# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))))<=>((s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))|((s(t_h4s_nums_num,X3)=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,X2)))))|(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))|(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,X3))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ch4s_arithmetics_EXPu_u_BASEu_u_LEu_u_IFF)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(24, axiom,![X3]:(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,X3))))=>![X1]:![X2]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_EXPu_u_BASEu_u_LEu_u_MONO)).
fof(27, axiom,![X1]:![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_LESSu_u_EQ)).
fof(31, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X2),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(32, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_LESSu_u_CASES)).
fof(33, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(36, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(38, axiom,![X1]:(~(s(t_h4s_nums_num,X1)=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,X1))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(39, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(42, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))=>~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_primu_u_recs_LESSu_u_NOTu_u_EQ)).
fof(43, 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/EXP__BASE__LE__IFF', ah4s_arithmetics_ONE)).
fof(50, axiom,![X16]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X16)))=s(t_h4s_nums_num,X16),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(52, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_ALTu_u_ZERO)).
fof(55, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,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,X1)=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,h4s_nums_0))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_EXPu_u_EQu_u_1)).
fof(57, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X1)=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,X2)))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_EXPu_u_EQu_u_0)).
fof(58, axiom,![X14]:![X16]:(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,X16),s(t_h4s_nums_num,X14))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X16))))|s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_ZEROu_u_LTu_u_EXP)).
fof(60, axiom,![X1]: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,X1)))=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/EXP__BASE__LE__IFF', ah4s_arithmetics_EXPu_u_1u_c0)).
fof(61, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X2),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/EXP__BASE__LE__IFF', ah4s_arithmetics_EXP0u_c0)).
fof(63, axiom,![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_numu_u_CASES)).
fof(88, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
