# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value)))))))=>(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,X2),X4)))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X3)))<=>s(t_h4s_fcps_cart(t_bool,X2),X4)=s(t_h4s_fcps_cart(t_bool,X2),h4s_wordss_n2w(s(t_h4s_nums_num,X3))))),file('i/f/words/w2w__eq__n2w', ch4s_wordss_w2wu_u_equ_u_n2w)).
fof(15, axiom,![X14]:![X15]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))))),file('i/f/words/w2w__eq__n2w', ah4s_arithmetics_NOTu_u_LESS)).
fof(21, axiom,![X13]:![X14]:![X15]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X13))))),file('i/f/words/w2w__eq__n2w', ah4s_arithmetics_LESSu_u_LESSu_u_EQu_u_TRANS)).
fof(24, axiom,![X13]:![X14]:![X15]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X13))))),file('i/f/words/w2w__eq__n2w', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(26, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/words/w2w__eq__n2w', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(30, axiom,![X14]:![X15]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))))),file('i/f/words/w2w__eq__n2w', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(34, axiom,![X2]:![X19]:?[X14]:(s(t_h4s_fcps_cart(t_bool,X2),X19)=s(t_h4s_fcps_cart(t_bool,X2),h4s_wordss_n2w(s(t_h4s_nums_num,X14)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value))))))),file('i/f/words/w2w__eq__n2w', ah4s_wordss_rangedu_u_wordu_u_nchotomy)).
fof(36, axiom,![X2]:![X14]:s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X2),h4s_wordss_n2w(s(t_h4s_nums_num,X14)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value))))),file('i/f/words/w2w__eq__n2w', ah4s_wordss_w2nu_u_n2w)).
fof(40, axiom,![X1]:![X2]:![X19]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,X2),X19)))=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,X2),X19))))),file('i/f/words/w2w__eq__n2w', ah4s_wordss_w2wu_u_def)).
fof(49, axiom,~(p(s(t_bool,f))),file('i/f/words/w2w__eq__n2w', aHLu_FALSITY)).
fof(57, axiom,![X10]:((p(s(t_bool,X10))=>p(s(t_bool,f)))<=>s(t_bool,X10)=s(t_bool,f)),file('i/f/words/w2w__eq__n2w', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(60, axiom,![X14]:![X21]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X14))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,X21)),file('i/f/words/w2w__eq__n2w', ah4s_arithmetics_LESSu_u_MOD)).
fof(64, axiom,![X14]:![X15]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X14))),file('i/f/words/w2w__eq__n2w', ah4s_arithmetics_LESSu_u_EQ)).
fof(66, axiom,![X2]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value))))))=>s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X2),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,h4s_nums_0),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,X14)),file('i/f/words/w2w__eq__n2w', ah4s_wordss_BITSu_u_ZEROLu_u_DIMINDEX)).
fof(67, axiom,![X2]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value)))))=s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X2),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,h4s_nums_0),s(t_h4s_nums_num,X14))),file('i/f/words/w2w__eq__n2w', ah4s_wordss_MODu_u_DIMINDEX)).
fof(68, axiom,![X2]:s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value)))=s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value))))),file('i/f/words/w2w__eq__n2w', ah4s_wordss_dimwordu_u_def)).
fof(73, axiom,![X22]:![X20]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X22))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X22))))))),file('i/f/words/w2w__eq__n2w', ah4s_bits_TWOEXPu_u_MONO2)).
# SZS output end CNFRefutation
