# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/int_arith/INT__NUM__SUB', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/INT__NUM__SUB', 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/int_arith/INT__NUM__SUB', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))=>s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X7))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8)))))),file('i/f/int_arith/INT__NUM__SUB', ah4s_integers_INTu_u_SUB)).
fof(6, axiom,![X7]:![X8]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X7)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))),file('i/f/int_arith/INT__NUM__SUB', ah4s_integers_INTu_u_LT)).
fof(12, axiom,![X7]:![X8]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))))),file('i/f/int_arith/INT__NUM__SUB', ah4s_arithmetics_NOTu_u_LESS)).
fof(21, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/int_arith/INT__NUM__SUB', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(37, axiom,![X1]:((p(s(t_bool,X1))=>p(s(t_bool,f)))<=>s(t_bool,X1)=s(t_bool,f)),file('i/f/int_arith/INT__NUM__SUB', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(39, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X7),file('i/f/int_arith/INT__NUM__SUB', ah4s_numerals_numeralu_u_distribu_c1)).
fof(42, axiom,![X7]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X7)))),file('i/f/int_arith/INT__NUM__SUB', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(51, axiom,![X7]:![X8]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X8))))),file('i/f/int_arith/INT__NUM__SUB', ah4s_arithmetics_NOTu_u_LEQ)).
fof(52, axiom,![X7]:![X8]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))),file('i/f/int_arith/INT__NUM__SUB', ah4s_arithmetics_ADDu_u_SYM)).
fof(55, axiom,![X19]:![X7]:![X8]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X7))))),file('i/f/int_arith/INT__NUM__SUB', ah4s_arithmetics_SUBu_u_RIGHTu_u_ADD)).
fof(60, axiom,![X10]:![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10)))=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X10))))),file('i/f/int_arith/INT__NUM__SUB', ah4s_integers_intu_u_sub0)).
fof(71, axiom,![X19]:![X7]:![X8]:(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X19)))<=>(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,X7)|(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_0))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X19))))))),file('i/f/int_arith/INT__NUM__SUB', ah4s_arithmetics_SUBu_u_LEFTu_u_EQ)).
fof(73, axiom,![X7]:![X8]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X7)))),file('i/f/int_arith/INT__NUM__SUB', ah4s_arithmetics_SUBu_u_LESSu_u_EQ)).
fof(76, axiom,![X7]: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,X7)))))=s(t_h4s_nums_num,X7),file('i/f/int_arith/INT__NUM__SUB', ah4s_numerals_numeralu_u_addu_c0)).
fof(89, axiom,![X7]:![X8]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X7))),file('i/f/int_arith/INT__NUM__SUB', ah4s_arithmetics_LESSu_u_EQ)).
fof(122, axiom,![X9]:![X15]:![X16]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X16),s(X9,X15)))=s(X9,X16),file('i/f/int_arith/INT__NUM__SUB', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(124, axiom,![X9]:![X15]:![X16]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X16),s(X9,X15)))=s(X9,X15),file('i/f/int_arith/INT__NUM__SUB', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(133, conjecture,![X7]:![X8]:s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8)))))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X7))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X7))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8))))))),file('i/f/int_arith/INT__NUM__SUB', ch4s_intu_u_ariths_INTu_u_NUMu_u_SUB)).
# SZS output end CNFRefutation
