# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),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,X2)))))))=>?[X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))))),file('i/f/bit/EXISTS__BIT__LT', ch4s_bits_EXISTSu_u_BITu_u_LT)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bit/EXISTS__BIT__LT', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bit/EXISTS__BIT__LT', aHLu_FALSITY)).
fof(10, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/bit/EXISTS__BIT__LT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X5]:((p(s(t_bool,X5))=>p(s(t_bool,f)))<=>s(t_bool,X5)=s(t_bool,f)),file('i/f/bit/EXISTS__BIT__LT', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(26, axiom,![X21]:![X1]:![X22]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),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,X21)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X21))))),file('i/f/bit/EXISTS__BIT__LT', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(27, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/bit/EXISTS__BIT__LT', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(29, axiom,![X1]:![X2]:![X23]:((~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))&(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X23))),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,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,X2))))))))=>?[X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X3))))&(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))))),file('i/f/bit/EXISTS__BIT__LT', ah4s_bits_EXISTSu_u_BITu_u_INu_u_RANGE)).
fof(30, axiom,![X1]:![X22]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X1))),file('i/f/bit/EXISTS__BIT__LT', ah4s_arithmetics_LESSu_u_EQ)).
fof(33, axiom,![X1]:![X22]:(~(s(t_h4s_nums_num,X22)=s(t_h4s_nums_num,X1))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X22)))))),file('i/f/bit/EXISTS__BIT__LT', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(34, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=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,X1))),file('i/f/bit/EXISTS__BIT__LT', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(35, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X1),file('i/f/bit/EXISTS__BIT__LT', ah4s_numerals_numeralu_u_distribu_c1)).
fof(38, 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/EXISTS__BIT__LT', ah4s_numerals_TWOu_u_EXPu_u_THMu_c0)).
fof(39, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/bit/EXISTS__BIT__LT', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
