# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))),file('i/f/bit/BITS__SUC__THM', ch4s_bits_BITSu_u_SUCu_u_THM)).
fof(10, axiom,![X1]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X13))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_ADDu_u_SYM)).
fof(14, axiom,![X7]:![X4]:![X5]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X5),s(X7,X4)))=s(X7,X5),file('i/f/bit/BITS__SUC__THM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(15, axiom,![X7]:![X4]:![X5]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X5),s(X7,X4)))=s(X7,X4),file('i/f/bit/BITS__SUC__THM', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(21, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))))))=>s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))),file('i/f/bit/BITS__SUC__THM', ah4s_bits_BITSu_u_SUC)).
fof(22, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))=>s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/bit/BITS__SUC__THM', ah4s_bits_BITSu_u_ZERO)).
fof(26, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bit/BITS__SUC__THM', ah4s_numerals_numeralu_u_lteu_c1)).
fof(28, axiom,~(p(s(t_bool,f))),file('i/f/bit/BITS__SUC__THM', aHLu_FALSITY)).
fof(29, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/bit/BITS__SUC__THM', aHLu_BOOLu_CASES)).
fof(34, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/bit/BITS__SUC__THM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(35, axiom,![X6]:((p(s(t_bool,X6))=>p(s(t_bool,f)))<=>s(t_bool,X6)=s(t_bool,f)),file('i/f/bit/BITS__SUC__THM', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(36, axiom,![X1]:![X13]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X13))))),file('i/f/bit/BITS__SUC__THM', ah4s_arithmetics_NOTu_u_LESS)).
# SZS output end CNFRefutation
