# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_nums_0))))&(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,h4s_nums_0))))))&![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))))))=>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,h4s_nums_suc(s(t_h4s_nums_num,X2)))))))))))=>![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X3))))),file('i/f/rat/rat__of__num__ind', ch4s_rats_ratu_u_ofu_u_numu_u_ind)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/rat/rat__of__num__ind', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(38, 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/rat/rat__of__num__ind', ah4s_nums_INDUCTION)).
fof(42, axiom,![X23]:(s(t_h4s_nums_num,X23)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X23)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/rat/rat__of__num__ind', ah4s_arithmetics_numu_u_CASES)).
# SZS output end CNFRefutation
