# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/TC__eq__NRC', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/TC__eq__NRC', aHLu_FALSITY)).
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/TC__eq__NRC', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(14, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/TC__eq__NRC', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(35, axiom,![X9]:![X18]:![X6]:![X19]:(p(s(t_bool,h4s_relations_tc(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(X9,X6),s(X9,X18))))<=>?[X10]:(p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(X9,X6))),s(X9,X10))))&p(s(t_bool,h4s_relations_rtc(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(X9,X10),s(X9,X18)))))),file('i/f/arithmetic/TC__eq__NRC', ah4s_relations_EXTENDu_u_RTCu_u_TCu_u_EQN)).
fof(36, axiom,![X9]:![X10]:![X6]:![X20]:![X19]:(p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20))),s(X9,X6),s(X9,X10))))<=>?[X18]:(p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(X9,X6))),s(X9,X18))))&p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(t_h4s_nums_num,X20),s(X9,X18),s(X9,X10)))))),file('i/f/arithmetic/TC__eq__NRC', ah4s_arithmetics_NRC0u_c1)).
fof(37, axiom,![X9]:![X10]:![X6]:![X19]:(p(s(t_bool,h4s_relations_rtc(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(X9,X6),s(X9,X10))))<=>?[X20]:p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(t_h4s_nums_num,X20),s(X9,X6),s(X9,X10))))),file('i/f/arithmetic/TC__eq__NRC', ah4s_arithmetics_RTCu_u_equ_u_NRC)).
fof(38, conjecture,![X9]:![X10]:![X6]:![X19]:(p(s(t_bool,h4s_relations_tc(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(X9,X6),s(X9,X10))))<=>?[X20]:p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(X9,t_fun(X9,t_bool)),X19),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20))),s(X9,X6),s(X9,X10))))),file('i/f/arithmetic/TC__eq__NRC', ch4s_arithmetics_TCu_u_equ_u_NRC)).
# SZS output end CNFRefutation
