# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))))=>s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,X3)))=s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))),file('i/f/words/word__index', ch4s_wordss_wordu_u_index)).
fof(5, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/words/word__index', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X1]:![X2]:![X24]:![X3]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,X3)))=s(t_bool,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))),s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_fun(t_h4s_nums_num,t_bool)),h4s_combins_fail(s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_bool,X24))),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,X3))))),file('i/f/words/word__index', ah4s_wordss_wordu_u_indexu_u_n2w)).
fof(35, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/words/word__index', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(39, axiom,![X2]:![X27]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X27))))),file('i/f/words/word__index', ah4s_arithmetics_NOTu_u_LESS)).
fof(43, axiom,![X2]:(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X2)))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/words/word__index', ah4s_numerals_numeralu_u_distribu_c18)).
fof(45, axiom,![X1]:![X28]:?[X2]:(s(t_h4s_fcps_cart(t_bool,X1),X28)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X2)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))))),file('i/f/words/word__index', ah4s_wordss_rangedu_u_wordu_u_nchotomy)).
fof(53, axiom,~(p(s(t_bool,f))),file('i/f/words/word__index', aHLu_FALSITY)).
fof(55, axiom,![X13]:((p(s(t_bool,X13))=>p(s(t_bool,f)))<=>s(t_bool,X13)=s(t_bool,f)),file('i/f/words/word__index', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(56, axiom,![X13]:(s(t_bool,f)=s(t_bool,X13)<=>~(p(s(t_bool,X13)))),file('i/f/words/word__index', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(71, axiom,![X1]:![X11]:![X12]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X12),s(X1,X11)))=s(X1,X11),file('i/f/words/word__index', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(72, axiom,![X1]:![X11]:![X12]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X12),s(X1,X11)))=s(X1,X12),file('i/f/words/word__index', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(75, axiom,![X2]:![X27]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X27),s(t_h4s_nums_num,X2))),file('i/f/words/word__index', ah4s_arithmetics_MINu_u_DEF)).
fof(77, axiom,![X21]:![X1]:![X8]:![X32]:s(X1,h4s_combins_fail(s(X1,X8),s(X21,X32)))=s(X1,X8),file('i/f/words/word__index', ah4s_combins_FAILu_u_DEF)).
# SZS output end CNFRefutation
