# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(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,X2),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bits_log2),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bits_log2),s(t_h4s_nums_num,X1)))))))),file('i/f/bit/LOG2__LE__MONO', ch4s_bits_LOG2u_u_LEu_u_MONO)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bit/LOG2__LE__MONO', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bit/LOG2__LE__MONO', aHLu_FALSITY)).
fof(8, axiom,![X9]:![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X10))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9)))))),file('i/f/bit/LOG2__LE__MONO', ah4s_numerals_numeralu_u_ltu_c5)).
fof(9, axiom,![X1]:![X2]:![X11]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X11))))&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,X2),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_logroots_log(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_logroots_log(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X1)))))))),file('i/f/bit/LOG2__LE__MONO', ah4s_logroots_LOGu_u_LEu_u_MONO)).
fof(10, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/bit/LOG2__LE__MONO', aHLu_BOOLu_CASES)).
fof(13, axiom,![X9]:![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))),file('i/f/bit/LOG2__LE__MONO', ah4s_numerals_numeralu_u_distribu_c22)).
fof(14, axiom,![X9]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bit/LOG2__LE__MONO', ah4s_numerals_numeralu_u_ltu_c2)).
fof(15, axiom,s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bits_log2)=s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_logroots_log(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/bit/LOG2__LE__MONO', ah4s_bits_LOG2u_u_def)).
# SZS output end CNFRefutation
