# 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,X1),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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ch4s_arithmetics_Xu_u_LTu_u_EXPu_u_Xu_u_IFF)).
fof(24, axiom,![X17]:(~(s(t_h4s_nums_num,X17)=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,X17))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(25, axiom,![X17]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
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/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_ONE)).
fof(36, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X1),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(37, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(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,X2))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_Xu_u_LTu_u_EXPu_u_X)).
fof(43, axiom,![X17]:![X18]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X18)))=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,X17)=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,X18)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_EXPu_u_EQu_u_1)).
fof(45, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_exp(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,X17)))=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/X__LT__EXP__X__IFF', ah4s_arithmetics_EXPu_u_1u_c0)).
fof(46, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_ALTu_u_ZERO)).
fof(50, axiom,![X17]:![X18]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X17)=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,X18)))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_EXPu_u_EQu_u_0)).
fof(53, axiom,![X17]: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,X17)))))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_primu_u_recs_LESSu_u_0)).
fof(56, axiom,![X18]:(s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_nums_0)|?[X17]:s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_numu_u_CASES)).
fof(58, axiom,![X17]:![X18]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X17))),file('i/f/arithmetic/X__LT__EXP__X__IFF', ah4s_arithmetics_LESSu_u_MONOu_u_EQ)).
# SZS output end CNFRefutation
