# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUB__ELIM__THM', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUB__ELIM__THM', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/SUB__ELIM__THM', aHLu_BOOLu_CASES)).
fof(10, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/SUB__ELIM__THM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X11]:![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))),file('i/f/arithmetic/SUB__ELIM__THM', ah4s_arithmetics_ADDu_u_SYM)).
fof(14, axiom,![X11]:![X12]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))))),file('i/f/arithmetic/SUB__ELIM__THM', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(16, axiom,![X11]:![X12]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,X12)<=>s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/SUB__ELIM__THM', ah4s_arithmetics_ADDu_u_INVu_u_0u_u_EQ)).
fof(18, axiom,![X14]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,X15),file('i/f/arithmetic/SUB__ELIM__THM', ah4s_arithmetics_ADDu_u_SUB)).
fof(19, axiom,![X11]:![X12]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))))),file('i/f/arithmetic/SUB__ELIM__THM', ah4s_arithmetics_LESSu_u_EQu_u_CASES)).
fof(20, axiom,![X11]:![X12]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))))<=>?[X13]:s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X13)))),file('i/f/arithmetic/SUB__ELIM__THM', ah4s_arithmetics_LESSu_u_EQu_u_EXISTS)).
fof(21, conjecture,![X16]:![X15]:![X17]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X17),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X16))))))<=>![X18]:((s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X18)))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X17),s(t_h4s_nums_num,h4s_nums_0)))))&(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X18)))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X17),s(t_h4s_nums_num,X18))))))),file('i/f/arithmetic/SUB__ELIM__THM', ch4s_arithmetics_SUBu_u_ELIMu_u_THM)).
# SZS output end CNFRefutation
