $$ ":" -- nat_num) :|--
+ lookup_context (mk_bv_num o theory_of)) st
+
+fun appl (app as (Sym (n, _), _)) = lookup_context mk_app app :|-- (fn
+ SOME app' => Scan.succeed app'
+ | NONE => scan_exn ("unknown function: " ^ quote n))
+
+fun constant st = ((sym >> rpair []) :|-- appl) st
+
+fun expr_id st = (id :|-- (fn i => lookup_context lookup_expr i :|-- (fn
+ SOME e => Scan.succeed e
+ | NONE => scan_exn ("unknown term id: " ^ quote (string_of_int i))))) st
+
+fun arg st = Scan.first [expr_id, number, bv_number, constant] st
+
+fun application st = par ((sym -- Scan.repeat1 (sep arg)) :|-- appl) st
+
+fun variables st = par (this "vars" |-- seps1 (par (name |-- sep sort))) st
+
+fun patterns st = seps (par ((this ":pat" || this ":nopat") |-- seps1 id)) st
+
+fun quant_kind st = st |> (
+ this "forall" >> K (mk_forall o theory_of) ||
+ this "exists" >> K (mk_exists o theory_of))
+
+fun quantifier st =
+ (par (quant_kind -- sep variables --| patterns -- sep arg) :|--
+ lookup_context (fn cx => fn ((mk_q, Ts), body) => mk_q cx Ts body)) st
+
+fun expr k =
+ Scan.first [bound, quantifier, application, number, bv_number, constant] :|--
+ with_context (pair NONE oo add_expr k)
+
+fun rule_name st = ((name >> `(Symtab.lookup rule_names)) :|-- (fn
+ (SOME r, _) => Scan.succeed r
+ | (NONE, n) => scan_exn ("unknown proof rule: " ^ quote n))) st
+
+fun rule f k =
+ bra (rule_name -- seps id) --| $$ ":" -- sep arg #->
+ with_context (pair (f k) oo add_proof_step k)
+
+fun decl st = (this "decl" |-- sep name --| sep (this "::") -- sep sort :|--
+ with_context (pair NONE oo add_decl)) st
+
+fun def st = (id --| sep (this ":=")) st
+
+fun node st = st |> (
+ decl ||
+ def :|-- (fn k => sep (expr k) || sep (rule (K NONE) k)) ||
+ rule SOME ~1)
+
+
+(* overall parser *)
+
+(* Currently, terms are parsed bottom-up (i.e., along with parsing the proof
+ text line by line), but proofs are reconstructed top-down (i.e. by an
+ in-order top-down traversal of the proof tree/graph). The latter approach
+ was taken because some proof texts comprise irrelevant proof steps which
+ will thus not be reconstructed. This approach might also be beneficial
+ for constructing terms, but it would also increase the complexity of the
+ (otherwise rather modular) code. *)
+
+fun parse ctxt typs terms proof_text =
+ make_context ctxt typs terms
+ |> with_info (fold (parse_line node) proof_text)
+ ||> finish
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_proof_reconstruction.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,821 @@
+(* Title: HOL/Tools/SMT/z3_proof_reconstruction.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Proof reconstruction for proofs found by Z3.
+*)
+
+signature Z3_PROOF_RECONSTRUCTION =
+sig
+ val trace_assms: bool Config.T
+ val reconstruct: string list * SMT_Translate.recon -> Proof.context ->
+ thm * Proof.context
+ val setup: theory -> theory
+end
+
+structure Z3_Proof_Reconstruction: Z3_PROOF_RECONSTRUCTION =
+struct
+
+structure P = Z3_Proof_Parser
+structure T = Z3_Proof_Tools
+structure L = Z3_Proof_Literals
+
+fun z3_exn msg = raise SMT_Solver.SMT ("Z3 proof reconstruction: " ^ msg)
+
+
+
+(** net of schematic rules **)
+
+val z3_ruleN = "z3_rule"
+
+local
+ val description = "declaration of Z3 proof rules"
+
+ val eq = Thm.eq_thm
+
+ structure Z3_Rules = Generic_Data
+ (
+ type T = thm Net.net
+ val empty = Net.empty
+ val extend = I
+ val merge = Net.merge eq
+ )
+
+ val prep = `Thm.prop_of o Simplifier.rewrite_rule [L.rewrite_true]
+
+ fun ins thm net = Net.insert_term eq (prep thm) net handle Net.INSERT => net
+ fun del thm net = Net.delete_term eq (prep thm) net handle Net.DELETE => net
+
+ val add = Thm.declaration_attribute (Z3_Rules.map o ins)
+ val del = Thm.declaration_attribute (Z3_Rules.map o del)
+in
+
+fun get_schematic_rules ctxt = Net.content (Z3_Rules.get (Context.Proof ctxt))
+
+fun by_schematic_rule ctxt ct =
+ the (T.net_instance (Z3_Rules.get (Context.Proof ctxt)) ct)
+
+val z3_rules_setup =
+ Attrib.setup (Binding.name z3_ruleN) (Attrib.add_del add del) description #>
+ PureThy.add_thms_dynamic (Binding.name z3_ruleN, Net.content o Z3_Rules.get)
+
+end
+
+
+
+(** proof tools **)
+
+fun named ctxt name prover ct =
+ let val _ = SMT_Solver.trace_msg ctxt I ("Z3: trying " ^ name ^ " ...")
+ in prover ct end
+
+fun NAMED ctxt name tac i st =
+ let val _ = SMT_Solver.trace_msg ctxt I ("Z3: trying " ^ name ^ " ...")
+ in tac i st end
+
+fun pretty_goal ctxt thms t =
+ [Pretty.block [Pretty.str "proposition: ", Syntax.pretty_term ctxt t]]
+ |> not (null thms) ? cons (Pretty.big_list "assumptions:"
+ (map (Display.pretty_thm ctxt) thms))
+
+fun try_apply ctxt thms =
+ let
+ fun try_apply_err ct = Pretty.string_of (Pretty.chunks [
+ Pretty.big_list ("Z3 found a proof," ^
+ " but proof reconstruction failed at the following subgoal:")
+ (pretty_goal ctxt thms (Thm.term_of ct)),
+ Pretty.str ("Adding a rule to the lemma group " ^ quote z3_ruleN ^
+ " might solve this problem.")])
+
+ fun apply [] ct = error (try_apply_err ct)
+ | apply (prover :: provers) ct =
+ (case try prover ct of
+ SOME thm => (SMT_Solver.trace_msg ctxt I "Z3: succeeded"; thm)
+ | NONE => apply provers ct)
+
+ in apply o cons (named ctxt "schematic rules" (by_schematic_rule ctxt)) end
+
+
+
+(** theorems and proofs **)
+
+(* theorem incarnations *)
+
+datatype theorem =
+ Thm of thm | (* theorem without special features *)
+ MetaEq of thm | (* meta equality "t == s" *)
+ Literals of thm * L.littab
+ (* "P1 & ... & Pn" and table of all literals P1, ..., Pn *)
+
+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 = mk_meta_eq (thm_of p)
+
+fun literals_of (Literals (_, lits)) = lits
+ | literals_of p = L.make_littab [thm_of p]
+
+
+(* proof representation *)
+
+datatype proof = Unproved of P.proof_step | Proved of theorem
+
+
+
+(** core proof rules **)
+
+(* assumption *)
+
+val (trace_assms, trace_assms_setup) =
+ Attrib.config_bool "z3_trace_assms" (K false)
+
+local
+ val remove_trigger = @{lemma "trigger t p == p"
+ by (rule eq_reflection, rule trigger_def)}
+
+ val prep_rules = [@{thm Let_def}, remove_trigger, L.rewrite_true]
+
+ fun rewrite_conv ctxt eqs = Simplifier.full_rewrite
+ (Simplifier.context ctxt Simplifier.empty_ss addsimps eqs)
+
+ fun rewrites ctxt eqs = map (Conv.fconv_rule (rewrite_conv ctxt eqs))
+
+ fun trace ctxt thm =
+ if Config.get ctxt trace_assms
+ then tracing (Display.string_of_thm ctxt thm)
+ else ()
+
+ fun lookup_assm ctxt assms ct =
+ (case T.net_instance assms ct of
+ SOME thm => (trace ctxt thm; thm)
+ | _ => z3_exn ("not asserted: " ^
+ quote (Syntax.string_of_term ctxt (Thm.term_of ct))))
+in
+fun prepare_assms ctxt unfolds assms =
+ let
+ val unfolds' = rewrites ctxt [L.rewrite_true] unfolds
+ val assms' = rewrites ctxt (union Thm.eq_thm unfolds' prep_rules) assms
+ in (unfolds', T.thm_net_of assms') end
+
+fun asserted _ NONE ct = Thm (Thm.assume ct)
+ | asserted ctxt (SOME (unfolds, assms)) ct =
+ let val revert_conv = rewrite_conv ctxt unfolds
+ in Thm (T.with_conv revert_conv (lookup_assm ctxt assms) ct) end
+end
+
+
+
+(* P = Q ==> P ==> Q or P --> Q ==> P ==> Q *)
+local
+ val meta_iffD1 = @{lemma "P == Q ==> P ==> (Q::bool)" by simp}
+ val meta_iffD1_c = T.precompose2 Thm.dest_binop meta_iffD1
+
+ val iffD1_c = T.precompose2 (Thm.dest_binop o Thm.dest_arg) @{thm iffD1}
+ val mp_c = T.precompose2 (Thm.dest_binop o Thm.dest_arg) @{thm mp}
+in
+fun mp (MetaEq thm) p = Thm (Thm.implies_elim (T.compose meta_iffD1_c thm) p)
+ | mp p_q p =
+ let
+ val pq = thm_of p_q
+ val thm = T.compose iffD1_c pq handle THM _ => T.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 is_sublit conj t = L.exists_lit conj (fn u => u aconv t)
+
+ fun derive conj t lits idx ptab =
+ let
+ val lit = the (L.get_first_lit (is_sublit conj t) lits)
+ val ls = L.explode conj false false [t] lit
+ val lits' = fold L.insert_lit ls (L.delete_lit lit lits)
+
+ fun upd (Proved thm) = Proved (Literals (thm_of thm, lits'))
+ | upd p = p
+ in (the (L.lookup_lit lits' t), Inttab.map_entry idx upd ptab) end
+
+ fun lit_elim conj (p, idx) ct ptab =
+ let val lits = literals_of p
+ in
+ (case L.lookup_lit lits (T.term_of ct) of
+ SOME lit => (Thm lit, ptab)
+ | NONE => apfst Thm (derive conj (T.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 = L.explode 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 = T.precompose dest_ccontr @{thm ccontr}
+in
+fun lemma thm ct =
+ let
+ val cu = Thm.capply @{cterm Not} (Thm.dest_arg ct)
+ val hyps = map_filter (try HOLogic.dest_Trueprop) (#hyps (Thm.rep_thm thm))
+ in Thm (T.compose ccontr (T.under_assumption (intro hyps thm) cu)) end
+end
+
+
+
+(* \/{P1, ..., Pn, Q1, ..., Qn}, ~P1, ..., ~Pn ==> \/{Q1, ..., Qn} *)
+local
+ val explode_disj = L.explode false true false
+ val join_disj = L.join false
+ fun unit thm thms th =
+ let val t = @{term Not} $ T.prop_of thm and ts = map T.prop_of thms
+ in join_disj (L.make_littab (thms @ explode_disj ts th)) t end
+
+ fun dest_arg2 ct = Thm.dest_arg (Thm.dest_arg ct)
+ fun dest ct = pairself dest_arg2 (Thm.dest_binop ct)
+ val contrapos = T.precompose2 dest @{lemma "(~P ==> ~Q) ==> Q ==> P" by fast}
+in
+fun unit_resolution thm thms ct =
+ Thm.capply @{cterm Not} (Thm.dest_arg ct)
+ |> T.under_assumption (unit thm thms)
+ |> Thm o T.discharge thm o T.compose contrapos
+end
+
+
+
+(* P ==> P == True or P ==> P == False *)
+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 & *)
+fun distributivity ctxt = Thm o try_apply ctxt [] [
+ named ctxt "fast" (T.by_tac (Classical.best_tac HOL_cs))]
+ (* FIXME: not very well tested *)
+
+
+
+(* 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 lits = L.true_thm :: L.explode conj1 true (conj1 <> conj2) [] thm
+ in L.join conj2 (L.make_littab lits) (Thm.term_of ct2) end
+
+ fun prove rule (ct1, conj1) (ct2, conj2) =
+ T.under_assumption (prove' conj1 conj2 ct2) ct1 COMP rule
+
+ fun prove_def_axiom ct =
+ let val (ct1, ct2) = Thm.dest_binop (Thm.dest_arg 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 T.with_conv (dis_conv T.unfold_distinct_conv) prv 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 T.with_conv (dis_conv T.unfold_distinct_conv) prv ct end
+ | _ => raise CTERM ("prove_def_axiom", [ct]))
+ end
+
+ val rewr_if =
+ @{lemma "(if P then Q1 else Q2) = ((P --> Q1) & (~P --> Q2))" by simp}
+in
+fun def_axiom ctxt = Thm o try_apply ctxt [] [
+ named ctxt "conj/disj/distinct" prove_def_axiom,
+ T.by_abstraction ctxt [] (fn ctxt' =>
+ named ctxt' "simp+fast" (T.by_tac (
+ Simplifier.simp_tac (HOL_ss addsimps [rewr_if])
+ THEN_ALL_NEW Classical.best_tac HOL_cs)))]
+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 = T.match_instantiate Thm.dest_arg
+
+ fun apply_rule ct =
+ (case get_first (try (inst_rule ct)) intro_rules of
+ SOME thm => thm
+ | NONE => raise CTERM ("intro_def", [ct]))
+in
+fun intro_def ct = T.make_hyp_def (apply_rule ct) #>> Thm
+
+fun apply_def thm =
+ get_first (try (fn rule => MetaEq (thm COMP rule))) apply_rules
+ |> the_default (Thm thm)
+end
+
+
+
+(* negation normal form *)
+
+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 vars qs p ct =
+ T.as_meta_eq ct
+ |> T.by_tac (nnf_quant_tac (T.varify vars (meta_eq_of p)) qs)
+
+ fun prove_nnf ctxt = try_apply ctxt [] [
+ named ctxt "conj/disj" L.prove_conj_disj_eq]
+in
+fun nnf ctxt vars ps ct =
+ (case T.term_of ct of
+ _ $ (l as Const _ $ Abs _) $ (r as Const _ $ Abs _) =>
+ if l aconv r
+ then MetaEq (Thm.reflexive (Thm.dest_arg (Thm.dest_arg ct)))
+ else MetaEq (nnf_quant vars quant_rules1 (hd ps) ct)
+ | _ $ (@{term Not} $ (Const _ $ Abs _)) $ (Const _ $ Abs _) =>
+ MetaEq (nnf_quant vars quant_rules2 (hd ps) ct)
+ | _ =>
+ let
+ val nnf_rewr_conv = Conv.arg_conv (Conv.arg_conv
+ (T.unfold_eqs ctxt (map (Thm.symmetric o meta_eq_of) ps)))
+ in Thm (T.with_conv nnf_rewr_conv (prove_nnf ctxt) ct) end)
+end
+
+
+
+(** equality proof rules **)
+
+(* |- t = t *)
+fun refl ct = MetaEq (Thm.reflexive (Thm.dest_arg (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 trans1 = @{lemma "s == t ==> t = u ==> s == u" by simp}
+ val trans2 = @{lemma "s = t ==> t == u ==> s == u" by simp}
+ val trans3 = @{lemma "s = t ==> t = u ==> s == u" by simp}
+in
+fun trans (MetaEq thm1) (MetaEq thm2) = MetaEq (Thm.transitive thm1 thm2)
+ | trans (MetaEq thm) q = MetaEq (thm_of q COMP (thm COMP trans1))
+ | trans p (MetaEq thm) = MetaEq (thm COMP (thm_of p COMP trans2))
+ | trans p q = MetaEq (thm_of q COMP (thm_of p COMP trans3))
+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 L.is_conj (prove_eq_exn f)
+ | @{term "op |"} => prove_nary L.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 lookup = AList.lookup (op aconv) (map (`Thm.prop_of o meta_eq_of) eqs)
+ val cp = Thm.dest_binop (Thm.dest_arg ct)
+ in MetaEq (prove_eq_exn lookup cp handle MONO => mono lookup cp) end
+end
+
+
+
+(* |- f a b = f b a (where f is equality) *)
+local
+ val rule = @{lemma "a = b == b = a" by (atomize(full)) (rule eq_commute)}
+in
+fun commutativity ct = MetaEq (T.match_instantiate I (T.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) ==> (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}]
+in
+fun quant_intro vars p ct =
+ let
+ val thm = meta_eq_of p
+ val rules' = T.varify vars thm :: rules
+ val cu = T.as_meta_eq ct
+ in MetaEq (T.by_tac (REPEAT_ALL_NEW (Tactic.match_tac rules')) cu) end
+end
+
+
+
+(* |- ((ALL x. P x) | Q) = (ALL x. P x | Q) *)
+fun pull_quant ctxt = Thm o try_apply ctxt [] [
+ named ctxt "fast" (T.by_tac (Classical.fast_tac HOL_cs))]
+ (* FIXME: not very well tested *)
+
+
+
+(* |- (ALL x. P x & Q x) = ((ALL x. P x) & (ALL x. Q x)) *)
+fun push_quant ctxt = Thm o try_apply ctxt [] [
+ named ctxt "fast" (T.by_tac (Classical.fast_tac HOL_cs))]
+ (* FIXME: not very well tested *)
+
+
+
+(* |- (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}
+
+ fun elim_unused_conv ctxt =
+ Conv.params_conv ~1 (K (Conv.arg_conv (Conv.arg1_conv
+ (More_Conv.rewrs_conv [elim_all, elim_ex])))) ctxt
+
+ fun elim_unused_tac ctxt =
+ REPEAT_ALL_NEW (
+ Tactic.match_tac [@{thm refl}, @{thm iff_allI}, @{thm iff_exI}]
+ ORELSE' CONVERSION (elim_unused_conv ctxt))
+in
+fun elim_unused_vars ctxt = Thm o T.by_tac (elim_unused_tac ctxt)
+end
+
+
+
+(* |- (ALL x1 ... xn. ~(x1 = t1 & ... xn = tn) | P x1 ... xn) = P t1 ... tn *)
+fun dest_eq_res ctxt = Thm o try_apply ctxt [] [
+ named ctxt "fast" (T.by_tac (Classical.fast_tac HOL_cs))]
+ (* FIXME: not very well tested *)
+
+
+
+(* |- ~(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 T.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 pair2 (a, b) (c, d) = [(a, c), (b, d)]
+ 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 ([], (pair2 (dest f sk') (p, c))) sk')
+ |> Conv.fconv_rule (Thm.beta_conversion true)
+
+ fun kind (Const (@{const_name Ex}, _) $ _) = (sk_ex_rule, I, I)
+ | kind (@{term Not} $ (Const (@{const_name All}, _) $ _)) =
+ (sk_all_rule, Thm.dest_arg, Thm.capply @{cterm Not})
+ | kind t = raise TERM ("skolemize", [t])
+
+ fun dest_abs_type (Abs (_, T, _)) = T
+ | dest_abs_type t = raise TERM ("dest_abs_type", [t])
+
+ fun bodies_of thy lhs rhs =
+ let
+ val (rule, dest, make) = kind (Thm.term_of lhs)
+
+ fun dest_body idx cbs ct =
+ let
+ val cb = Thm.dest_arg (dest ct)
+ val T = dest_abs_type (Thm.term_of cb)
+ val cv = Thm.cterm_of thy (Var (("x", idx), T))
+ val cu = make (Drule.beta_conv cb cv)
+ val cbs' = (cv, cb) :: cbs
+ in
+ (snd (Thm.first_order_match (cu, rhs)), rev cbs')
+ handle Pattern.MATCH => dest_body (idx+1) cbs' cu
+ end
+ in (rule, dest_body 1 [] lhs) end
+
+ fun transitive f thm = Thm.transitive thm (f (Thm.rhs_of thm))
+
+ fun sk_step (rule, elim) (cv, mct, cb) ((is, thm), ctxt) =
+ (case mct of
+ SOME ct =>
+ ctxt
+ |> T.make_hyp_def (inst_sk rule (Thm.instantiate_cterm ([], is) cb) ct)
+ |>> pair ((cv, ct) :: is) o Thm.transitive thm
+ | NONE => ((is, transitive (Conv.rewr_conv elim) thm), ctxt))
+in
+fun skolemize ct ctxt =
+ let
+ val (lhs, rhs) = Thm.dest_binop (Thm.dest_arg ct)
+ val (rule, (ctab, cbs)) = bodies_of (ProofContext.theory_of ctxt) lhs rhs
+ fun lookup_var (cv, cb) = (cv, AList.lookup (op aconvc) ctab cv, cb)
+ in
+ (([], Thm.reflexive lhs), ctxt)
+ |> fold (sk_step rule) (map lookup_var cbs)
+ |>> MetaEq o snd
+ end
+end
+
+
+
+(** theory proof rules **)
+
+(* theory lemmas: linear arithmetic, arrays *)
+
+fun th_lemma ctxt simpset thms = Thm o try_apply ctxt thms [
+ T.by_abstraction ctxt thms (fn ctxt' => T.by_tac (
+ NAMED ctxt' "arith" (Arith_Data.arith_tac ctxt')
+ ORELSE' NAMED ctxt' "simp+arith" (Simplifier.simp_tac simpset THEN_ALL_NEW
+ Arith_Data.arith_tac ctxt')))]
+
+
+
+(* 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_Simps = Named_Thms
+(
+ val name = "z3_simp"
+ val description = "simplification rules for Z3 proof reconstruction"
+)
+
+local
+ fun spec_meta_eq_of thm =
+ (case try (fn th => th RS @{thm spec}) thm of
+ SOME thm' => spec_meta_eq_of thm'
+ | NONE => mk_meta_eq thm)
+
+ fun prep (Thm thm) = spec_meta_eq_of thm
+ | prep (MetaEq thm) = thm
+ | prep (Literals (thm, _)) = spec_meta_eq_of thm
+
+ fun unfold_conv ctxt ths =
+ Conv.arg_conv (Conv.binop_conv (T.unfold_eqs ctxt (map prep ths)))
+
+ fun with_conv _ [] prv = prv
+ | with_conv ctxt ths prv = T.with_conv (unfold_conv ctxt ths) prv
+
+ val unfold_conv =
+ Conv.arg_conv (Conv.binop_conv (Conv.try_conv T.unfold_distinct_conv))
+ val prove_conj_disj_eq = T.with_conv unfold_conv L.prove_conj_disj_eq
+in
+
+fun rewrite ctxt simpset ths = Thm o with_conv ctxt ths (try_apply ctxt [] [
+ named ctxt "conj/disj/distinct" prove_conj_disj_eq,
+ T.by_abstraction ctxt [] (fn ctxt' => T.by_tac (
+ NAMED ctxt' "simp" (Simplifier.simp_tac simpset)
+ THEN_ALL_NEW (
+ NAMED ctxt' "fast" (Classical.fast_tac HOL_cs)
+ ORELSE' NAMED ctxt' "arith" (Arith_Data.arith_tac ctxt'))))])
+
+end
+
+
+
+(** proof reconstruction **)
+
+(* tracing and checking *)
+
+local
+ fun count_rules ptab =
+ let
+ fun count (_, Unproved _) (solved, total) = (solved, total + 1)
+ | count (_, Proved _) (solved, total) = (solved + 1, total + 1)
+ in Inttab.fold count ptab (0, 0) end
+
+ fun header idx r (solved, total) =
+ "Z3: #" ^ string_of_int idx ^ ": " ^ P.string_of_rule r ^ " (goal " ^
+ string_of_int (solved + 1) ^ " of " ^ string_of_int total ^ ")"
+
+ fun check ctxt idx r ps ct p =
+ let val thm = thm_of p |> tap (Thm.join_proofs o single)
+ in
+ if (Thm.cprop_of thm) aconvc ct then ()
+ else z3_exn (Pretty.string_of (Pretty.big_list ("proof step failed: " ^
+ quote (P.string_of_rule r) ^ " (#" ^ string_of_int idx ^ ")")
+ (pretty_goal ctxt (map (thm_of o fst) ps) (Thm.prop_of thm) @
+ [Pretty.block [Pretty.str "expected: ",
+ Syntax.pretty_term ctxt (Thm.term_of ct)]])))
+ end
+in
+fun trace_rule idx prove r ps ct (cxp as (ctxt, ptab)) =
+ let
+ val _ = SMT_Solver.trace_msg ctxt (header idx r o count_rules) ptab
+ val result as (p, cxp' as (ctxt', _)) = prove r ps ct cxp
+ val _ = if not (Config.get ctxt' SMT_Solver.trace) then ()
+ else check ctxt' idx r ps ct p
+ in result end
+end
+
+
+(* overall reconstruction procedure *)
+
+fun not_supported r =
+ raise Fail ("Z3: proof rule not implemented: " ^ quote (P.string_of_rule r))
+
+fun prove ctxt unfolds assms vars =
+ let
+ val assms' = Option.map (prepare_assms ctxt unfolds) assms
+ val simpset = T.make_simpset ctxt (Z3_Simps.get ctxt)
+
+ fun step r ps ct (cxp as (cx, ptab)) =
+ (case (r, ps) of
+ (* core rules *)
+ (P.TrueAxiom, _) => (Thm L.true_thm, cxp)
+ | (P.Asserted, _) => (asserted cx assms' ct, cxp)
+ | (P.Goal, _) => (asserted cx assms' ct, cxp)
+ | (P.ModusPonens, [(p, _), (q, _)]) => (mp q (thm_of p), cxp)
+ | (P.ModusPonensOeq, [(p, _), (q, _)]) => (mp q (thm_of p), cxp)
+ | (P.AndElim, [(p, i)]) => and_elim (p, i) ct ptab ||> pair cx
+ | (P.NotOrElim, [(p, i)]) => not_or_elim (p, i) ct ptab ||> pair cx
+ | (P.Hypothesis, _) => (Thm (Thm.assume ct), cxp)
+ | (P.Lemma, [(p, _)]) => (lemma (thm_of p) ct, cxp)
+ | (P.UnitResolution, (p, _) :: ps) =>
+ (unit_resolution (thm_of p) (map (thm_of o fst) ps) ct, cxp)
+ | (P.IffTrue, [(p, _)]) => (iff_true (thm_of p), cxp)
+ | (P.IffFalse, [(p, _)]) => (iff_false (thm_of p), cxp)
+ | (P.Distributivity, _) => (distributivity cx ct, cxp)
+ | (P.DefAxiom, _) => (def_axiom cx ct, cxp)
+ | (P.IntroDef, _) => intro_def ct cx ||> rpair ptab
+ | (P.ApplyDef, [(p, _)]) => (apply_def (thm_of p), cxp)
+ | (P.IffOeq, [(p, _)]) => (p, cxp)
+ | (P.NnfPos, _) => (nnf cx vars (map fst ps) ct, cxp)
+ | (P.NnfNeg, _) => (nnf cx vars (map fst ps) ct, cxp)
+
+ (* equality rules *)
+ | (P.Reflexivity, _) => (refl ct, cxp)
+ | (P.Symmetry, [(p, _)]) => (symm p, cxp)
+ | (P.Transitivity, [(p, _), (q, _)]) => (trans p q, cxp)
+ | (P.Monotonicity, _) => (monotonicity (map fst ps) ct, cxp)
+ | (P.Commutativity, _) => (commutativity ct, cxp)
+
+ (* quantifier rules *)
+ | (P.QuantIntro, [(p, _)]) => (quant_intro vars p ct, cxp)
+ | (P.PullQuant, _) => (pull_quant cx ct, cxp)
+ | (P.PushQuant, _) => (push_quant cx ct, cxp)
+ | (P.ElimUnusedVars, _) => (elim_unused_vars cx ct, cxp)
+ | (P.DestEqRes, _) => (dest_eq_res cx ct, cxp)
+ | (P.QuantInst, _) => (quant_inst ct, cxp)
+ | (P.Skolemize, _) => skolemize ct cx ||> rpair ptab
+
+ (* theory rules *)
+ | (P.ThLemma, _) =>
+ (th_lemma cx simpset (map (thm_of o fst) ps) ct, cxp)
+ | (P.Rewrite, _) => (rewrite cx simpset [] ct, cxp)
+ | (P.RewriteStar, ps) =>
+ (rewrite cx simpset (map fst ps) ct, cxp)
+
+ | (P.NnfStar, _) => not_supported r
+ | (P.CnfStar, _) => not_supported r
+ | (P.TransitivityStar, _) => not_supported r
+ | (P.PullQuantStar, _) => not_supported r
+
+ | _ => raise Fail ("Z3: proof rule " ^ quote (P.string_of_rule r) ^
+ " has an unexpected number of arguments."))
+
+ fun conclude idx rule prop (ps, cxp) =
+ trace_rule idx step rule ps prop cxp
+ |-> (fn p => apsnd (Inttab.update (idx, Proved p)) #> pair p)
+
+ fun lookup idx (cxp as (cx, ptab)) =
+ (case Inttab.lookup ptab idx of
+ SOME (Unproved (P.Proof_Step {rule, prems, prop})) =>
+ fold_map lookup prems cxp
+ |>> map2 rpair prems
+ |> conclude idx rule prop
+ | SOME (Proved p) => (p, cxp)
+ | NONE => z3_exn ("unknown proof id: " ^ quote (string_of_int idx)))
+
+ fun result (p, (cx, _)) = (thm_of p, cx)
+ in
+ (fn (idx, ptab) => result (lookup idx (ctxt, Inttab.map Unproved ptab)))
+ end
+
+fun reconstruct (output, {typs, terms, unfolds, assms}) ctxt =
+ P.parse ctxt typs terms output
+ |> (fn (idx, (ptab, vars, cx)) => prove cx unfolds assms vars (idx, ptab))
+
+val setup = trace_assms_setup #> z3_rules_setup #> Z3_Simps.setup
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_proof_tools.ML Wed May 12 23:54:02 2010 +0200
@@ -0,0 +1,368 @@
+(* Title: HOL/Tools/SMT/z3_proof_tools.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Helper functions required for Z3 proof reconstruction.
+*)
+
+signature Z3_PROOF_TOOLS =
+sig
+ (* accessing and modifying terms *)
+ val term_of: cterm -> term
+ val prop_of: thm -> term
+ val mk_prop: cterm -> cterm
+ val as_meta_eq: cterm -> cterm
+
+ (* theorem nets *)
+ val thm_net_of: thm list -> thm Net.net
+ val net_instance: thm Net.net -> cterm -> thm option
+
+ (* proof combinators *)
+ val under_assumption: (thm -> thm) -> cterm -> thm
+ val with_conv: conv -> (cterm -> thm) -> cterm -> thm
+ val discharge: thm -> thm -> thm
+ val varify: string list -> thm -> thm
+ val unfold_eqs: Proof.context -> thm list -> conv
+ val match_instantiate: (cterm -> cterm) -> cterm -> thm -> thm
+ val by_tac: (int -> tactic) -> cterm -> thm
+ val make_hyp_def: thm -> Proof.context -> thm * Proof.context
+ val by_abstraction: Proof.context -> thm list -> (Proof.context -> cterm ->
+ thm) -> cterm -> thm
+
+ (* a faster COMP *)
+ type compose_data
+ val precompose: (cterm -> cterm list) -> thm -> compose_data
+ val precompose2: (cterm -> cterm * cterm) -> thm -> compose_data
+ val compose: compose_data -> thm -> thm
+
+ (* unfolding of 'distinct' *)
+ val unfold_distinct_conv: conv
+
+ (* simpset *)
+ val make_simpset: Proof.context -> thm list -> simpset
+end
+
+structure Z3_Proof_Tools: Z3_PROOF_TOOLS =
+struct
+
+
+
+(* accessing terms *)
+
+val dest_prop = (fn @{term Trueprop} $ t => t | t => t)
+
+fun term_of ct = dest_prop (Thm.term_of ct)
+fun prop_of thm = dest_prop (Thm.prop_of thm)
+
+val mk_prop = Thm.capply @{cterm Trueprop}
+
+val (eqT, eq) = `(hd o Thm.dest_ctyp o Thm.ctyp_of_term) @{cpat "op =="}
+fun mk_meta_eq_cterm ct cu =
+ let val inst = ([(eqT, Thm.ctyp_of_term ct)], [])
+ in Thm.mk_binop (Thm.instantiate_cterm inst eq) ct cu end
+
+fun as_meta_eq ct = uncurry mk_meta_eq_cterm (Thm.dest_binop (Thm.dest_arg ct))
+
+
+
+(* theorem nets *)
+
+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 maybe_instantiate ct thm =
+ try Thm.first_order_match (Thm.cprop_of thm, ct)
+ |> Option.map (fn inst => Thm.instantiate inst thm)
+
+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
+
+
+
+(* proof combinators *)
+
+fun under_assumption f ct =
+ let val ct' = 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 discharge p pq = Thm.implies_elim pq p
+
+fun varify vars = Drule.generalize ([], vars)
+
+fun unfold_eqs _ [] = Conv.all_conv
+ | unfold_eqs ctxt eqs =
+ More_Conv.top_sweep_conv (K (More_Conv.rewrs_conv eqs)) ctxt
+
+fun match_instantiate f ct thm =
+ Thm.instantiate (Thm.match (f (Thm.cprop_of thm), ct)) thm
+
+fun by_tac tac ct = Goal.norm_result (Goal.prove_internal [] ct (K (tac 1)))
+
+(* |- c x == t x ==> P (c x) ~~> c == t |- P (c x) *)
+fun make_hyp_def thm ctxt =
+ let
+ val (lhs, rhs) = Thm.dest_binop (Thm.cprem_of thm 1)
+ val (cf, cvs) = Drule.strip_comb lhs
+ val eq = mk_meta_eq_cterm 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
+ yield_singleton Assumption.add_assumes eq ctxt
+ |>> Thm.implies_elim thm o fold apply cvs
+ end
+
+
+
+(* abstraction *)
+
+local
+
+fun typ_of ct = #T (Thm.rep_cterm ct)
+fun certify ctxt = Thm.cterm_of (ProofContext.theory_of ctxt)
+
+fun abs_context ctxt = (ctxt, Termtab.empty, 1, false)
+
+fun context_of (ctxt, _, _, _) = ctxt
+
+fun replace (cv, ct) = Thm.forall_elim ct o Thm.forall_intr cv
+
+fun abs_instantiate (_, tab, _, beta_norm) =
+ fold replace (map snd (Termtab.dest tab)) #>
+ beta_norm ? Conv.fconv_rule (Thm.beta_conversion true)
+
+fun generalize cvs =
+ let
+ val no_name = ""
+
+ fun dest (Free (n, _)) = n
+ | dest _ = no_name
+
+ fun gen vs (t as Free (n, _)) =
+ let val i = find_index (equal n) vs
+ in
+ if i >= 0 then insert (op aconvc) (nth cvs i) #> pair (Bound i)
+ else pair t
+ end
+ | gen vs (t $ u) = gen vs t ##>> gen vs u #>> (op $)
+ | gen vs (Abs (n, T, t)) =
+ gen (no_name :: vs) t #>> (fn u => Abs (n, T, u))
+ | gen _ t = pair t
+
+ in (fn ct => gen (map (dest o Thm.term_of) cvs) (Thm.term_of ct) []) end
+
+fun fresh_abstraction cvs ct (cx as (ctxt, tab, idx, beta_norm)) =
+ let val (t, cvs') = generalize cvs ct
+ in
+ (case Termtab.lookup tab t of
+ SOME (cv, _) => (cv, cx)
+ | NONE =>
+ let
+ val (n, ctxt') = yield_singleton Variable.variant_fixes "x" ctxt
+ val cv = certify ctxt (Free (n, map typ_of cvs' ---> typ_of ct))
+ val cv' = Drule.list_comb (cv, cvs')
+ val e = (t, (cv, fold_rev Thm.cabs cvs' ct))
+ val beta_norm' = beta_norm orelse not (null cvs')
+ in (cv', (ctxt', Termtab.update e tab, idx + 1, beta_norm')) end)
+ end
+
+fun abs_arg f cvs ct =
+ let val (cf, cu) = Thm.dest_comb ct
+ in f cvs cu #>> Thm.capply cf end
+
+fun abs_comb f g cvs ct =
+ let val (cf, cu) = Thm.dest_comb ct
+ in f cvs cf ##>> g cvs cu #>> uncurry Thm.capply end
+
+fun abs_list f g cvs ct =
+ (case Thm.term_of ct of
+ Const (@{const_name Nil}, _) => pair ct
+ | Const (@{const_name Cons}, _) $ _ $ _ =>
+ abs_comb (abs_arg f) (abs_list f g) cvs ct
+ | _ => g cvs ct)
+
+fun abs_abs f cvs ct =
+ let val (cv, cu) = Thm.dest_abs NONE ct
+ in f (cv :: cvs) cu #>> Thm.cabs cv end
+
+val is_atomic = (fn _ $ _ => false | Abs _ => false | _ => true)
+val is_arithT = (fn @{typ int} => true | @{typ real} => true | _ => false)
+fun is_number t =
+ (case try HOLogic.dest_number t of
+ SOME (T, _) => is_arithT T
+ | NONE => false)
+
+fun abstract (ext_logic, with_theories) =
+ let
+ fun abstr1 cvs ct = abs_arg abstr cvs ct
+ and abstr2 cvs ct = abs_comb abstr1 abstr cvs ct
+ and abstr3 cvs ct = abs_comb abstr2 abstr cvs ct
+ and abstr_abs cvs ct = abs_arg (abs_abs abstr) cvs ct
+
+ and abstr cvs ct =
+ (case Thm.term_of ct of
+ @{term Trueprop} $ _ => abstr1 cvs ct
+ | @{term "op ==>"} $ _ $ _ => abstr2 cvs ct
+ | @{term True} => pair ct
+ | @{term False} => pair ct
+ | @{term Not} $ _ => abstr1 cvs ct
+ | @{term "op &"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op |"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op -->"} $ _ $ _ => abstr2 cvs ct
+ | Const (@{const_name "op ="}, _) $ _ $ _ => abstr2 cvs ct
+ | Const (@{const_name distinct}, _) $ _ =>
+ if ext_logic then abs_arg (abs_list abstr fresh_abstraction) cvs ct
+ else fresh_abstraction cvs ct
+ | Const (@{const_name If}, _) $ _ $ _ $ _ =>
+ if ext_logic then abstr3 cvs ct else fresh_abstraction cvs ct
+ | Const (@{const_name All}, _) $ _ =>
+ if ext_logic then abstr_abs cvs ct else fresh_abstraction cvs ct
+ | Const (@{const_name Ex}, _) $ _ =>
+ if ext_logic then abstr_abs cvs ct else fresh_abstraction cvs ct
+ | @{term "uminus :: int => _"} $ _ => abstr1 cvs ct
+ | @{term "uminus :: real => _"} $ _ => abstr1 cvs ct
+ | @{term "op + :: int => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op + :: real => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op - :: int => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op - :: real => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op * :: int => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op * :: real => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op div :: int => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op mod :: int => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op / :: real => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op < :: int => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op < :: real => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op <= :: int => _"} $ _ $ _ => abstr2 cvs ct
+ | @{term "op <= :: real => _"} $ _ $ _ => abstr2 cvs ct
+ | Const (@{const_name apply}, _) $ _ $ _ => abstr2 cvs ct
+ | Const (@{const_name fun_upd}, _) $ _ $ _ $ _ => abstr3 cvs ct
+ | t =>
+ if is_atomic t orelse is_number t then pair ct
+ else fresh_abstraction cvs ct)
+ in abstr [] end
+
+fun with_prems thms f ct =
+ fold_rev (Thm.mk_binop @{cterm "op ==>"} o Thm.cprop_of) thms ct
+ |> f
+ |> fold (fn prem => fn th => Thm.implies_elim th prem) thms
+
+in
+
+fun by_abstraction ctxt thms prove = with_prems thms (fn ct =>
+ let val (cu, cx) = abstract (true, true) ct (abs_context ctxt)
+ in abs_instantiate cx (prove (context_of cx) cu) end)
+
+end
+
+
+
+(* a faster COMP *)
+
+type compose_data = cterm list * (cterm -> cterm list) * thm
+
+fun list2 (x, y) = [x, y]
+
+fun precompose f rule = (f (Thm.cprem_of rule 1), f, rule)
+fun precompose2 f rule = precompose (list2 o f) rule
+
+fun compose (cvs, f, rule) thm =
+ discharge thm (Thm.instantiate ([], cvs ~~ f (Thm.cprop_of thm)) rule)
+
+
+
+(* unfolding of 'distinct' *)
+
+local
+ val set1 = @{lemma "x ~: set [] == ~False" by simp}
+ val set2 = @{lemma "x ~: set [x] == False" by simp}
+ val set3 = @{lemma "x ~: set [y] == x ~= y" by simp}
+ val set4 = @{lemma "x ~: set (x # ys) == False" by simp}
+ val set5 = @{lemma "x ~: set (y # ys) == x ~= y & x ~: set ys" by simp}
+
+ fun set_conv ct =
+ (More_Conv.rewrs_conv [set1, set2, set3, set4] else_conv
+ (Conv.rewr_conv set5 then_conv Conv.arg_conv set_conv)) ct
+
+ val dist1 = @{lemma "distinct [] == ~False" by simp}
+ val dist2 = @{lemma "distinct [x] == ~False" by simp}
+ val dist3 = @{lemma "distinct (x # xs) == x ~: set xs & distinct xs"
+ by simp}
+
+ fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
+in
+fun unfold_distinct_conv ct =
+ (More_Conv.rewrs_conv [dist1, dist2] else_conv
+ (Conv.rewr_conv dist3 then_conv binop_conv set_conv unfold_distinct_conv)) ct
+end
+
+
+
+(* simpset *)
+
+local
+ val antisym_le1 = mk_meta_eq @{thm order_class.antisym_conv}
+ val antisym_le2 = mk_meta_eq @{thm linorder_class.antisym_conv2}
+ val antisym_less1 = mk_meta_eq @{thm linorder_class.antisym_conv1}
+ val antisym_less2 = mk_meta_eq @{thm linorder_class.antisym_conv3}
+
+ fun eq_prop t thm = HOLogic.mk_Trueprop t aconv Thm.prop_of thm
+ fun dest_binop ((c as Const _) $ t $ u) = (c, t, u)
+ | dest_binop t = raise TERM ("dest_binop", [t])
+
+ fun prove_antisym_le ss t =
+ let
+ val (le, r, s) = dest_binop t
+ val less = Const (@{const_name less}, Term.fastype_of le)
+ val prems = Simplifier.prems_of_ss ss
+ in
+ (case find_first (eq_prop (le $ s $ r)) prems of
+ NONE =>
+ find_first (eq_prop (HOLogic.mk_not (less $ r $ s))) prems
+ |> Option.map (fn thm => thm RS antisym_less1)
+ | SOME thm => SOME (thm RS antisym_le1))
+ end
+ handle THM _ => NONE
+
+ fun prove_antisym_less ss t =
+ let
+ val (less, r, s) = dest_binop (HOLogic.dest_not t)
+ val le = Const (@{const_name less_eq}, Term.fastype_of less)
+ val prems = prems_of_ss ss
+ in
+ (case find_first (eq_prop (le $ r $ s)) prems of
+ NONE =>
+ find_first (eq_prop (HOLogic.mk_not (less $ s $ r))) prems
+ |> Option.map (fn thm => thm RS antisym_less2)
+ | SOME thm => SOME (thm RS antisym_le2))
+ end
+ handle THM _ => NONE
+in
+
+fun make_simpset ctxt rules = Simplifier.context ctxt (HOL_ss
+ addsimps @{thms field_simps}
+ addsimps [@{thm times_divide_eq_right}, @{thm times_divide_eq_left}]
+ 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}
+ addsimps @{thms array_rules}
+ 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),
+ Simplifier.simproc @{theory} "antisym_le" ["(x::'a::order) <= y"]
+ (K prove_antisym_le),
+ Simplifier.simproc @{theory} "antisym_less" ["~ (x::'a::linorder) < y"]
+ (K prove_antisym_less)]
+ addsimps rules)
+
+end
+
+end