# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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__EQ__0', ch4s_arithmetics_EXPu_u_EQu_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/EXP__EQ__0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/EXP__EQ__0', aHLu_FALSITY)).
fof(13, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/arithmetic/EXP__EQ__0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(14, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/arithmetic/EXP__EQ__0', aHLu_BOOLu_CASES)).
fof(16, 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__EQ__0', ah4s_nums_NOTu_u_SUC)).
fof(17, 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__EQ__0', ah4s_arithmetics_numu_u_CASES)).
fof(18, 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__EQ__0', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(19, 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__EQ__0', ah4s_arithmetics_EXP0u_c0)).
fof(20, 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__EQ__0', ah4s_arithmetics_EXP0u_c1)).
fof(21, 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__EQ__0', ah4s_arithmetics_ONE)).
fof(22, axiom,![X1]:![X2]:~(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/EXP__EQ__0', ah4s_arithmetics_NOTu_u_EXPu_u_0)).
fof(23, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>(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))),file('i/f/arithmetic/EXP__EQ__0', ah4s_arithmetics_MULTu_u_EQu_u_0)).
# SZS output end CNFRefutation
