# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_u_3e(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_lists_list(t_h4s_nums_num),X2))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),X2)))))))=>(p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_numu_u_fromu_u_binu_u_list),s(t_h4s_lists_list(t_h4s_nums_num),X2))))))<=>s(t_h4s_nums_num,h4s_lists_el(s(t_h4s_nums_num,X1),s(t_h4s_lists_list(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/numposrep/BIT__num__from__bin__list', ch4s_numposreps_BITu_u_numu_u_fromu_u_binu_u_list)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/numposrep/BIT__num__from__bin__list', aHLu_TRUTH)).
fof(8, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/numposrep/BIT__num__from__bin__list', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X11]:![X12]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X12)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))),file('i/f/numposrep/BIT__num__from__bin__list', ah4s_numerals_numeralu_u_distribu_c22)).
fof(12, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X11),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,X11),file('i/f/numposrep/BIT__num__from__bin__list', ah4s_arithmetics_EXPu_u_1u_c1)).
fof(13, axiom,![X11]:![X13]:(p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X11))))<=>s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X11)))=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/numposrep/BIT__num__from__bin__list', ah4s_bits_BITu_u_def)).
fof(14, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X14)))=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/numposrep/BIT__num__from__bin__list', ah4s_bits_SUCu_u_SUB)).
fof(15, axiom,![X11]:![X2]:![X15]:s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X11),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))))),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,X15))),s(t_h4s_nums_num,X2))))))),file('i/f/numposrep/BIT__num__from__bin__list', ah4s_bits_BITSu_u_THM)).
fof(16, axiom,s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_numu_u_fromu_u_binu_u_list)=s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/numposrep/BIT__num__from__bin__list', ah4s_numposreps_numu_u_fromu_u_binu_u_listu_u_def)).
fof(17, axiom,![X1]:![X2]:![X13]:((p(s(t_bool,h4s_primu_u_recs_u_3c(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,X13))))&(p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_u_3e(s(t_h4s_nums_num,X13))),s(t_h4s_lists_list(t_h4s_nums_num),X2))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),X2))))))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(s(t_h4s_nums_num,X13))),s(t_h4s_lists_list(t_h4s_nums_num),X2))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1))))),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_lists_el(s(t_h4s_nums_num,X1),s(t_h4s_lists_list(t_h4s_nums_num),X2)))),file('i/f/numposrep/BIT__num__from__bin__list', ah4s_numposreps_l2nu_u_DIGIT)).
fof(18, axiom,![X11]:![X12]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X12))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))))),file('i/f/numposrep/BIT__num__from__bin__list', ah4s_numerals_numeralu_u_ltu_c5)).
fof(19, axiom,![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numposrep/BIT__num__from__bin__list', ah4s_numerals_numeralu_u_ltu_c2)).
fof(20, axiom,~(p(s(t_bool,f))),file('i/f/numposrep/BIT__num__from__bin__list', aHLu_FALSITY)).
fof(23, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/numposrep/BIT__num__from__bin__list', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
