# 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))))|?[X3]: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,X3)))))))),file('i/f/arithmetic/EXISTS__NUM', ch4s_arithmetics_EXISTSu_u_NUM)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/EXISTS__NUM', aHLu_FALSITY)).
fof(39, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/arithmetic/EXISTS__NUM', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(56, axiom,![X3]:(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/EXISTS__NUM', ah4s_arithmetics_numu_u_CASES)).
fof(71, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/arithmetic/EXISTS__NUM', aHLu_BOOLu_CASES)).
fof(72, axiom,![X7]:((p(s(t_bool,f))=>p(s(t_bool,X7)))<=>p(s(t_bool,t))),file('i/f/arithmetic/EXISTS__NUM', ah4s_bools_IMPu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
