# 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)),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,X2))))<=>![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,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)),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(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)))))))))))),file('i/f/arithmetic/SUC__ELIM__THM', ch4s_arithmetics_SUCu_u_ELIMu_u_THM)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUC__ELIM__THM', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUC__ELIM__THM', aHLu_FALSITY)).
fof(13, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(17, axiom,![X2]: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,X2)))))),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_primu_u_recs_LESSu_u_0)).
fof(18, axiom,![X2]:![X13]:~((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))))))),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_arithmetics_LESSu_u_LESSu_u_SUC)).
fof(19, axiom,![X2]:![X13]:(s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,X2)|(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2))))|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13)))))),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_arithmetics_LESSu_u_LESSu_u_CASES)).
fof(22, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X13),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_arithmetics_SUBu_u_0u_c1)).
fof(24, axiom,![X2]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13))),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_arithmetics_SUBu_u_MONOu_u_EQ)).
fof(25, axiom,![X2]:![X13]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_arithmetics_SUBu_u_LEFTu_u_SUC)).
fof(26, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(27, 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/SUC__ELIM__THM', ah4s_arithmetics_ONE)).
fof(28, axiom,![X13]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),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/SUC__ELIM__THM', ah4s_arithmetics_ADD1)).
fof(30, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_arithmetics_ALTu_u_ZERO)).
fof(32, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/arithmetic/SUC__ELIM__THM', aHLu_BOOLu_CASES)).
fof(33, axiom,![X2]:![X13]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13))))),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_arithmetics_NOTu_u_LESS)).
fof(34, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X4),s(X6,X3)))=s(X6,X4),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(35, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X4),s(X6,X3)))=s(X6,X3),file('i/f/arithmetic/SUC__ELIM__THM', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
