0.00/0.03	NO
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	Infeasibility Problem:
0.00/0.03	(VAR vNonEmpty:S x:S)
0.00/0.03	(RULES
0.00/0.03	p(s(x:S)) -> x:S
0.00/0.03	pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
0.00/0.03	pos(s(0)) -> ttrue
0.00/0.03	pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue
0.00/0.03	pos(0) -> ffalse
0.00/0.03	s(p(x:S)) -> x:S
0.00/0.03	)
0.00/0.03	
0.00/0.03	Infeasibility Conditions:
0.00/0.03	pos(p(x:S)) ->* ttrue
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	Obtaining a proof using Prover9. Prover9 Output:
0.00/0.03	============================== Prover9 ===============================
0.00/0.03	Prover9 (64) version 2009-11A, November 2009.
0.00/0.03	Process 11100 was started by sandbox on n005.star.cs.uiowa.edu,
0.00/0.03	Thu Jun 11 09:56:51 2020
0.00/0.03	The command was "./prover9 -f /tmp/prover91804289383846930886.in".
0.00/0.03	============================== end of head ===========================
0.00/0.03	
0.00/0.03	============================== INPUT =================================
0.00/0.03	
0.00/0.03	% Reading from file /tmp/prover91804289383846930886.in
0.00/0.03	
0.00/0.03	assign(max_seconds,300).
0.00/0.03	
0.00/0.03	formulas(assumptions).
0.00/0.03	arrowStar_s0(x,x) # label(reflexivity).
0.00/0.03	arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(transitivity).
0.00/0.03	arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence).
0.00/0.03	arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence).
0.00/0.03	arrow_s0(x1,y) -> arrow_s0(f4(x1),f4(y)) # label(congruence).
0.00/0.03	arrow_s0(f2(f4(x1)),x1) # label(repacement).
0.00/0.03	arrowStar_s0(f3(x1),f7) -> arrow_s0(f3(f2(x1)),f7) # label(repacement).
0.00/0.03	arrow_s0(f3(f4(f5)),f8) # label(repacement).
0.00/0.03	arrowStar_s0(f3(x1),f8) -> arrow_s0(f3(f4(x1)),f8) # label(repacement).
0.00/0.03	arrow_s0(f3(f5),f7) # label(repacement).
0.00/0.03	arrow_s0(f4(f2(x1)),x1) # label(repacement).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	formulas(goals).
0.00/0.03	(exists x3 arrowStar_s0(f3(f2(x3)),f8)) # label(goal).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	============================== end of input ==========================
0.00/0.03	
0.00/0.03	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.00/0.03	
0.00/0.03	% Formulas that are not ordinary clauses:
0.00/0.03	1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(transitivity) # label(non_clause).  [assumption].
0.00/0.03	2 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	3 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	4 arrow_s0(x1,y) -> arrow_s0(f4(x1),f4(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	5 arrowStar_s0(f3(x1),f7) -> arrow_s0(f3(f2(x1)),f7) # label(repacement) # label(non_clause).  [assumption].
0.00/0.03	6 arrowStar_s0(f3(x1),f8) -> arrow_s0(f3(f4(x1)),f8) # label(repacement) # label(non_clause).  [assumption].
0.00/0.03	7 (exists x3 arrowStar_s0(f3(f2(x3)),f8)) # label(goal) # label(non_clause) # label(goal).  [goal].
0.00/0.03	
0.00/0.03	============================== end of process non-clausal formulas ===
0.00/0.03	
0.00/0.03	============================== PROCESS INITIAL CLAUSES ===============
0.00/0.03	
0.00/0.03	% Clauses before input processing:
0.00/0.03	
0.00/0.03	formulas(usable).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	formulas(sos).
0.00/0.03	arrowStar_s0(x,x) # label(reflexivity).  [assumption].
0.00/0.03	-arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(transitivity).  [clausify(1)].
0.00/0.03	-arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence).  [clausify(2)].
0.00/0.03	-arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).  [clausify(3)].
0.00/0.03	-arrow_s0(x,y) | arrow_s0(f4(x),f4(y)) # label(congruence).  [clausify(4)].
0.00/0.03	arrow_s0(f2(f4(x)),x) # label(repacement).  [assumption].
0.00/0.03	-arrowStar_s0(f3(x),f7) | arrow_s0(f3(f2(x)),f7) # label(repacement).  [clausify(5)].
0.00/0.03	arrow_s0(f3(f4(f5)),f8) # label(repacement).  [assumption].
0.00/0.03	-arrowStar_s0(f3(x),f8) | arrow_s0(f3(f4(x)),f8) # label(repacement).  [clausify(6)].
0.00/0.03	arrow_s0(f3(f5),f7) # label(repacement).  [assumption].
0.00/0.03	arrow_s0(f4(f2(x)),x) # label(repacement).  [assumption].
0.00/0.03	-arrowStar_s0(f3(f2(x)),f8) # label(goal).  [deny(7)].
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	formulas(demodulators).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	============================== PREDICATE ELIMINATION =================
0.00/0.03	
0.00/0.03	No predicates eliminated.
0.00/0.03	
0.00/0.03	============================== end predicate elimination =============
0.00/0.03	
0.00/0.03	Auto_denials:
0.00/0.03	  % copying label goal to answer in negative clause
0.00/0.03	
0.00/0.03	Term ordering decisions:
0.00/0.03	Predicate symbol precedence:  predicate_order([ arrow_s0, arrowStar_s0 ]).
0.00/0.03	Function symbol precedence:  function_order([ f7, f8, f5, f3, f4, f2 ]).
0.00/0.03	After inverse_order:  (no changes).
0.00/0.03	Unfolding symbols: (none).
0.00/0.03	
0.00/0.03	Auto_inference settings:
0.00/0.03	  % set(neg_binary_resolution).  % (HNE depth_diff=-5)
0.00/0.03	  % clear(ordered_res).  % (HNE depth_diff=-5)
0.00/0.03	  % set(ur_resolution).  % (HNE depth_diff=-5)
0.00/0.03	    % set(ur_resolution) -> set(pos_ur_resolution).
0.00/0.03	    % set(ur_resolution) -> set(neg_ur_resolution).
0.00/0.03	
0.00/0.03	Auto_process settings:  (no changes).
0.00/0.03	
0.00/0.03	kept:      8 arrowStar_s0(x,x) # label(reflexivity).  [assumption].
0.00/0.03	kept:      9 -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(transitivity).  [clausify(1)].
0.00/0.03	kept:      10 -arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence).  [clausify(2)].
0.00/0.03	kept:      11 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).  [clausify(3)].
0.00/0.03	kept:      12 -arrow_s0(x,y) | arrow_s0(f4(x),f4(y)) # label(congruence).  [clausify(4)].
0.00/0.03	kept:      13 arrow_s0(f2(f4(x)),x) # label(repacement).  [assumption].
0.00/0.03	kept:      14 -arrowStar_s0(f3(x),f7) | arrow_s0(f3(f2(x)),f7) # label(repacement).  [clausify(5)].
0.00/0.03	kept:      15 arrow_s0(f3(f4(f5)),f8) # label(repacement).  [assumption].
0.00/0.03	kept:      16 -arrowStar_s0(f3(x),f8) | arrow_s0(f3(f4(x)),f8) # label(repacement).  [clausify(6)].
0.00/0.03	kept:      17 arrow_s0(f3(f5),f7) # label(repacement).  [assumption].
0.00/0.03	kept:      18 arrow_s0(f4(f2(x)),x) # label(repacement).  [assumption].
0.00/0.03	kept:      19 -arrowStar_s0(f3(f2(x)),f8) # label(goal) # answer(goal).  [deny(7)].
0.00/0.03	
0.00/0.03	============================== end of process initial clauses ========
0.00/0.03	
0.00/0.03	============================== CLAUSES FOR SEARCH ====================
0.00/0.03	
0.00/0.03	% Clauses after input processing:
0.00/0.03	
0.00/0.03	formulas(usable).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	formulas(sos).
0.00/0.03	8 arrowStar_s0(x,x) # label(reflexivity).  [assumption].
0.00/0.03	9 -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(transitivity).  [clausify(1)].
0.00/0.03	10 -arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence).  [clausify(2)].
0.00/0.03	11 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).  [clausify(3)].
0.00/0.03	12 -arrow_s0(x,y) | arrow_s0(f4(x),f4(y)) # label(congruence).  [clausify(4)].
0.00/0.03	13 arrow_s0(f2(f4(x)),x) # label(repacement).  [assumption].
0.00/0.03	14 -arrowStar_s0(f3(x),f7) | arrow_s0(f3(f2(x)),f7) # label(repacement).  [clausify(5)].
0.00/0.03	15 arrow_s0(f3(f4(f5)),f8) # label(repacement).  [assumption].
0.00/0.03	16 -arrowStar_s0(f3(x),f8) | arrow_s0(f3(f4(x)),f8) # label(repacement).  [clausify(6)].
0.00/0.03	17 arrow_s0(f3(f5),f7) # label(repacement).  [assumption].
0.00/0.03	18 arrow_s0(f4(f2(x)),x) # label(repacement).  [assumption].
0.00/0.03	19 -arrowStar_s0(f3(f2(x)),f8) # label(goal) # answer(goal).  [deny(7)].
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	formulas(demodulators).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	============================== end of clauses for search =============
0.00/0.03	
0.00/0.03	============================== SEARCH ================================
0.00/0.03	
0.00/0.03	% Starting search at 0.00 seconds.
0.00/0.03	
0.00/0.03	given #1 (I,wt=3): 8 arrowStar_s0(x,x) # label(reflexivity).  [assumption].
0.00/0.03	
0.00/0.03	given #2 (I,wt=9): 9 -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(transitivity).  [clausify(1)].
0.00/0.03	
0.00/0.03	given #3 (I,wt=8): 10 -arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence).  [clausify(2)].
0.00/0.03	
0.00/0.03	given #4 (I,wt=8): 11 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).  [clausify(3)].
0.00/0.03	
0.00/0.03	given #5 (I,wt=8): 12 -arrow_s0(x,y) | arrow_s0(f4(x),f4(y)) # label(congruence).  [clausify(4)].
0.00/0.03	
0.00/0.03	given #6 (I,wt=5): 13 arrow_s0(f2(f4(x)),x) # label(repacement).  [assumption].
0.00/0.03	
0.00/0.03	given #7 (I,wt=9): 14 -arrowStar_s0(f3(x),f7) | arrow_s0(f3(f2(x)),f7) # label(repacement).  [clausify(5)].
0.00/0.03	
0.00/0.03	given #8 (I,wt=5): 15 arrow_s0(f3(f4(f5)),f8) # label(repacement).  [assumption].
0.00/0.03	
0.00/0.03	given #9 (I,wt=9): 16 -arrowStar_s0(f3(x),f8) | arrow_s0(f3(f4(x)),f8) # label(repacement).  [clausify(6)].
0.00/0.03	
0.00/0.03	given #10 (I,wt=4): 17 arrow_s0(f3(f5),f7) # label(repacement).  [assumption].
0.00/0.03	
0.00/0.03	given #11 (I,wt=5): 18 arrow_s0(f4(f2(x)),x) # label(repacement).  [assumption].
0.00/0.03	
0.00/0.03	given #12 (I,wt=5): 19 -arrowStar_s0(f3(f2(x)),f8) # label(goal) # answer(goal).  [deny(7)].
0.00/0.03	
0.00/0.03	given #13 (A,wt=7): 20 arrow_s0(f3(f2(f4(x))),f3(x)).  [ur(11,a,13,a)].
0.00/0.03	
0.00/0.03	============================== PROOF =================================
0.00/0.03	
0.00/0.03	% Proof 1 at 0.00 (+ 0.00) seconds: goal.
0.00/0.03	% Length of proof is 13.
0.00/0.03	% Level of proof is 4.
0.00/0.03	% Maximum clause weight is 9.000.
0.00/0.03	% Given clauses 13.
0.00/0.03	
0.00/0.03	1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(transitivity) # label(non_clause).  [assumption].
0.00/0.03	3 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	7 (exists x3 arrowStar_s0(f3(f2(x3)),f8)) # label(goal) # label(non_clause) # label(goal).  [goal].
0.00/0.03	8 arrowStar_s0(x,x) # label(reflexivity).  [assumption].
0.00/0.03	9 -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(transitivity).  [clausify(1)].
0.00/0.03	11 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).  [clausify(3)].
0.00/0.03	13 arrow_s0(f2(f4(x)),x) # label(repacement).  [assumption].
0.00/0.03	15 arrow_s0(f3(f4(f5)),f8) # label(repacement).  [assumption].
0.00/0.03	19 -arrowStar_s0(f3(f2(x)),f8) # label(goal) # answer(goal).  [deny(7)].
0.00/0.03	20 arrow_s0(f3(f2(f4(x))),f3(x)).  [ur(11,a,13,a)].
0.00/0.03	26 arrowStar_s0(f3(f4(f5)),f8).  [ur(9,a,15,a,b,8,a)].
0.00/0.03	40 -arrowStar_s0(f3(x),f8) # answer(goal).  [ur(9,a,20,a,c,19,a)].
0.00/0.03	41 $F # answer(goal).  [resolve(40,a,26,a)].
0.00/0.03	
0.00/0.03	============================== end of proof ==========================
0.00/0.03	
0.00/0.03	============================== STATISTICS ============================
0.00/0.03	
0.00/0.03	Given=13. Generated=35. Kept=33. proofs=1.
0.00/0.03	Usable=13. Sos=15. Demods=0. Limbo=4, Disabled=12. Hints=0.
0.00/0.03	Kept_by_rule=0, Deleted_by_rule=0.
0.00/0.03	Forward_subsumed=2. Back_subsumed=0.
0.00/0.03	Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
0.00/0.03	New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
0.00/0.03	Demod_attempts=0. Demod_rewrites=0.
0.00/0.03	Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
0.00/0.03	Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=9.
0.00/0.03	Megabytes=0.09.
0.00/0.03	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
0.00/0.03	
0.00/0.03	============================== end of statistics =====================
0.00/0.03	
0.00/0.03	============================== end of search =========================
0.00/0.03	
0.00/0.03	THEOREM PROVED
0.00/0.03	
0.00/0.03	Exiting with 1 proof.
0.00/0.03	
0.00/0.03	Process 11100 exit (max_proofs) Thu Jun 11 09:56:51 2020
0.00/0.03	
0.00/0.03	
0.00/0.03	The problem is feasible.
0.00/20.08	EOF