# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((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,X2),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))&~(s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3)))=s(t_h4s_nums_num,h4s_nums_0)))=>![X4]:p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4))))))))),file('i/f/transc/DIVISION__LBOUND__LT', ch4s_transcs_DIVISIONu_u_LBOUNDu_u_LT)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/transc/DIVISION__LBOUND__LT', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/transc/DIVISION__LBOUND__LT', aHLu_FALSITY)).
fof(9, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X4]:![X8]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X4))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_ORu_u_LESS)).
fof(12, axiom,![X4]:![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_LESSu_u_IMPu_u_LESSu_u_ORu_u_EQ)).
fof(13, axiom,![X4]:![X8]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X8))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(14, axiom,![X4]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_LEu_c0)).
fof(16, axiom,![X1]:![X2]:![X3]:(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,X2),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))=>s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3)))))=s(t_h4s_realaxs_real,X1)),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_transcs_DIVISIONu_u_RHS)).
fof(17, axiom,![X1]:![X2]:![X3]:(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,X2),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))=>![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))))=>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),X3),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),X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4)))))))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_transcs_DIVISIONu_u_LT)).
fof(18, axiom,![X1]:![X2]:![X3]:(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,X2),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))=>![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))))=>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),X3),s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3)))))))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_transcs_DIVISIONu_u_GT)).
fof(21, axiom,![X1]:![X2]:![X3]:(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,X2),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))<=>(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_realaxs_real,X2)&(![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))))=>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),X3),s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4)))))))))&![X4]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))))=>s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,X4)))=s(t_h4s_realaxs_real,X1))))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_transcs_DIVISIONu_u_THM)).
fof(22, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/transc/DIVISION__LBOUND__LT', aHLu_BOOLu_CASES)).
fof(23, axiom,![X4]:![X8]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X8)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X4))),file('i/f/transc/DIVISION__LBOUND__LT', ah4s_arithmetics_GREATERu_u_EQ)).
# SZS output end CNFRefutation
