# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/integer/EQ__ADDL', ch4s_integers_EQu_u_ADDL)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integer/EQ__ADDL', aHLu_FALSITY)).
fof(22, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,X14),file('i/f/integer/EQ__ADDL', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(23, axiom,![X15]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))),file('i/f/integer/EQ__ADDL', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(24, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X15),file('i/f/integer/EQ__ADDL', ah4s_numerals_numeralu_u_distribu_c1)).
fof(25, axiom,![X15]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/integer/EQ__ADDL', ah4s_numerals_numeralu_u_distribu_c27)).
fof(26, axiom,![X15]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))),file('i/f/integer/EQ__ADDL', ah4s_arithmetics_ADDu_u_SYM)).
fof(29, axiom,![X15]:![X14]:(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,X15)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))))),file('i/f/integer/EQ__ADDL', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(30, axiom,![X13]:![X15]:![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X13))),file('i/f/integer/EQ__ADDL', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(33, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/integer/EQ__ADDL', aHLu_BOOLu_CASES)).
fof(37, axiom,p(s(t_bool,t)),file('i/f/integer/EQ__ADDL', aHLu_TRUTH)).
# SZS output end CNFRefutation
