# 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))))&(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),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,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X3)))),file('i/f/arithmetic/MOD__TIMES__SUB', ch4s_arithmetics_MODu_u_TIMESu_u_SUB)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MOD__TIMES__SUB', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MOD__TIMES__SUB', aHLu_FALSITY)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/arithmetic/MOD__TIMES__SUB', aHLu_BOOLu_CASES)).
fof(13, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/arithmetic/MOD__TIMES__SUB', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(14, axiom,![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))))=>![X2]:![X1]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),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)))),file('i/f/arithmetic/MOD__TIMES__SUB', ah4s_arithmetics_MODu_u_TIMES)).
fof(15, axiom,![X3]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/MOD__TIMES__SUB', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(16, axiom,![X3]:![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X3))),file('i/f/arithmetic/MOD__TIMES__SUB', ah4s_arithmetics_MULTu_c1)).
fof(17, axiom,![X9]:(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_0)|?[X3]:s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3)))),file('i/f/arithmetic/MOD__TIMES__SUB', ah4s_arithmetics_numu_u_CASES)).
fof(18, axiom,![X10]:![X11]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))))=>![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/MOD__TIMES__SUB', ah4s_arithmetics_LESSu_u_EQu_u_ADDu_u_SUB)).
# SZS output end CNFRefutation
