# 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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),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))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/ONE__LT__EXP', ch4s_arithmetics_ONEu_u_LTu_u_EXP)).
fof(2, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(23, axiom,![X16]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(24, axiom,![X16]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X16))))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(26, axiom,![X16]:(~(s(t_h4s_nums_num,X16)=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,X16))))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(27, 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/ONE__LT__EXP', ah4s_arithmetics_ONE)).
fof(28, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X2),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(29, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_ALTu_u_ZERO)).
fof(31, axiom,![X2]:![X18]:(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,X18))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X2))))))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_Xu_u_LTu_u_EXPu_u_X)).
fof(33, axiom,![X2]:![X18]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,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,X18))))|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_Xu_u_LTu_u_EXPu_u_Xu_u_IFF)).
fof(37, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),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/ONE__LT__EXP', ah4s_arithmetics_EXP0u_c0)).
fof(39, axiom,![X16]: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,X16)))=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/ONE__LT__EXP', ah4s_arithmetics_EXPu_u_1u_c0)).
fof(40, axiom,![X16]:![X17]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X16),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,X16)=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_nums_0))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_EXPu_u_EQu_u_1)).
fof(41, axiom,![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/ONE__LT__EXP', ah4s_arithmetics_ZEROu_u_LTu_u_EXP)).
fof(42, axiom,![X16]:![X17]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X16)=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/ONE__LT__EXP', ah4s_arithmetics_EXPu_u_EQu_u_0)).
fof(49, axiom,![X16]:![X17]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X16))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_LESSu_u_EQ)).
fof(55, axiom,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,h4s_nums_0)))))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_primu_u_recs_LESSu_u_0u_u_0)).
fof(58, axiom,![X16]:![X17]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))|s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(61, axiom,![X16]:![X17]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_LESSu_u_CASES)).
fof(63, axiom,![X16]:![X17]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))))),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(74, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ONE__LT__EXP', ah4s_arithmetics_MULTu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
