# 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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))))=>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,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ch4s_arithmetics_ONEu_u_LTu_u_MULTu_u_IMP)).
fof(2, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(23, axiom,![X13]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(26, axiom,![X13]:(~(s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,h4s_nums_0))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(27, axiom,![X2]:![X13]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_LTu_u_MULTu_u_LCANCEL)).
fof(28, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),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/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_MULTu_u_CLAUSESu_c3)).
fof(29, axiom,![X2]:![X13]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_LTu_u_MULTu_u_RCANCEL)).
fof(33, axiom,![X13]:![X14]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_MULTu_u_EQu_u_0)).
fof(34, axiom,![X13]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X13))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_MULTu_c1)).
fof(40, axiom,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,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_ONE)).
fof(41, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,X9),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(42, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_BIT10)).
fof(43, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_ALTu_u_ZERO)).
fof(44, axiom,![X13]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_ADDu_u_COMM)).
fof(45, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,X13),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_ADDu_c0)).
fof(48, axiom,![X2]:![X13]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2))))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_LESSu_u_MONOu_u_ADD)).
fof(52, axiom,![X13]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_ADDu_u_CLAUSESu_c2)).
fof(53, axiom,![X13]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(54, axiom,![X13]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))))=>?[X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,X14)),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_LESSu_u_ADD)).
fof(56, axiom,![X13]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_primu_u_recs_LESSu_u_0)).
fof(57, axiom,![X13]:![X14]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_LESSu_u_MONOu_u_EQ)).
fof(58, axiom,![X13]:~(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_arithmetics_SUCu_u_NOT)).
fof(61, axiom,![X13]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X13))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_primu_u_recs_SUCu_u_LESS)).
fof(62, axiom,![X13]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13))))))<=>(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,X13)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))),file('i/f/arithmetic/ONE__LT__MULT__IMP', ah4s_primu_u_recs_LESSu_u_THM)).
# SZS output end CNFRefutation
