# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/words/w2w__lt', aHLu_TRUTH)).
fof(7, axiom,![X7]:![X8]:![X9]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X7),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,X8),X9))))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X8),X9)))))),file('i/f/words/w2w__lt', ah4s_wordss_w2nu_u_w2wu_u_le)).
fof(14, axiom,![X1]:((p(s(t_bool,X1))=>p(s(t_bool,f)))<=>s(t_bool,X1)=s(t_bool,f)),file('i/f/words/w2w__lt', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(20, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/words/w2w__lt', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(30, axiom,![X31]:![X25]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X31)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X31),s(t_h4s_nums_num,X25))))),file('i/f/words/w2w__lt', ah4s_arithmetics_NOTu_u_LESS)).
fof(41, axiom,![X8]:![X23]:![X24]:s(X8,h4s_bools_cond(s(t_bool,f),s(X8,X24),s(X8,X23)))=s(X8,X23),file('i/f/words/w2w__lt', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(42, axiom,![X8]:![X9]:?[X31]:(s(t_h4s_fcps_cart(t_bool,X8),X9)=s(t_h4s_fcps_cart(t_bool,X8),h4s_wordss_n2w(s(t_h4s_nums_num,X31)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X31),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value))))))),file('i/f/words/w2w__lt', ah4s_wordss_rangedu_u_wordu_u_nchotomy)).
fof(43, axiom,![X8]:![X31]:s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X8),h4s_wordss_n2w(s(t_h4s_nums_num,X31)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X31),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value))))),file('i/f/words/w2w__lt', ah4s_wordss_w2nu_u_n2w)).
fof(45, axiom,![X31]:![X25]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X31)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X31))),s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X31))),file('i/f/words/w2w__lt', ah4s_arithmetics_MINu_u_DEF)).
fof(98, axiom,![X31]:![X44]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X44),s(t_h4s_nums_num,X31))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X44),s(t_h4s_nums_num,X31)))=s(t_h4s_nums_num,X44)),file('i/f/words/w2w__lt', ah4s_arithmetics_LESSu_u_MOD)).
fof(124, axiom,![X32]:![X31]:![X25]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X32),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X31))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X32),s(t_h4s_nums_num,X25))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X32),s(t_h4s_nums_num,X31)))))),file('i/f/words/w2w__lt', ah4s_arithmetics_MINu_u_LTu_c1)).
fof(126, axiom,![X31]:![X25]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X31)))=s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X31),s(t_h4s_nums_num,X25))),file('i/f/words/w2w__lt', ah4s_arithmetics_MINu_u_COMM)).
fof(133, conjecture,![X7]:![X8]:![X9]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X7),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,X8),X9))))),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value)))))),file('i/f/words/w2w__lt', ch4s_wordss_w2wu_u_lt)).
# SZS output end CNFRefutation
