# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/toto/charOrd__lt__lem', aHLu_TRUTH)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/toto/charOrd__lt__lem', aHLu_BOOLu_CASES)).
fof(15, axiom,![X1]:(s(t_bool,t)=s(t_bool,X1)<=>p(s(t_bool,X1))),file('i/f/toto/charOrd__lt__lem', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(17, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/toto/charOrd__lt__lem', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(18, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/toto/charOrd__lt__lem', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(19, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/toto/charOrd__lt__lem', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(39, axiom,![X15]:![X21]:![X22]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X21))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X21))),s(t_h4s_nums_num,X15)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X15))))),file('i/f/toto/charOrd__lt__lem', ah4s_arithmetics_LESSu_u_TRANS)).
fof(49, axiom,![X21]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X21))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/toto/charOrd__lt__lem', ah4s_numerals_numeralu_u_lteu_c1)).
fof(50, axiom,![X13]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(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_strings_ord(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,X13)))))=s(t_h4s_nums_num,X13)),file('i/f/toto/charOrd__lt__lem', ah4s_strings_ORDu_u_CHRu_u_RWT)).
fof(51, axiom,![X9]:![X23]:![X6]:![X13]:?[X24]:((p(s(t_bool,X24))<=>s(X9,X6)=s(X9,X23))&s(t_h4s_totos_cpn,happ(s(t_fun(X9,t_h4s_totos_cpn),happ(s(t_fun(X9,t_fun(X9,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(X9,t_fun(X9,t_bool)),X13))),s(X9,X6))),s(X9,X23)))=s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,X24),s(t_h4s_totos_cpn,h4s_totos_equal),s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X13),s(X9,X6))),s(X9,X23))),s(t_h4s_totos_cpn,h4s_totos_less),s(t_h4s_totos_cpn,h4s_totos_greater)))))),file('i/f/toto/charOrd__lt__lem', ah4s_totos_TOu_u_ofu_u_LinearOrder0)).
fof(52, axiom,~(s(t_h4s_totos_cpn,h4s_totos_equal)=s(t_h4s_totos_cpn,h4s_totos_less)),file('i/f/toto/charOrd__lt__lem', ah4s_totos_allu_u_cpnu_u_distinctu_c3)).
fof(53, axiom,~(s(t_h4s_totos_cpn,h4s_totos_greater)=s(t_h4s_totos_cpn,h4s_totos_less)),file('i/f/toto/charOrd__lt__lem', ah4s_totos_allu_u_cpnu_u_distinctu_c4)).
fof(55, axiom,s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord)=s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))),file('i/f/toto/charOrd__lt__lem', ah4s_totos_numOrd0)).
fof(56, axiom,![X18]:![X17]:s(t_h4s_totos_cpn,h4s_totos_charord(s(t_h4s_strings_char,X17),s(t_h4s_strings_char,X18)))=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_numord),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,X17))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,X18))))),file('i/f/toto/charOrd__lt__lem', ah4s_totos_charOrd0)).
fof(57, conjecture,![X18]:![X17]:(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_numord),s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X18)))=s(t_h4s_totos_cpn,h4s_totos_less)=>(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),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,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(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_bool,t)=>s(t_h4s_totos_cpn,h4s_totos_charord(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,X17))),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,X18)))))=s(t_h4s_totos_cpn,h4s_totos_less))),file('i/f/toto/charOrd__lt__lem', ch4s_totos_charOrdu_u_ltu_u_lem)).
# SZS output end CNFRefutation
