# 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_realaxs_real,X2)=s(t_h4s_realaxs_real,X1)<=>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))),file('i/f/transc/DIVISION__EQ', ch4s_transcs_DIVISIONu_u_EQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/transc/DIVISION__EQ', aHLu_TRUTH)).
fof(8, axiom,![X6]:(s(t_bool,t)=s(t_bool,X6)<=>p(s(t_bool,X6))),file('i/f/transc/DIVISION__EQ', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(10, axiom,![X9]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/transc/DIVISION__EQ', ah4s_nums_NOTu_u_SUC)).
fof(11, axiom,![X10]:(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_0)|?[X9]:s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))),file('i/f/transc/DIVISION__EQ', ah4s_arithmetics_numu_u_CASES)).
fof(13, 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)&(![X9]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),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,X9))),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,X9)))))))))&![X9]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X9),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,X9)))=s(t_h4s_realaxs_real,X1))))),file('i/f/transc/DIVISION__EQ', ah4s_transcs_DIVISIONu_u_THM)).
fof(14, 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))))=>![X9]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),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,X9)))))))))),file('i/f/transc/DIVISION__EQ', ah4s_transcs_DIVISIONu_u_LT)).
fof(15, axiom,![X9]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))))),file('i/f/transc/DIVISION__EQ', ah4s_primu_u_recs_LESSu_u_SUCu_u_REFL)).
fof(16, axiom,![X10]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))=s(t_h4s_nums_num,X10),file('i/f/transc/DIVISION__EQ', ah4s_primu_u_recs_PRE0u_c1)).
fof(17, axiom,![X10]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X10)))),file('i/f/transc/DIVISION__EQ', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(18, axiom,![X9]:![X10]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))),file('i/f/transc/DIVISION__EQ', ah4s_arithmetics_GREATERu_u_EQ)).
fof(20, axiom,![X15]:![X8]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X15))))=>~(s(t_h4s_realaxs_real,X8)=s(t_h4s_realaxs_real,X15))),file('i/f/transc/DIVISION__EQ', ah4s_reals_REALu_u_LTu_u_IMPu_u_NE)).
fof(21, axiom,~(p(s(t_bool,f))),file('i/f/transc/DIVISION__EQ', aHLu_FALSITY)).
fof(24, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/transc/DIVISION__EQ', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
