# 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,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))<=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/integral/LT_c1', ch4s_integrals_LTu_c1)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integral/LT_c1', aHLu_FALSITY)).
fof(9, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/integral/LT_c1', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(21, axiom,![X12]:![X13]:![X14]:((p(s(t_bool,X14))<=>s(t_bool,X13)=s(t_bool,X12))<=>((p(s(t_bool,X14))|(p(s(t_bool,X13))|p(s(t_bool,X12))))&((p(s(t_bool,X14))|(~(p(s(t_bool,X12)))|~(p(s(t_bool,X13)))))&((p(s(t_bool,X13))|(~(p(s(t_bool,X12)))|~(p(s(t_bool,X14)))))&(p(s(t_bool,X12))|(~(p(s(t_bool,X13)))|~(p(s(t_bool,X14))))))))),file('i/f/integral/LT_c1', ah4s_sats_dcu_u_eq)).
fof(25, axiom,![X14]:![X1]:![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,X1),s(t_h4s_nums_num,X14)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X14))))),file('i/f/integral/LT_c1', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(26, axiom,![X1]:![X2]:(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,X2),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))),file('i/f/integral/LT_c1', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(28, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/integral/LT_c1', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(29, axiom,![X1]:![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))),file('i/f/integral/LT_c1', ah4s_arithmetics_LESSu_u_EQ)).
fof(30, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(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,X1),s(t_h4s_nums_num,X2))))),file('i/f/integral/LT_c1', ah4s_arithmetics_NOTu_u_LESS)).
fof(31, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X2),file('i/f/integral/LT_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(32, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/integral/LT_c1', ah4s_arithmetics_ADDu_u_SYM)).
fof(34, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/integral/LT_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(35, axiom,![X14]:![X1]:![X2]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X14)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X14))),file('i/f/integral/LT_c1', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(36, axiom,![X1]:![X2]:(~(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,h4s_nums_suc(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,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2)))))),file('i/f/integral/LT_c1', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(37, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=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,X1))),file('i/f/integral/LT_c1', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(38, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/integral/LT_c1', ah4s_numerals_numeralu_u_distribu_c27)).
fof(40, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/integral/LT_c1', aHLu_BOOLu_CASES)).
fof(43, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))))),file('i/f/integral/LT_c1', ah4s_numerals_numeralu_u_distribu_c2)).
fof(44, axiom,![X1]: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,X1)))))=s(t_h4s_nums_num,X1),file('i/f/integral/LT_c1', ah4s_numerals_numeralu_u_addu_c0)).
fof(47, axiom,p(s(t_bool,t)),file('i/f/integral/LT_c1', aHLu_TRUTH)).
fof(50, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/integral/LT_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
