# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]: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,X1),X2))),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value)))))),file('i/f/words/w2n__lt', ch4s_wordss_w2nu_u_lt)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/words/w2n__lt', aHLu_FALSITY)).
fof(4, axiom,![X3]:((p(s(t_bool,X3))=>p(s(t_bool,f)))<=>s(t_bool,X3)=s(t_bool,f)),file('i/f/words/w2n__lt', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(6, axiom,![X5]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5)))),file('i/f/words/w2n__lt', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(8, axiom,![X9]:![X5]:![X10]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X5))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X9)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))))),file('i/f/words/w2n__lt', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(9, axiom,![X10]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X10)))),file('i/f/words/w2n__lt', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(12, axiom,![X5]:![X10]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X5)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X10))))),file('i/f/words/w2n__lt', ah4s_arithmetics_NOTu_u_LESS)).
fof(31, axiom,![X5]:![X10]:(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,X5)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X5))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X10)))))),file('i/f/words/w2n__lt', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(35, axiom,![X5]:![X10]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X5))))=>?[X9]:s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9)))),file('i/f/words/w2n__lt', ah4s_arithmetics_LESSu_u_EQUALu_u_ADD)).
fof(41, axiom,![X12]:![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X12))))=>(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,X4)<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X12)))))),file('i/f/words/w2n__lt', ah4s_arithmetics_Xu_u_MODu_u_Yu_u_EQu_u_X)).
fof(42, axiom,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value)))))),file('i/f/words/w2n__lt', ah4s_wordss_ZEROu_u_LTu_u_dimword)).
fof(43, axiom,![X5]:![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X5)))=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,X5))),file('i/f/words/w2n__lt', ah4s_arithmetics_LESSu_u_EQ)).
fof(45, axiom,![X5]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/words/w2n__lt', ah4s_numerals_numeralu_u_ltu_c2)).
fof(52, axiom,![X1]:![X5]:s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X5)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))),file('i/f/words/w2n__lt', ah4s_wordss_w2nu_u_n2w)).
fof(64, axiom,![X1]:![X2]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X2)))))=s(t_h4s_fcps_cart(t_bool,X1),X2),file('i/f/words/w2n__lt', ah4s_wordss_n2wu_u_w2n)).
fof(66, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/words/w2n__lt', aHLu_BOOLu_CASES)).
fof(67, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/words/w2n__lt', ah4s_bools_NOTu_u_CLAUSESu_c2)).
fof(78, axiom,![X21]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),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,h4s_nums_0),file('i/f/words/w2n__lt', ah4s_arithmetics_MODu_u_1)).
fof(80, axiom,![X5]:![X10]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/words/w2n__lt', ah4s_arithmetics_MULTu_u_EQu_u_0)).
# SZS output end CNFRefutation
