# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/bit/BITS__ZERO4', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bit/BITS__ZERO4', 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/bit/BITS__ZERO4', aHLu_BOOLu_CASES)).
fof(15, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/bit/BITS__ZERO4', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(18, axiom,![X1]:((p(s(t_bool,X1))=>p(s(t_bool,f)))<=>s(t_bool,X1)=s(t_bool,f)),file('i/f/bit/BITS__ZERO4', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(22, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/bit/BITS__ZERO4', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(23, axiom,![X18]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/bit/BITS__ZERO4', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(24, axiom,![X18]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))))))),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_SUBu_c1)).
fof(25, axiom,![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X19),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_ADDu_u_0)).
fof(27, axiom,![X18]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19))),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_ADDu_u_SYM)).
fof(28, axiom,![X18]:![X19]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X18))),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_LESSu_u_EQ)).
fof(29, axiom,![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X19),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_SUBu_u_0u_c1)).
fof(31, axiom,![X20]:![X18]:![X19]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X20)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20))))),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(33, axiom,![X20]:![X18]:![X19]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X20))),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(34, axiom,![X18]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X18))),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(36, axiom,![X21]:![X18]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X18))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,X21)),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_MULTu_u_DIV)).
fof(37, axiom,![X21]:s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X21),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,X21),file('i/f/bit/BITS__ZERO4', ah4s_arithmetics_DIVu_u_1)).
fof(39, axiom,![X18]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bit/BITS__ZERO4', ah4s_numerals_numeralu_u_lteu_c1)).
fof(40, axiom,s(t_h4s_nums_num,h4s_arithmetics_exp(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,h4s_nums_0)))=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/bit/BITS__ZERO4', ah4s_numerals_TWOu_u_EXPu_u_THMu_c0)).
fof(41, axiom,![X18]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_exp(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,X18)))))),file('i/f/bit/BITS__ZERO4', ah4s_bits_ZEROu_u_LTu_u_TWOEXP)).
fof(42, axiom,![X18]:![X22]:![X23]:s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,h4s_arithmetics_exp(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,X22))))),s(t_h4s_nums_num,h4s_arithmetics_exp(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,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,X22))))))),file('i/f/bit/BITS__ZERO4', ah4s_bits_BITSu_u_THM)).
fof(43, conjecture,![X22]:![X23]:![X24]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X23))))=>s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,h4s_arithmetics_exp(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,X22)))))))=s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X24)))),file('i/f/bit/BITS__ZERO4', ch4s_bits_BITSu_u_ZERO4)).
# SZS output end CNFRefutation
