# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))),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_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/DOUBLE__LT', ch4s_arithmetics_DOUBLEu_u_LT)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/DOUBLE__LT', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/DOUBLE__LT', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/DOUBLE__LT', aHLu_BOOLu_CASES)).
fof(7, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/arithmetic/DOUBLE__LT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(21, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/arithmetic/DOUBLE__LT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(22, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/arithmetic/DOUBLE__LT', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(42, axiom,![X13]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X13))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))),file('i/f/arithmetic/DOUBLE__LT', ah4s_primu_u_recs_SUCu_u_LESS)).
fof(43, axiom,![X13]:![X14]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))&~(s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X13))))),file('i/f/arithmetic/DOUBLE__LT', ah4s_arithmetics_LESSu_u_NOTu_u_SUC)).
fof(44, axiom,![X13]:p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X13)))))),file('i/f/arithmetic/DOUBLE__LT', ah4s_arithmetics_EVENu_u_DOUBLE)).
fof(45, axiom,![X13]:p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X13)))))))),file('i/f/arithmetic/DOUBLE__LT', ah4s_arithmetics_ODDu_u_DOUBLE)).
fof(46, axiom,![X14]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),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/DOUBLE__LT', ah4s_arithmetics_ADD1)).
fof(47, axiom,![X13]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X13))))<=>~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X13)))))),file('i/f/arithmetic/DOUBLE__LT', ah4s_arithmetics_EVENu_u_ODD)).
# SZS output end CNFRefutation
