# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![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_arithmetics_exp(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/ZERO__LT__EXP', ch4s_arithmetics_ZEROu_u_LTu_u_EXP)).
fof(3, axiom,![X5]:(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0)|?[X6]:s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6)))),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_arithmetics_numu_u_CASES)).
fof(5, axiom,![X5]:(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,X5)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5))))),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_arithmetics_LESSu_u_0u_u_CASES)).
fof(6, axiom,![X6]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(27, axiom,![X6]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6)))))),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_primu_u_recs_LESSu_u_SUCu_u_REFL)).
fof(28, axiom,![X6]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X6))))),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(37, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X5),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__LT__EXP', ah4s_arithmetics_EXP0u_c0)).
fof(38, axiom,![X6]:![X5]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X6)=s(t_h4s_nums_num,h4s_nums_0)&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5)))))),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_arithmetics_EXPu_u_EQu_u_0)).
fof(41, 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/arithmetic/ZERO__LT__EXP', ah4s_arithmetics_ONE)).
fof(43, axiom,![X6]:![X5]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X6)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_arithmetics_MULTu_u_EQu_u_0)).
fof(51, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_arithmetics_ALTu_u_ZERO)).
fof(75, axiom,![X6]:![X5]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X6))))),file('i/f/arithmetic/ZERO__LT__EXP', ah4s_arithmetics_EXP0u_c1)).
# SZS output end CNFRefutation
