Selecting the Given Clause

At each iteration of the main loop, Prover9 selects a given clause from the sos list, moves it to the usable list, and makes inferences from it and other clauses in the usable list.

A basic way to select the given clause is to always select the lightest clause in sos. Otter has the ability to mix two methods of selecting the given clause in a ratio determined by a parameter --- selecting the lightest clause and selecting the oldest clause. This method adds a breadth-first component to the search. See the pick_given_ratio parameter below.

Prover9 uses six components in selecting the given clause. The following six options are used.

assign(age_part, n).     % default n=1, range [0 .. INT_MAX]

assign(weight_part, n).  % default n=0, range [0 .. INT_MAX]

assign(false_part, n).   % default n=4, range [0 .. INT_MAX]

assign(true_part, n).    % default n=4, range [0 .. INT_MAX]

assign(random_part, n).  % default n=0, range [0 .. INT_MAX]

assign(hints_part, n).   % default n=INT_MAX, range [0 .. INT_MAX]

These six parameters work together to specify a 6-way ratio for selection of the given clauses:

age_part refers to the clause with lowest ID (the oldest clause),
weight_part refers to the (oldest) clause with lowest weight,
false_part refers to the (oldest) lightest false clause,
true_part refers to the (oldest) lightest true clause,
random_part refers to a (pseudo-) random clause,
hints_part refers to the lightest clause that matches a hint.
The false/true distinction is determined by a set of interpretations. The default interpretation is that negative clauses are false and non-negative clauses are true. To use explicit interpretations, see the section on semantic guidance.
Under the default interpretation, for example, if age_part = 1, false_part = 2, and true_part = 3, given clauses will be selected in a cycle of size six: one clause by lowest ID, then two clauses because they are the lightest negative (i.e., false) clauses, then three clauses because they are the lightest non-negative (i.e., true) clauses. And so on.
If a clause of required type is not available, that component of the ratio is simply skipped. For example, with ratio in the preceding paragraph, if no false clauses are available, the cycle has size four (one part age, 3 parts true clauses) until some false clauses become available.
Note that the default value of hints_part is INT_MAX. This means that whenever the selection cycle gets to the hints_part, clauses that match hints will be selected as long as any are available.

When a given clause is printed, its sequence number, the reason it was selected, its weight, and its ID are also shown as in the following excerpt.

given #1  (I,wt=7): 9 x v y = y v x.  [input].
...
given #18 (T,wt=5): 28 x v x = x.  [para(13(a,1),14(a,1,2))].
given #19 (A,wt=11): 18 x ^ (y ^ z) = y ^ (x ^ z).  [para(11(a,1),12(a,1,1)),demod(12(2))].
given #20 (F,wt=21): 43 x ^ (((x v y) ^ z) v ((x v z) ^ y)) = (x ^ z) v (x ^ y) # label(false).  [para(11(a,1),32(a,1,2,2))].

The selection codes are A=age, W=weight, F=false, T=true, H=hints, R=random, and I=input (see flag input_sos_first).

More selection criteria will likely be added in future versions of Prover9.

Other Options

set(default_parts).      % default set
clear(default_parts).

If this flag is cleared, all of the selection parts, including hints, are set to 0. If it is set, the selection parts are reset to their defaults. This flag operates by making the following changes.

  clear(default_parts) -> assign(hints_part, 0).
  clear(default_parts) -> assign(weight_part, 0).
  clear(default_parts) -> assign(age_part, 0).
  clear(default_parts) -> assign(false_part, 0).
  clear(default_parts) -> assign(true_part, 0).
  clear(default_parts) -> assign(random_part, 0).

  set(default_parts) -> assign(hints_part, INT_MAX).
  set(default_parts) -> assign(weight_part, 0).
  set(default_parts) -> assign(age_part, 1).
  set(default_parts) -> assign(false_part, 4).
  set(default_parts) -> assign(true_part, 4).
  set(default_parts) -> assign(random_part, 0).

assign(pick_given_ratio, n).  % default n=0, range [0 .. INT_MAX]

If n>0, the given clauses are chosen in the ratio one part by age, and n parts by weight. The false/true distinction is ignored. This parameter works by making the following changes. (Note that this parameter does not alter hints_part, so that clauses matching hints may still be selected.)
  assign(pick_given_ratio, n) -> assign(age_part, 1).
  assign(pick_given_ratio, n) -> assign(weight_part, n).
  assign(pick_given_ratio, n) -> assign(false_part, 0).
  assign(pick_given_ratio, n) -> assign(true_part, 0).
  assign(pick_given_ratio, n) -> assign(random_part, 0).

set(lightest_first).
clear(lightest_first).    % default clear

If this flag is set, the given clauses are selected by weight, lightest first. This flag operates by making the following changes. (Note that this flag does not alter hints_part, so that clauses matching hints may still be selected.)
  set(lightest_first) -> assign(weight_part, 1).
  set(lightest_first) -> assign(age_part, 0).
  set(lightest_first) -> assign(false_part, 0).
  set(lightest_first) -> assign(true_part, 0).
  set(lightest_first) -> assign(random_part, 0).

set(breadth_first).
clear(breadth_first).    % default clear

If this flag is set, the sos list operates as a queue, giving a breadth-first search. That is, the oldest clause is selected as the given clause. This flag operates by making the following changes. (Note that this flag does not alter hints_part, so that clauses matching hints may still be selected.)
  set(breadth_first) -> assign(age_part, 1).
  set(breadth_first) -> assign(weight_part, 0).
  set(breadth_first) -> assign(false_part, 0).
  set(breadth_first) -> assign(true_part, 0).
  set(breadth_first) -> assign(random_part, 0).

set(random_given).
clear(random_given).    % default clear

If this flag is set, a random clause is selected from the sos list. This flag operates by making the following changes. (Note that this flag does not alter hints_part, so that clauses matching hints may still be selected.)
  set(random_given) -> assign(random_part, 1).
  set(random_given) -> assign(age_part, 0).
  set(random_given) -> assign(weight_part, 0).
  set(random_given) -> assign(false_part, 0).
  set(random_given) -> assign(true_part, 0).

assign(random_seed, n).  % default n=0, range [-1 .. INT_MAX]

This parameter determines the seed for the (pseudo-) random number generator, which is used for the parameter random_part (and maybe also for other purposes). The system library functions rand() and srand() are used for random number generation.
If n ≥ 0, it is used as the seed. If n = -1, Prover9 selects a seed, based on the value of the system clock; in this case, Prover9 jobs are not reproducibe.

set(input_sos_first).    % default set
clear(input_sos_first).

If this flag is set, the clauses in the initial sos list are selected as given clauses (in the order in which they occur in the sos list) before any derived clauses are selected. This flag allows heavy input clauses to enter the search right away. After the initial clauses have been selected, the ordinary selection ratio, takes over.

Next Section: Inference Rules