# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))))))=>![X3]:?[X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X2))))))),file('i/f/arithmetic/STRICTLY__INCREASING__UNBOUNDED', ch4s_arithmetics_STRICTLYu_u_INCREASINGu_u_UNBOUNDED)).
fof(2, axiom,~(p(s(t_bool,f0))),file('i/f/arithmetic/STRICTLY__INCREASING__UNBOUNDED', aHLu_FALSITY)).
fof(20, axiom,![X1]:(![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))))))=>p(s(t_bool,h4s_bools_oneu_u_one(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1))))),file('i/f/arithmetic/STRICTLY__INCREASING__UNBOUNDED', ah4s_arithmetics_STRICTLYu_u_INCREASINGu_u_ONEu_u_ONE)).
fof(21, axiom,![X1]:(p(s(t_bool,h4s_bools_oneu_u_one(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1))))=>![X3]:?[X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X2))))))),file('i/f/arithmetic/STRICTLY__INCREASING__UNBOUNDED', ah4s_arithmetics_ONEu_u_ONEu_u_UNBOUNDED)).
fof(23, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f0)),file('i/f/arithmetic/STRICTLY__INCREASING__UNBOUNDED', aHLu_BOOLu_CASES)).
fof(25, axiom,p(s(t_bool,t)),file('i/f/arithmetic/STRICTLY__INCREASING__UNBOUNDED', aHLu_TRUTH)).
fof(27, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/arithmetic/STRICTLY__INCREASING__UNBOUNDED', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
