# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:![X5]:![X6]:(p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool)))),X2),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X4))),s(t_bool,X5))),s(t_bool,X6))))<=>((s(t_bool,X5)=s(t_bool,X6)&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value)))))))))|(p(s(t_bool,X5))&~(p(s(t_bool,X6))))))=>![X7]:(![X3]:![X4]:![X5]:s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool)))),X7),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X4))),s(t_bool,X5)))=s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool)))),X2),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X4))),s(t_bool,X5)))=>![X4]:![X3]:s(t_bool,h4s_wordss_wordu_u_le(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X3))),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X4)))))=s(t_bool,h4s_bools_let(s(t_fun(t_bool,t_bool),h4s_bools_let(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool)))),X7),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X4))),s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))),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,X3))))),s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))),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,X4))))))),file('i/f/words/word__le__n2w', ch4s_wordss_wordu_u_leu_u_n2w)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/words/word__le__n2w', aHLu_TRUTH)).
fof(7, axiom,![X14]:![X1]:![X12]:![X10]:s(X14,h4s_bools_let(s(t_fun(X1,X14),X10),s(X1,X12)))=s(X14,happ(s(t_fun(X1,X14),X10),s(X1,X12))),file('i/f/words/word__le__n2w', ah4s_bools_LETu_u_THM)).
fof(8, axiom,![X1]:![X15]:s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X15)))))=s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))),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,X15))),file('i/f/words/word__le__n2w', ah4s_wordss_wordu_u_msbu_u_n2w)).
fof(10, axiom,![X1]:![X15]:s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X15)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))),file('i/f/words/word__le__n2w', ah4s_wordss_w2nu_u_n2w)).
fof(11, axiom,![X1]:![X4]:![X3]:(p(s(t_bool,h4s_wordss_wordu_u_le(s(t_h4s_fcps_cart(t_bool,X1),X3),s(t_h4s_fcps_cart(t_bool,X1),X4))))<=>((s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X3)))=s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X4)))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X3))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X4)))))))|(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X3))))&~(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X4)))))))),file('i/f/words/word__le__n2w', ah4s_wordss_WORDu_u_LE)).
fof(12, axiom,~(p(s(t_bool,f))),file('i/f/words/word__le__n2w', aHLu_FALSITY)).
fof(13, axiom,![X13]:(s(t_bool,X13)=s(t_bool,t)|s(t_bool,X13)=s(t_bool,f)),file('i/f/words/word__le__n2w', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
