YES

Problem 1: 

Infeasibility Problem:
[(VAR vNonEmpty vNonEmpty)
(STRATEGY CONTEXTSENSITIVE
(a)
(b)
(c)
(fSNonEmpty)
)
(RULES
a -> b
a -> c
b -> c | b ->* c
)
]

Infeasibility Conditions:
b ->* c

Problem 1: 

Obtaining a model using Mace4:

 -> Usable Rules:
b -> c | b ->* c

 -> Mace4 Output:
============================== Mace4 =================================
Mace4 (64) version 2009-11A, November 2009.
Process 3355955 was started by sandbox2 on z002.star.cs.uiowa.edu,
Tue Jul 30 09:32:55 2024
The command was "./mace4 -c -f /tmp/mace43355942-2.in".
============================== end of head ===========================

============================== INPUT =================================

% Reading from file /tmp/mace43355942-2.in

assign(max_seconds,100).

formulas(assumptions).
->*(b,c) -> ->(b,c) # label(replacement).
->*(x,x) # label(reflexivity).
->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
end_of_list.

formulas(goals).
->*(b,c) # label(goal).
end_of_list.

============================== end of input ==========================

============================== PROCESS NON-CLAUSAL FORMULAS ==========

% Formulas that are not ordinary clauses:
1 ->*(b,c) -> ->(b,c) # label(replacement) # label(non_clause).  [assumption].
2 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
3 ->*(b,c) # label(goal) # label(non_clause) # label(goal).  [goal].

============================== end of process non-clausal formulas ===

============================== CLAUSES FOR SEARCH ====================

formulas(mace4_clauses).
-->*(b,c) | ->(b,c) # label(replacement).
->*(x,x) # label(reflexivity).
-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
-->*(b,c) # label(goal).
end_of_list.

============================== end of clauses for search =============

% There are no natural numbers in the input.

============================== DOMAIN SIZE 2 =========================

============================== MODEL =================================

interpretation( 2, [number=1, seconds=0], [

        function(b, [ 0 ]),

        function(c, [ 1 ]),

        relation(->*(_,_), [
			   1, 0,
			   0, 1 ]),

        relation(->(_,_), [
			   0, 0,
			   0, 0 ])
]).

============================== end of model ==========================

============================== STATISTICS ============================

For domain size 2.

Current CPU time: 0.00 seconds (total CPU time: 0.01 seconds).
Ground clauses: seen=12, kept=8.
Selections=4, assignments=4, propagations=6, current_models=1.
Rewrite_terms=6, rewrite_bools=12, indexes=2.
Rules_from_neg_clauses=1, cross_offs=1.

============================== end of statistics =====================

User_CPU=0.01, System_CPU=0.00, Wall_clock=0.

Exiting with 1 model.

Process 3355955 exit (max_models) Tue Jul 30 09:32:55 2024
The process finished Tue Jul 30 09:32:55 2024


Mace4 cooked interpretation:

% number = 1
% seconds = 0

% Interpretation of size 2

b = 0.

c = 1.

  ->*(0,0).
- ->*(0,1).
- ->*(1,0).
  ->*(1,1).

- ->(0,0).
- ->(0,1).
- ->(1,0).
- ->(1,1).


The problem is infeasible.