# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_2comp(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_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))))),file('i/f/words/WORD__LESS__0__word__T_c2', ch4s_wordss_WORDu_u_LESSu_u_0u_u_wordu_u_Tu_c2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/words/WORD__LESS__0__word__T_c2', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/words/WORD__LESS__0__word__T_c2', aHLu_FALSITY)).
fof(5, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)<=>p(s(t_bool,X2))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(11, axiom,![X2]:(s(t_bool,f)=s(t_bool,X2)<=>~(p(s(t_bool,X2)))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(54, axiom,![X5]:![X18]:![X19]:(p(s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,X5),X19),s(t_h4s_fcps_cart(t_bool,X5),X18))))<=>((s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X5),X19)))=s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X5),X18)))&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,X5),X19))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X5),X18)))))))|(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X5),X19))))&~(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X5),X18)))))))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_wordss_WORDu_u_LT)).
fof(55, axiom,![X5]:p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X5),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,X5),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)))))))))))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_wordss_wordu_u_msbu_u_wordu_u_T)).
fof(59, axiom,![X5]:~(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X5),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_wordss_WORDu_u_0u_u_POS)).
fof(63, axiom,![X12]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X12)))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(64, axiom,![X12]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_numerals_numeralu_u_distribu_c27)).
fof(66, axiom,![X12]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_numerals_numeralu_u_distribu_c17)).
fof(67, axiom,![X23]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X23)))=s(t_h4s_nums_num,X23),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(70, axiom,![X10]:![X12]:![X23]:(s(t_h4s_nums_num,X23)=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10)))<=>(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,X12)|(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,h4s_nums_0))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10))))))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_arithmetics_SUBu_u_LEFTu_u_EQ)).
fof(72, axiom,![X10]:![X12]:![X23]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X12))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X10))))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(73, axiom,![X12]:![X23]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X12)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X23))))),file('i/f/words/WORD__LESS__0__word__T_c2', ah4s_arithmetics_NOTu_u_LESS)).
fof(79, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/words/WORD__LESS__0__word__T_c2', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
