rationalize slicing format

--- a/src/HOL/Tools/Sledgehammer/sledgehammer.ML	Mon Jan 31 16:09:23 2022 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer.ML	Mon Jan 31 16:09:23 2022 +0100
@@ -313,7 +313,8 @@
               (case max_facts of
                 SOME n => n
               | NONE =>
-                0 |> fold (Integer.max o default_max_facts_of_prover ctxt) provers
+                0 |> fold (fn prover => Integer.max (fst (fst (get_default_slice ctxt prover))))
+                    provers
                   |> mode = Auto_Try ? (fn n => n div auto_try_max_facts_divisor))
             val ({elapsed, ...}, factss) = Timing.timing
               (relevant_facts ctxt params (hd provers) max_max_facts fact_override hyp_ts concl_t)

--- a/src/HOL/Tools/Sledgehammer/sledgehammer_atp_systems.ML	Mon Jan 31 16:09:23 2022 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_atp_systems.ML	Mon Jan 31 16:09:23 2022 +0100
@@ -12,7 +12,8 @@
   type atp_formula_role = ATP_Problem.atp_formula_role
   type atp_failure = ATP_Proof.atp_failure
 
-  type atp_slice = (int * string) * atp_format * string * string * bool * string
+  type base_slice = int * string
+  type atp_slice = atp_format * string * string * bool * string
   type atp_config =
     {exec : string list * string list,
      arguments : Proof.context -> bool -> string -> Time.time -> Path.T ->
@@ -20,9 +21,9 @@
      proof_delims : (string * string) list,
      known_failures : (atp_failure * string) list,
      prem_role : atp_formula_role,
-     best_slices : Proof.context -> atp_slice list,
-     best_max_mono_iters : int,
-     best_max_new_mono_instances : int}
+     good_slices : Proof.context -> (base_slice * atp_slice) list,
+     good_max_mono_iters : int,
+     good_max_new_mono_instances : int}
 
   val default_max_mono_iters : int
   val default_max_new_mono_instances : int
@@ -46,7 +47,7 @@
   val spass_H2SOS : string
   val isabelle_scala_function: string list * string list
   val remote_atp : string -> string -> string list -> (string * string) list ->
-    (atp_failure * string) list -> atp_formula_role -> (Proof.context -> atp_slice) ->
+    (atp_failure * string) list -> atp_formula_role -> (Proof.context -> base_slice * atp_slice) ->
     string * (unit -> atp_config)
   val add_atp : string * (unit -> atp_config) -> theory -> theory
   val get_atp : theory -> string -> (unit -> atp_config)
@@ -76,7 +77,8 @@
 val default_max_mono_iters = 3 (* FUDGE *)
 val default_max_new_mono_instances = 100 (* FUDGE *)
 
-type atp_slice = (int * string) * atp_format * string * string * bool * string
+type base_slice = int * string
+type atp_slice = atp_format * string * string * bool * string
 
 type atp_config =
   {exec : string list * string list,
@@ -85,11 +87,11 @@
    proof_delims : (string * string) list,
    known_failures : (atp_failure * string) list,
    prem_role : atp_formula_role,
-   best_slices : Proof.context -> atp_slice list,
-   best_max_mono_iters : int,
-   best_max_new_mono_instances : int}
+   good_slices : Proof.context -> (base_slice * atp_slice) list,
+   good_max_mono_iters : int,
+   good_max_new_mono_instances : int}
 
-(* "best_slices" must be found empirically, taking a holistic approach since the
+(* "good_slices" must be found empirically, taking a holistic approach since the
    ATPs are run in parallel. Each slice has the format
 
      (time_frac, ((max_facts, fact_filter), format, type_enc,
@@ -168,11 +170,11 @@
    proof_delims = tstp_proof_delims,
    known_failures = known_szs_status_failures,
    prem_role = Hypothesis,
-   best_slices =
+   good_slices =
      (* FUDGE *)
-     K [((60, meshN), THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, "")],
-   best_max_mono_iters = default_max_mono_iters - 1 (* FUDGE *),
-   best_max_new_mono_instances = default_max_new_mono_instances}
+     K [((60, meshN), (THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, ""))],
+   good_max_mono_iters = default_max_mono_iters - 1 (* FUDGE *),
+   good_max_new_mono_instances = default_max_new_mono_instances}
 
 val agsyhol = (agsyholN, fn () => agsyhol_config)
 
@@ -190,11 +192,11 @@
       (TimedOut, ": Timeout"),
       (GaveUp, ": Unknown")],
    prem_role = Hypothesis,
-   best_slices = fn _ =>
+   good_slices =
      (* FUDGE *)
-     [((100, meshN), TF1, "poly_native", liftingN, false, "")],
-   best_max_mono_iters = default_max_mono_iters,
-   best_max_new_mono_instances = default_max_new_mono_instances}
+     K [((100, meshN), (TF1, "poly_native", liftingN, false, ""))],
+   good_max_mono_iters = default_max_mono_iters,
+   good_max_new_mono_instances = default_max_new_mono_instances}
 
 val alt_ergo = (alt_ergoN, fn () => alt_ergo_config)
 
@@ -287,7 +289,7 @@
       (TimedOut, "time limit exceeded")] @
      known_szs_status_failures,
    prem_role = Conjecture,
-   best_slices = fn ctxt =>
+   good_slices = fn ctxt =>
      let
        val heuristic = Config.get ctxt e_selection_heuristic
        val (format, enc, main_lam_trans) =
@@ -300,17 +302,17 @@
      in
        (* FUDGE *)
        if heuristic = e_smartN then
-         [((128, meshN), format, enc, main_lam_trans, false, e_fun_weightN),
-          ((128, mashN), format, enc, main_lam_trans, false, e_sym_offset_weightN),
-          ((91, mepoN), format, enc, main_lam_trans, false, e_autoN),
-          ((1000, meshN), format, "poly_guards??", main_lam_trans, false, e_sym_offset_weightN),
-          ((256, mepoN), format, enc, liftingN, false, e_fun_weightN),
-          ((64, mashN), format, enc, combsN, false, e_fun_weightN)]
+         [((128, meshN), (format, enc, main_lam_trans, false, e_fun_weightN)),
+          ((128, mashN), (format, enc, main_lam_trans, false, e_sym_offset_weightN)),
+          ((91, mepoN), (format, enc, main_lam_trans, false, e_autoN)),
+          ((1000, meshN), (format, "poly_guards??", main_lam_trans, false, e_sym_offset_weightN)),
+          ((256, mepoN), (format, enc, liftingN, false, e_fun_weightN)),
+          ((64, mashN), (format, enc, combsN, false, e_fun_weightN))]
        else
-         [((500, meshN), format, enc, combsN, false, heuristic)]
+         [((500, meshN), (format, enc, combsN, false, heuristic))]
      end,
-   best_max_mono_iters = default_max_mono_iters,
-   best_max_new_mono_instances = default_max_new_mono_instances}
+   good_max_mono_iters = default_max_mono_iters,
+   good_max_new_mono_instances = default_max_new_mono_instances}
 
 val e = (eN, fn () => e_config)
 
@@ -328,11 +330,11 @@
      [(ProofIncomplete, "% SZS output start CNFRefutation")] @
      known_szs_status_failures,
    prem_role = Hypothesis,
-   best_slices =
+   good_slices =
      (* FUDGE *)
-     K [((150, meshN), FOF, "mono_guards??", liftingN, false, "")],
-   best_max_mono_iters = default_max_mono_iters,
-   best_max_new_mono_instances = default_max_new_mono_instances}
+     K [((150, meshN), (FOF, "mono_guards??", liftingN, false, ""))],
+   good_max_mono_iters = default_max_mono_iters,
+   good_max_new_mono_instances = default_max_new_mono_instances}
 
 val iprover = (iproverN, fn () => iprover_config)
 
@@ -353,11 +355,11 @@
       (GaveUp, "No.of.Axioms")] @
      known_szs_status_failures,
    prem_role = Hypothesis,
-   best_slices =
+   good_slices =
      (* FUDGE *)
-     K [((40, meshN), THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, "")],
-   best_max_mono_iters = default_max_mono_iters - 1 (* FUDGE *),
-   best_max_new_mono_instances = default_max_new_mono_instances}
+     K [((40, meshN), (THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, ""))],
+   good_max_mono_iters = default_max_mono_iters - 1 (* FUDGE *),
+   good_max_new_mono_instances = default_max_new_mono_instances}
 
 val leo2 = (leo2N, fn () => leo2_config)
 
@@ -374,11 +376,11 @@
    proof_delims = tstp_proof_delims,
    known_failures = known_szs_status_failures,
    prem_role = Hypothesis,
-   best_slices =
+   good_slices =
      (* FUDGE *)
-     K [((512, meshN), TH1, "mono_native_higher", keep_lamsN, false, "")],
-   best_max_mono_iters = default_max_mono_iters - 1 (* FUDGE *),
-   best_max_new_mono_instances = default_max_new_mono_instances}
+     K [((512, meshN), (TH1, "mono_native_higher", keep_lamsN, false, ""))],
+   good_max_mono_iters = default_max_mono_iters - 1 (* FUDGE *),
+   good_max_new_mono_instances = default_max_new_mono_instances}
 
 val leo3 = (leo3N, fn () => leo3_config)
 
@@ -397,11 +399,11 @@
      [("% SZS output start Proof", "% SZS output end Proof")],
    known_failures = known_szs_status_failures,
    prem_role = Hypothesis,
-   best_slices =
+   good_slices =
      (* FUDGE *)
-     K [((150, meshN), THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, "")],
-   best_max_mono_iters = default_max_mono_iters - 1 (* FUDGE *),
-   best_max_new_mono_instances = default_max_new_mono_instances}
+     K [((150, meshN), (THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, ""))],
+   good_max_mono_iters = default_max_mono_iters - 1 (* FUDGE *),
+   good_max_new_mono_instances = default_max_new_mono_instances}
 
 val satallax = (satallaxN, fn () => satallax_config)
 
@@ -434,18 +436,18 @@
         (Unprovable, "No formulae and clauses found in input file"),
         (InternalError, "Please report this error")],
      prem_role = Conjecture,
-     best_slices = fn _ =>
+     good_slices =
        (* FUDGE *)
-       [((150, meshN), format, "mono_native", combsN, true, ""),
-        ((500, meshN), format, "mono_native", liftingN, true, spass_H2SOS),
-        ((50, meshN), format,  "mono_native", liftingN, true, spass_H2LR0LT0),
-        ((250, meshN), format, "mono_native", combsN, true, spass_H2NuVS0),
-        ((1000, mepoN), format, "mono_native", liftingN, true, spass_H1SOS),
-        ((150, meshN), format, "poly_guards??", liftingN, false, spass_H2NuVS0Red2),
-        ((300, meshN), format, "mono_native", combsN, true, spass_H2SOS),
-        ((100, meshN), format, "mono_native", combs_and_liftingN, true, spass_H2)],
-     best_max_mono_iters = default_max_mono_iters,
-     best_max_new_mono_instances = default_max_new_mono_instances}
+       K [((150, meshN), (format, "mono_native", combsN, true, "")),
+        ((500, meshN), (format, "mono_native", liftingN, true, spass_H2SOS)),
+        ((50, meshN), (format,  "mono_native", liftingN, true, spass_H2LR0LT0)),
+        ((250, meshN), (format, "mono_native", combsN, true, spass_H2NuVS0)),
+        ((1000, mepoN), (format, "mono_native", liftingN, true, spass_H1SOS)),
+        ((150, meshN), (format, "poly_guards??", liftingN, false, spass_H2NuVS0Red2)),
+        ((300, meshN), (format, "mono_native", combsN, true, spass_H2SOS)),
+        ((100, meshN), (format, "mono_native", combs_and_liftingN, true, spass_H2))],
+     good_max_mono_iters = default_max_mono_iters,
+     good_max_new_mono_instances = default_max_new_mono_instances}
   end
 
 val spass = (spassN, fn () => spass_config)
@@ -480,13 +482,13 @@
       (Interrupted, "Aborted by signal SIGINT")] @
      known_szs_status_failures,
    prem_role = Hypothesis,
-   best_slices = fn ctxt =>
+   good_slices =
      (* FUDGE *)
-     [((500, meshN), TX1, "mono_native_fool", combs_or_liftingN, false, sosN),
-      ((150, meshN), TX1, "poly_native_fool", combs_or_liftingN, false, sosN),
-      ((50, meshN), TX1, "mono_native_fool", combs_or_liftingN, false, no_sosN)],
-   best_max_mono_iters = default_max_mono_iters,
-   best_max_new_mono_instances = 2 * default_max_new_mono_instances (* FUDGE *)}
+     K [((500, meshN), (TX1, "mono_native_fool", combs_or_liftingN, false, sosN)),
+      ((150, meshN), (TX1, "poly_native_fool", combs_or_liftingN, false, sosN)),
+      ((50, meshN), (TX1, "mono_native_fool", combs_or_liftingN, false, no_sosN))],
+   good_max_mono_iters = default_max_mono_iters,
+   good_max_new_mono_instances = 2 * default_max_new_mono_instances (* FUDGE *)}
 
 val vampire = (vampireN, fn () => vampire_config)
 
@@ -500,14 +502,14 @@
    proof_delims = [("SZS status Theorem", "")],
    known_failures = known_szs_status_failures,
    prem_role = Hypothesis,
-   best_slices =
+   good_slices =
      (* FUDGE *)
-     K [((250, meshN), TF0, "mono_native", combsN, false, ""),
-        ((125, mepoN), TF0, "mono_native", combsN, false, ""),
-        ((62, mashN), TF0, "mono_native", combsN, false, ""),
-        ((31, meshN), TF0, "mono_native", combsN, false, "")],
-   best_max_mono_iters = default_max_mono_iters,
-   best_max_new_mono_instances = 2 * default_max_new_mono_instances (* FUDGE *)}
+     K [((250, meshN), (TF0, "mono_native", combsN, false, "")),
+      ((125, mepoN), (TF0, "mono_native", combsN, false, "")),
+      ((62, mashN), (TF0, "mono_native", combsN, false, "")),
+      ((31, meshN), (TF0, "mono_native", combsN, false, ""))],
+   good_max_mono_iters = default_max_mono_iters,
+   good_max_new_mono_instances = 2 * default_max_new_mono_instances (* FUDGE *)}
 
 val z3_tptp = (z3_tptpN, fn () => z3_tptp_config)
 
@@ -528,15 +530,15 @@
        [(TimedOut, "SZS status ResourceOut")] @   (* odd way of timing out *)
        known_szs_status_failures,
      prem_role = Hypothesis,
-     best_slices = fn _ =>
-       [((512, meshN), format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-pragmatic --tptp-def-as-rewrite --rewrite-before-cnf=true --max-inferences=1 --ho-unif-max-depth=1 --ho-max-elims=0 --ho-max-app-projections=0 --ho-max-rigid-imitations=1 --ho-max-identifications=0 --boolean-reasoning=bool-hoist --bool-hoist-simpl=true --bool-select=LI --recognize-injectivity=true --ext-rules=ext-family --ext-rules-max-depth=1 --ho-choice-inst=true --ho-prim-enum=none --ho-elim-leibniz=0 --interpret-bool-funs=true --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --ho-unif-level=pragmatic-framework --select=bb+e-selection2 --post-cnf-lambda-lifting=true -q \"4|prefer-sos|pnrefined(2,1,1,1,2,2,2)\" -q \"6|prefer-processed|conjecture-relative-struct(1.5,3.5,2,3)\" -q \"1|const|fifo\" -q \"4|prefer-ground|orient-lmax(2,1,2,1,1)\" -q \"4|defer-sos|conjecture-relative-struct(1,5,2,3)\" --avatar=off --recognize-injectivity=true --ho-neg-ext=true --e-timeout=2 --ho-pattern-decider=true --ho-fixpoint-decider=true --e-max-derived=50 --ignore-orphans=true --e-auto=true --presaturate=true --e-call-point=0.1"),
-        ((256, mashN), format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-pragmatic --tptp-def-as-rewrite --rewrite-before-cnf=true --mode=ho-competitive --boolean-reasoning=simpl-only --ext-rules=ext-family --ext-rules-max-depth=1 --ho-prim-enum=none --avatar=off --recognize-injectivity=true --ho-elim-leibniz=1 --ho-unif-level=pragmatic-framework --no-max-vars --max-inferences=2 --ho-unif-max-depth=1 -q \"6|prefer-sos|pnrefined(1,1,1,2,2,2,0.5)\" -q \"6|const|conjecture-relative-var(1.02,l,f)\" -q \"1|prefer-processed|fifo\" -q \"1|prefer-non-goals|conjecture-relative-var(1,l,f)\" -q \"4|prefer-easy-ho|conjecture-relative-var(1.01,s,f)\" --select=e-selection16 --ho-choice-inst=true --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --e-timeout=3 --e-auto=true --sine=50 --sine-tolerance=1.0 --sine-depth-max=3 --sine-depth-min=1 --sine-trim-implications=true --ho-unif-level=pragmatic-framework --e-encode-lambdas=lift --scan-clause-ac=false --kbo-weight-fun=lambda-def-invfreqrank --e-call-point=0.1"),
-        ((128, mepoN), format, "mono_native_higher_fool", keep_lamsN, false, "-nc --tptp-def-as-rewrite --rewrite-before-cnf=true --mode=ho-competitive --boolean-reasoning=simpl-only --ext-rules=off --ho-prim-enum=full --ho-prim-max=1 --avatar=off --recognize-injectivity=true --ho-elim-leibniz=4 --ho-unif-level=full-framework --no-max-vars -q \"2|prefer-goals|conjecture-relative-e(0.5,1,100,100,100,100,1.5,1.5,1)\" -q \"4|const|conjecture-relative-e(0.1,1,100,100,100,100,1.5,1.5,1.5)\" -q \"1|prefer-processed|fifo\" -q \"1|prefer-non-goals|conjecture-relative-e(0.5,1,100,100,100,100,1.5,1.5,1.5)\" -q \"4|prefer-sos|pnrefined(1,1,1,1,2,1.5,2)\" --select=ho-selection5 --ho-choice-inst=true --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --e-timeout=5 --e-call-point=0.25 --e-auto=true --sine=50 --sine-tolerance=2 --sine-depth-max=4 --sine-depth-min=1 --e-max-derived=96 --e-encode-lambdas=lift --scan-clause-ac=false --kbo-weight-fun=arity0 --prec-gen-fun=invfreq_conj"),
-        ((1024, meshN), format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-pragmatic -nc --tptp-def-as-rewrite --rewrite-before-cnf=true --mode=ho-competitive --boolean-reasoning=simpl-only --ext-rules=ext-family --ext-rules-max-depth=1 --ho-prim-enum=none --avatar=off --recognize-injectivity=true --ho-elim-leibniz=1 --ho-unif-level=pragmatic-framework --no-max-vars --max-inferences=4 --ho-max-app-projections=1 --ho-max-elims=0 --ho-max-rigid-imitations=2 --ho-max-identifications=0 --ho-unif-max-depth=3 -q \"6|prefer-sos|pnrefined(1,1,1,2,2,2,0.5)\" -q \"6|const|conjecture-relative-var(1.02,l,f)\" -q \"1|prefer-processed|fifo\" -q \"1|prefer-non-goals|conjecture-relative-var(1,l,f)\" -q \"4|prefer-easy-ho|conjecture-relative-var(1.01,s,f)\" --select=e-selection7 --ho-choice-inst=true --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --e-timeout=7 --sine=50 --sine-tolerance=1 --sine-depth-max=2 --sine-depth-min=1 --e-max-derived=64 --sine-ignore-k-most-common-syms=2 --sine-trim-implications=true --e-encode-lambdas=lift --scan-clause-ac=false --lambdasup=0 --kbo-weight-fun=lambda-def-invfreqrank --demod-in-var-args=true --bool-demod=true --lambda-demod=true --e-call-point=0.1"),
-        ((64, meshN), format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-comb-complete --boolean-reasoning=simpl-only --ext-rules=off --kbo-weight-fun=lambda-def-sqarity --ho-prim-enum=none --tptp-def-as-rewrite -q \"4|prefer-sos|orient-lmax(2,1,2,1,1)\" -q \"4|defer-sos|conjecture-relative-var(1,s,f)\" -q \"3|const|default\" -q \"1|prefer-processed|fifo\" --ho-elim-leibniz=1 --select=NoSelection --solve-formulas=true --lazy-cnf=true --lazy-cnf-kind=simp --lazy-cnf-renaming-threshold=8 --sine=60 --sine-tolerance=2 --sine-depth-max=5 --sine-depth-min=1 --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --e-timeout=3 --e-auto=true --e-max-derived=50 --e-encode-lambdas=ignore --scan-clause-ac=false --presaturate=true --comb-b-penalty=3 --comb-c-penalty=3 --comb-k-penalty=1 --comb-s-penalty=5 --subvarsup=false --e-call-point=0.15"),
-        ((512, meshN), format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-pragmatic --boolean-reasoning=simpl-only --ho-unif-max-depth=0 --ho-prim-enum=none -q \"2|prefer-ho-steps|conjecture-relative-e(0.1,0.5,100,100,100,100,1.5,1.5,1.5)\" -q \"1|prefer-sos|pnrefined(1,1,1,2,2,2,0.5)\" -q \"2|prefer-ground|default\" -q \"2|prefer-empty-trail|conjecture-relative-e(0.1,0.5,100,100,100,100,1.5,1.5,1.5)\" -q \"1|prefer-processed|fifo\" --select=bb+e-selection7 --ho-pattern-decider=false --ho-fixpoint-decider=true --ho-solid-decider=false --sine=150 --sine-tolerance=2 --sine-depth-max=3 --sine-depth-min=1 --prec-gen-fun=invfreqhack --lazy-cnf=true --lazy-cnf-kind=simp --lazy-cnf-renaming-threshold=2 --fluid-log-hoist=false --tptp-def-as-rewrite --rewrite-before-cnf=true --ho-prim-enum=eq --ho-prim-enum-add-var=true --ho-prim-max=1 --ho-prim-enum-early-bird=true -o tptp --avatar=eager --split-only-ground=true")],
-     best_max_mono_iters = default_max_mono_iters,
-     best_max_new_mono_instances = default_max_new_mono_instances}
+     good_slices =
+       K [((512, meshN), (format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-pragmatic --tptp-def-as-rewrite --rewrite-before-cnf=true --max-inferences=1 --ho-unif-max-depth=1 --ho-max-elims=0 --ho-max-app-projections=0 --ho-max-rigid-imitations=1 --ho-max-identifications=0 --boolean-reasoning=bool-hoist --bool-hoist-simpl=true --bool-select=LI --recognize-injectivity=true --ext-rules=ext-family --ext-rules-max-depth=1 --ho-choice-inst=true --ho-prim-enum=none --ho-elim-leibniz=0 --interpret-bool-funs=true --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --ho-unif-level=pragmatic-framework --select=bb+e-selection2 --post-cnf-lambda-lifting=true -q \"4|prefer-sos|pnrefined(2,1,1,1,2,2,2)\" -q \"6|prefer-processed|conjecture-relative-struct(1.5,3.5,2,3)\" -q \"1|const|fifo\" -q \"4|prefer-ground|orient-lmax(2,1,2,1,1)\" -q \"4|defer-sos|conjecture-relative-struct(1,5,2,3)\" --avatar=off --recognize-injectivity=true --ho-neg-ext=true --e-timeout=2 --ho-pattern-decider=true --ho-fixpoint-decider=true --e-max-derived=50 --ignore-orphans=true --e-auto=true --presaturate=true --e-call-point=0.1")),
+        ((256, mashN), (format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-pragmatic --tptp-def-as-rewrite --rewrite-before-cnf=true --mode=ho-competitive --boolean-reasoning=simpl-only --ext-rules=ext-family --ext-rules-max-depth=1 --ho-prim-enum=none --avatar=off --recognize-injectivity=true --ho-elim-leibniz=1 --ho-unif-level=pragmatic-framework --no-max-vars --max-inferences=2 --ho-unif-max-depth=1 -q \"6|prefer-sos|pnrefined(1,1,1,2,2,2,0.5)\" -q \"6|const|conjecture-relative-var(1.02,l,f)\" -q \"1|prefer-processed|fifo\" -q \"1|prefer-non-goals|conjecture-relative-var(1,l,f)\" -q \"4|prefer-easy-ho|conjecture-relative-var(1.01,s,f)\" --select=e-selection16 --ho-choice-inst=true --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --e-timeout=3 --e-auto=true --sine=50 --sine-tolerance=1.0 --sine-depth-max=3 --sine-depth-min=1 --sine-trim-implications=true --ho-unif-level=pragmatic-framework --e-encode-lambdas=lift --scan-clause-ac=false --kbo-weight-fun=lambda-def-invfreqrank --e-call-point=0.1")),
+        ((128, mepoN), (format, "mono_native_higher_fool", keep_lamsN, false, "-nc --tptp-def-as-rewrite --rewrite-before-cnf=true --mode=ho-competitive --boolean-reasoning=simpl-only --ext-rules=off --ho-prim-enum=full --ho-prim-max=1 --avatar=off --recognize-injectivity=true --ho-elim-leibniz=4 --ho-unif-level=full-framework --no-max-vars -q \"2|prefer-goals|conjecture-relative-e(0.5,1,100,100,100,100,1.5,1.5,1)\" -q \"4|const|conjecture-relative-e(0.1,1,100,100,100,100,1.5,1.5,1.5)\" -q \"1|prefer-processed|fifo\" -q \"1|prefer-non-goals|conjecture-relative-e(0.5,1,100,100,100,100,1.5,1.5,1.5)\" -q \"4|prefer-sos|pnrefined(1,1,1,1,2,1.5,2)\" --select=ho-selection5 --ho-choice-inst=true --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --e-timeout=5 --e-call-point=0.25 --e-auto=true --sine=50 --sine-tolerance=2 --sine-depth-max=4 --sine-depth-min=1 --e-max-derived=96 --e-encode-lambdas=lift --scan-clause-ac=false --kbo-weight-fun=arity0 --prec-gen-fun=invfreq_conj")),
+        ((1024, meshN), (format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-pragmatic -nc --tptp-def-as-rewrite --rewrite-before-cnf=true --mode=ho-competitive --boolean-reasoning=simpl-only --ext-rules=ext-family --ext-rules-max-depth=1 --ho-prim-enum=none --avatar=off --recognize-injectivity=true --ho-elim-leibniz=1 --ho-unif-level=pragmatic-framework --no-max-vars --max-inferences=4 --ho-max-app-projections=1 --ho-max-elims=0 --ho-max-rigid-imitations=2 --ho-max-identifications=0 --ho-unif-max-depth=3 -q \"6|prefer-sos|pnrefined(1,1,1,2,2,2,0.5)\" -q \"6|const|conjecture-relative-var(1.02,l,f)\" -q \"1|prefer-processed|fifo\" -q \"1|prefer-non-goals|conjecture-relative-var(1,l,f)\" -q \"4|prefer-easy-ho|conjecture-relative-var(1.01,s,f)\" --select=e-selection7 --ho-choice-inst=true --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --e-timeout=7 --sine=50 --sine-tolerance=1 --sine-depth-max=2 --sine-depth-min=1 --e-max-derived=64 --sine-ignore-k-most-common-syms=2 --sine-trim-implications=true --e-encode-lambdas=lift --scan-clause-ac=false --lambdasup=0 --kbo-weight-fun=lambda-def-invfreqrank --demod-in-var-args=true --bool-demod=true --lambda-demod=true --e-call-point=0.1")),
+        ((64, meshN), (format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-comb-complete --boolean-reasoning=simpl-only --ext-rules=off --kbo-weight-fun=lambda-def-sqarity --ho-prim-enum=none --tptp-def-as-rewrite -q \"4|prefer-sos|orient-lmax(2,1,2,1,1)\" -q \"4|defer-sos|conjecture-relative-var(1,s,f)\" -q \"3|const|default\" -q \"1|prefer-processed|fifo\" --ho-elim-leibniz=1 --select=NoSelection --solve-formulas=true --lazy-cnf=true --lazy-cnf-kind=simp --lazy-cnf-renaming-threshold=8 --sine=60 --sine-tolerance=2 --sine-depth-max=5 --sine-depth-min=1 --try-e=\"$E_HOME/eprover\" --tmp-dir=\"$ISABELLE_TMP_PREFIX\" --e-timeout=3 --e-auto=true --e-max-derived=50 --e-encode-lambdas=ignore --scan-clause-ac=false --presaturate=true --comb-b-penalty=3 --comb-c-penalty=3 --comb-k-penalty=1 --comb-s-penalty=5 --subvarsup=false --e-call-point=0.15")),
+        ((512, meshN), (format, "mono_native_higher_fool", keep_lamsN, false, "--mode=ho-pragmatic --boolean-reasoning=simpl-only --ho-unif-max-depth=0 --ho-prim-enum=none -q \"2|prefer-ho-steps|conjecture-relative-e(0.1,0.5,100,100,100,100,1.5,1.5,1.5)\" -q \"1|prefer-sos|pnrefined(1,1,1,2,2,2,0.5)\" -q \"2|prefer-ground|default\" -q \"2|prefer-empty-trail|conjecture-relative-e(0.1,0.5,100,100,100,100,1.5,1.5,1.5)\" -q \"1|prefer-processed|fifo\" --select=bb+e-selection7 --ho-pattern-decider=false --ho-fixpoint-decider=true --ho-solid-decider=false --sine=150 --sine-tolerance=2 --sine-depth-max=3 --sine-depth-min=1 --prec-gen-fun=invfreqhack --lazy-cnf=true --lazy-cnf-kind=simp --lazy-cnf-renaming-threshold=2 --fluid-log-hoist=false --tptp-def-as-rewrite --rewrite-before-cnf=true --ho-prim-enum=eq --ho-prim-enum-add-var=true --ho-prim-max=1 --ho-prim-enum-early-bird=true -o tptp --avatar=eager --split-only-ground=true"))],
+     good_max_mono_iters = default_max_mono_iters,
+     good_max_new_mono_instances = default_max_new_mono_instances}
   end
 
 val zipperposition = (zipperpositionN, fn () => zipperposition_config)
@@ -581,7 +583,7 @@
 
 val isabelle_scala_function = (["SCALA_HOME"], ["bin/scala"])
 
-fun remote_config system_name system_versions proof_delims known_failures prem_role best_slice =
+fun remote_config system_name system_versions proof_delims known_failures prem_role good_slice =
   {exec = isabelle_scala_function,
    arguments = fn _ => fn _ => fn command => fn timeout => fn problem => fn _ =>
      [the_remote_system system_name system_versions,
@@ -590,19 +592,19 @@
    proof_delims = union (op =) tstp_proof_delims proof_delims,
    known_failures = known_failures @ known_says_failures,
    prem_role = prem_role,
-   best_slices = fn ctxt => [best_slice ctxt],
-   best_max_mono_iters = default_max_mono_iters,
-   best_max_new_mono_instances = default_max_new_mono_instances} : atp_config
+   good_slices = fn ctxt => [good_slice ctxt],
+   good_max_mono_iters = default_max_mono_iters,
+   good_max_new_mono_instances = default_max_new_mono_instances} : atp_config
 
-fun remotify_config system_name system_versions best_slice
+fun remotify_config system_name system_versions good_slice
     ({proof_delims, known_failures, prem_role, ...} : atp_config) =
-  remote_config system_name system_versions proof_delims known_failures prem_role best_slice
+  remote_config system_name system_versions proof_delims known_failures prem_role good_slice
 
-fun remote_atp name system_name system_versions proof_delims known_failures prem_role best_slice =
+fun remote_atp name system_name system_versions proof_delims known_failures prem_role good_slice =
   (remote_prefix ^ name, fn () =>
-     remote_config system_name system_versions proof_delims known_failures prem_role best_slice)
-fun remotify_atp (name, config) system_name system_versions best_slice =
-  (remote_prefix ^ name, remotify_config system_name system_versions best_slice o config)
+     remote_config system_name system_versions proof_delims known_failures prem_role good_slice)
+fun remotify_atp (name, config) system_name system_versions good_slice =
+  (remote_prefix ^ name, remotify_config system_name system_versions good_slice o config)
 
 fun gen_remote_waldmeister name type_enc =
   remote_atp name "Waldmeister" ["710"] tstp_proof_delims
@@ -611,30 +613,30 @@
       (Crashed, "Unrecoverable Segmentation Fault")]
      @ known_szs_status_failures)
     Hypothesis
-    (K ((50, meshN), CNF_UEQ, type_enc, combsN, false, "") (* FUDGE *))
+    (K ((50, meshN), (CNF_UEQ, type_enc, combsN, false, "")) (* FUDGE *))
 
 val remote_agsyhol =
   remotify_atp agsyhol "agsyHOL" ["1.0", "1"]
-    (K ((60, meshN), THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, "") (* FUDGE *))
+    (K ((60, meshN), (THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, "")) (* FUDGE *))
 val remote_alt_ergo =
   remotify_atp alt_ergo "Alt-Ergo" ["0.95.2"]
-    (K ((250, meshN), TF1, "poly_native", keep_lamsN, false, "") (* FUDGE *))
+    (K ((250, meshN), (TF1, "poly_native", keep_lamsN, false, "")) (* FUDGE *))
 val remote_e =
   remotify_atp e "E" ["2.0", "1.9.1", "1.8"]
-    (K ((750, meshN), TF0, "mono_native", combsN, false, "") (* FUDGE *))
+    (K ((750, meshN), (TF0, "mono_native", combsN, false, "")) (* FUDGE *))
 val remote_iprover =
   remotify_atp iprover "iProver" ["0.99"]
-    (K ((150, meshN), FOF, "mono_guards??", liftingN, false, "") (* FUDGE *))
+    (K ((150, meshN), (FOF, "mono_guards??", liftingN, false, "")) (* FUDGE *))
 val remote_leo2 =
   remotify_atp leo2 "LEO-II" ["1.5.0", "1.4", "1.3", "1.2", "1"]
-    (K ((40, meshN), THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", liftingN, false, "") (* FUDGE *))
+    (K ((40, meshN), (THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", liftingN, false, "")) (* FUDGE *))
 val remote_leo3 =
   remotify_atp leo3 "Leo-III" ["1.1"]
-    (K ((150, meshN), THF (Polymorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "poly_native_higher", keep_lamsN, false, "") (* FUDGE *))
+    (K ((150, meshN), (THF (Polymorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "poly_native_higher", keep_lamsN, false, "")) (* FUDGE *))
 val remote_waldmeister = gen_remote_waldmeister waldmeisterN "raw_mono_tags??"
 val remote_zipperposition =
   remotify_atp zipperposition "Zipperpin" ["2.1", "2.0"]
-    (K ((512, meshN), THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, "") (* FUDGE *))
+    (K ((512, meshN), (THF (Monomorphic, {with_ite = false, with_let = false}, THF_Without_Choice), "mono_native_higher", keep_lamsN, false, "")) (* FUDGE *))
 
 
 (* Dummy prover *)
@@ -645,11 +647,11 @@
    proof_delims = [],
    known_failures = known_szs_status_failures,
    prem_role = prem_role,
-   best_slices =
-     K [((200, "mepo"), format, type_enc,
-        if is_format_higher_order format then keep_lamsN else combsN, uncurried_aliases, "")],
-   best_max_mono_iters = default_max_mono_iters,
-   best_max_new_mono_instances = default_max_new_mono_instances}
+   good_slices =
+     K [((200, "mepo"), (format, type_enc,
+      if is_format_higher_order format then keep_lamsN else combsN, uncurried_aliases, ""))],
+   good_max_mono_iters = default_max_mono_iters,
+   good_max_new_mono_instances = default_max_new_mono_instances}
 
 val dummy_fof =
   (dummy_fofN, fn () => dummy_config Hypothesis FOF "mono_guards??" false)

--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover.ML	Mon Jan 31 16:09:23 2022 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover.ML	Mon Jan 31 16:09:23 2022 +0100
@@ -14,6 +14,7 @@
   type fact = Sledgehammer_Fact.fact
   type proof_method = Sledgehammer_Proof_Methods.proof_method
   type play_outcome = Sledgehammer_Proof_Methods.play_outcome
+  type base_slice = Sledgehammer_ATP_Systems.base_slice
   type atp_slice = Sledgehammer_ATP_Systems.atp_slice
 
   datatype mode = Auto_Try | Try | Normal | Minimize | MaSh
@@ -62,9 +63,7 @@
      factss : (string * fact list) list,
      found_proof : string -> unit}
 
-  datatype prover_slice =
-    ATP_Slice of atp_slice
-  | SMT_Slice of int * string
+  type prover_slice = base_slice * atp_slice option
 
   type prover_result =
     {outcome : atp_failure option,
@@ -199,9 +198,7 @@
    factss : (string * fact list) list,
    found_proof : string -> unit}
 
-datatype prover_slice =
-  ATP_Slice of atp_slice
-| SMT_Slice of int * string
+type prover_slice = base_slice * atp_slice option
 
 type prover_result =
   {outcome : atp_failure option,

--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover_atp.ML	Mon Jan 31 16:09:23 2022 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover_atp.ML	Mon Jan 31 16:09:23 2022 +0100
@@ -112,11 +112,11 @@
     val thy = Proof.theory_of state
     val ctxt = Proof.context_of state
 
-    val ATP_Slice ((best_max_facts, best_fact_filter), format, best_type_enc, best_lam_trans,
-      best_uncurried_aliases, extra) = slice
+    val ((good_max_facts, good_fact_filter), SOME (good_format, good_type_enc, good_lam_trans,
+      good_uncurried_aliases, extra)) = slice
 
-    val {exec, arguments, proof_delims, known_failures, prem_role, best_max_mono_iters,
-      best_max_new_mono_instances, ...} = get_atp thy name ()
+    val {exec, arguments, proof_delims, known_failures, prem_role, good_max_mono_iters,
+      good_max_new_mono_instances, ...} = get_atp thy name ()
 
     val full_proofs = isar_proofs |> the_default (mode = Minimize)
     val local_name = perhaps (try (unprefix remote_prefix)) name
@@ -166,8 +166,8 @@
           let
             val ctxt =
               ctxt
-              |> repair_monomorph_context max_mono_iters best_max_mono_iters max_new_mono_instances
-                   best_max_new_mono_instances
+              |> repair_monomorph_context max_mono_iters good_max_mono_iters max_new_mono_instances
+                   good_max_new_mono_instances
             (* pseudo-theorem involving the same constants as the subgoal *)
             val subgoal_th =
               Logic.list_implies (hyp_ts, concl_t) |> Skip_Proof.make_thm thy
@@ -183,31 +183,31 @@
             |> maps (fn (name, rths) => map (pair name o zero_var_indexes o snd) rths)
           end
 
-        val effective_fact_filter = fact_filter |> the_default best_fact_filter
+        val effective_fact_filter = fact_filter |> the_default good_fact_filter
         val facts = get_facts_of_filter effective_fact_filter factss
         val num_facts =
           (case max_facts of
-            NONE => best_max_facts
+            NONE => good_max_facts
           | SOME max_facts => max_facts)
           |> Integer.min (length facts)
         val strictness = if strict then Strict else Non_Strict
-        val type_enc = type_enc |> choose_type_enc strictness best_type_enc format
+        val type_enc = type_enc |> choose_type_enc strictness good_type_enc good_format
         val run_timeout = slice_timeout slices timeout
         val generous_run_timeout = if mode = MaSh then one_day else run_timeout
         val ({elapsed, ...}, atp_problem_data as (atp_problem, _, _, _)) = Timing.timing (fn () =>
           let
             val sound = is_type_enc_sound type_enc
-            val generate_info = (case format of DFG _ => true | _ => false)
+            val generate_info = (case good_format of DFG _ => true | _ => false)
             val readable_names = not (Config.get ctxt atp_full_names)
-            val lam_trans = lam_trans |> the_default best_lam_trans
-            val uncurried_aliases = uncurried_aliases |> the_default best_uncurried_aliases
+            val lam_trans = lam_trans |> the_default good_lam_trans
+            val uncurried_aliases = uncurried_aliases |> the_default good_uncurried_aliases
           in
             facts
             |> not sound ? filter_out (is_dangerous_prop ctxt o Thm.prop_of o snd)
             |> take num_facts
             |> not (is_type_enc_polymorphic type_enc) ? monomorphize_facts
             |> map (apsnd Thm.prop_of)
-            |> generate_atp_problem ctxt generate_info format prem_role type_enc atp_mode
+            |> generate_atp_problem ctxt generate_info good_format prem_role type_enc atp_mode
               lam_trans uncurried_aliases readable_names true hyp_ts concl_t
           end) ()
 
@@ -233,7 +233,7 @@
 
         val _ =
           atp_problem
-          |> lines_of_atp_problem format ord ord_info
+          |> lines_of_atp_problem good_format ord ord_info
           |> (exec <> isabelle_scala_function) ?
             cons ("% " ^ command ^ "\n" ^ (if comment = "" then "" else "% " ^ comment ^ "\n"))
           |> File.write_list prob_path
@@ -268,7 +268,7 @@
             | NONE => (found_proof name; NONE))
           | _ => outcome)
       in
-        (atp_problem_data, (output, run_time, facts, atp_proof, outcome), (format, type_enc))
+        (atp_problem_data, (output, run_time, facts, atp_proof, outcome), (good_format, type_enc))
       end
 
     (* If the problem file has not been exported, remove it; otherwise, export

--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover_minimize.ML	Mon Jan 31 16:09:23 2022 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover_minimize.ML	Mon Jan 31 16:09:23 2022 +0100
@@ -17,7 +17,6 @@
 
   val is_prover_supported : Proof.context -> string -> bool
   val is_prover_installed : Proof.context -> string -> bool
-  val default_max_facts_of_prover : Proof.context -> string -> int
   val get_prover : Proof.context -> mode -> string -> prover
   val get_default_slice : Proof.context -> string -> prover_slice
 
@@ -53,16 +52,6 @@
 fun is_prover_installed ctxt =
   is_smt_prover ctxt orf is_atp_installed (Proof_Context.theory_of ctxt)
 
-fun default_max_facts_of_prover ctxt name =
-  let val thy = Proof_Context.theory_of ctxt in
-    if is_atp thy name then
-      fold (Integer.max o fst o #1) (#best_slices (get_atp thy name ()) ctxt) 0
-    else if is_smt_prover ctxt name then
-      SMT_Solver.default_max_relevant ctxt name
-    else
-      error ("No such prover: " ^ name)
-  end
-
 fun get_prover ctxt mode name =
   let val thy = Proof_Context.theory_of ctxt in
     if is_atp thy name then run_atp mode name
@@ -73,9 +62,9 @@
 fun get_default_slice ctxt name =
   let val thy = Proof_Context.theory_of ctxt in
     if is_atp thy name then
-      ATP_Slice (List.last (#best_slices (get_atp thy name ()) ctxt))
+      apsnd SOME (List.last (#good_slices (get_atp thy name ()) ctxt))
     else if is_smt_prover ctxt name then
-      SMT_Slice (SMT_Solver.default_max_relevant ctxt name, "")
+      ((SMT_Solver.default_max_relevant ctxt name, ""), NONE)
     else
       error ("No such prover: " ^ name)
   end

--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover_smt.ML	Mon Jan 31 16:09:23 2022 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover_smt.ML	Mon Jan 31 16:09:23 2022 +0100
@@ -116,10 +116,10 @@
   let
     val ctxt = Proof.context_of state
 
-    val SMT_Slice (best_max_facts, best_fact_filter) = slice
+    val ((best_max_facts, best_fact_filter), _) = slice
 
     val effective_fact_filter = fact_filter |> the_default best_fact_filter
-    val facts = get_facts_of_filter effective_fact_filter factss
+    val facts = take best_max_facts (get_facts_of_filter effective_fact_filter factss)
 
     val {outcome, filter_result = {fact_ids, atp_proof, ...}, used_from, run_time} =
       smt_filter name params state goal subgoal facts

--- a/src/HOL/Tools/Sledgehammer/sledgehammer_tactics.ML	Mon Jan 31 16:09:23 2022 +0100
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_tactics.ML	Mon Jan 31 16:09:23 2022 +0100
@@ -33,7 +33,7 @@
     val params as {provers, induction_rules, max_facts, ...} = default_params thy override_params
     val name = hd provers
     val prover = get_prover ctxt mode name
-    val default_max_facts = default_max_facts_of_prover ctxt name
+    val default_max_facts = fst (fst (get_default_slice ctxt name))
     val (_, hyp_ts, concl_t) = ATP_Util.strip_subgoal goal i ctxt
     val keywords = Thy_Header.get_keywords' ctxt
     val css_table = clasimpset_rule_table_of ctxt