# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))),file('i/f/integer/LT__ADD2', ch4s_integers_LTu_u_ADD2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integer/LT__ADD2', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/integer/LT__ADD2', aHLu_FALSITY)).
fof(9, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/integer/LT__ADD2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X6]:((p(s(t_bool,X6))=>p(s(t_bool,f)))<=>s(t_bool,X6)=s(t_bool,f)),file('i/f/integer/LT__ADD2', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(14, axiom,![X13]:![X14]:![X15]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X13))))),file('i/f/integer/LT__ADD2', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(16, axiom,![X14]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))),file('i/f/integer/LT__ADD2', ah4s_arithmetics_ADDu_u_SYM)).
fof(18, axiom,![X13]:![X14]:![X15]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X13)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))),file('i/f/integer/LT__ADD2', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(19, axiom,![X14]:![X15]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X14))),file('i/f/integer/LT__ADD2', ah4s_arithmetics_LESSu_u_EQ)).
fof(20, axiom,![X14]:![X15]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))))),file('i/f/integer/LT__ADD2', ah4s_arithmetics_NOTu_u_LESS)).
fof(21, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,X15),file('i/f/integer/LT__ADD2', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(22, axiom,![X14]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X14))),file('i/f/integer/LT__ADD2', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(24, axiom,![X14]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X14)))))=s(t_h4s_nums_num,X14),file('i/f/integer/LT__ADD2', ah4s_numerals_numeralu_u_addu_c0)).
fof(26, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/integer/LT__ADD2', aHLu_BOOLu_CASES)).
fof(28, axiom,![X14]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14)))),file('i/f/integer/LT__ADD2', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
