# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:?[X2]:((p(s(t_bool,X2))<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))&s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,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))))),s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/arithmetic/ZERO__EXP', ch4s_arithmetics_ZEROu_u_EXP)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/ZERO__EXP', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/ZERO__EXP', aHLu_FALSITY)).
fof(10, axiom,![X6]:![X4]:![X5]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X5),s(X6,X4)))=s(X6,X5),file('i/f/arithmetic/ZERO__EXP', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(11, axiom,![X6]:![X4]:![X5]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X5),s(X6,X4)))=s(X6,X4),file('i/f/arithmetic/ZERO__EXP', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(15, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_MULTu_c0)).
fof(16, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_nums_0)))=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/arithmetic/ZERO__EXP', ah4s_arithmetics_EXP0u_c0)).
fof(17, axiom,![X14]:(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0)|?[X13]:s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_numu_u_CASES)).
fof(18, axiom,![X13]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_EXP0u_c1)).
# SZS output end CNFRefutation
