# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/NRC__1', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/NRC__1', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/NRC__1', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/arithmetic/NRC__1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X9]:![X12]:![X6]:![X13]:(p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(X9,t_fun(X9,t_bool)),X13),s(t_h4s_nums_num,h4s_nums_0),s(X9,X6),s(X9,X12))))<=>s(X9,X6)=s(X9,X12)),file('i/f/arithmetic/NRC__1', ah4s_arithmetics_NRC0u_c0)).
fof(10, axiom,![X9]:![X12]:![X6]:![X14]:![X13]:(p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(X9,t_fun(X9,t_bool)),X13),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(X9,X6),s(X9,X12))))<=>?[X15]:(p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X13),s(X9,X6))),s(X9,X15))))&p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(X9,t_fun(X9,t_bool)),X13),s(t_h4s_nums_num,X14),s(X9,X15),s(X9,X12)))))),file('i/f/arithmetic/NRC__1', ah4s_arithmetics_NRC0u_c1)).
fof(11, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/NRC__1', ah4s_arithmetics_ONE)).
fof(12, conjecture,![X9]:![X12]:![X6]:![X13]:s(t_bool,h4s_arithmetics_nrc(s(t_fun(X9,t_fun(X9,t_bool)),X13),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(X9,X6),s(X9,X12)))=s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X13),s(X9,X6))),s(X9,X12))),file('i/f/arithmetic/NRC__1', ch4s_arithmetics_NRCu_u_1)).
# SZS output end CNFRefutation
