# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(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,X1))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))&s(t_h4s_nums_num,h4s_arithmetics_mod(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,X1)))=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/ONE__MOD__IFF', ch4s_arithmetics_ONEu_u_MODu_u_IFF)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/ONE__MOD__IFF', aHLu_TRUTH)).
fof(8, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(12, axiom,![X1]:![X11]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_primu_u_recs_LESSu_u_MONO)).
fof(14, axiom,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_primu_u_recs_LESSu_u_0)).
fof(15, axiom,![X1]:~(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_arithmetics_SUCu_u_NOT)).
fof(16, axiom,![X11]:(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_arithmetics_numu_u_CASES)).
fof(17, axiom,![X12]:![X1]:![X11]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X12)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))))),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_arithmetics_LESSu_u_TRANS)).
fof(18, axiom,![X6]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(19, 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/ONE__MOD__IFF', ah4s_arithmetics_ONE)).
fof(20, axiom,![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(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,X1))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(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,X1)))=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/ONE__MOD__IFF', ah4s_arithmetics_ONEu_u_MOD)).
fof(22, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_arithmetics_ALTu_u_ZERO)).
fof(23, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ONE__MOD__IFF', ah4s_arithmetics_MODu_u_ONE)).
fof(24, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/ONE__MOD__IFF', aHLu_FALSITY)).
fof(29, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/arithmetic/ONE__MOD__IFF', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
