# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_nums_0))))&![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))))))),file('i/f/arithmetic/FORALL__NUM__THM', ch4s_arithmetics_FORALLu_u_NUMu_u_THM)).
fof(2, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/arithmetic/FORALL__NUM__THM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_nums_0))))&![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))))))=>![X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/FORALL__NUM__THM', ah4s_nums_INDUCTION)).
fof(14, axiom,![X1]:(?[X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))=>?[X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))&![X16]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X2))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X16)))))))),file('i/f/arithmetic/FORALL__NUM__THM', ah4s_arithmetics_WOP)).
fof(20, axiom,![X7]:![X1]:(~(?[X8]:p(s(t_bool,happ(s(t_fun(X7,t_bool),X1),s(X7,X8)))))<=>![X8]:~(p(s(t_bool,happ(s(t_fun(X7,t_bool),X1),s(X7,X8)))))),file('i/f/arithmetic/FORALL__NUM__THM', ah4s_bools_NOTu_u_EXISTSu_u_THM)).
fof(21, axiom,![X7]:![X21]:![X1]:(?[X8]:(s(X7,X8)=s(X7,X21)&p(s(t_bool,happ(s(t_fun(X7,t_bool),X1),s(X7,X8)))))<=>p(s(t_bool,happ(s(t_fun(X7,t_bool),X1),s(X7,X21))))),file('i/f/arithmetic/FORALL__NUM__THM', ah4s_bools_UNWINDu_u_THM2)).
# SZS output end CNFRefutation
