# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(~(s(t_h4s_fcps_cart(t_bool,X1),X2)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))=>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),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,X1),X2),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(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_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X2))))))),file('i/f/words/WORD__PRED__THM', ch4s_wordss_WORDu_u_PREDu_u_THM)).
fof(8, axiom,![X10]:![X2]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X10)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X2))))),file('i/f/words/WORD__PRED__THM', ah4s_arithmetics_NOTu_u_LESS)).
fof(9, axiom,![X1]:![X4]:(~(s(t_h4s_fcps_cart(t_bool,X1),X4)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))=>s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,X1),X4),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(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_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X4)))),file('i/f/words/WORD__PRED__THM', ah4s_wordss_SUCu_u_WORDu_u_PRED)).
fof(10, axiom,![X10]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/words/WORD__PRED__THM', ah4s_numerals_numeralu_u_distribu_c27)).
fof(11, axiom,![X10]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/words/WORD__PRED__THM', ah4s_numerals_numeralu_u_lteu_c1)).
fof(12, axiom,![X10]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10)))),file('i/f/words/WORD__PRED__THM', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(14, axiom,![X10]:![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X10)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X10))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X2)))))),file('i/f/words/WORD__PRED__THM', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(15, axiom,![X10]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X10))),file('i/f/words/WORD__PRED__THM', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(16, axiom,~(p(s(t_bool,f))),file('i/f/words/WORD__PRED__THM', aHLu_FALSITY)).
fof(17, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/words/WORD__PRED__THM', aHLu_BOOLu_CASES)).
fof(20, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X2),file('i/f/words/WORD__PRED__THM', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(21, axiom,![X10]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X2))),file('i/f/words/WORD__PRED__THM', ah4s_arithmetics_ADDu_u_SYM)).
fof(22, axiom,![X11]:![X10]:![X2]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X11)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/words/WORD__PRED__THM', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(23, axiom,p(s(t_bool,t)),file('i/f/words/WORD__PRED__THM', aHLu_TRUTH)).
fof(25, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/words/WORD__PRED__THM', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
