1		% (c) 2019-2025 Lehrstuhl fuer Softwaretechnik und Programmiersprachen,
2		% Heinrich Heine Universitaet Duesseldorf
3		% This software is licenced under EPL 1.0 (http://www.eclipse.org/org/documents/epl-v10.html)
4
5		:- module(cdclt_sat_solver, [b_to_cnf_safe/3,
6		create_solver_state/1,
7		sat/3,
8		sat/4,
9		sat/5,
10		restarts/1,
11		is_backjumping/0,
12		announce_bt_from_smt_solution/0,
13		store_idl_unsat_core/1,
14		log_theory_propagation_sat_stack/4,
15		set_variable_references_in_clauses/3,
16		remove_idl_unsat_core/0,
17		unit_propagate_cnf/4,
18		get_bindings_from_ids/6,
19		portray_cnf/1,
20		cnf_to_smt/2,
21		clear_pending_theory_propagations/0,
22		unfixed_deferred_set_error_occurred/0,
23		severe_error_occurred/0,
24		assignment_timeout_occurred/0,
25		log_det_theory_timeout/1,
26		sat_bindings_to_smt_formula/2]).
27
28		:- meta_predicate asserta_once(0).
29		:- meta_predicate retract_if_exists(0).
30		:- meta_predicate retract_once(0).
31		:- meta_predicate bt_asserta(0).
32		:- meta_predicate bt_retract(0).
33
34		:- use_module(library(lists)).
35		:- use_module(library(sets), [subtract/3]).
36		:- use_module(library(heaps)).
37		:- use_module(library(ordsets)).
38		:- use_module(library(timeout)).
39		:- use_module(library(samsort)).
40		:- use_module(library(plunit)).
41
42		:- use_module(smt_solvers_interface(ast_optimizer_for_smt)).
43		:- use_module(cdclt_solver('cdclt_stats')).
44		:- use_module(cdclt_solver('cdclt_pred_to_sat')).
45		:- use_module(cdclt_solver('cdclt_settings')).
46		:- use_module(cdclt_solver('symmetry_check/sat_symmetry_breaking')).
47		:- use_module(probsrc(b_global_sets), [list_contains_unfixed_deferred_set_id/1]).
48		:- use_module(probsrc(bsyntaxtree),[get_texpr_expr/2,
49		find_typed_identifier_uses/3,
50		safe_create_texpr/4,
51		create_texpr/4,
52		disjunct_predicates/2,
53		conjunct_predicates/2,
54		conjunction_to_list/2]).
55		:- use_module(probsrc(debug)).
56		:- use_module(probsrc(preferences), [temporary_set_preference/3,
57		reset_temporary_preference/2]).
58		:- use_module(probsrc(error_manager), [add_internal_error/2,
59		add_error_fail/3,
60		check_error_occured/2,
61		error_occurred_in_error_scope/0]).
62		:- use_module(probsrc(translate), [translate_bexpression/2]).
63		:- use_module(extrasrc(unsat_cores), [unsat_core_with_fixed_conjuncts/3,
64		unsat_chr_core_list_with_auto_time_limit/5]).
65		:- use_module(probsrc(module_information), [module_info/2]).
66		:- use_module(extension('banditfuzz/welldef')).
67
68		:- use_module(extension('fibonacci_heap/fibonacci_heap')).
69		%:- use_module(probsrc(tools_portability), [exists_source/1]).
70
71		:- module_info(group, cdclt).
72		:- module_info(description,'This module provides the SAT solver for CDCL(T) implementing CDCL with backjumping and further improvements.').
73
74		:- public solver_name/1. % but not used at the moment
75		:- dynamic solver_name/1, backjump_clause/6, backjump_level/1, conflict_stats/3, saved_phase/2, restarts/1,
76		bt_from_smt_solution/0, is_restart/0,
77		%exclude_sat_solution_clause/1,
78		total_lbd_sum/1, recent_lbds_dl/2, recent_stack_sizes_dl/2, luby_counter/1,
79		%amount_clause_reductions/1,
80		amount_learned_clauses/1, idl_unsat_core/1, pending_theory_prop/2, unfixed_deferred_set_error/0, assignment_count_on_cur_level/1,
81		glue_level/3, glue_clauses/1, allow_partial_model/0, assignment_timeout_occurred/0.
82
83		%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
84		% A sat solver utilising delay declaration to implement watched literals.
85		% Authors: Jacob Howe and Andy King
86		%
87		% Extended for CDCL(T) with first UIP conflict-driven clause learning,
88		% theory propagation, branching heuristics, phase saving for rapid restarts,
89		% learned clause reduction, clause minimization, random restarts, and static SMT symmetry breaking.
90		%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
91
92		% possible improvements:
93		% (- FirstNewCutscheme (cf. https://www.aaai.org/Papers/JAIR/Vol22/JAIR-2210.pdf))
94		% [] improve implying constraint detection (e.g., :cdclt x > y & gt : {x+1} & y > gt)
95		% -> might be overkill at some point
96		% [] clause minimization (cf. Definition 9, "Towards Understanding and Harnessing the Potential of Clause Learning")
97		% [] check out "Advances in Symmetry Breaking for SAT Modulo Theories" by Dinliwal et al. for static SMT symmetry breaking
98
99		%:- if(exists_source(library(mutdict))).
100		%:- use_module(library(mutdict)).
101		%:- else.
102		% mutdict throws a segmentation fault in SICStus 4.8.0, don't use it until the bug is fixed
103		:- use_module(library(avl)).
104		%mutdict_empty(Dict) :-
105		% get_mutable(Avl, Dict),
106		% empty_avl(Avl).
107
108		new_mutdict(Dict) :-
109		empty_avl(Avl),
110		create_mutable(Avl, Dict).
111
112		mutdict_put(Dict, Key, Value) :-
113		get_mutable(Avl, Dict),
114		avl_store(Key, Avl, Value, NewAvl),
115		update_mutable(NewAvl, Dict).
116
117		mutdict_get(Dict, Key, Value) :-
118		get_mutable(Avl, Dict),
119		avl_fetch(Key, Avl, Value).
120
121		mutdict_keys(Dict, Keys) :-
122		get_mutable(Avl, Dict),
123		avl_domain(Avl, Keys).
124
125		mutdict_update(Dict, Key, OldValue, NewValue) :-
126		get_mutable(Avl, Dict),
127		avl_change(Key, Avl, OldValue, NewAvl, NewValue),
128		update_mutable(NewAvl, Dict).
129
130		%mutdict_delete(Dict, Key) :-
131		% get_mutable(Avl, Dict),
132		% avl_delete(Key, Avl, _, NewAvl),
133		% update_mutable(NewAvl, Dict).
134
135		mutdict_items(Dict, Items) :-
136		get_mutable(Avl, Dict),
137		avl_to_list(Avl, Items).
138
139		%mutdict_values(Dict, Values) :-
140		% get_mutable(Avl, Dict),
141		% avl_range(Avl, Values).
142		%:- endif.
143
144		pretty_print_clause([], []).
145		pretty_print_clause([_-Pol-Var-Name|T], [Pol-Var-Name|NT]) :-
146		pretty_print_clause(T, NT).
147
148		pretty_print_vars([], []).
149		pretty_print_vars([strip-Var|T], [NVar|NT]) :-
150		!,
151		pretty_print_clause(Var, NVar),
152		pretty_print_vars(T, NT).
153		pretty_print_vars([Var|T], [Var|NT]) :-
154		pretty_print_vars(T, NT).
155
156		debug_format_sat(_, _) :-
157		print_logs(false),
158		!.
159		debug_format_sat(Msg, Vars) :-
160		append(Msg, " (CDCL(T) SAT Solver)~n", NCodes),
161		atom_codes(NMsg, NCodes),
162		pretty_print_vars(Vars, NVars),
163		format(NMsg, NVars), !.
164
165		debug_format_sat(_, _, _) :-
166		print_logs(false),
167		!.
168		debug_format_sat(Msg, Vars, Pred) :-
169		format(Msg, Vars),
170		translate:print_bexpr(Pred), nl, !.
171
172		unfixed_deferred_set_error_occurred :-
173		unfixed_deferred_set_error.
174
175		assignment_count_on_cur_level(0).
176
177		reset_assignment_count_on_level :-
178		retract(assignment_count_on_cur_level(Old)),
179		asserta(assignment_count_on_cur_level(0)),
180		( true
181		; retract(assignment_count_on_cur_level(_)),
182		asserta(assignment_count_on_cur_level(Old)),
183		fail
184		).
185
186		get_next_assignment_count_on_level(NCount) :-
187		retract(assignment_count_on_cur_level(Count)),
188		NCount is Count + 1,
189		asserta(assignment_count_on_cur_level(NCount)),
190		( true
191		; retract(assignment_count_on_cur_level(_)),
192		asserta(assignment_count_on_cur_level(Count)),
193		fail
194		).
195
196		clear_pending_theory_propagations :-
197		retractall_once(pending_theory_prop(_,_)).
198
199		% this is just to replay the same order as is propagated to ProB using coroutines
200		plvar_sort(_-(_-_-_-(_,(DLevel1,ACount1),_,_)), _-(_-_-_-(_,(DLevel2,ACount2),_,_))) :-
201		ground(DLevel1), ground(DLevel2),
202		( DLevel1 < DLevel2
203		-> true
204		; DLevel1 == DLevel2
205		-> ACount1 < ACount2
206		; fail
207		).
208
209		sat_bindings_to_smt_formula(PlVars, SmtFormula) :-
210		mutdict_items(PlVars, PlItems),
211		samsort(plvar_sort, PlItems, SPlItems),
212		sat_bindings_to_smt_formula_aux(SPlItems, b(truth,pred,[]), SmtFormula).
213
214		sat_bindings_to_smt_formula_aux([], Acc, Acc).
215		sat_bindings_to_smt_formula_aux([_-(PrologVar-_-TTheoryConstraint-_)|T], Acc, SmtFormula) :-
216		ground(PrologVar),
217		!,
218		get_smt_formula_for_sat_pol(TTheoryConstraint, PrologVar, TheoryConstraint),
219		safe_create_texpr(conjunct(Acc,TheoryConstraint), pred, [], NAcc),
220		sat_bindings_to_smt_formula_aux(T, NAcc, SmtFormula).
221		sat_bindings_to_smt_formula_aux([_|T], Acc, SmtFormula) :-
222		sat_bindings_to_smt_formula_aux(T, Acc, SmtFormula).
223
224		%% get_bindings_from_ids(+SatVars, -StackBindings, -SatBindings, -SatVarNames, -IdPrologVarTuples, -PrologSatVarTriple).
225		% Given a set of boolean B identifiers. Create a list of bindings containing terms bind/2
226		% and a list of tuples of B identifier and corresponding Prolog variable used for sat solving.
227		% StackBindings contain the bind/2 terms as well as the StackInfo in order to unify Prolog variables in b_to_cnf_safe/3.
228		get_bindings_from_ids(SatVars, StackBindings, SatBindings, SatVarNames, IdPrologVarTuples, PrologSatVarTriple) :-
229		new_mutdict(EmptyDict),
230		get_bindings_from_ids_acc(SatVars, [], [], [], [], EmptyDict, StackBindings, SatBindings, SatVarNames, IdPrologVarTuples, PrologSatVarTriple), !.
231
232		get_bindings_from_ids_acc([], AccStackBindings, AccBindings, AccNames, AccTuples, AccPlVars, AccStackBindings, AccBindings, AccNames, AccTuples, AccPlVars).
233		get_bindings_from_ids_acc([b(identifier(Name),IdType,IdInfo)|T], AccStackBindings, AccBindings, AccNames, AccTuples, AccPlVars, StackBindings, SatBindings, SatVarNames, IdPrologVarTuples, PrologSatVarTriple) :-
234		NewAccBindings = [bind(Name,PrologVar)|AccBindings],
235		% we add Prolog variables for stack infos to each var so that we do not have to maintain a genuine stack
236		StackInfo = (_PropType, _Level, _Pol, _OriginalClause),
237		NewAccStackBindings = [bind(Name,PrologVar)-StackInfo|AccStackBindings],
238		NewAccTuples = [(b(identifier(Name),IdType,IdInfo),PrologVar,StackInfo)|AccTuples],
239		!,
240		( member(smt_formula(SmtFormula), IdInfo)
241		-> mutdict_put(AccPlVars, Name, PrologVar-Name-SmtFormula-StackInfo)
242		; % plain SAT variable which is not reified with a theory solver, e.g., introduced by CNF optimization rewriting
243		OptEq = b(equal(b(identifier(Name),boolean,[]),b(boolean_true,boolean,[])),pred,[]),
244		mutdict_put(AccPlVars, Name, PrologVar-Name-OptEq-StackInfo)
245		),
246		get_bindings_from_ids_acc(T, NewAccStackBindings, NewAccBindings, [Name|AccNames], NewAccTuples, AccPlVars, StackBindings, SatBindings, SatVarNames, IdPrologVarTuples, PrologSatVarTriple).
247		get_bindings_from_ids_acc([_|T], AccStackBindings, AccBindings, AccNames, AccTuples, AccPlVars, StackBindings, SatBindings, SatVarNames, IdPrologVarTuples, PrologSatVarTriple) :-
248		get_bindings_from_ids_acc(T, AccStackBindings, AccBindings, AccNames, AccTuples, AccPlVars, StackBindings, SatBindings, SatVarNames, IdPrologVarTuples, PrologSatVarTriple).
249
250		%% sat(+SolverName, +SolverEnv, +Clauses).
251		% SolverEnv is a list [sat_vars:_, sat_varnames:_, sat_bindings:_, t2b_env:_, pl_vars:_].
252		% sat_vars are boolean b/3 identifier ASTs for corresponding SAT variables in Clauses.
253		% sat_bindings is a list of terms bind/2 as used by the ProB constraint solver.
254		% t2b_env is the environment mapping SAT variable names and theory formulae used to
255		% translate B predicates to SAT.
256		% pl_vars is a dict of tuples PrologVar-SatVarName-SmtFormula-StackInfo.
257		sat(SolverName, SolverEnv, Clauses) :-
258		debug_format_sat("Start SAT solving with solver ~w ", [SolverName]),
259		init_dynamic_solver_state(SolverName),
260		create_solver_state(StateMutable),
261		get_from_solver_env(SolverEnv, binary_clause_vars, VarsFromBinaryClauses),
262		init_decision_heuristic(StateMutable, VarsFromBinaryClauses, Clauses),
263		sat_stateful_pre(SolverEnv, StateMutable, Clauses).
264
265		%% sat(+SolverName, +SolverEnv, +StateMutable, +Clauses).
266		sat(SolverName, SolverEnv, StateMutable, Clauses) :-
267		sat(SolverName, SolverEnv, StateMutable, Clauses, []).
268
269		%% sat(+SolverName, +SolverEnv, +StateMutable, +Clauses, +Options).
270		% Options:
271		% allow_partial_model: only for SMT solving: possibly does not assign all SAT variables,
272		% but the reification with ProB ensures that all coroutines are triggered
273		sat(SolverName, SolverEnv, StateMutable, Clauses, Options) :-
274		debug_format_sat("Start SAT solving with solver ~w ", [SolverName]),
275		init_dynamic_solver_state(SolverName),
276		( memberchk(allow_partial_model, Options)
277		-> asserta(allow_partial_model)
278		; true
279		),
280		get_from_solver_env(SolverEnv, binary_clause_vars, VarsFromBinaryClauses),
281		init_decision_heuristic(StateMutable, VarsFromBinaryClauses, Clauses),
282		sat_stateful_pre(SolverEnv, StateMutable, Clauses).
283
284		% Wrapper for sat_stateful_restart_cp/3 to enable backjumping to level 0 several times.
285		sat_stateful_pre(SolverEnv, StateMutable, Clauses) :-
286		\+ severe_error_occurred,
287		sat_stateful_restart_cp(SolverEnv, StateMutable, Clauses).
288
289		sat_stateful_restart_cp(SolverEnv, StateMutable, Clauses) :-
290		( sat_stateful(SolverEnv, StateMutable, Clauses)
291		; % we either learned a unit-clause from conflict analysis or randomly restart
292		% in both cases, we learn all asserted backjump clauses
293		retract(backjump_level(0)),
294		( retract(is_restart)
295		-> debug_format_sat("backjump to level 0 random restart", []),
296		backjump_clause(LearnFromLevel,_,_,_,_,_)
297		; debug_format_sat("backjump to level 0", []),
298		LearnFromLevel = 0
299		),
300		learn_backjump_clause(LearnFromLevel, SolverEnv, StateMutable),
301		sat_stateful_pre(SolverEnv, StateMutable, Clauses)
302		).
303
304		%% sat_stateful(+Clauses, +StateMutable, +Clauses).
305		% CDCL with first UIP conflict-driven clause learning, two-watched literals, EVSIDS branching heuristic,
306		% random glucose restarts, and phase saving for rapid restarts.
307		% See create_solver_state/1 for variable StateMutable.
308		sat_stateful(SolverEnv, StateMutable, Clauses) :-
309		problem_setup(SolverEnv, StateMutable, Clauses),
310		%static_sat_symmetry_breaking(Clauses, SolverEnv, CurLevelMut, NewSolverEnv),
311		elim_vars(SolverEnv, StateMutable).
312
313		%% elim_vars(+SolverEnv, +StateMutable).
314		elim_vars(SolverEnv, StateMutable) :-
315		\+ severe_error_occurred,
316		get_full_state(StateMutable, cur_level, CurLevel),
317		NextLevel is CurLevel + 1,
318		reset_assignment_count_on_level,
319		( % solution found
320		fibonacci_heap:is_empty
321		-> true
322		; elim_vars_from_asserted_heuristic_rapid_restart(SolverEnv, StateMutable, NextLevel)
323		).
324
325		learn_backjump_clause(CurLevel, SolverEnv, StateMutable) :-
326		retract(backjump_clause(BjLevel, BjClause, _, BjSatVars, UsedVars, AC)),
327		( CurLevel == BjLevel
328		-> true
329		; add_error_fail(learn_backjump_clause, 'Inconsistent backjump level: ', [BjLevel,CurLevel])
330		),
331		get_from_solver_env(SolverEnv, pl_vars, PlVars),
332		set_variable_references_in_clause(PlVars, BjClause, BjClauseRef),
333		clause_setup(SolverEnv, StateMutable, BjClauseRef),
334		update_heuristic_scores_for_vars(BjSatVars, AC),
335		( bump_scores_for_bj_clause_only(true)
336		; % additionally bump scores for all variables used during conflict analysis
337		bump_scores_for_bj_clause_only(false),
338		update_heuristic_scores_for_vars(UsedVars, AC)
339		), !.
340
341		possibly_backjump(_, _, _).
342		possibly_backjump(SolverEnv, StateMutable, NextLevel) :-
343		% backjumping to a level other than 0; skip for restart since we then backjump to level 0
344		\+ is_restart,
345		backjump_level(C),
346		debug_format_sat("Current level is ~w and bj level is ~w", [NextLevel,C]),
347		C == NextLevel,
348		retract(backjump_level(C)),
349		debug_format_sat("~nbackjump branch prop level ~w", [NextLevel]),
350		learn_backjump_clause(C, SolverEnv, StateMutable),
351		possibly_bump_glue_variable_scores(NextLevel),
352		possibly_backjump(SolverEnv, StateMutable, NextLevel).
353
354		possibly_bump_glue_variable_scores(CurLevel) :-
355		( ( glue_bumping(true),
356		glue_clauses(GC),
357		GC \== 0
358		)
359		-> bump_glue_variable_scores(GC, CurLevel)
360		; true
361		).
362
363		bump_glue_variable_scores(GC, CurLevel) :-
364		( bt_retract(glue_level(GlueVar,GlueLevel,AlreadyBumped))
365		-> ( ( \+ AlreadyBumped,
366		GlueLevel > CurLevel
367		)
368		-> fibonacci_heap:get_priority_of(GlueVar, Score),
369		bump_glue_variable_score(Score, GlueVar, GlueLevel, GC),
370		bump_glue_variable_scores(GC, CurLevel),
371		bt_asserta(glue_level(GlueVar,GlueLevel,true))
372		; bump_glue_variable_scores(GC, CurLevel),
373		bt_asserta(glue_level(GlueVar,GlueLevel,AlreadyBumped))
374		)
375		; true
376		).
377
378		bump_glue_variable_score(Score, SatVarName, GlueLevel, GC) :-
379		GlueBump is Score * (GlueLevel/GC),
380		NScore is Score + GlueBump,
381		fibonacci_heap:update_bt(SatVarName, NScore).
382
383		%% elim_vars_from_asserted_heuristic_rapid_restart(+SolverEnv, +StateMutable, +NextLevel).
384		elim_vars_from_asserted_heuristic_rapid_restart(SolverEnv, StateMutable, NextLevel) :-
385		\+ backjump_level(_),
386		\+ idl_unsat_core(_),
387		get_sat_var_with_max_heuristic(SatVarName, MaxScore),
388		get_from_solver_env(SolverEnv, pl_vars, PlVars),
389		mutdict_get(PlVars, SatVarName, Var-SatVarName-_-StackInfo), % we need the variable's references
390		debug_format_sat("Max heuristic value with score ~w is ~w", [MaxScore,SatVarName]),
391		possibly_backjump(SolverEnv, StateMutable, NextLevel),
392		( saved_phase(SatVarName, SavedPol)
393		-> % restore phase/polarity from cache for rapid restart
394		SelectedPol = SavedPol,
395		retract(saved_phase(SatVarName, _)), % don't undo when backtracking
396		debug_format_sat("Restore phase of ~w", [SatVarName])
397		; % uninformed phase/polarity selection: start with truth
398		SelectedPol = pred_true
399		),
400		elim_var_for_phase(SatVarName, StackInfo, SelectedPol, Var, SolverEnv, StateMutable, NextLevel).
401
402		%% elim_var_for_phase(+SatVarName, +StackInfo, +SavedPol, +Var, +SolverEnv, +StateMutable, +NextLevel).
403		elim_var_for_phase(SatVarName, StackInfo, SavedPol, Var, SolverEnv, StateMutable, NextLevel) :-
404		( ground(Var)
405		-> add_error_fail(elim_var_for_phase, 'Decision variable is already ground: probably an error in the decision heuristic.', [SatVarName])
406		; true
407		),
408		update_full_state(StateMutable, cur_level, NextLevel),
409		get_next_assignment_count_on_level(ACount),
410		( StackInfo = (branch,(NextLevel,ACount),SavedPol,_OriginalClause),
411		bt_log_sat_stack(StateMutable, SatVarName, SavedPol),
412		debug_format_sat("Decide variable ~w with polarity ~w on level ~w", [SatVarName,SavedPol,NextLevel]),
413		log_boolean_decision,
414		Var = SavedPol
415		; \+ backjump_level(_),
416		\+ severe_error_occurred,
417		negate_polarity(SavedPol, NegSavedPol),
418		StackInfo = (branch,(NextLevel,ACount),NegSavedPol,_OriginalClause),
419		bt_log_sat_stack(StateMutable, SatVarName, NegSavedPol),
420		debug_format_sat("Decide variable ~w with polarity ~w on level ~w", [SatVarName,NegSavedPol,NextLevel]),
421		log_boolean_decision,
422		Var = NegSavedPol
423		),
424		elim_vars(SolverEnv, StateMutable).
425
426		%% checkout_sat_variable(+SatVarName, +OriginalClause).
427		% Remove a SAT variable's information if it has been propagated.
428		checkout_sat_variable(SatVarName, OriginalClause) :-
429		delete_from_heuristic(SatVarName),
430		retract_if_exists(saved_phase(SatVarName, _)),
431		( allow_partial_model
432		-> worsen_scores_for_vars_in_clause(OriginalClause)
433		; true
434		).
435
436		worsen_scores_for_vars_in_clause([]).
437		worsen_scores_for_vars_in_clause([_-_-_-SatVarName|T]) :-
438		( fibonacci_heap:get_priority_of_silent_fail(SatVarName, Score)
439		-> ( Score > 1,
440		fibonacci_heap:dec_priority_of_bt(SatVarName, 1)
441		; Score =< 1,
442		fibonacci_heap:delete_elm_bt(SatVarName)
443		),
444		worsen_scores_for_vars_in_clause(T)
445		; worsen_scores_for_vars_in_clause(T)
446		).
447
448		problem_setup(_, _, []).
449		problem_setup(SolverEnv, StateMutable, [Clause|Clauses]) :-
450		clause_setup(SolverEnv, StateMutable, Clause),
451		problem_setup(SolverEnv, StateMutable, Clauses).
452
453		clause_setup(SolverEnv, StateMutable, Clause) :-
454		Clause = [StackInfo-Pol-Var-SatVarName|Triples],
455		set_watch(SolverEnv, StateMutable, Clause, Triples, Var, Pol, SatVarName, StackInfo).
456
457		set_polarity_of_var_explicitly(_, _, [], []).
458		set_polarity_of_var_explicitly(SatVarName, Pol, [CPol-CVar-CName|T], ConflictClause) :-
459		var(CVar),
460		SatVarName == CName,
461		!,
462		ConflictClause = [CPol-Pol-CName|T].
463		set_polarity_of_var_explicitly(SatVarName, Pol, [Triple|T], [Triple|NT]) :-
464		set_polarity_of_var_explicitly(SatVarName, Pol, T, NT).
465
466		set_watch(_, _, OriginalClause, [], Var, Pol, SatVarName, _) :-
467		Var == Pol,
468		checkout_sat_variable(SatVarName, OriginalClause).
469		set_watch(SolverEnv, StateMutable, OriginalClause, [], Var, Pol, _, _) :-
470		ground(Var),
471		Var \== Pol,
472		\+ severe_error_occurred,
473		\+ backjump_level(_),
474		debug_format_sat("sat conflict", []),
475		clause_learning(true),
476		possibly_bt_from_smt_solution(SolverEnv,StateMutable, _, _),
477		get_full_state(StateMutable, current_stack_size, StackSize),
478		get_full_state(StateMutable, cur_level, CurLevel),
479		assignment_count_on_cur_level(ACount),
480		ACount \== 1, % at least one unit-propagation for CDCL, otherwise just backtrack to the last decision
481		compute_and_assert_backjump_clause(SolverEnv, StateMutable, StackSize, CurLevel, OriginalClause),
482		fail.
483		set_watch(SolverEnv, StateMutable, OriginalClause, [], Var, Pol, SatVarName, StackInfo) :-
484		var(Var),
485		\+ severe_error_occurred,
486		\+ backjump_level(_),
487		get_full_state(StateMutable, cur_level, CurLevel),
488		debug_format_sat("unit propagation of ~w with polarity ~w on level ~w due to clause ~w", [SatVarName,Pol,CurLevel,strip-OriginalClause]),
489		%translate:print_bexpr(TheoryFormula),nl,
490		get_next_assignment_count_on_level(ACount),
491		StackInfo = (unit,(CurLevel,ACount),Pol,OriginalClause),
492		bt_log_sat_stack(StateMutable, SatVarName, Pol),
493		log_unit_propagation,
494		( checkout_sat_variable(SatVarName, OriginalClause),
495		Var = Pol,
496		( true
497		; % remove idl unsat core from higher decision level when backtracking
498		remove_idl_unsat_core,
499		fail
500		)
501		; % theory conflict: if Var = Pol triggered a SAT conflict instead,
502		% a backjump clause has been computed and backjump_level/1 is asserted
503		clause_learning(true),
504		\+ severe_error_occurred,
505		\+ backjump_level(_), % skip when backjumping
506		get_last_decision_level(StateMutable, LastDLevel), % skip if no decision so far
507		LastDLevel > 0, % just backtrack if last decision level is 1 or 0
508		possibly_bt_from_smt_solution(SolverEnv,StateMutable, SatVarName, Pol),
509		( learn_idl_core(StateMutable, SolverEnv, SatVarName, Pol)
510		-> true
511		; debug_format_sat("theory conflict on level ~w", [CurLevel]),
512		get_conflict_clause_for_theory_conflict(SolverEnv, SatVarName, Pol, SolverEnv, TConflictClause),
513		% explicitly set the polarity which failed to be assigned above in line 414 for conflict analysis (possibly part of the unsat core)
514		set_polarity_of_var_explicitly(SatVarName, Pol, TConflictClause, ConflictClause),
515		( ConflictClause = [SStackInfo-CPol-SingletonVar-SingletonName]
516		-> % singleton theory conflict: backjump to level 0
517		debug_format_sat("backjump to level 0 after finding singleton theory conflict for SAT variable ~w", [SingletonName]),
518		( ground(SingletonVar)
519		-> negate_polarity(SingletonVar, NSingletonPol)
520		; % static WD PO theory contradiction
521		debug_format_sat("Force static theory conflict of WD condition to be false for ~w.", [SingletonName]),
522		NSingletonPol = CPol
523		),
524		BjClause = [SStackInfo-NSingletonPol-SingletonVar-SingletonName],
525		debug_format_sat("learn unit clause ~w", [strip-BjClause]),
526		BjLevel = 0,
527		compute_lbd_score(BjClause, LbdScore),
528		count_found_conflict(NewTotal, _, _),
529		asserta(backjump_clause(BjLevel, BjClause, LbdScore, [SingletonName], [], NewTotal)),
530		asserta(backjump_level(BjLevel))
531		; get_maximum_decision_level(ConflictClause, ConflictLevel),
532		% it can be the case that ProB first recognizes unsatisfiable after grounding waitflags; the last decision level is then not necessarily the conflict level
533		debug_format_sat("theory conflict on level ~w after unsat core computation", [ConflictLevel]),
534		get_full_state(StateMutable, current_stack_size, StackSize),
535		compute_and_assert_backjump_clause_get_level(SolverEnv, StateMutable, StackSize, ConflictLevel, ConflictClause, _BjLevel)
536		)
537		),
538		fail
539		).
540		set_watch(SolverEnv, StateMutable, OriginalClause, [StackInfo2-Pol2-Var2-Name2|Triples], Var1, Pol1, Name1, StackInfo1):-
541		\+ backjump_level(_),
542		watch(SolverEnv, StateMutable, OriginalClause, StackInfo1, Var1, Pol1, Name1, StackInfo2, Var2, Pol2, Name2, Triples).
543
544		:- block watch(?, ?, ?, ?, -, ?, ?, ?, -, ?, ?, ?).
545		watch(SolverEnv, StateMutable, OriginalClause, StackInfo1, Var1, Pol1, Name1, StackInfo2, Var2, Pol2, Name2, Triples) :-
546		( nonvar(Var1)
547		-> update_watch(SolverEnv, StateMutable, OriginalClause, StackInfo1, Var1, Pol1, Name1, StackInfo2, Var2, Pol2, Name2, Triples)
548		; update_watch(SolverEnv, StateMutable, OriginalClause, StackInfo2, Var2, Pol2, Name2, StackInfo1, Var1, Pol1, Name1, Triples)
549		).
550
551		update_watch(SolverEnv, StateMutable, OriginalClause, _, Var1, Pol1, Name1, StackInfo2, Var2, Pol2, Name2, Triples) :-
552		( Var1 == Pol1
553		-> checkout_sat_variable(Name1, OriginalClause)
554		; set_watch(SolverEnv, StateMutable, OriginalClause, Triples, Var2, Pol2, Name2, StackInfo2)
555		).
556
557		retract_once(Assertion) :-
558		retract(Assertion),
559		!.
560
561		severe_error_occurred :-
562		error_occurred_in_error_scope,
563		check_error_occured(ErrorName, _),
564		ErrorName \= warning(_),
565		ErrorName \== clpfd_overflow,
566		ErrorName \== smt_symmetry_breaking,
567		ErrorName \== well_definedness_error,
568		ErrorName \== smt_solvers_interface,
569		ErrorName \== internal_error(smt_solvers_interface).
570
571		%% is_backjumping.
572		is_backjumping :-
573		backjump_level(_).
574
575		assert_update_pending_theory_propagation(SatVarName, Pol) :-
576		retract(pending_theory_prop(SatVarName,_)),
577		!,
578		asserta(pending_theory_prop(SatVarName,Pol)).
579		assert_update_pending_theory_propagation(SatVarName, Pol) :-
580		asserta(pending_theory_prop(SatVarName,Pol)).
581
582		% We use a time limit in b_interpreter:b_convert_bool_timeout/7 which is observed here.
583		% It can be the case that ProB/CLP(FD) exceeds the predefined global time limit
584		% when assigning a SAT variable in the deterministic propagation phase (b_convert_bool).
585		% Simply setting a time limit on the SAT variable's unification in the SAT solver is not possible
586		% since CDCL etc. would also be affected by this time limit due to coroutines.
587		:- block log_det_theory_timeout(-).
588		log_det_theory_timeout(TORes) :-
589		( TORes == time_out
590		-> asserta(assignment_timeout_occurred)
591		; true
592		).
593
594		%% log_theory_propagation_sat_stack(+StateMutable, +SatVarName, +SatPrologVar, +StackInfo).
595		log_theory_propagation_sat_stack(StateMutable, SatVarName, SatPrologVar, StackInfo) :-
596		get_full_state(StateMutable, cur_level, CurLevel),
597		log_theory_propagation,
598		!,
599		debug_format_sat("Theory propagation of ~w with polarity ~w", [SatVarName,SatPrologVar]),
600		( SatPrologVar == pred_true -> Pol = pred_true; Pol = pred_false),
601		assert_update_pending_theory_propagation(SatVarName, Pol),
602		% explanation (OriginalClause) is computed lazily for conflict analysis if necessary, see explain_theory_propagation/5
603		get_next_assignment_count_on_level(ACount),
604		StackInfo = (theory,(CurLevel,ACount),Pol,_),
605		bt_log_sat_stack(StateMutable, SatVarName, Pol).
606
607		%% learn_idl_core(+StateMutable, +SolverEnv, +LastSatVarName, +FailedPol).
608		learn_idl_core(StateMutable, SolverEnv, LastSatVarName, FailedPol) :-
609		retract(idl_unsat_core(Core)),
610		remove_idl_unsat_core,
611		!,
612		get_from_solver_env(SolverEnv, pl_vars, PlVars),
613		get_conflict_clause_from_unsat_core(Core, SolverEnv, TConflictClause),
614		% explicitly assign the polarity which was undone due to the conflict
615		set_polarity_of_var_explicitly(LastSatVarName, FailedPol, TConflictClause, TTConflictClause),
616		set_variable_references_in_clause(PlVars, TTConflictClause, ConflictClause),
617		get_full_state(StateMutable, current_stack_size, StackSize),
618		get_full_state(StateMutable, cur_level, CurLevel),
619		compute_and_assert_backjump_clause(SolverEnv, StateMutable, StackSize, CurLevel, ConflictClause).
620
621		save_phase(SatVarName, Pol) :-
622		(retract(saved_phase(SatVarName, _)), !; true),
623		asserta(saved_phase(SatVarName, Pol)).
624
625		% Log variable assignments.
626		% Effect is undone when backtracking. Cache phase when backtracking and unassigning a variable.
627		bt_log_sat_stack(StateMutable, SatVarName, Pol) :-
628		increase_stack_size(StateMutable),
629		( true
630		; save_phase(SatVarName, Pol),
631		fail
632		).
633
634		increase_stack_size(StateMutable) :-
635		get_full_state(StateMutable, current_stack_size, Old),
636		New is Old + 1, !,
637		update_full_state(StateMutable, current_stack_size, New).
638
639		%% possibly_bt_from_smt_solution(+SolverEnv,+StateMutable, +SatVarName, +Pol).
640		% Backtracking from an SMT solution which should not be handled as a theory conflict.
641		possibly_bt_from_smt_solution(_SolverEnv,StateMutable, _SatVarName, _Pol) :-
642		retract(bt_from_smt_solution),
643		!,
644		%( ground(SatVarName)
645		%-> get_complete_theory_lemma_fixed_binding(SolverEnv, SatVarName, Pol, TheoryLemmaClause)
646		%; get_complete_theory_lemma(SolverEnv, TheoryLemmaClause)
647		%),
648		% backjump to the last decision level without computing a conflict clause
649		% but excluding the last SAT solution when backtracking after finding an SMT solution
650		get_last_decision_level(StateMutable, Level),
651		%asserta(exclude_sat_solution_clause(TheoryLemmaClause)), % not used currently
652		asserta(backjump_level(Level)),
653		fail.
654		possibly_bt_from_smt_solution(_,_, _, _).
655
656		% Just wrap with negation but prevent double negation.
657		negate_smt_formula(b(negation(Smt),pred,_), NegSmt) :-
658		!,
659		NegSmt = Smt.
660		negate_smt_formula(Smt, b(negation(Smt),pred,[])).
661
662		% iterate over all Prolog variables to find the propagated literals: usually a stack is used but we store stack infos besides each
663		% variable in the clauses; explanation of theory propagations is rare and maintaining a genuine stack is more expensive
664		get_propagated_sat_vars([], _, []).
665		get_propagated_sat_vars([SatVarName-(_-_-_-(_,(Level,_ACount),Pol,_))|T], TheoryPropLevel, SatVarNameTuples) :-
666		ground(Level),
667		Level < TheoryPropLevel,
668		!,
669		SatVarNameTuples = [(SatVarName-Pol)|NT],
670		get_propagated_sat_vars(T, TheoryPropLevel, NT).
671		get_propagated_sat_vars([_|T], TheoryPropLevel, NT) :-
672		get_propagated_sat_vars(T, TheoryPropLevel, NT).
673
674		%% explain_theory_propagation(+SolverEnv, +TheoryPropSatVar, +TheoryPropLevel, +TheoryPropPol, -ExplainingClause).
675		explain_theory_propagation(SolverEnv, TheoryPropSatVar, _, _, ExplainingClause) :-
676		minimize_theory_explanations(false),
677		!,
678		debug_format_sat("Use complete lemma for theory explanation of ~w", [TheoryPropSatVar]),
679		get_from_solver_env(SolverEnv, sat_bindings, SatBindings),
680		get_clause_from_ground_bindings(SatBindings, _, _, [], TExplainingClause),
681		get_from_solver_env(SolverEnv, pl_vars, PlVars),
682		set_variable_references_in_clause(PlVars, TExplainingClause, ExplainingClause),
683		debug_format_sat("finished explanation.", []).
684		explain_theory_propagation(SolverEnv, TheoryPropSatVar, TheoryPropLevel, TheoryPropPol, ExplainingClause) :-
685		debug_format_sat("Explain theory propagation of ~w", [TheoryPropSatVar]),
686		get_from_solver_env(SolverEnv, pl_vars, PlVars),
687		mutdict_items(PlVars, PlVarsList),
688		get_propagated_sat_vars(PlVarsList, TheoryPropLevel, SatVarNameTuples),
689		get_from_solver_env(SolverEnv, sat_vars, SatVars),
690		get_smt_formula_from_vars_for_sat_pol(SatVars, TheoryPropSatVar, TheoryPropPol, SmtFormula),
691		negate_smt_formula(SmtFormula, NegSmt),
692		debug_format_sat("Compute unsat core for explanation: ", [], NegSmt),
693		get_explanation_candidate_formula(SatVars, SatVarNameTuples, CandidateFormula),
694		( SatVarNameTuples = [_]
695		-> safe_create_texpr(conjunct(CandidateFormula,NegSmt), pred, [], UnsatCore)
696		; temporary_set_preference(time_out, 25, Change1),
697		temporary_set_preference(unsat_core_algorithm, linear, Change2),
698		call_cleanup(unsat_core_with_fixed_conjuncts(CandidateFormula, NegSmt, TTUnsatCore),
699		(reset_temporary_preference(unsat_core_algorithm, Change2),
700		reset_temporary_preference(time_out, Change1))),
701		safe_create_texpr(conjunct(TTUnsatCore,NegSmt), pred, [], TUnsatCore),
702		( strip_pos_keep_toplevel_conj(TUnsatCore, UnsatCore)
703		-> true
704		; add_error_fail(strip_pos_keep_toplevel_conj, 'Removing WD POs for CDCL(T) failed for explaining theory propagation.', [unsat_core_with_wd:TUnsatCore])
705		)
706		),
707		get_from_solver_env(SolverEnv, t2b_env, T2BEnv),
708		debug_format_sat("Computed unsat core for explanation: ", [], UnsatCore),
709		(
710		(
711		predicate_to_sat(only_reuse, [], SatVars, T2BEnv, UnsatCore, _NewEnv, _, UnsatCoreSat, _NewSatVars),
712		sat_conj_negate_to_clause(UnsatCoreSat, TExplainingClause)
713		)
714		-> true
715		; add_error_fail(sat_conj_negate_to_clause, 'Explaining theory propagation failed: Explanation cannot be transformed to SAT.', [unsat_core:UnsatCore])
716		),
717		debug_format_sat("finished explanation.", []),
718		set_variable_references_in_clause(PlVars, TExplainingClause, TTExplainingClause),
719		sort(TTExplainingClause, ExplainingClause).
720
721		get_explanation_candidate_formula(SatVars, [SatVarName-Pol|T], CandidateFormula) :-
722		get_smt_formula_from_vars_for_sat_pol(SatVars, SatVarName, Pol, SmtFormula),
723		!,
724		get_explanation_candidate_formula_acc(SatVars, T, SmtFormula, CandidateFormula).
725		get_explanation_candidate_formula(SatVars, [_|T], CandidateFormula) :-
726		% can be artificial SAT variable introduced by cnf rewriting
727		get_explanation_candidate_formula(SatVars, T, CandidateFormula).
728
729		get_explanation_candidate_formula_acc(_, [], Acc, Acc).
730		get_explanation_candidate_formula_acc(SatVars, [SatVarName-Pol|T], Acc, CandidateFormula) :-
731		get_smt_formula_from_vars_for_sat_pol(SatVars, SatVarName, Pol, SmtFormula),
732		!,
733		safe_create_texpr(conjunct(SmtFormula,Acc), pred, [], NAcc),
734		get_explanation_candidate_formula_acc(SatVars, T, NAcc, CandidateFormula).
735		get_explanation_candidate_formula_acc(SatVars, [_|T], Acc, CandidateFormula) :-
736		get_explanation_candidate_formula_acc(SatVars, T, Acc, CandidateFormula).
737
738		get_smt_formula_from_vars_for_sat_pol(SatVars, SatVarName, Pol, SmtFormula) :-
739		memberchk(b(identifier(SatVarName),_,Info), SatVars),
740		member(smt_formula(TSmtFormula), Info),
741		get_smt_formula_for_sat_pol(TSmtFormula, Pol, SmtFormula).
742
743		get_smt_formula_for_sat_pol(TSmtFormula, Pol, SmtFormula) :-
744		( Pol == pred_true
745		-> SmtFormula = TSmtFormula
746		; TSmtFormula = b(negation(SmtFormula),pred,[])
747		-> true
748		; TSmtFormula = b(_,_,Info),
749		SmtFormula = b(negation(TSmtFormula),pred,Info)
750		).
751
752		%% get_sat_var_with_max_heuristic(-SatVarName, -MaxScore).
753		get_sat_var_with_max_heuristic(SatVarName, MaxScore) :-
754		%\+ fibonacci_heap:is_empty,
755		( print_logs(true)
756		-> fibonacci_heap:get_max_priority(MaxScore)
757		; MaxScore = -1
758		),
759		fibonacci_heap:get_and_remove_max_value_bt(SatVarName).
760
761		retract_if_exists(Assertion) :-
762		( cdclt_sat_solver:Assertion
763		-> retract(cdclt_sat_solver:Assertion)
764		; true
765		).
766
767		% Periodically decay heuristic scores for VSIDS heuristic.
768		% Not undone when backtracking.
769		possibly_decay_heuristic_values :-
770		decision_heuristic(vsids),
771		conflict_stats(total(AC), _, _),
772		AC \== 0,
773		vsids_decay_frequency(I),
774		C is AC mod I,
775		C == 0,
776		debug_format_sat("~nDecay heuristic scores", []),
777		!,
778		vsids_decay_value(Val),
779		decay_heuristic_values(Val).
780		possibly_decay_heuristic_values.
781
782		%% decay_heuristic_values(+DecayValue).
783		% Not undone when backtracking.
784		decay_heuristic_values(DecayValue) :-
785		Decay is (1/DecayValue),
786		fibonacci_heap:mult_priority_of_all(Decay).
787
788		%% init_decision_heuristic(+StateMutable, +VarsFromBinaryClauses, +Clauses).
789		% Each variable is initially assigned the number of its occurrences in all clauses as its score.
790		% Variable scores are not split for polarities.
791		init_decision_heuristic(StateMutable, VarsFromBinaryClauses, Clauses) :-
792		count_var_occurrences_in_clauses(Clauses, VarScoreTuples),
793		binary_boost_factor(BoostFactor),
794		add_heuristic_tuples(StateMutable, BoostFactor, VarsFromBinaryClauses, VarScoreTuples).
795
796		add_heuristic_tuples(_, _, _, []).
797		add_heuristic_tuples(StateMutable, BoostFactor, VarsFromBinaryClauses, [SatVarName-Score|T]) :-
798		( select(SatVarName, VarsFromBinaryClauses, TVarsFromBinaryClauses)
799		-> NScore is Score * BoostFactor
800		; NScore = Score,
801		TVarsFromBinaryClauses = VarsFromBinaryClauses
802		),
803		fibonacci_heap:push(NScore, SatVarName),
804		add_heuristic_tuples(StateMutable, BoostFactor, TVarsFromBinaryClauses, T).
805
806		count_var_occurrences_in_clauses(Clauses, DictItems) :-
807		new_mutdict(Dict),
808		count_var_occurrences_dict(Dict, Clauses), !,
809		mutdict_items(Dict, DictItems), !.
810
811		count_var_occurrences_dict(_, []).
812		count_var_occurrences_dict(Dict, [Clause|T]) :-
813		count_var_occurrences_from_clause_dict(Dict, Clause),
814		count_var_occurrences_dict(Dict, T).
815
816		count_var_occurrences_from_clause_dict(_, []).
817		count_var_occurrences_from_clause_dict(Dict, [_-_-Pol-SatVarName|T]) :-
818		var(Pol), % skip variables that are already propagated by deterministic unit propagation
819		!,
820		( mutdict_get(Dict, SatVarName, Score)
821		-> Score1 is Score + 1,
822		mutdict_update(Dict, SatVarName, _, Score1)
823		; mutdict_put(Dict, SatVarName, 1)
824		),
825		count_var_occurrences_from_clause_dict(Dict, T).
826		count_var_occurrences_from_clause_dict(Dict, [_|T]) :-
827		count_var_occurrences_from_clause_dict(Dict, T).
828
829		update_heuristic_scores_for_vars(UsedVars, AC) :-
830		decision_heuristic(Type),
831		update_heuristic_scores(AC, Type, UsedVars).
832
833		%% update_heuristic_scores(+AmountOfConflitsAtLevel, +Type, +SatVarNames).
834		% Type is either vsids, evsids, vmtf or acids.
835		% SatVarNames are the variable names occurring in learned clauses.
836		update_heuristic_scores(_, _, []).
837		update_heuristic_scores(TotalConflicts, Type, [SatVarName|T]) :-
838		( fibonacci_heap:get_priority_of_silent_fail(SatVarName, OldScore)
839		-> bump_heuristic_score_for_type(Type, TotalConflicts, OldScore, NewScore),
840		fibonacci_heap:update(SatVarName, NewScore),
841		update_heuristic_scores(TotalConflicts, Type, T)
842		; % SAT variable has already been propagated.
843		% For instance, this is the case when learning a clause on a level greater zero while
844		% a specific SAT variable of this clause has already been propagated on a previous level.
845		update_heuristic_scores(TotalConflicts, Type, T)
846		).
847
848		% v_s + 1
849		bump_heuristic_score_for_type(vsids, _, OldScore, NewScore) :-
850		NewScore is OldScore + 1.
851		% k
852		bump_heuristic_score_for_type(vmtf, TotalConflicts, _, NewScore) :-
853		NewScore is TotalConflicts.
854		% (v_s + k) / 2
855		bump_heuristic_score_for_type(acids, TotalConflicts, OldScore, NewScore) :-
856		NewScore is (OldScore + TotalConflicts) / 2.
857		% v_s + f^(-k), where f is evsids_f_value/1 and it is/was the k-th conflict when finding this clause via conflict analysis
858		bump_heuristic_score_for_type(evsids, TotalConflicts, OldScore, NewScore) :-
859		evsids_f_value(FVal),
860		catch(NewScore is OldScore + FVal**(-TotalConflicts), error(evaluation_error(float_overflow),_), NewScore = 1.35743634973696E+308).
861
862		% Literal Block Distance (LBD) as defined in "Predicting Learnt Clauses Quality in Modern SAT Solvers",
863		% i.e., the amount of different decision levels in a clause.
864		compute_lbd_score(BjClause, LbdScore) :-
865		compute_lbd_score(BjClause, [], LbdScore).
866
867		compute_lbd_score([], Acc, LbdScore) :-
868		length(Acc, LbdScore).
869		compute_lbd_score([(_,(Level,_),_,_)-_-_-_|T], Acc, LbdScore) :-
870		!,
871		ord_add_element(Acc, Level, NewAcc),
872		compute_lbd_score(T, NewAcc, LbdScore).
873
874		%% count_found_conflict(-NewTotal, -NewSinceRestart, -NewSinceReduction).
875		count_found_conflict(Total1, SRes1, SRed1) :-
876		log_conflict,
877		retract(conflict_stats(total(Total), since_restart(SRes), since_reduction(SRed))),
878		Total1 is Total + 1,
879		SRes1 is SRes + 1,
880		SRed1 is SRed + 1,
881		asserta(conflict_stats(total(Total1), since_restart(SRes1), since_reduction(SRed1))).
882
883		%% compute_and_assert_backjump_clause(+SolverEnv, +StateMutable, +StackSize, +ConflictClause).
884		compute_and_assert_backjump_clause(SolverEnv, StateMutable, StackSize, ConflictLevel, ConflictClause) :-
885		compute_and_assert_backjump_clause_get_level(SolverEnv, StateMutable, StackSize, ConflictLevel, ConflictClause, _).
886
887		cnf_to_smt(BoolPred, Smt) :-
888		BoolPred = b(Expr,_,_),
889		cnf_to_smt_e(Expr, Smt).
890
891		cnf_to_smt_e(falsity, b(falsity,pred,[])).
892		cnf_to_smt_e(truth, b(truth,pred,[])).
893		cnf_to_smt_e(conjunct(A,B), Smt) :-
894		cnf_to_smt(A, NA),
895		cnf_to_smt(B, NB),
896		safe_create_texpr(conjunct(NA,NB), pred, [], Smt).
897		cnf_to_smt_e(disjunct(A,B), Smt) :-
898		cnf_to_smt(A, NA),
899		cnf_to_smt(B, NB),
900		safe_create_texpr(disjunct(NA,NB), pred, [], Smt).
901		cnf_to_smt_e(equal(b(identifier(_),_,Info),b(BoolExpr,boolean,_)), Smt) :-
902		member(smt_formula(TSmt), Info),
903		( BoolExpr == boolean_true
904		-> Smt = TSmt
905		; safe_create_texpr(negation(TSmt), pred, [], Smt)
906		).
907
908		/*cnf_to_smt([], _, Acc, SmtFromCnf) :-
909		conjunct_predicates(Acc, SmtFromCnf).
910		cnf_to_smt([Clause|T], PrologSatVarTriple, Acc, SmtFromCnf) :-
911		clause_to_smt(PrologSatVarTriple, Clause, SmtClause),
912		cnf_to_smt(T, PrologSatVarTriple, [SmtClause|Acc], SmtFromCnf).*/
913
914		%clause_to_smt(PlVars, Clause, SmtFormula) :-
915		% clause_to_smt(PlVars, Clause, [], SmtFormula).
916		%
917		%clause_to_smt(_, [], Acc, SmtFormula) :-
918		% disjunct_predicates(Acc, SmtFormula).
919		%clause_to_smt(PlVars, [_-Pol-_-SatVarName|T], Acc, SmtClause) :-
920		% mutdict_get(PlVars, SatVarName, _-SatVarName-TSmtFormula-_),
921		% !,
922		% get_smt_formula_for_sat_pol(TSmtFormula, Pol, SmtFormula),
923		% clause_to_smt(PlVars, T, [SmtFormula|Acc], SmtClause).
924		%clause_to_smt(_, [_-_-SatVarName|_], _, _) :-
925		% add_error_fail(clause_to_smt, 'Unknown SAT variable.', [SatVarName]).
926
927		bump_glue_levels([]).
928		bump_glue_levels([_-_-_-SatVarName|T]) :-
929		( retract(glue_level(SatVarName, GlueLevel,AlreadyBumped))
930		-> NGlueLevel is GlueLevel + 1
931		; NGlueLevel = 1,
932		AlreadyBumped = false
933		),
934		asserta(glue_level(SatVarName,NGlueLevel,AlreadyBumped)),
935		bump_glue_levels(T).
936
937		%% compute_and_assert_backjump_clause_get_level(+SolverEnv, +StateMutable, +StackSize, +ConflictLevel, +ConflictClause, -BjLevel).
938		compute_and_assert_backjump_clause_get_level(SolverEnv, StateMutable, StackSize, ConflictLevel, ConflictClause, BjLevel) :-
939		get_last_decision_level(StateMutable, _),
940		%possibly_discard_learned_clauses, % TODO: adapt to new bj clause handling; yet, forgetting clauses has not shown to be beneficial so far
941		debug_format_sat("~nConflict clause is ~w", [strip-ConflictClause]),
942		debug_format_sat("~nStart CDCL..", []),
943		( (
944		get_backjump_clause_conflict_resolution(SolverEnv, StateMutable, ConflictLevel, ConflictClause, BjClause, BjLevel, BjSatVars, UsedVars),
945		BjLevel \== -1
946		)
947		; add_error_fail(compute_and_assert_backjump_clause_get_level, 'SMT solver\'s conflict resolution failed', [])
948		),
949		debug_format_sat("done.", []),
950		debug_format_sat("Backjump clause is ~w", [strip-BjClause]),
951		debug_format_sat("Backjump level is ~w", [BjLevel]),
952		compute_lbd_score(BjClause, LbdScore),
953		debug_format_sat("LBD Score is ~w", [LbdScore]),
954		( ( glue_bumping(true),
955		LbdScore == 2
956		)
957		-> retract(glue_clauses(Old)),
958		New is Old + 1,
959		asserta(glue_clauses(New)),
960		bump_glue_levels(BjClause)
961		; true
962		),
963		count_found_conflict(NewTotal, NewSinceRestart, _),
964		asserta(backjump_clause(BjLevel, BjClause, LbdScore, BjSatVars, UsedVars, NewTotal)),
965		asserta(backjump_level(BjLevel)),
966		store_recent_stack_size(StackSize),
967		count_learned_clause,
968		possibly_decay_heuristic_values,
969		( \+ clear_lbd_values_or_fail(StateMutable),
970		BjLevel \== 0
971		-> store_recent_lbd_score(LbdScore),
972		update_total_lbd_sum(LbdScore),
973		(random_restart(NewTotal, NewSinceRestart), !; true)
974		; true
975		), !.
976
977		count_learned_clause :-
978		retract(amount_learned_clauses(Old)),
979		New is Old + 1,
980		asserta(amount_learned_clauses(New)).
981
982		%% store_recent_lbd_score(+LbdScore).
983		% The stored list of recent LBDs is a difference list and we insert at the end of the list.
984		% The first LBD is thus the oldest one and removed when exceeding the maximum size
985		% defined by recent_lbd_threshold/1.
986		store_recent_lbd_score(LbdScore) :-
987		retract(recent_lbds_dl(Lbds-Diff, Amount)),
988		glucose_restart_recent_lbds_threshold(Thresh),
989		Diff = [LbdScore|NDiff],
990		( Amount < Thresh
991		-> Amount1 is Amount + 1,
992		asserta(recent_lbds_dl(Lbds-NDiff, Amount1))
993		; Lbds = [_|RLbds],
994		asserta(recent_lbds_dl(RLbds-NDiff, Amount))
995		).
996
997		store_recent_stack_size(StackSize) :-
998		retract(recent_stack_sizes_dl(StackSizes-Diff, Amount)),
999		glucose_restart_trail_threshold(Thresh),
1000		Diff = [StackSize|NDiff],
1001		( Amount < Thresh
1002		-> Amount1 is Amount + 1,
1003		asserta(recent_stack_sizes_dl(StackSizes-NDiff, Amount1))
1004		; StackSizes = [_|RStackSizes],
1005		asserta(recent_stack_sizes_dl(RStackSizes-NDiff, Amount))
1006		).
1007
1008		%% update_total_lbd_sum(+LbdScore).
1009		update_total_lbd_sum(LbdScore) :-
1010		retract(total_lbd_sum(Old)),
1011		New is Old + LbdScore,
1012		asserta(total_lbd_sum(New)).
1013
1014		%% random_restart(+AmountOfConflicts, +AmountOfConflictsSinceRestart).
1015		% "Randomly" restart after an amount of conflicts since the last restart.
1016		random_restart(_AC, ACR) :-
1017		restart_policy(luby),
1018		random_luby_restart(ACR), !.
1019		random_restart(AC, _ACR) :-
1020		restart_policy(glucose),
1021		random_glucose_restart(AC), !.
1022
1023		do_random_restart :-
1024		log_restart,
1025		retract(restarts(OldR)),
1026		NewR is OldR + 1,
1027		asserta(restarts(NewR)),
1028		retract(backjump_level(_)),
1029		asserta(backjump_level(0)),
1030		retract(conflict_stats(total(Total), _, since_reduction(SRed))),
1031		asserta(conflict_stats(total(Total), since_restart(0), since_reduction(SRed))),
1032		asserta_once(is_restart),
1033		debug_format_sat("~nRandom restart", []).
1034
1035		%% random_glucose_restart(+AmountOfConflicts).
1036		% Restart search if recent_lbds_dl/2 contains exactly glucose_restart_recent_lbds_threshold/1 amount
1037		% of most recent LBDs and RecentAvg * Proportion > TotalAvg is satisfied, i.e., the recently learned clauses'
1038		% LBDs got too large.
1039		random_glucose_restart(AC) :-
1040		total_lbd_sum(TotalLbdSum),
1041		TotalAvg is TotalLbdSum / AC,
1042		recent_lbds_dl(RLbds-[], LbdAmount),
1043		glucose_restart_recent_lbds_threshold(LbdThresh),
1044		LbdAmount == LbdThresh, % queue of recent LBDs is full
1045		sumlist(RLbds, RSum),
1046		RecentAvg is RSum / LbdAmount,
1047		glucose_restart_margin_ratio(Proportion),
1048		debug_format_sat("~nTotalAvg: ~w~nRecentAvg: ~w", [TotalAvg,RecentAvg]),
1049		( RecentAvg * Proportion > TotalAvg
1050		-> do_random_restart,
1051		clear_recent_lbds_state
1052		; true
1053		).
1054
1055		% Favor SAT instances too by possibly clearing the recent LBD queue.
1056		% Assumption: The queue of recent LBDs is full.
1057		clear_lbd_values_or_fail(StateMutable) :-
1058		glucose_restart_trail_threshold(TrailThresh),
1059		glucose_restart_stack_avg_factor(StackSizeFactor),
1060		recent_stack_sizes_dl(StackSizes-[], AmountStackSizes),
1061		AmountStackSizes == TrailThresh, % queue of recent stack sizes on conflict is full
1062		get_full_state(StateMutable, current_stack_size, StackSize),
1063		sumlist(StackSizes, SSum),
1064		StackSizesAvg is SSum / AmountStackSizes,
1065		StackSize > StackSizeFactor * StackSizesAvg,
1066		clear_recent_lbds_state.
1067
1068		clear_recent_lbds_state :-
1069		retract(recent_lbds_dl(_, _)),
1070		asserta(recent_lbds_dl(Diff-Diff, 0)).
1071
1072		%% random_luby_restart(+AmountOfConflictsSinceRestart).
1073		% The amount of conflicts when to restart is defined by the Luby sequence,
1074		% i.e., 1,1,2,1,1,2,4,1,1,2,1,1,2,4,8,.. etc., (cf. "Optimal speedup of Las Vegas algorithms")
1075		% using a unit length of 32 (see luby_counter/1).
1076		random_luby_restart(ACR) :-
1077		restart_policy(luby),
1078		get_next_luby_value(Luby),
1079		!,
1080		( ACR == Luby
1081		-> retract_once(luby_counter(_)),
1082		do_random_restart
1083		; true
1084		).
1085		random_luby_restart(_) :-
1086		add_error_fail(random_restart, 'No more values in predefined Luby sequence', []).
1087
1088		get_next_luby_value(LubyValue) :-
1089		luby_counter(Luby),
1090		luby_restart_unit_length(UnitLength),
1091		LubyValue is UnitLength * Luby,
1092		!.
1093
1094		%% get_sat_solution_exclusion_clauses(+PlVars, -ExclClausesNoRef).
1095		% We exclude SAT solutions when backtracking from finding an SMT solution to find a different assignment.
1096		/*get_sat_solution_exclusion_clauses(PlVars, ExclClausesNoRef) :-
1097		findall(ExclClause,
1098		(exclude_sat_solution_clause(TExclClause), set_variable_references_in_clause(PlVars, TExclClause, ExclClause)),
1099		ExclClausesNoRef), !.*/
1100
1101		%% set_variable_references_in_clauses(+PlVars, +Clauses, -RefClauses).
1102		set_variable_references_in_clauses(_, [], []).
1103		set_variable_references_in_clauses(PlVars, [Clause|T], [RefClause|NT]) :-
1104		set_variable_references_in_clause(PlVars, Clause, RefClause),
1105		set_variable_references_in_clauses(PlVars, T, NT).
1106
1107		%% set_variable_references_in_clause(+PlVars, +Clause, -RefClauses).
1108		% We need to set the correct variable references in a new learned clause
1109		% to trigger co-routines etc.
1110		set_variable_references_in_clause(_, [], Out) :- !, Out = [].
1111		set_variable_references_in_clause(PlVars, [_-Pol-_-Name|T], [StackInfo-Pol-Var-Name|NT]) :-
1112		mutdict_get(PlVars, Name, TVar-Name-_-TStackInfo),
1113		!,
1114		Var = TVar,
1115		StackInfo = TStackInfo,
1116		set_variable_references_in_clause(PlVars, T, NT).
1117		set_variable_references_in_clause(_, [_-_-_-Name|_], _) :-
1118		add_error_fail(set_variable_references_in_clause, 'Cannot set references: unknown SAT variable.', [Name]).
1119
1120		get_from_solver_env(SolverEnv, Key, OutValue) :-
1121		get_from_solver_env_ordered(Key, SolverEnv, Value),
1122		!,
1123		OutValue = Value.
1124		get_from_solver_env(SolverEnv, Key, _) :-
1125		add_error_fail(get_from_solver_env,
1126		'Wrong key or corrupt solver environment in CDCL(T) SAT solver',
1127		[solver_env:SolverEnv,key:Key]).
1128
1129		get_from_solver_env_ordered(sat_vars, [sat_vars:SatVars,_,_,_,_,_], SatVars).
1130		get_from_solver_env_ordered(sat_varnames, [_,sat_varnames:SatVarNames,_,_,_,_], SatVarNames).
1131		get_from_solver_env_ordered(sat_bindings, [_,_,sat_bindings:SatBindings,_,_,_], SatBindings).
1132		get_from_solver_env_ordered(t2b_env, [_,_,_,t2b_env:Env,_,_], Env).
1133		get_from_solver_env_ordered(pl_vars, [_,_,_,_,pl_vars:PlVars,_], PlVars).
1134		get_from_solver_env_ordered(binary_clause_vars, [_,_,_,_,_,binary_clause_vars:VarsFromBinaryClauses], VarsFromBinaryClauses).
1135
1136		bt_asserta(Assertion) :-
1137		asserta(Assertion); (retract(Assertion), !, fail).
1138
1139		bt_retract(Assertion) :-
1140		( retract(Assertion)
1141		-> ( true
1142		; asserta(Assertion),
1143		!,
1144		fail
1145		)
1146		; fail
1147		).
1148
1149		%% get_unsat_core_from_smt_formula(+FullFormula, +LastVarName, -UnsatCore).
1150		% Assumption: unsat core computation only removes constraints and does not deduce new ones.
1151		% Fails if +FullFormula is satisfiable.
1152		get_unsat_core_from_smt_formula(FullFormula, LastVarName, UnsatCore) :-
1153		debug_format_sat("Compute unsat core for: ", [], FullFormula),
1154		preferences:temporary_set_preference(time_out, 25, Change),
1155		call_cleanup(time_out(unsat_chr_core_list_with_auto_time_limit(FullFormula, 30000,
1156		[auto_time_out_factor(180), % we add 80 %
1157		ignore_if_sol_found,
1158		inspect_quantifiers(false)], GlobalRes, CoreList), 30000, TimeoutResult),
1159		reset_temporary_preference(time_out, Change)),
1160		!,
1161		( GlobalRes = solution(_)
1162		-> % the present theory conflict only occurs within the current state of ProB's waitflag store; there is at least one choice point
1163		% in the theory solver which needs to be evaluated; we thus do not learn from this "spurious counterexample" but
1164		% trigger chronological backtracking instead of backjumping
1165		debug_format_sat("Spurious counterexample found. Skip backjumping and use chronological backtracking instead.", []),
1166		fail
1167		; GlobalRes == time_out
1168		-> % ignore core if global result is timeout
1169		TUnsatCore = FullFormula
1170		; TimeoutResult == time_out
1171		-> % don't waste too much time in unsat core computation
1172		debug_format_sat("Canceled unsat core computation due to exceeding a timeout" ,[]),
1173		TUnsatCore = FullFormula
1174		; ( CoreList == []
1175		-> add_error_fail(get_conflict_clause_for_theory_conflict, 'Conflict clause in SMT solving is not a conflict.', [LastVarName])
1176		; conjunct_predicates(CoreList, TUnsatCore)
1177		)
1178		),
1179		debug_format_sat("Computed unsat core with added WD POs: ", [], TUnsatCore),
1180		( strip_pos_keep_toplevel_conj(TUnsatCore, UnsatCore)
1181		-> true
1182		; add_error_fail(strip_pos_keep_toplevel_conj, 'Removing WD POs for CDCL(T) failed.', [unsat_core_with_wd:TUnsatCore])
1183		),
1184		debug_format_sat("Computed unsat core: ", [], UnsatCore).
1185
1186		%% get_conflict_clause_for_theory_conflict(+LastVarName, +LastVarValue, +SolverEnv, -ConflictClause).
1187		% Translate current sat solution, which is a theory conflict, to the theory and compute
1188		% the (minimum) unsat core. Return the negated theory conflict as a conflict clause.
1189		% Note that an SMT formula passed to the theory solver is always a conjunction and
1190		% thus the negated unsat core is a disjunction (clause).
1191		get_conflict_clause_for_theory_conflict(SolverEnv, LastVarName, LastVarValue, SolverEnv, ConflictClause) :-
1192		( retract(idl_unsat_core(UnsatCore))
1193		-> true
1194		; get_from_solver_env(SolverEnv, sat_bindings, SatBindingsNoLast),
1195		get_from_solver_env(SolverEnv, sat_vars, SatVars),
1196		sat_to_predicate_from_solution(SatBindingsNoLast, SatVars, SmtFormulaNoLast),
1197		findall(bind(PendingName,PendingPol), pending_theory_prop(PendingName,PendingPol), PendingTheoryProps),
1198		sat_to_predicate_from_solution([bind(LastVarName,LastVarValue)|PendingTheoryProps], SatVars, FixedConj),
1199		safe_create_texpr(conjunct(FixedConj,SmtFormulaNoLast), pred, [] , FullFormula),
1200		get_unsat_core_from_smt_formula(FullFormula, LastVarName, UnsatCore)
1201		), !,
1202		find_typed_identifier_uses(UnsatCore, [], UsedIds),
1203		( list_contains_unfixed_deferred_set_id(UsedIds)
1204		-> asserta(unfixed_deferred_set_error)
1205		; true
1206		),
1207		get_conflict_clause_from_unsat_core(UnsatCore, SolverEnv, TConflictClause),
1208		sort(TConflictClause, TTConflictClause), % there can be duplicates due to added top-level WD POs; important to remove
1209		( TTConflictClause = [_]
1210		-> % currently undiscovered static theory contradiction; SAT variable might not be propagated yet if added WD PO
1211		ConflictClause = TTConflictClause
1212		; % remove not propagated top-level WD POs; we enforce WD POs in the theory solver but it can
1213		% be the case that a theory conflict occurs before the WD POs are propagated in the SAT solver
1214		remove_not_propagated(TTConflictClause, LastVarName, ConflictClause)
1215		),
1216		!.
1217
1218		remove_not_propagated([], _, []).
1219		remove_not_propagated([Pol-Var-Name|T], LastVarName, [Pol-Var-Name|NT]) :-
1220		( ground(Var)
1221		; Name == LastVarName
1222		),
1223		!,
1224		remove_not_propagated(T, LastVarName, NT).
1225		remove_not_propagated([_-_-Name|T], LastVarName, NT) :-
1226		debug_format_sat("Remove not propagated SAT variable ~w from conflict clause.", [Name]),
1227		remove_not_propagated(T, LastVarName, NT).
1228
1229		%% get_conflict_clause_from_unsat_core(+UnsatCore, +SolverEnv, -ConflictClause).
1230		get_conflict_clause_from_unsat_core(UnsatCore, SolverEnv, ConflictClause) :-
1231		get_from_solver_env(SolverEnv, sat_vars, SatVars),
1232		get_from_solver_env(SolverEnv, t2b_env, T2BEnv),
1233		get_from_solver_env(SolverEnv, pl_vars, PlVars),
1234		predicate_to_sat(only_reuse, [], SatVars, T2BEnv, UnsatCore, _NewEnv, _, UnsatCoreSat, _NewSatVars),
1235		sat_conj_negate_to_clause(UnsatCoreSat, TConflictClause),
1236		set_variable_references_in_clause(PlVars, TConflictClause, ConflictClause),
1237		!.
1238		get_conflict_clause_from_unsat_core(_, _, _) :-
1239		add_error_fail(get_conflict_clause_from_unsat_core, 'Unsat core to conflict clause failed.', []).
1240
1241		:- public get_complete_theory_lemma/2. % not used at the moment, for Spider
1242		%% get_complete_theory_lemma(+SolverEnv, -TheoryLemmaClause) :-
1243		% Return the complete unsatisfiable SMT formula as a conflict clause.
1244		get_complete_theory_lemma(SolverEnv, TheoryLemmaClause) :-
1245		get_complete_theory_lemma_fixed_binding(SolverEnv, _, _, TheoryLemmaClause).
1246
1247		%% get_complete_theory_lemma_fixed_binding(+SolverEnv, +SatVarName, +SatVarPol, -TheoryLemmaClause).
1248		% Enforce +SatVarName to have +SatVarPol binding. This is important for theory conflicts since the last
1249		% binding has been undone when backtracking. This is not applied if both inputs are variables, e.g., for SAT conflicts.
1250		get_complete_theory_lemma_fixed_binding(SolverEnv, SatVarName, SatVarPol, TheoryLemmaClause) :-
1251		get_from_solver_env(SolverEnv, pl_vars, PlVars),
1252		get_from_solver_env(SolverEnv, sat_bindings, SatBindings),
1253		get_clause_from_negated_ground_bindings(SatBindings, SatVarName, SatVarPol, TTheoryLemmaClause),
1254		set_variable_references_in_clause(PlVars, TTheoryLemmaClause, TheoryLemmaClause), !.
1255
1256		%% get_clause_from_negated_ground_bindings(+SatBindings, +FSatVarName, +FSatVarPol, -TheoryLemmaClause) :-
1257		% FSatVarName: name of SAT variable whose binding should be set to +FSatVarPol
1258		get_clause_from_negated_ground_bindings(SatBindings, FSatVarName, FSatVarPol, TheoryLemmaClause) :-
1259		get_clause_from_negated_ground_bindings(SatBindings, FSatVarName, FSatVarPol, [], TheoryLemmaClause).
1260
1261		get_clause_from_negated_ground_bindings([], _, _, Acc, Acc).
1262		get_clause_from_negated_ground_bindings([bind(SatVarName,_)|T], FSatVarName, FSatVarPol, Acc, TheoryLemmaClause) :-
1263		% theory propagations during grounding are possibly undone in the stack if finding a contradiction during grounding waitflags
1264		% we restore such pending theory propagations here
1265		pending_theory_prop(SatVarName, SatVarPol),
1266		!,
1267		negate_polarity(SatVarPol, NegPol),
1268		get_clause_from_negated_ground_bindings(T, FSatVarName, FSatVarPol, [_-NegPol-_-SatVarName|Acc], TheoryLemmaClause).
1269		get_clause_from_negated_ground_bindings([bind(SatVarName,_)|T], FSatVarName, FSatVarPol, Acc, TheoryLemmaClause) :-
1270		% set fixed polarity
1271		SatVarName == FSatVarName,
1272		!,
1273		negate_polarity(FSatVarPol, NegPol),
1274		get_clause_from_negated_ground_bindings(T, FSatVarName, FSatVarPol, [_-NegPol-_-SatVarName|Acc], TheoryLemmaClause).
1275		get_clause_from_negated_ground_bindings([bind(SatVarName,Pol)|T], FSatVarName, FSatVarPol, Acc, TheoryLemmaClause) :-
1276		ground(Pol),
1277		!,
1278		negate_polarity(Pol, NegPol),
1279		get_clause_from_negated_ground_bindings(T, FSatVarName, FSatVarPol, [_-NegPol-_-SatVarName|Acc], TheoryLemmaClause).
1280		get_clause_from_negated_ground_bindings([_|T], FSatVarName, FSatVarPol, Acc, TheoryLemmaClause) :-
1281		get_clause_from_negated_ground_bindings(T, FSatVarName, FSatVarPol, Acc, TheoryLemmaClause).
1282
1283		get_clause_from_ground_bindings([], _, _, Acc, Acc).
1284		get_clause_from_ground_bindings([bind(SatVarName,_)|T], FSatVarName, FSatVarPol, Acc, TheoryLemmaClause) :-
1285		% theory propagations during grounding are possibly undone in the stack if finding a contradiction during grounding waitflags
1286		% we restore such pending theory propagations here
1287		pending_theory_prop(SatVarName, SatVarPol),
1288		!,
1289		get_clause_from_ground_bindings(T, FSatVarName, FSatVarPol, [_-SatVarPol-_-SatVarName|Acc], TheoryLemmaClause).
1290		get_clause_from_ground_bindings([bind(SatVarName,Pol)|T], FSatVarName, FSatVarPol, Acc, TheoryLemmaClause) :-
1291		ground(Pol),
1292		!,
1293		get_clause_from_ground_bindings(T, FSatVarName, FSatVarPol, [_-Pol-_-SatVarName|Acc], TheoryLemmaClause).
1294		get_clause_from_ground_bindings([_|T], FSatVarName, FSatVarPol, Acc, TheoryLemmaClause) :-
1295		get_clause_from_ground_bindings(T, FSatVarName, FSatVarPol, Acc, TheoryLemmaClause).
1296
1297		% Fail if no decision has been made so far, i.e., the decision level is set to -1.
1298		get_last_decision_level(StateMutable, Level) :-
1299		get_full_state(StateMutable, cur_level, TLevel),
1300		TLevel > 0,
1301		!,
1302		Level = TLevel.
1303
1304		%negate_polarities([], []).
1305		%negate_polarities([StackInfo-Pol-Var-Name|T], [StackInfo-NPol-Var-Name|NT]) :-
1306		% negate_polarity(Pol, NPol),
1307		% negate_polarities(T, NT).
1308
1309		get_maximum_decision_level([(_,(Level,_),_,_)-_-_-_|T], ConflictLevel) :-
1310		!,
1311		get_maximum_decision_level(T, Level, ConflictLevel).
1312		get_maximum_decision_level([_-_-_-Name|_], _) :-
1313		add_error_fail(get_maximum_decision_level, 'The SAT variable has not been decided yet', [Name]).
1314
1315		get_maximum_decision_level([], Acc, Acc).
1316		get_maximum_decision_level([(_,(Level,_),_,_)-_-_-_|T], Acc, ConflictLevel) :-
1317		!,
1318		( Level > Acc
1319		-> NAcc = Level
1320		; NAcc = Acc
1321		),
1322		get_maximum_decision_level(T, NAcc, ConflictLevel).
1323		get_maximum_decision_level([_-_-_-Name|_], _, _) :-
1324		add_error_fail(get_maximum_decision_level, 'The SAT variable has not been decided yet', [Name]).
1325
1326		get_maximum_decision_level_other_than_current([_], _, _, BjLevel) :-
1327		% zero if learning a unit clause
1328		!,
1329		BjLevel = 0.
1330		get_maximum_decision_level_other_than_current(BjClause, BjLevelAcc, CurLevel, BjLevel) :-
1331		get_maximum_decision_level_other_than_current_not_unit(BjClause, BjLevelAcc, CurLevel, BjLevel).
1332
1333		get_maximum_decision_level_other_than_current_not_unit([], BjLevelAcc, _, BjLevelAcc).
1334		get_maximum_decision_level_other_than_current_not_unit([(_,(Level,_),_,_)-_-_-_|T], BjLevelAcc, CurLevel, BjLevel) :-
1335		( (Level \== CurLevel,
1336		Level > BjLevelAcc
1337		)
1338		-> NBjLevelAcc = Level
1339		; NBjLevelAcc = BjLevelAcc
1340		),
1341		get_maximum_decision_level_other_than_current_not_unit(T, NBjLevelAcc, CurLevel, BjLevel).
1342
1343		%% get_antecedent_assignments(+SolverEnv, +ConflictDLevel, +SatVarName, +RPol, +RPropType, +ROriginalClause, -Antecedent).
1344		get_antecedent_assignments(_, _, SatVarName, _, _, ROriginalClause, Antecedent) :-
1345		is_list(ROriginalClause),
1346		!,
1347		select(_-_-_-SatVarName, ROriginalClause, TAntecedent), !,
1348		Antecedent = TAntecedent.
1349		get_antecedent_assignments(SolverEnv, ConflictDLevel, SatVarName, RPol, theory, ROriginalClause, Antecedent) :-
1350		\+ is_list(ROriginalClause),
1351		!,
1352		explain_theory_propagation(SolverEnv, SatVarName, ConflictDLevel, RPol, OriginalClause),
1353		ROriginalClause = OriginalClause,
1354		select(_-_-_-SatVarName, OriginalClause, TAntecedent), !,
1355		Antecedent = TAntecedent.
1356		get_antecedent_assignments(_, _, SatVarName, _, _, _, _) :-
1357		add_error_fail(get_antecedent_assignments, 'No antecedent assignments since variable has not been propagated.', SatVarName).
1358
1359		%% join_assignments(+A1, +A2, +A2Full, -Joined).
1360		join_assignments([], _, A, A).
1361		join_assignments([StackInfo-Pol-Var-Name|T], A2, A3, Res) :-
1362		( select(_-_-_-Name, A2, A4) % removes dups assuming that A2 has no dups
1363		-> join_assignments(T, A4, A3, Res)
1364		; join_assignments(T, A2, [StackInfo-Pol-Var-Name|A3], Res)
1365		).
1366
1367		%% resolve(+SolverEnv, +TBjClause, +Resolver, +ROriginalClause, -NTBjClause).
1368		% +Resolver is a SAT variable name to resolve next (i.e., expand its antecedent assignments).
1369		resolve(SolverEnv, TBjClause, ConflictDLevel, Resolver, RPol, RPropType, ROriginalClause, NTBjClause) :-
1370		get_antecedent_assignments(SolverEnv, ConflictDLevel, Resolver, RPol, RPropType, ROriginalClause, Antecedent),
1371		join_assignments(Antecedent, TBjClause, TBjClause, TNTBjClause), % important to not have duplicates
1372		select(_-_-_-Resolver, TNTBjClause, NTBjClause).
1373
1374		add_used_vars_to_mutdict([], _).
1375		add_used_vars_to_mutdict([_-_-_-SatVarName|T], VarNamesDict) :-
1376		\+ mutdict_get(VarNamesDict, SatVarName, _),
1377		!,
1378		mutdict_put(VarNamesDict, SatVarName, SatVarName),
1379		add_used_vars_to_mutdict(T, VarNamesDict).
1380		add_used_vars_to_mutdict([_|T], VarNamesDict) :-
1381		add_used_vars_to_mutdict(T, VarNamesDict).
1382
1383		get_variables_used_in_cdcl(ResolvedSoFar, BjClause, UsedVars) :-
1384		add_used_vars_to_mutdict(BjClause, ResolvedSoFar),
1385		mutdict_keys(ResolvedSoFar, UsedVars).
1386
1387		get_variable_names_in_clause([], []).
1388		get_variable_names_in_clause([_-_-_-SatVarName|T], [SatVarName|NT]) :-
1389		get_variable_names_in_clause(T, NT).
1390
1391		% sort in reversed stack order
1392		reversed_stack_sort((_,(DLevel1,ACount1),_,_)-_-_-_, (_,(DLevel2,ACount2),_,_)-_-_-_) :-
1393		ground(DLevel1), ground(DLevel2),
1394		( DLevel1 > DLevel2
1395		-> true
1396		; DLevel1 == DLevel2
1397		-> ACount1 > ACount2
1398		; fail
1399		).
1400
1401		:- dynamic part_of_first_uip/1.
1402
1403		% See https://cca.informatik.uni-freiburg.de/papers/SoerenssonBiere-SAT09.pdf
1404		% Generate the 1-UIP clause. Mark all its literals. Remove those implied variables which have all their antecedent literals marked.
1405		minimize_clause(SolverEnv, ConflictDLevel, BjClause, local, MinBjClause) :-
1406		mark_literals(BjClause),
1407		remove_where_all_antecedent_marked(BjClause, SolverEnv, ConflictDLevel, MinBjClause).
1408		% Generate the 1-UIP clause. Mark its literals. Implied variables in 1-UIP clause are candidates for removal.
1409		% Search implication graph. Start from antecedent literals of candidate. Stop at marked literals or decisions.
1410		% If search always ends at marked literals, the candidate can be removed.
1411		minimize_clause(SolverEnv, ConflictDLevel, BjClause, recursive, MinBjClause) :-
1412		mark_literals(BjClause),
1413		remove_recursively_stop_marked(BjClause, SolverEnv, ConflictDLevel, MinBjClause).
1414
1415		remove_recursively_stop_marked([], _, _, []).
1416		remove_recursively_stop_marked([(PropType,_,_,OriginalClause)-_-Pol-SatVarName|T], SolverEnv, ConflictDLevel, MinBjClause) :-
1417		PropType \== branch,
1418		get_antecedent_assignments(SolverEnv, ConflictDLevel, SatVarName, Pol, PropType, OriginalClause, Antecedent),
1419		samsort(reversed_stack_sort, Antecedent, SAntecedent), % reverse assignment order
1420		recursively_inspect_antecedent(SAntecedent, SolverEnv, ConflictDLevel),
1421		!,
1422		remove_recursively_stop_marked(T, SolverEnv, ConflictDLevel, MinBjClause).
1423		remove_recursively_stop_marked([Lit|T], SolverEnv, ConflictDLevel, [Lit|NT]) :-
1424		remove_recursively_stop_marked(T, SolverEnv, ConflictDLevel, NT).
1425
1426		recursively_inspect_antecedent([], _, _).
1427		recursively_inspect_antecedent([(PropType,_,_,OriginalClause)-_-Pol-SatVarName|T], SolverEnv, ConflictDLevel) :-
1428		recursive_search_stops_at_marked_or_decision(PropType, OriginalClause, Pol, SatVarName, SolverEnv, ConflictDLevel),
1429		recursively_inspect_antecedent(T, SolverEnv, ConflictDLevel).
1430
1431		recursive_search_stops_at_marked_or_decision(_, _, _, SatVarName, _, _) :-
1432		part_of_first_uip(SatVarName),
1433		!.
1434		recursive_search_stops_at_marked_or_decision(PropType, OriginalClause, Pol, SatVarName, SolverEnv, ConflictDLevel) :-
1435		PropType \== branch,
1436		get_antecedent_assignments(SolverEnv, ConflictDLevel, SatVarName, Pol, PropType, OriginalClause, Antecedent),
1437		recursively_inspect_antecedent(Antecedent, SolverEnv, ConflictDLevel).
1438
1439		all_literals_are_marked([]).
1440		all_literals_are_marked([_-_-_-SatVarName|T]) :-
1441		part_of_first_uip(SatVarName),
1442		!,
1443		all_literals_are_marked(T).
1444
1445		remove_where_all_antecedent_marked([], _, _, []).
1446		remove_where_all_antecedent_marked([(PropType,_,_,OriginalClause)-_-Pol-SatVarName|T], SolverEnv, ConflictDLevel, MinBjClause) :-
1447		PropType == unit,
1448		get_antecedent_assignments(SolverEnv, ConflictDLevel, SatVarName, Pol, PropType, OriginalClause, Antecedent),
1449		all_literals_are_marked(Antecedent),
1450		!,
1451		remove_where_all_antecedent_marked(T, SolverEnv, ConflictDLevel, MinBjClause).
1452		remove_where_all_antecedent_marked([Lit|T], SolverEnv, ConflictDLevel, [Lit|NT]) :-
1453		remove_where_all_antecedent_marked(T, SolverEnv, ConflictDLevel, NT).
1454
1455		mark_literals(Lits) :-
1456		retractall(part_of_first_uip(_)),
1457		mark_literals_state(Lits).
1458
1459		mark_literals_state([]).
1460		mark_literals_state([_-_-_-SatVarName|T]) :-
1461		asserta(part_of_first_uip(SatVarName)),
1462		mark_literals_state(T).
1463
1464		%% get_backjump_clause_conflict_resolution(+SolverEnv, +StateMutable, +ConflictLevel, +ConflictClause, -BjClause, -BjLevel, -BjSatVars, -UsedVars).
1465		% In the conflict graph each node corresponds to a variable assignment.
1466		% The predecessors of node x are the antecedent assignments A^w(x) corresponding
1467		% to the unit clause w (in its original form) that led to the propagation of x (logical implications).
1468		% The directed edges from the nodes in A^w(x) to node x are all labeled with w.
1469		% Nodes that have no predecessor correspond to decision/branching assignments
1470		% (cf. GRASP: A Search Algorithm for Propositional Satisfiability, by Marques-Silva and Sakallah).
1471		% As an improvement, we apply first UIP clause learning (cf. Efficient Conflict Driven Learning in a Boolean Satisfiability Solver, Zhang et al.).
1472		% Compute the conflict graph for a conflicting unit-propagation of a variable and extract a backjump clause.
1473		% -UsedVars are the SAT variables used during conflict analysis that are not part of the final bj clause (can be necessary for branching heuristic).
1474		% -BjSatVars are the SAT variables in the final bj clause.
1475		% Notes:
1476		% - the variable references in the returned clause are not yet set
1477		% - we do not create an actual graph but apply Boolean resolution
1478		get_backjump_clause_conflict_resolution(SolverEnv, StateMutable, ConflictLevel, ConflictClause, BjClause, BjLevel, BjSatVars, UsedVars) :-
1479		get_last_decision_level(StateMutable, _),
1480		new_mutdict(ResolvedSoFar),
1481		get_backjump_clause_and_level(SolverEnv, ConflictLevel, ResolvedSoFar, ConflictClause, BjClause, BjLevel, TUsedVars),
1482		get_variable_names_in_clause(BjClause, BjSatVars),
1483		subtract(TUsedVars, BjSatVars, UsedVars).
1484
1485		%% get_backjump_clause_and_level(+SolverEnv, +ConflictDLevel, +ResolvedSoFar, +TBjClause, -BjClause, -BjLevel, -UsedVars).
1486		get_backjump_clause_and_level(SolverEnv, ConflictDLevel, ResolvedSoFar, TBjClause, MinBjClause, BjLevel, UsedVars) :-
1487		get_backjump_clause_and_level_sub(ConflictDLevel, 0, _, TBjClause, Resolver-RPol-RPropType-ROriginalClause, ThisLevelCount),
1488		( ThisLevelCount == 1
1489		-> % break, first UIP
1490		BjClause = TBjClause,
1491		clause_minimization(ClauseMinType),
1492		( ClauseMinType \== none
1493		-> ( minimize_clause(SolverEnv, ConflictDLevel, BjClause, ClauseMinType, MinBjClause), !
1494		; add_error_fail(minimize_clause, 'Clause minimization failed: ', [BjClause])
1495		)
1496		; MinBjClause = BjClause
1497		),
1498		get_maximum_decision_level_other_than_current(MinBjClause, 0, ConflictDLevel, BjLevel),
1499		get_variables_used_in_cdcl(ResolvedSoFar, MinBjClause, UsedVars)
1500		; ground(Resolver),
1501		resolve(SolverEnv, TBjClause, ConflictDLevel, Resolver, RPol, RPropType, ROriginalClause, NToExpand),
1502		mutdict_put(ResolvedSoFar, Resolver, Resolver),
1503		get_backjump_clause_and_level(SolverEnv, ConflictDLevel, ResolvedSoFar, NToExpand, MinBjClause, BjLevel, UsedVars)
1504		).
1505
1506		get_backjump_clause_and_level_sub(_, ThisLevelCountAcc, ResolverAcc-_-RPol-RPropType-ROriginalClause, [], ResolverAcc-RPol-RPropType-ROriginalClause, ThisLevelCountAcc).
1507		get_backjump_clause_and_level_sub(ConflictDLevel, ThisLevelCountAcc, ResolverAcc-RACount-RPol-RPropType-ROriginalClause, [(PropType,(Level,ACount),_,OriginalClause)-Pol-_-SatVarName|T], Resolver, ThisLevelCount) :-
1508		( Level == ConflictDLevel
1509		-> NThisLevelCountAcc is ThisLevelCountAcc + 1
1510		; NThisLevelCountAcc = ThisLevelCountAcc
1511		),
1512		( (
1513		Level == ConflictDLevel,
1514		% unit or theory propagation
1515		PropType \== branch,
1516		% use last assigned literal to resolve next
1517		( var(ResolverAcc)
1518		; ACount > RACount
1519		)
1520		)
1521		-> NResolverAcc = SatVarName-ACount-Pol-PropType-OriginalClause
1522		; NResolverAcc = ResolverAcc-RACount-RPol-RPropType-ROriginalClause
1523		),
1524		get_backjump_clause_and_level_sub(ConflictDLevel, NThisLevelCountAcc, NResolverAcc, T, Resolver, ThisLevelCount).
1525
1526		negate_polarity(pred_true, pred_false).
1527		negate_polarity(pred_false, pred_true).
1528
1529		retractall_once(Assertion) :-
1530		retractall(cdclt_sat_solver:Assertion),
1531		!.
1532
1533		asserta_once(Assertion) :-
1534		call(cdclt_sat_solver:Assertion),
1535		!.
1536		asserta_once(Assertion) :-
1537		asserta(cdclt_sat_solver:Assertion).
1538
1539		b_pred_or_bool_true(X) :- X == truth; X == boolean_true; X == value(pred_true).
1540		%b_pred_or_bool_false(X) :- X == falsity; X == boolean_false; X == value(pred_false).
1541
1542		sat_conj_negate_to_clause(Pred, Clause) :-
1543		conjunction_to_list(Pred, List),
1544		maplist(sat_equality_negate_to_literal, List, Clause).
1545
1546		sat_equality_negate_to_literal(b(equal(ID,Pol),pred,_), _-NegPol-_-Name) :-
1547		ID = b(identifier(Name),_,_),
1548		Pol = b(Value,boolean,_),
1549		( b_pred_or_bool_true(Value)
1550		-> NegPol = pred_false
1551		; NegPol = pred_true
1552		).
1553
1554		%%%%% Solver State
1555		create_solver_state(StateMutable) :-
1556		State = [cur_level:0,current_stack_size:0],
1557		create_mutable(solver_state(State), StateMutable).
1558
1559		%% get_full_state(+StateMutable, +Key, -Datum).
1560		% We assume an order of the SolverState to prevent using member.
1561		get_full_state(StateMutable, Key, Datum) :-
1562		get_mutable(solver_state(SolverState), StateMutable),
1563		get_full_state_ordered(Key, SolverState, Datum), !.
1564
1565		get_full_state_ordered(cur_level, [cur_level:CurLevel,_], CurLevel).
1566		get_full_state_ordered(current_stack_size, [_,current_stack_size:Size], Size).
1567
1568		%% delete_from_heuristic(+SatVarName).
1569		delete_from_heuristic(SatVarName) :-
1570		( fibonacci_heap:elm_exists(SatVarName)
1571		-> fibonacci_heap:delete_elm_bt(SatVarName)
1572		; % it can be the case that SatVarName has already been removed
1573		% from the mutable due to coroutines etc.; succeed in this case
1574		true
1575		).
1576
1577		%% update_full_state(+StateMutable, +Key, +Datum).
1578		% We assume an order of the SolverState to prevent using member.
1579		update_full_state(StateMutable, Key, Datum) :-
1580		get_mutable(solver_state(SolverState), StateMutable),
1581		update_full_state_ordered(Key, Datum, SolverState, NewSolverState), !,
1582		update_mutable(solver_state(NewSolverState), StateMutable).
1583
1584		update_full_state_ordered(cur_level, NewDatum, [cur_level:_,B], [cur_level:NewDatum,B]).
1585		update_full_state_ordered(current_stack_size, NewDatum, [A,current_stack_size:_], [A,current_stack_size:NewDatum]).
1586
1587		%% Initialize the dynamic solver state for a specific solver.
1588		init_dynamic_solver_state(SolverName) :-
1589		fibonacci_heap:init,
1590		clean_dynamic_solver_state,
1591		clear_pending_theory_propagations,
1592		asserta(solver_name(SolverName)),
1593		asserta(restarts(0)),
1594		asserta(glue_clauses(0)),
1595		%asserta(amount_clause_reductions(0)),
1596		asserta(assignment_count_on_cur_level(0)),
1597		asserta(amount_learned_clauses(0)),
1598		asserta(conflict_stats(total(0), since_restart(0), since_reduction(0))),
1599		asserta(recent_lbds_dl(Diff1-Diff1, 0)),
1600		asserta(recent_stack_sizes_dl(Diff2-Diff2, 0)),
1601		asserta(total_lbd_sum(0)),
1602		init_luby_sequence.
1603
1604		clean_dynamic_solver_state :-
1605		retractall(assignment_timeout_occurred),
1606		retractall(allow_partial_model),
1607		retractall(unfixed_deferred_set_error),
1608		retractall(assignment_count_on_cur_level(_)),
1609		retractall(pending_theory_prop(_,_)),
1610		retractall(glue_clauses(_)),
1611		retractall(glue_level(_,_,_)),
1612		retractall(solver_name(_)),
1613		retractall(restarts(_)),
1614		retractall(is_restart),
1615		retractall(bt_from_smt_solution),
1616		retractall(recent_lbds_dl(_, _)),
1617		retractall(recent_stack_sizes_dl(_, _)),
1618		retractall(saved_phase(_, _)),
1619		%retractall(amount_clause_reductions(_)),
1620		retractall(amount_learned_clauses(_)),
1621		retractall(luby_counter(_)),
1622		%retractall(exclude_sat_solution_clause(_)),
1623		retractall(total_lbd_sum(_)),
1624		retractall(conflict_stats(_, _, _)),
1625		retractall(idl_unsat_core(_)),
1626		retractall(backjump_level(_)),
1627		retractall(backjump_clause(_, _, _, _, _, _)).
1628
1629		%% Remove dynamically stored unsat core found by the IDL solver.
1630		remove_idl_unsat_core :-
1631		retractall_once(idl_unsat_core(_)).
1632
1633		%% Store an unsat core found by the IDL solver in the SMT solver's dynamic state.
1634		store_idl_unsat_core(Core) :-
1635		assignment_count_on_cur_level(ACount),
1636		ACount > 1, % at least one unit propagation on this level, otherwise just backtrack
1637		retractall_once(idl_unsat_core(_)),
1638		asserta(idl_unsat_core(Core)).
1639
1640		%% Announce backtracking after a solution has been found in order to backtrack to search for another solution.
1641		%% We have to be able to distinguish between backtracking due to not finding a solution or backtracking
1642		%% triggered by the user to find another solution.
1643		announce_bt_from_smt_solution :-
1644		asserta(bt_from_smt_solution).
1645		%%%%%
1646
1647		%% b_to_cnf_safe(+In, +State, -Out).
1648		b_to_cnf_safe(In, State, Out) :-
1649		b_to_cnf(In, State, TOut),
1650		!,
1651		Out = TOut.
1652		b_to_cnf_safe(_, _, _) :-
1653		add_internal_error('B to CNF conversion failed ', cdclt),
1654		fail.
1655
1656		%% b_to_cnf(+In, +State, -Out).
1657		% Accepts predicates with conjunction, disjunction, and equality of SAT variables. No negations.
1658		b_to_cnf(In, State, Out) :-
1659		get_texpr_expr(In, Expr),
1660		b_to_cnf_aux(Expr, State, Res, []),
1661		!,
1662		Res = Out.
1663		b_to_cnf(In, _, _) :-
1664		translate_bexpression(In, PPIn),
1665		!,
1666		add_error_fail(b_to_cnf, 'CNF conversion failed', PPIn).
1667
1668		b_to_cnf(b(Expr,_,_Info), State) -->
1669		!,
1670		b_to_cnf_aux(Expr, State).
1671		b_to_cnf(In, _, _, _) :-
1672		add_error_fail(b_to_cnf, 'Not properly wrapped:', In).
1673
1674		b_to_cnf_aux(X, _) -->
1675		{X == truth}, !,
1676		[].
1677		b_to_cnf_aux(X, _) -->
1678		{X == falsity}, !,
1679		[[]].
1680		b_to_cnf_aux(equal(A,B), State) -->
1681		{get_texpr_expr(B, Expr),
1682		Expr == boolean_true,
1683		get_texpr_expr(A, identifier(Name))},
1684		!,
1685		{member(bind(Name,Res)-StackInfo, State)},
1686		[[StackInfo-pred_true-Res-Name]].
1687		b_to_cnf_aux(equal(A,B), State) -->
1688		{get_texpr_expr(B, Expr),
1689		Expr == boolean_false,
1690		get_texpr_expr(A, identifier(Name)),
1691		member(bind(Name,Res)-StackInfo, State)},
1692		[[StackInfo-pred_false-Res-Name]].
1693		b_to_cnf_aux(disjunct(D1,D2), State) -->
1694		b_to_cnf_disj_aux(D1, D2, State).
1695		b_to_cnf_aux(conjunct(A,B), State) -->
1696		b_to_cnf(A, State),
1697		b_to_cnf(B, State).
1698
1699		b_to_cnf_disj_aux(D1, D2, State) -->
1700		{get_texpr_expr(D1, conjunct(A,B))}, !,
1701		{create_texpr(disjunct(A,D2), pred, [], DJ1),
1702		create_texpr(disjunct(B,D2), pred, [], DJ2)},
1703		b_to_cnf_aux(conjunct(DJ1,DJ2), State).
1704		b_to_cnf_disj_aux(D1, D2, State) -->
1705		{get_texpr_expr(D2, conjunct(A,B))}, !,
1706		{create_texpr(disjunct(D1,A), pred, [], DJ1),
1707		create_texpr(disjunct(D1,B), pred, [], DJ2)},
1708		b_to_cnf_aux(conjunct(DJ1,DJ2), State).
1709		b_to_cnf_disj_aux(D1, D2, State, Res, Acc) :-
1710		b_to_cnf(D1, State, Res1),
1711		b_to_cnf(D2, State, Res2),
1712		!,
1713		( Res1 = []
1714		-> Res = Acc
1715		; Res1 = [[]]
1716		-> append(Res2,Acc,Res)
1717		; Res2 = []
1718		-> Res = Acc
1719		; Res2 = [[]]
1720		-> append(Res1,Acc,Res)
1721		; ( Res1 = [ResD1],
1722		Res2 = [ResD2]
1723		)
1724		-> Res = [Res12|Acc],
1725		append(ResD1, ResD2, Res12)
1726		; join_clauses(Res1,Res2,Res,Acc)
1727		-> true
1728		; add_error_fail(b_to_cnf_disj, 'Cannot join clauses: ', Res1:Res2)
1729		).
1730
1731		join_clauses([], _) --> [].
1732		join_clauses([Clause1|T], Clauses2) -->
1733		join_clauses_aux(Clause1,Clauses2),
1734		join_clauses(T,Clauses2).
1735
1736		join_clauses_aux(_, []) --> [].
1737		join_clauses_aux(Clause1, [Clause2|T]) -->
1738		{append(Clause1, Clause2, NewClause)},
1739		[NewClause],
1740		join_clauses_aux(Clause1, T).
1741
1742
1743		% Used for random restarts.
1744		% First restart is after 32nd conflict, second after additional 32 conflicts,
1745		% third after additional 64 conflicts etc.
1746		init_luby_sequence :-
1747		retractall(luby_counter(_)),
1748		% unit length of 32
1749		% 1,1,2,1,1,2,4,1,1,2,1,1,2,4,8,..
1750		assertz(luby_counter(1)), assertz(luby_counter(1)), assertz(luby_counter(2)), assertz(luby_counter(1)), assertz(luby_counter(1)),
1751		assertz(luby_counter(2)), assertz(luby_counter(4)), assertz(luby_counter(1)), assertz(luby_counter(1)), assertz(luby_counter(2)),
1752		assertz(luby_counter(1)), assertz(luby_counter(1)), assertz(luby_counter(2)), assertz(luby_counter(4)), assertz(luby_counter(8)),
1753		assertz(luby_counter(1)), assertz(luby_counter(1)), assertz(luby_counter(2)), assertz(luby_counter(1)), assertz(luby_counter(1)),
1754		assertz(luby_counter(2)), assertz(luby_counter(4)), assertz(luby_counter(8)), assertz(luby_counter(16)), assertz(luby_counter(1)),
1755		assertz(luby_counter(1)), assertz(luby_counter(2)), assertz(luby_counter(1)), assertz(luby_counter(1)), assertz(luby_counter(2)),
1756		assertz(luby_counter(4)), assertz(luby_counter(8)), assertz(luby_counter(16)), assertz(luby_counter(32)), assertz(luby_counter(1)),
1757		assertz(luby_counter(1)), assertz(luby_counter(2)), assertz(luby_counter(1)), assertz(luby_counter(1)), assertz(luby_counter(2)),
1758		assertz(luby_counter(4)), assertz(luby_counter(8)), assertz(luby_counter(16)), assertz(luby_counter(32)), assertz(luby_counter(64)),
1759		assertz(luby_counter(1)), assertz(luby_counter(1)), assertz(luby_counter(2)), assertz(luby_counter(1)), assertz(luby_counter(1)),
1760		assertz(luby_counter(2)), assertz(luby_counter(4)), assertz(luby_counter(8)), assertz(luby_counter(16)), assertz(luby_counter(32)),
1761		assertz(luby_counter(64)), assertz(luby_counter(128)).
1762
1763		% ----------------
1764
1765		%% simplify_cnf(+CNF, -Simplified).
1766		% Boolean resolution.
1767		simplify_cnf([], []).
1768		simplify_cnf([Clause|T], NewCnf) :-
1769		simplify_clause(Clause, _, Simplified, IsTrue), !,
1770		Simplified \== [], % contradiction if a clause is empty
1771		( IsTrue == true
1772		-> NewCnf = NT % remove true clauses
1773		; NewCnf = [Simplified|NT]
1774		),
1775		simplify_cnf(T, NT).
1776
1777		simplify_clause([], IsTrue, [], IsTrue).
1778		simplify_clause([_-Pol-Var-_|T], IsTrueAcc, NT, IsTrue) :-
1779		ground(Var),
1780		Pol \== Var,
1781		!,
1782		simplify_clause(T, IsTrueAcc, NT, IsTrue).
1783		simplify_clause([StackInfo-Pol-Var-SatVarName|T], IsTrueAcc, [StackInfo-Pol-Var-SatVarName|NT], IsTrue) :-
1784		( Pol == Var
1785		-> IsTrueAcc = true
1786		; true
1787		),
1788		simplify_clause(T, IsTrueAcc, NT, IsTrue).
1789
1790		clause_order(_-_-_-A3, _-_-_-B3) :- A3 @< B3.
1791
1792		%% unit_propagate_cnf(+SolverEnv, +StateMutable, +Clauses, -NewClauses).
1793		% A simple unit propagation, useful to run before reification.
1794		% Removes duplicates from each clause.
1795		% Important to identify all unit clauses, b_to_cnf does not check for unique sat variables in clauses.
1796		% An exhaustive unit-propagation prior to the reification is not beneficial
1797		% since simplifying a CNF is slow compared to using watched literals in sat/4.
1798		% Note: It is important to remove duplicates, e.g., using sort/2. Otherwise, a conflict clause with duplicates
1799		% would lead to failure for first UIP CDCL (first UIP not recognized due to duplicate decision level).
1800		unit_propagate_cnf(SolverEnv, StateMutable, Clauses, NewClauses) :-
1801		unit_prop_clause_sort(true, SolverEnv, StateMutable, Clauses, _, _, TNewClauses), !,
1802		simplify_cnf(TNewClauses, NewClauses).
1803
1804		propagate_unit_clause([StackInfo-Pol-PrologVar-SatVarName], StateMutable, RAcc) :-
1805		( PrologVar == Pol
1806		-> % duplicate unit clause already propagated
1807		true
1808		; PrologVar = Pol,
1809		RAcc = true,
1810		debug_format_sat("deterministic unit propagation of ~w with polarity ~w before reification", [SatVarName,Pol]),
1811		get_next_assignment_count_on_level(ACount),
1812		StackInfo = (unit,(0,ACount),Pol,[_-Pol-PrologVar-SatVarName]),
1813		bt_log_sat_stack(StateMutable, SatVarName, Pol),
1814		log_unit_propagation
1815		).
1816
1817		%% unit_prop_clause_sort(+Sort, +SolverEnv, +StateMutable, +CNF, +RAcc, -Resolved, -NewClauses).
1818		% Removes duplicates from each clause if +Sort is true.
1819		% Logs if a variable has been unit propagated in -Resolved using +RAcc.
1820		unit_prop_clause_sort(_, _, _, [], RAcc, RAcc, []).
1821		unit_prop_clause_sort(Sort, SolverEnv, StateMutable, [[StackInfo-Pol-PrologVar-SatVarName]|T], RAcc, Resolved, NT) :-
1822		propagate_unit_clause([StackInfo-Pol-PrologVar-SatVarName], StateMutable, RAcc),
1823		!,
1824		unit_prop_clause_sort(Sort, SolverEnv, StateMutable, T, RAcc, Resolved, NT).
1825		unit_prop_clause_sort(Sort, SolverEnv, StateMutable, [Clause|T], RAcc, Resolved, NewClauses) :-
1826		( Sort = true
1827		-> remove_dups(Clause, TNewClause),
1828		% clause_order ensures that watched literals are initially set to the same variables for stronger propagation
1829		samsort(clause_order, TNewClause, NewClause)
1830		; NewClause = Clause
1831		),
1832		( NewClause = [_-_-_-_]
1833		-> propagate_unit_clause(NewClause, StateMutable, RAcc),
1834		NewClauses = NT
1835		; NewClauses = [NewClause|NT]
1836		), !,
1837		unit_prop_clause_sort(Sort, SolverEnv, StateMutable, T, RAcc, Resolved, NT).
1838
1839		% ----------------
1840
1841		portray_cnf(Clauses) :- length(Clauses,Len), format('CNF with ~w clauses:~n',[Len]),
1842		maplist(portray_sat_clause,Clauses).
1843
1844		portray_sat_clause(Clause) :- write(' '),maplist(portray_literal,Clause),nl.
1845
1846		portray_literal(pred_false-PrologVar-ID) :- !, format('- ~w(~w) ',[ID,PrologVar]).
1847		portray_literal(pred_true-PrologVar-ID) :- !, format(' ~w(~w) ',[ID,PrologVar]).
1848		portray_literal(Lit) :- format(' *** UNKNOWN: ~w ',[Lit]).
1849
1850		% ----------------
1851
1852		/*
1853		%% static_sat_symmetry_breaking(+Clauses, +SolverEnv, +CurLevelMut, -NewSolverEnv).
1854		% Static SAT symmetry breaking after unit propagation of problem_setup/3 but only once, e.g., not after a restart or bj to level 0
1855		% Can only be used for pure SAT solving.
1856		static_sat_symmetry_breaking(_, SolverEnv, _, NewSolverEnv) :-
1857		static_sat_symmetry_breaking(false),
1858		!,
1859		NewSolverEnv = SolverEnv.
1860		static_sat_symmetry_breaking(Clauses, SolverEnv, CurLevelMut, NewSolverEnv) :-
1861		\+ symmetry_breaking_pred(_, _),
1862		!,
1863		get_symmetry_breaking_predicates(Clauses, SBPsConjNoRef, NewSatVars),
1864		asserta(symmetry_breaking_pred(SBPsConjNoRef,NewSatVars)),
1865		static_sat_symmetry_breaking(Clauses, SolverEnv, CurLevelMut, NewSolverEnv).
1866		static_sat_symmetry_breaking(_, SolverEnv, CurLevelMut, NewSolverEnv) :-
1867		get_asserted_symmetry_breaking_pred(SolverEnv, SBPsConj, NewSolverEnv),
1868		problem_setup(NewSolverEnv, CurLevelMut, SBPsConj).
1869
1870		get_asserted_symmetry_breaking_pred(SolverEnv, SBPsConj, NewSolverEnv) :-
1871		symmetry_breaking_pred(SBPsConjNoRef, NewSatVars),
1872		add_symmetry_breaking_eqs_to_solver_env(NewSatVars, SolverEnv, NewSolverEnv),
1873		get_from_solver_env(NewSolverEnv, pl_vars, PlVars),
1874		set_variable_references_in_clauses(PlVars, SBPsConjNoRef, SBPsConj),
1875		findall(Var, (member(Var, NewSatVars), bt_asserta(heuristic_tuple(Var,1))), _).
1876
1877		%% add_symmetry_breaking_eqs_to_solver_env(+NewSatVars, +SolverEnv, -NewSolverEnv).
1878		% Symmetry breaking might introduce new SAT variables for equalities inbetween cycles of permutations.
1879		% We update the solver environment and create the corresponding SMT formulas for equalities here.
1880		% This is necessary, e.g., if a SAT variable corresponding to an equality introduced
1881		% from symmetry breaking is involved in a conflict.
1882		add_symmetry_breaking_eqs_to_solver_env(NewSatVars, SolverEnv, NewSolverEnv) :-
1883		SolverEnv = [sat_vars:SatVars,sat_varnames:SatVarNames,sat_bindings:SatBindings,t2b_env:Env,pl_vars:PrologSatVarTriple],
1884		add_symmetry_breaking_eqs_to_solver_env(NewSatVars, SatVars, SatVarNames, SatBindings, Env, PrologSatVarTriple, NSatVars, NSatVarNames, NSatBindings, NEnv, NPrologSatVarTriple),
1885		NewSolverEnv = [sat_vars:NSatVars,sat_varnames:NSatVarNames,sat_bindings:NSatBindings,t2b_env:NEnv,pl_vars:NPrologSatVarTriple].
1886
1887		add_symmetry_breaking_eqs_to_solver_env([], SatVars, SatVarNames, SatBindings, Env, PrologSatVarTriple, SatVars, SatVarNames, SatBindings, Env, PrologSatVarTriple).
1888		add_symmetry_breaking_eqs_to_solver_env([NewSatVarName-EqClauses|T], SatVars, SatVarNames, SatBindings, Env, PrologSatVarTriple, NSatVars, NSatVarNames, NSatBindings, NEnv, NPrologSatVarTriple) :-
1889		maplist(clause_to_smt_disjunction(SatVars), EqClauses, EqSmtClauses),
1890		conjunct_predicates(EqSmtClauses, EqSmt1), % all true
1891		maplist(negate_smt_formula, EqSmtClauses, NegEqSmtClauses),
1892		conjunct_predicates(NegEqSmtClauses, EqSmt2), % or all false
1893		EqSmt = b(disjunct(EqSmt1,EqSmt2),pred,[]),
1894		SatVars1 = [b(identifier(NewSatVarName),boolean,[smt_formula(EqSmt),eq_symmetry_break])|SatVars],
1895		SatVarNames1 = [NewSatVarName|SatVarNames],
1896		SatBindings1 = [bind(NewSatVarName,Var)|SatBindings],
1897		PrologSatVarTriple1 = [Var-NewSatVarName-EqSmt|PrologSatVarTriple],
1898		Env1 = [(EqSmt,b(identifier(NewSatVarName),boolean,[]))|Env],
1899		add_symmetry_breaking_eqs_to_solver_env(T, SatVars1, SatVarNames1, SatBindings1, Env1, PrologSatVarTriple1, NSatVars, NSatVarNames, NSatBindings, NEnv, NPrologSatVarTriple).
1900
1901		%clause_to_smt_disjunction(_, [], b(truth,pred,[])).
1902		clause_to_smt_disjunction(SatVars, [Pol-_-SatVarName|T], SmtDisj) :-
1903		get_smt_formula_from_vars_for_sat_pol(SatVars, SatVarName, Pol, SmtFormula),
1904		clause_to_smt_disjunction(SatVars, T, SmtFormula, SmtDisj).
1905
1906		clause_to_smt_disjunction(_, [], Acc, Acc).
1907		clause_to_smt_disjunction(SatVars, [Pol-_-SatVarName|T], Acc, SmtDisj) :-
1908		get_smt_formula_from_vars_for_sat_pol(SatVars, SatVarName, Pol, SmtFormula),
1909		NAcc = b(disjunct(SmtFormula,Acc),pred,[]),
1910		clause_to_smt_disjunction(SatVars, T, NAcc, SmtDisj).
1911		*/
1912
1913		/*
1914		% Remove half of the clauses every "frequency_constant + constant_factor * x" conflicts,
1915		% where x is the amount of clause reductions so far. We keep clauses with a small LBD forever.
1916		possibly_discard_learned_clauses :-
1917		conflict_stats(_, _, since_reduction(SRed)),
1918		cdclt_settings:discard_learned_clauses_frequency_constant(Frequency),
1919		SRed >= Frequency, % first check to improve performance
1920		amount_clause_reductions(Reductions),
1921		cdclt_settings:discard_learned_clauses_constant_factor(Factor),
1922		Threshold is Frequency + Factor * Reductions,
1923		SRed == Threshold,
1924		!,
1925		log_set_of_learned_clauses_reduction,
1926		debug_format_sat("~nDiscard half of learned clauses..", []),
1927		cdclt_settings:discard_clause_greater_lbd(LbdLimit),
1928		amount_learned_clauses(ALC),
1929		Half is ALC // 2,
1930		NReductions is Reductions + 1,
1931		retract(amount_clause_reductions(_)),
1932		asserta(amount_clause_reductions(NReductions)),
1933		discard_half_of_learned_clauses_greater_lbd(0, Half, LbdLimit, Removed),
1934		log_forgotten_clauses(Removed),
1935		retract(amount_learned_clauses(Old)),
1936		New is Old - Removed,
1937		asserta(amount_learned_clauses(New)),
1938		retract(conflict_stats(total(Total), since_restart(SRRed), _)),
1939		asserta(conflict_stats(total(Total), since_restart(SRRed), since_reduction(0))), !.
1940		possibly_discard_learned_clauses.
1941		% Remove half of the clauses learned so far.
1942		% We keep clauses with an LBD smaller than cdclt_settings:discard_clause_greater_lbd/1
1943		% forever. Thus it is not guaranteed that exactly half of the clauses are deleted if
1944		% a lot of high quality clauses have been learned.
1945		discard_half_of_learned_clauses_greater_lbd(C, Half, LbdLimit, Removed) :-
1946		C =< Half,
1947		retract(backjump_clause(BjLevel, BjClause, LbdScore, BjSatVars, UsedVars, AC)),
1948		!,
1949		( LbdScore > LbdLimit
1950		-> C1 is C + 1,
1951		discard_half_of_learned_clauses_greater_lbd(C1, Half, LbdLimit, Removed)
1952		; discard_half_of_learned_clauses_greater_lbd(C, Half, LbdLimit, Removed),
1953		asserta(backjump_clause(BjLevel, BjClause, LbdScore, BjSatVars, UsedVars, AC))
1954		).
1955		discard_half_of_learned_clauses_greater_lbd(C, _, _, C).
1956		*/