# 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,p(s(t_bool,t)),file('i/f/arithmetic/EXP__BASE__LE__IFF', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/EXP__BASE__LE__IFF', aHLu_FALSITY)).
fof(17, axiom,![X6]:(s(t_bool,t)=s(t_bool,X6)<=>p(s(t_bool,X6))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(19, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(22, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(23, 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(25, 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(26, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(27, 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(28, axiom,![X1]:~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_NOTu_u_SUCu_u_LESSu_u_EQu_u_0)).
fof(31, axiom,![X1]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_nums_NOTu_u_SUC)).
fof(34, 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(35, 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(36, 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(37, 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(38, axiom,![X1]:![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_LESSu_u_MONOu_u_EQ)).
fof(39, 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(40, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/arithmetic/EXP__BASE__LE__IFF', aHLu_BOOLu_CASES)).
fof(41, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_EXP0u_c1)).
fof(42, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/EXP__BASE__LE__IFF', ah4s_arithmetics_MULTu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
