# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:?[X5]:((p(s(t_bool,X5))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0))&s(X1,h4s_indu_u_types_fcons(s(X1,X4),s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,X2)))=s(X1,h4s_bools_cond(s(t_bool,X5),s(X1,X4),s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))),file('i/f/ind_type/FCONS__DEST', ch4s_indu_u_types_FCONSu_u_DEST)).
fof(4, axiom,![X1]:![X9]:![X10]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X10),s(X1,X9)))=s(X1,X10),file('i/f/ind_type/FCONS__DEST', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(5, axiom,![X1]:![X9]:![X10]:s(X1,h4s_bools_cond(s(t_bool,f0),s(X1,X10),s(X1,X9)))=s(X1,X9),file('i/f/ind_type/FCONS__DEST', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(22, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/ind_type/FCONS__DEST', ah4s_arithmetics_SUBu_c0)).
fof(23, axiom,![X2]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X15))),file('i/f/ind_type/FCONS__DEST', ah4s_arithmetics_SUBu_u_MONOu_u_EQ)).
fof(24, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X15),file('i/f/ind_type/FCONS__DEST', ah4s_arithmetics_SUBu_u_0u_c1)).
fof(28, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/ind_type/FCONS__DEST', ah4s_arithmetics_ONE)).
fof(31, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/ind_type/FCONS__DEST', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(33, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/ind_type/FCONS__DEST', ah4s_arithmetics_ALTu_u_ZERO)).
fof(34, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/ind_type/FCONS__DEST', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(53, axiom,![X1]:![X3]:![X4]:s(X1,h4s_indu_u_types_fcons(s(X1,X4),s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_nums_0)))=s(X1,X4),file('i/f/ind_type/FCONS__DEST', ah4s_indu_u_types_FCONS0u_c0)).
fof(54, axiom,![X1]:![X2]:![X3]:![X4]:s(X1,h4s_indu_u_types_fcons(s(X1,X4),s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,X2))),file('i/f/ind_type/FCONS__DEST', ah4s_indu_u_types_FCONS0u_c1)).
fof(55, axiom,![X15]:(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/ind_type/FCONS__DEST', ah4s_arithmetics_numu_u_CASES)).
fof(56, axiom,![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))),file('i/f/ind_type/FCONS__DEST', ah4s_primu_u_recs_LESSu_u_0)).
fof(57, axiom,![X2]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/ind_type/FCONS__DEST', ah4s_nums_NOTu_u_SUC)).
fof(58, axiom,![X2]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/ind_type/FCONS__DEST', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(60, axiom,p(s(t_bool,t)),file('i/f/ind_type/FCONS__DEST', aHLu_TRUTH)).
fof(61, axiom,![X21]:(s(t_bool,X21)=s(t_bool,t)|s(t_bool,X21)=s(t_bool,f0)),file('i/f/ind_type/FCONS__DEST', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
