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 y:S)
0.00/0.03	(RULES
0.00/0.03	pin(x:S) -> pout(f(y:S)) | pin(x:S) ->* pout(g(y:S))
0.00/0.03	pin(x:S) -> pout(g(x:S))
0.00/0.03	)
0.00/0.03	
0.00/0.03	Infeasibility Conditions:
0.00/0.03	pin(x1:S) ->* pout(g(x2:S))
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 35362 was started by sandbox on n002.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(f5(x1),f5(y)) # label(congruence).
0.00/0.03	arrow_s0(x1,y) -> arrow_s0(f6(x1),f6(y)) # label(congruence).
0.00/0.03	arrowStar_s0(f2(x1),f6(f5(x2))) -> arrow_s0(f2(x1),f6(f3(x2))) # label(repacement).
0.00/0.03	arrow_s0(f2(x1),f6(f5(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 x4 exists x5 arrowStar_s0(f2(x5),f6(f5(x4)))) # 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(f5(x1),f5(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	5 arrow_s0(x1,y) -> arrow_s0(f6(x1),f6(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	6 arrowStar_s0(f2(x1),f6(f5(x2))) -> arrow_s0(f2(x1),f6(f3(x2))) # label(repacement) # label(non_clause).  [assumption].
0.00/0.03	7 (exists x4 exists x5 arrowStar_s0(f2(x5),f6(f5(x4)))) # 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(f5(x),f5(y)) # label(congruence).  [clausify(4)].
0.00/0.03	-arrow_s0(x,y) | arrow_s0(f6(x),f6(y)) # label(congruence).  [clausify(5)].
0.00/0.03	-arrowStar_s0(f2(x),f6(f5(y))) | arrow_s0(f2(x),f6(f3(y))) # label(repacement).  [clausify(6)].
0.00/0.03	arrow_s0(f2(x),f6(f5(x))) # label(repacement).  [assumption].
0.00/0.03	-arrowStar_s0(f2(x),f6(f5(y))) # 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([ f2, f6, f5, f3 ]).
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=-4)
0.00/0.03	  % clear(ordered_res).  % (HNE depth_diff=-4)
0.00/0.03	  % set(ur_resolution).  % (HNE depth_diff=-4)
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(f5(x),f5(y)) # label(congruence).  [clausify(4)].
0.00/0.03	kept:      13 -arrow_s0(x,y) | arrow_s0(f6(x),f6(y)) # label(congruence).  [clausify(5)].
0.00/0.03	kept:      14 -arrowStar_s0(f2(x),f6(f5(y))) | arrow_s0(f2(x),f6(f3(y))) # label(repacement).  [clausify(6)].
0.00/0.03	kept:      15 arrow_s0(f2(x),f6(f5(x))) # label(repacement).  [assumption].
0.00/0.03	kept:      16 -arrowStar_s0(f2(x),f6(f5(y))) # 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(f5(x),f5(y)) # label(congruence).  [clausify(4)].
0.00/0.03	13 -arrow_s0(x,y) | arrow_s0(f6(x),f6(y)) # label(congruence).  [clausify(5)].
0.00/0.03	15 arrow_s0(f2(x),f6(f5(x))) # label(repacement).  [assumption].
0.00/0.03	16 -arrowStar_s0(f2(x),f6(f5(y))) # 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(f5(x),f5(y)) # label(congruence).  [clausify(4)].
0.00/0.03	
0.00/0.03	given #6 (I,wt=8): 13 -arrow_s0(x,y) | arrow_s0(f6(x),f6(y)) # label(congruence).  [clausify(5)].
0.00/0.03	
0.00/0.03	given #7 (I,wt=6): 15 arrow_s0(f2(x),f6(f5(x))) # label(repacement).  [assumption].
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 8.
0.00/0.03	% Level of proof is 3.
0.00/0.03	% Maximum clause weight is 9.000.
0.00/0.03	% Given clauses 7.
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	7 (exists x4 exists x5 arrowStar_s0(f2(x5),f6(f5(x4)))) # 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	15 arrow_s0(f2(x),f6(f5(x))) # label(repacement).  [assumption].
0.00/0.03	16 -arrowStar_s0(f2(x),f6(f5(y))) # label(goal) # answer(goal).  [deny(7)].
0.00/0.03	21 arrowStar_s0(f2(x),f6(f5(x))).  [ur(9,a,15,a,b,8,a)].
0.00/0.03	22 $F # answer(goal).  [resolve(21,a,16,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=7. Generated=14. Kept=14. proofs=1.
0.00/0.03	Usable=7. Sos=1. Demods=0. Limbo=4, Disabled=10. Hints=0.
0.00/0.03	Kept_by_rule=0, Deleted_by_rule=0.
0.00/0.03	Forward_subsumed=0. Back_subsumed=1.
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=8.
0.00/0.03	Megabytes=0.06.
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 35362 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.
0.00/20.09	EOF