# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/ODD__ADD', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/ODD__ADD', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/ODD__ADD', aHLu_BOOLu_CASES)).
fof(6, axiom,![X10]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X10))))<=>~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/ODD__ADD', ah4s_arithmetics_EVENu_u_ODD)).
fof(10, axiom,![X10]:(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10))))))<=>~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/ODD__ADD', ah4s_arithmetics_ODD0u_c1)).
fof(18, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/arithmetic/ODD__ADD', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(19, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/ODD__ADD', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(26, axiom,![X10]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10))))))<=>~(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/ODD__ADD', ah4s_arithmetics_EVEN0u_c1)).
fof(31, axiom,![X10]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X10))))),file('i/f/arithmetic/ODD__ADD', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(82, axiom,![X10]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X10))))),file('i/f/arithmetic/ODD__ADD', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(89, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/arithmetic/ODD__ADD', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(110, axiom,![X10]:![X17]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X10))))))<=>s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X17)))=s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X10)))),file('i/f/arithmetic/ODD__ADD', ah4s_arithmetics_EVENu_u_ADD)).
fof(133, conjecture,![X10]:![X17]:(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X10))))))<=>~(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X17)))=s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X10))))),file('i/f/arithmetic/ODD__ADD', ch4s_arithmetics_ODDu_u_ADD)).
# SZS output end CNFRefutation
