# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/transc/DIVISION__LBOUND__LT', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/transc/DIVISION__LBOUND__LT', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/transc/DIVISION__LBOUND__LT', aHLu_BOOLu_CASES)).
fof(7, axiom,![X11]:![X12]:![X13]:(p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X11))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13))))<=>(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_realaxs_real,X12)&(![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13))))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13),s(t_h4s_nums_num,X14))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14)))))))))&![X14]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3eu_3d),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13))))))=>s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13),s(t_h4s_nums_num,X14)))=s(t_h4s_realaxs_real,X11))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_transcs_DIVISIONu_u_THM)).
fof(10, axiom,![X11]:![X12]:![X13]:(p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X11))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13))))=>![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13))))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14)))))))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_transcs_DIVISIONu_u_LT)).
fof(15, axiom,![X11]:![X12]:![X13]:(p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X11))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13))))=>(s(t_h4s_realaxs_real,X12)=s(t_h4s_realaxs_real,X11)<=>s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13)))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_transcs_DIVISIONu_u_EQ)).
fof(17, axiom,![X14]:![X15]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3eu_3d),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X15)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_GREATERu_u_EQ)).
fof(30, axiom,![X11]:![X12]:![X13]:(p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X11))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13))))=>![X20]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13),s(t_h4s_nums_num,X20))))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_transcs_DIVISIONu_u_LBOUND)).
fof(40, axiom,![X15]:(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_0)|?[X14]:s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14)))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_numu_u_CASES)).
fof(43, axiom,![X15]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15)))))=s(t_h4s_nums_num,X15),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_primu_u_recs_PRE0u_c1)).
fof(45, axiom,![X6]:~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X6))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_reals_REALu_u_LTu_u_REFL)).
fof(47, axiom,![X14]:![X15]:(p(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))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_ORu_u_LESS)).
fof(51, 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,X15),s(t_h4s_nums_num,X14))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_LESSu_u_IMPu_u_LESSu_u_ORu_u_EQ)).
fof(58, axiom,![X14]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_nums_NOTu_u_SUC)).
fof(65, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(69, 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/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_LESSu_u_CASES)).
fof(89, axiom,![X10]:![X6]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X10))))<=>(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X10))))|s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,X10))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_reals_REALu_u_LEu_u_LT)).
fof(133, conjecture,![X11]:![X12]:![X13]:((p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X11))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13))))&~(s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13)))=s(t_h4s_nums_num,h4s_nums_0)))=>![X14]:p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X13),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))))))))),file('i/f/transc/DIVISION__LBOUND__LT', ch4s_transcs_DIVISIONu_u_LBOUNDu_u_LT)).
# SZS output end CNFRefutation
