# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X3))))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X1)))))=>s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X2)))=s(t_h4s_nums_num,X1)),file('i/f/bit/LEAST__THM', ch4s_bits_LEASTu_u_THM)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bit/LEAST__THM', aHLu_FALSITY)).
fof(14, axiom,![X6]:((p(s(t_bool,X6))=>p(s(t_bool,f)))<=>s(t_bool,X6)=s(t_bool,f)),file('i/f/bit/LEAST__THM', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(28, axiom,![X14]:![X1]:![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X14)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X14))))),file('i/f/bit/LEAST__THM', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(33, axiom,![X8]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X8))))=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X2))))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X2))),s(t_h4s_nums_num,X8)))))),file('i/f/bit/LEAST__THM', ah4s_whiles_FULLu_u_LEASTu_u_INTRO)).
fof(35, axiom,![X1]:![X3]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3))))),file('i/f/bit/LEAST__THM', ah4s_arithmetics_NOTu_u_LESS)).
fof(36, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/bit/LEAST__THM', aHLu_BOOLu_CASES)).
fof(39, axiom,![X1]:![X3]:(~(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X1))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X3)))))),file('i/f/bit/LEAST__THM', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(41, axiom,p(s(t_bool,t)),file('i/f/bit/LEAST__THM', aHLu_TRUTH)).
fof(44, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/bit/LEAST__THM', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
