# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/integral/LT__LE', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integral/LT__LE', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/integral/LT__LE', aHLu_BOOLu_CASES)).
fof(16, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/integral/LT__LE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(19, axiom,![X1]:((p(s(t_bool,X1))=>p(s(t_bool,f)))<=>s(t_bool,X1)=s(t_bool,f)),file('i/f/integral/LT__LE', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(21, 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/integral/LT__LE', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(22, axiom,![X14]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),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,X13))),file('i/f/integral/LT__LE', ah4s_arithmetics_ADDu_u_SYM)).
fof(23, axiom,![X14]:![X13]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),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,X13))),s(t_h4s_nums_num,X14))),file('i/f/integral/LT__LE', ah4s_arithmetics_LESSu_u_EQ)).
fof(25, axiom,![X15]:![X14]:![X13]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),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)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X15))))),file('i/f/integral/LT__LE', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(26, 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/integral/LT__LE', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(27, axiom,![X14]:![X13]:(s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,X14)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),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)))))),file('i/f/integral/LT__LE', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(28, axiom,![X15]:![X14]:![X13]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X15)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))),file('i/f/integral/LT__LE', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(29, 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/integral/LT__LE', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(30, axiom,![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/integral/LT__LE', ah4s_numerals_numeralu_u_distribu_c27)).
fof(31, axiom,![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/integral/LT__LE', ah4s_numerals_numeralu_u_lteu_c1)).
fof(32, axiom,![X14]:![X13]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),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,X14))))|s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,X14))),file('i/f/integral/LT__LE', ah4s_integrals_LEu_u_LT)).
fof(33, conjecture,![X14]:![X13]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))))&~(s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,X14)))),file('i/f/integral/LT__LE', ch4s_integrals_LTu_u_LE)).
# SZS output end CNFRefutation
