# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_qku_u_numord),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_totos_cpn,h4s_totos_equal),file('i/f/toto/qk__numeralOrd_c0', ch4s_totos_qku_u_numeralOrdu_c0)).
fof(29, axiom,![X7]:![X25]:(p(s(t_bool,h4s_totos_totord(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),X25))))<=>(![X5]:![X8]:(s(t_h4s_totos_cpn,happ(s(t_fun(X7,t_h4s_totos_cpn),happ(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),X25),s(X7,X5))),s(X7,X8)))=s(t_h4s_totos_cpn,h4s_totos_equal)<=>s(X7,X5)=s(X7,X8))&(![X5]:![X8]:(s(t_h4s_totos_cpn,happ(s(t_fun(X7,t_h4s_totos_cpn),happ(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),X25),s(X7,X5))),s(X7,X8)))=s(t_h4s_totos_cpn,h4s_totos_greater)<=>s(t_h4s_totos_cpn,happ(s(t_fun(X7,t_h4s_totos_cpn),happ(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),X25),s(X7,X8))),s(X7,X5)))=s(t_h4s_totos_cpn,h4s_totos_less))&![X5]:![X8]:![X20]:((s(t_h4s_totos_cpn,happ(s(t_fun(X7,t_h4s_totos_cpn),happ(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),X25),s(X7,X5))),s(X7,X8)))=s(t_h4s_totos_cpn,h4s_totos_less)&s(t_h4s_totos_cpn,happ(s(t_fun(X7,t_h4s_totos_cpn),happ(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),X25),s(X7,X8))),s(X7,X20)))=s(t_h4s_totos_cpn,h4s_totos_less))=>s(t_h4s_totos_cpn,happ(s(t_fun(X7,t_h4s_totos_cpn),happ(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),X25),s(X7,X5))),s(X7,X20)))=s(t_h4s_totos_cpn,h4s_totos_less))))),file('i/f/toto/qk__numeralOrd_c0', ah4s_totos_TotOrd0)).
fof(30, axiom,p(s(t_bool,h4s_totos_totord(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_qku_u_numord)))),file('i/f/toto/qk__numeralOrd_c0', ah4s_totos_TOu_u_qku_u_numOrd)).
fof(46, axiom,![X26]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X26)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X26))),file('i/f/toto/qk__numeralOrd_c0', ah4s_numerals_numeralu_u_addu_c6)).
fof(48, 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/toto/qk__numeralOrd_c0', ah4s_numerals_numeralu_u_sucu_c0)).
fof(51, axiom,![X27]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X27))),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,X27),file('i/f/toto/qk__numeralOrd_c0', ah4s_arithmetics_SUCu_u_SUB1)).
fof(56, axiom,![X26]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X26),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X26),file('i/f/toto/qk__numeralOrd_c0', ah4s_numerals_numeralu_u_distribu_c1)).
fof(68, axiom,p(s(t_bool,t)),file('i/f/toto/qk__numeralOrd_c0', aHLu_TRUTH)).
fof(69, axiom,~(p(s(t_bool,f))),file('i/f/toto/qk__numeralOrd_c0', aHLu_FALSITY)).
fof(70, axiom,![X6]:(s(t_bool,t)=s(t_bool,X6)<=>p(s(t_bool,X6))),file('i/f/toto/qk__numeralOrd_c0', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(78, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/toto/qk__numeralOrd_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
