# 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_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(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/EVEN__EXP', aHLu_FALSITY)).
fof(8, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/arithmetic/EVEN__EXP', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(14, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/EVEN__EXP', aHLu_BOOLu_CASES)).
fof(15, 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(17, 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)).
fof(18, 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/EVEN__EXP', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(19, 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)).
# SZS output end CNFRefutation
