# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:?[X5]:((p(s(t_bool,X5))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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_fcps_dimindex(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value))))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))),s(t_h4s_nums_num,X4))))))&s(t_h4s_fcps_cart(t_bool,X1),happ(s(t_fun(t_h4s_nums_num,t_h4s_fcps_cart(t_bool,X1)),X3),s(t_h4s_nums_num,X4)))=s(t_h4s_fcps_cart(t_bool,X1),h4s_bools_cond(s(t_bool,X5),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_t),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X4))))))=>![X6]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_saturateu_u_w2w(s(t_h4s_fcps_cart(t_bool,X2),h4s_wordss_n2w(s(t_h4s_nums_num,X6)))))=s(t_h4s_fcps_cart(t_bool,X1),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_fcps_cart(t_bool,X1)),X3),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value)))))))),file('i/f/words/saturate__w2w__n2w', ch4s_wordss_saturateu_u_w2wu_u_n2w)).
fof(3, axiom,![X1]:![X2]:![X8]:![X9]:s(X1,h4s_bools_let(s(t_fun(X2,X1),X9),s(X2,X8)))=s(X1,happ(s(t_fun(X2,X1),X9),s(X2,X8))),file('i/f/words/saturate__w2w__n2w', ah4s_bools_LETu_u_THM)).
fof(5, axiom,![X6]:![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X6))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X6))),s(t_h4s_nums_num,X6))))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_MODu_u_LESS)).
fof(7, axiom,![X2]: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(X2),h4s_bools_theu_u_value)))))),file('i/f/words/saturate__w2w__n2w', ah4s_wordss_ZEROu_u_LTu_u_dimword)).
fof(10, axiom,![X1]:![X2]:![X15]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_saturateu_u_w2w(s(t_h4s_fcps_cart(t_bool,X2),X15)))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_saturateu_u_n2w(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X2),X15))))),file('i/f/words/saturate__w2w__n2w', ah4s_wordss_saturateu_u_w2wu_u_def)).
fof(11, axiom,![X2]:![X16]:![X17]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X17),s(X2,X16)))=s(X2,X17),file('i/f/words/saturate__w2w__n2w', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(14, axiom,![X2]:![X6]:s(t_h4s_fcps_cart(t_bool,X2),h4s_wordss_saturateu_u_n2w(s(t_h4s_nums_num,X6)))=s(t_h4s_fcps_cart(t_bool,X2),h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value))),s(t_h4s_nums_num,X6))),s(t_h4s_fcps_cart(t_bool,X2),h4s_wordss_wordu_u_t),s(t_h4s_fcps_cart(t_bool,X2),h4s_wordss_n2w(s(t_h4s_nums_num,X6))))),file('i/f/words/saturate__w2w__n2w', ah4s_wordss_saturateu_u_n2wu_u_def)).
fof(16, axiom,![X16]:![X17]:((p(s(t_bool,X17))=>p(s(t_bool,X16)))=>((p(s(t_bool,X16))=>p(s(t_bool,X17)))=>s(t_bool,X17)=s(t_bool,X16))),file('i/f/words/saturate__w2w__n2w', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(32, axiom,![X27]:![X6]:![X4]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X6))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X27)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X27))))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(33, axiom,![X4]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X4)))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(34, axiom,![X6]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X6)))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(35, axiom,![X27]:![X6]:![X4]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X6))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X27)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X27))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(36, axiom,![X2]:![X1]:s(t_bool,h4s_primu_u_recs_u_3c(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)))))=s(t_bool,h4s_primu_u_recs_u_3c(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_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))),file('i/f/words/saturate__w2w__n2w', ah4s_wordss_dimindexu_u_dimwordu_u_ltu_u_iso)).
fof(37, axiom,![X4]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X4),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_ADDu_u_0)).
fof(41, axiom,![X6]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6)))=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,X6))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(43, axiom,![X6]:![X4]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X6)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4))),s(t_h4s_nums_num,X6))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_LESSu_u_EQ)).
fof(45, axiom,![X2]:![X6]:s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X2),h4s_wordss_n2w(s(t_h4s_nums_num,X6)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X2),h4s_bools_theu_u_value))))),file('i/f/words/saturate__w2w__n2w', ah4s_wordss_w2nu_u_n2w)).
fof(46, axiom,p(s(t_bool,t)),file('i/f/words/saturate__w2w__n2w', aHLu_TRUTH)).
fof(47, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)|s(t_bool,X14)=s(t_bool,f)),file('i/f/words/saturate__w2w__n2w', aHLu_BOOLu_CASES)).
fof(54, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)<=>p(s(t_bool,X14))),file('i/f/words/saturate__w2w__n2w', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(55, axiom,~(p(s(t_bool,f))),file('i/f/words/saturate__w2w__n2w', aHLu_FALSITY)).
fof(60, axiom,![X14]:((p(s(t_bool,X14))=>p(s(t_bool,f)))<=>s(t_bool,X14)=s(t_bool,f)),file('i/f/words/saturate__w2w__n2w', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(66, axiom,![X6]:![X4]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X4))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_LESSu_u_EQu_u_MONO)).
fof(67, axiom,![X6]:![X4]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X6)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6))),s(t_h4s_nums_num,X4))))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_NOTu_u_LEQ)).
fof(68, axiom,![X6]:![X4]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X4))),file('i/f/words/saturate__w2w__n2w', ah4s_arithmetics_ADDu_u_SYM)).
# SZS output end CNFRefutation
