# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3))))=>(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X1)<=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3)))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/arithmetic/MULT__EQ__DIV', ch4s_arithmetics_MULTu_u_EQu_u_DIV)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MULT__EQ__DIV', aHLu_TRUTH)).
fof(4, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/arithmetic/MULT__EQ__DIV', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(8, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/arithmetic/MULT__EQ__DIV', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X8]:![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9))),file('i/f/arithmetic/MULT__EQ__DIV', ah4s_arithmetics_MULTu_u_COMM)).
fof(10, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X9),file('i/f/arithmetic/MULT__EQ__DIV', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(11, axiom,![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8))))=>![X10]:(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X8)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X8)))))),file('i/f/arithmetic/MULT__EQ__DIV', ah4s_arithmetics_DIVISION)).
fof(12, axiom,![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8))))=>![X10]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/MULT__EQ__DIV', ah4s_arithmetics_MODu_u_EQu_u_0)).
fof(13, axiom,![X11]:![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,X11)),file('i/f/arithmetic/MULT__EQ__DIV', ah4s_arithmetics_MULTu_u_DIV)).
fof(14, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/arithmetic/MULT__EQ__DIV', aHLu_BOOLu_CASES)).
fof(15, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MULT__EQ__DIV', aHLu_FALSITY)).
# SZS output end CNFRefutation
