# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X2)))))=>p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))),file('i/f/arithmetic/EVEN__EXP', ch4s_arithmetics_EVENu_u_EXP)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/EVEN__EXP', aHLu_TRUTH)).
fof(7, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/arithmetic/EVEN__EXP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(8, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/EVEN__EXP', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(14, axiom,![X1]:(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))<=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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/EVEN__EXP', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(46, 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/EVEN__EXP', ah4s_arithmetics_numu_u_CASES)).
fof(50, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1))))<=>~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/EVEN__EXP', ah4s_arithmetics_EVENu_u_ODD)).
fof(54, axiom,s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,t),file('i/f/arithmetic/EVEN__EXP', ah4s_arithmetics_EVEN0u_c0)).
fof(56, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))<=>(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X2))))|p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/EVEN__EXP', ah4s_arithmetics_EVENu_u_MULT)).
fof(61, 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/EVEN__EXP', ah4s_arithmetics_EXP0u_c1)).
# SZS output end CNFRefutation
