# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1)))))))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__distrib_c10', ch4s_numerals_numeralu_u_distribu_c10)).
fof(6, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/numeral/numeral__distrib_c10', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X18]:![X3]:![X4]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X4))))),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X18)))<=>(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X4)))))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X4)))))))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_NUMERALu_u_MULTu_u_EQu_u_DIVu_c1)).
fof(29, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit1(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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_BIT10)).
fof(33, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_ALTu_u_ZERO)).
fof(40, 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/numeral/numeral__distrib_c10', ah4s_arithmetics_ONE)).
fof(42, axiom,![X13]:![X1]:![X17]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X13),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))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X13)))))),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_LTu_u_MULTu_u_RCANCEL)).
fof(45, axiom,![X1]:(~(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,h4s_nums_0),s(t_h4s_nums_num,X1))))),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(46, axiom,![X1]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(47, axiom,![X4]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,X4),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(48, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))),file('i/f/numeral/numeral__distrib_c10', ah4s_numerals_numeralu_u_sucu_c1)).
fof(53, axiom,![X1]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17))),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_MULTu_u_COMM)).
fof(57, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,X17)))=s(t_h4s_nums_num,X17),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_MULTu_u_CLAUSESu_c2)).
fof(61, axiom,![X17]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),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/numeral/numeral__distrib_c10', ah4s_arithmetics_ADD1)).
fof(64, axiom,![X1]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_EXP0u_c1)).
fof(66, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1))))<=>?[X17]:s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,X17)))),file('i/f/numeral/numeral__distrib_c10', ah4s_arithmetics_EVENu_u_EXISTS)).
fof(72, axiom,p(s(t_bool,t)),file('i/f/numeral/numeral__distrib_c10', aHLu_TRUTH)).
fof(73, axiom,~(p(s(t_bool,f))),file('i/f/numeral/numeral__distrib_c10', aHLu_FALSITY)).
fof(75, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/numeral/numeral__distrib_c10', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
