# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/prelim/ordering2num__thm_c2', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/prelim/ordering2num__thm_c2', aHLu_FALSITY)).
fof(5, axiom,s(t_h4s_prelims_ordering,h4s_prelims_greater)=s(t_h4s_prelims_ordering,h4s_prelims_num2ordering(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/prelim/ordering2num__thm_c2', ah4s_prelims_GREATERu_u_def)).
fof(8, axiom,![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))<=>s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,h4s_prelims_num2ordering(s(t_h4s_nums_num,X8)))))=s(t_h4s_nums_num,X8)),file('i/f/prelim/ordering2num__thm_c2', ah4s_prelims_orderingu_u_BIJu_c1)).
fof(25, axiom,![X10]:![X19]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X19)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X19))),file('i/f/prelim/ordering2num__thm_c2', ah4s_numerals_numeralu_u_ltu_c3)).
fof(26, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_ALTu_u_ZERO)).
fof(27, axiom,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_suc(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/prelim/ordering2num__thm_c2', ah4s_arithmetics_TWO)).
fof(35, axiom,![X19]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X19),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/prelim/ordering2num__thm_c2', ah4s_arithmetics_EXP0u_c0)).
fof(37, axiom,![X6]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(46, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/prelim/ordering2num__thm_c2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(47, axiom,![X10]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X10))))),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(48, 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/prelim/ordering2num__thm_c2', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(66, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/prelim/ordering2num__thm_c2', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(78, axiom,![X10]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X19))),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_ADDu_u_COMM)).
fof(83, axiom,![X10]:![X19]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X10))))&~(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X10))))),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_LESSu_u_NOTu_u_SUC)).
fof(88, axiom,![X10]:![X19]:(~(s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,X10))<=>(p(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,X10))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X19)))))),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(92, axiom,![X10]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))=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,X10))),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(103, axiom,s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/prelim/ordering2num__thm_c2', ah4s_numpairs_triu_u_defu_c0)).
fof(107, axiom,![X10]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,X10),file('i/f/prelim/ordering2num__thm_c2', ah4s_numerals_numeralu_u_addu_c1)).
fof(108, axiom,![X10]:s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X10))))),file('i/f/prelim/ordering2num__thm_c2', ah4s_numpairs_triu_u_defu_c1)).
fof(109, axiom,![X10]:![X19]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X19)))))))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X19))))))),file('i/f/prelim/ordering2num__thm_c2', ah4s_numerals_numeralu_u_addu_c4)).
fof(113, axiom,s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/prelim/ordering2num__thm_c2', ah4s_numerals_numeralu_u_sucu_c0)).
fof(120, axiom,![X10]:~(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_SUCu_u_NOT)).
fof(128, axiom,![X28]:![X7]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X28))),s(t_h4s_nums_num,X28)))=s(t_h4s_nums_num,X7),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_ADDu_u_SUB)).
fof(129, axiom,![X28]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X28),s(t_h4s_nums_num,X28)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_SUBu_u_EQUALu_u_0)).
fof(132, axiom,![X10]:![X19]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X10)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X19))))),file('i/f/prelim/ordering2num__thm_c2', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(133, conjecture,s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,h4s_prelims_greater)))=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/prelim/ordering2num__thm_c2', ch4s_prelims_ordering2numu_u_thmu_c2)).
# SZS output end CNFRefutation
