0.00/0.00 % Leo-III: Strategy 1 (for '60') 21.10/10.51 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 21.10/10.51 % [INFO] Parsing done (304ms). 21.10/10.51 % [INFO] Running in sequential loop mode. 21.10/10.51 % [CONFIG] Using configuration: timeout(60) with strategy 21.10/10.51 % [INFO] eprover registered as external prover. 21.10/10.51 % [INFO] cvc4 registered as external prover. 21.10/10.51 % [INFO] Parsing finished. Scanning for conjecture ... 21.10/10.51 % [INFO] Found a conjecture and 185 axioms. Running axiom selection ... 21.10/10.51 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms). 21.10/10.51 % [INFO] Problem is higher-order (TPTP THF). 21.10/10.51 % [INFO] Type checking passed. Searching for refutation ... 21.10/10.51 % External prover 'e' found a proof! 21.10/10.51 % [INFO] Killing All external provers ... 21.10/10.51 % Time passed: 4993ms (effective reasoning time: 4191ms) 21.10/10.51 % Solved by strategy 21.10/10.51 % Axioms used in derivation (185): fact_144_length__induct, fact_26_div__mult__mult1, fact_104_mult__cancel__left, fact_31_nat__less__induct, fact_82_less__Suc__eq__0__disj, fact_20_mult__cancel2, fact_107_div__by__0, fact_6_nat__0__less__mult__iff, fact_156_split__div_H, fact_19_lessI, fact_95_n__less__m__mult__n, fact_157_le__less__div__conv, fact_111_mult__left__cancel, fact_155_length__product, fact_166_zero__le, fact_145_Ex__list__of__length, fact_130_mult__cancel2__gr0, fact_93_Euclidean__Division_Oless__mult__imp__div__less, fact_14_bot__nat__0_Onot__eq__extremum, fact_172_nat__leSuc0__conv, fact_59_not__less__less__Suc__eq, fact_135_ab__semigroup__mult__class_Omult__ac_I1_J, fact_87_nat__mult__less__cancel1, fact_92_Euclidean__Division_Odiv__eq__0__iff, fact_65_Suc__less__eq2, fact_139_gr__zeroI, fact_160_le0, fact_41_old_Onat_Oexhaust, fact_47_nat__induct, fact_103_mult__eq__0__iff, fact_113_mult__neg__pos, fact_149_list__decode_Ocases, fact_88_nat__mult__eq__cancel1, fact_1_div__mult__self1__is__m, fact_167_ge__less__neq__conv, fact_36_nat__neq__iff, fact_147_neq__if__length__neq, fact_53_infinite__descent0, fact_23_mult__is__0, fact_119_mult__strict__left__mono, fact_78_Suc__mult__cancel1, fact_17_Suc__less__eq, fact_29_linorder__neqE__nat, fact_50_old_Onat_Odistinct_I2_J, fact_143_length__induct, fact_32_less__irrefl__nat, fact_40_old_Onat_Oinducts, fact_10_less__Suc0, fact_55_less__zeroE, fact_131_zero__reorient, fact_133_mult_Ocommute, fact_71_less__SucE, fact_125_div__less__conv, fact_21_mult__cancel1, fact_106_div__0, fact_181_mult__mono_H, fact_164_nat__mult__le__cancel__disj, fact_90_mult__less__mono1, fact_9_one__eq__mult__iff, fact_128_bits__div__by__0, fact_39_not0__implies__Suc, fact_153_length__product, fact_146_Ex__list__of__length, fact_57_not__gr0, fact_68_less__Suc__eq, fact_77_mult__0, fact_140_gr__implies__gr0, fact_180_mult__left__mono, fact_8_mult__eq__1__iff, fact_25_div__mult__mult2, fact_74_Suc__lessD, fact_109_divisors__zero, fact_79_div__mult2__eq, fact_137_gr__implies__not__zero, fact_67_not__less__eq, fact_129_not__gr__zero, fact_27_n__not__Suc__n, fact_44_Suc__neq__Zero, fact_120_mult__strict__right__mono, fact_98_nonzero__mult__div__cancel__right, fact_179_mult__right__mono, fact_60_strict__inc__induct, fact_110_no__zero__divisors, fact_49_old_Onat_Odistinct_I1_J, fact_151_less__numeral__extra_I3_J, fact_16_neq0__conv, fact_54_gr__implies__not0, fact_138_not__less__zero, fact_70_less__SucI, fact_34_less__not__refl2, fact_33_less__not__refl3, fact_169_greater__le__neq__conv, fact_132_mult_Oleft__commute, fact_69_Ex__less__Suc, fact_118_zero__less__mult__pos2, fact_48_nat_OdiscI, fact_51_nat_Odistinct_I1_J, fact_73_Suc__lessE, fact_170_le__greater__neq__conv, fact_121_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_102_mult__zero__right, fact_76_nat__mult__eq__cancel__disj, fact_52_bot__nat__0_Oextremum__strict, fact_4_div__by__Suc__0, fact_116_mult__pos__neg2, fact_85_gr0__conv__Suc, fact_42_Zero__not__Suc, fact_80_lift__Suc__mono__less__iff, fact_178_split__mult__neg__le, fact_114_mult__pos__neg, fact_84_All__less__Suc2, fact_86_Ex__less__Suc2, fact_115_mult__pos__pos, fact_168_less__ge__neq__conv, fact_63_Suc__less__SucD, fact_91_Suc__mult__less__cancel1, fact_56_not__less0, fact_72_Suc__lessI, fact_134_mult_Oassoc, fact_163_mult__le__cancel2, fact_148_neq__if__length__neq, fact_124_Util__Div_Oless__mult__imp__div__less, fact_89_mult__less__mono2, fact_75_Nat_OlessE, fact_81_lift__Suc__mono__less, fact_171_nat__geSucSuc0__conv, fact_165_le__numeral__extra_I3_J, fact_62_less__trans__Suc, fact_35_less__not__refl, fact_154_length__product, fact_142_nat__grSuc0__conv, fact_100_less__div__Suc__mult, fact_150_exists__least__lemma, fact_18_Suc__mono, fact_161_Suc__le__mono, fact_13_nat_Oinject, fact_176_mult__nonneg__nonpos, fact_64_less__antisym, fact_38_size__neq__size__imp__neq, fact_61_less__Suc__induct, fact_182_mult__mono, fact_5_mult__less__cancel2, conj_1, fact_175_mult__nonpos__nonneg, fact_127_bits__div__0, fact_174_mult__nonneg__nonpos2, fact_3_div__less, fact_94_n__less__n__mult__m, fact_105_mult__cancel__right, fact_117_zero__less__mult__pos, fact_83_gr0__implies__Suc, fact_7_nat__mult__less__cancel__disj, fact_158_le__zero__eq, fact_28_Suc__inject, fact_101_mult__zero__left, fact_45_zero__induct, fact_24_div__mult__mult1__if, fact_152_length__product, fact_122_div__eq__0__conv, fact_177_mult__nonneg__nonneg, fact_112_mult__right__cancel, fact_0_div__mult__self__is__m, fact_58_gr0I, fact_46_diff__induct, fact_173_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_12_old_Onat_Oinject, fact_159_bot__nat__0_Oextremum, fact_162_one__le__mult__iff, fact_136_zero__less__iff__neq__zero, fact_37_size__neq__size__imp__neq, fact_96_one__less__mult, fact_30_infinite__descent, fact_2_nat__mult__div__cancel__disj, fact_66_All__less__Suc, fact_22_mult__0__right, fact_99_nonzero__mult__div__cancel__left, fact_123_div__eq__0__conv_H, conj_0, fact_126_div__less__imp__less__mult, fact_97_nat__mult__div__cancel1, fact_43_Zero__neq__Suc, fact_15_less__nat__zero__code, fact_108_mult__not__zero, fact_141_nat__lessSucSuc0__conv, fact_11_zero__less__Suc 21.10/10.51 % No. of inferences in proof: 374 21.10/10.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4993 ms resp. 4191 ms w/o parsing 21.10/10.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 21.10/10.51 thf(list_P1891567085od_a_a_type, type, list_P1891567085od_a_a: $tType). 21.10/10.51 thf(list_P1458844246od_a_a_type, type, list_P1458844246od_a_a: $tType). 21.10/10.51 thf(list_P319927492_a_a_a_type, type, list_P319927492_a_a_a: $tType). 21.10/10.51 thf(list_P1467822637od_a_a_type, type, list_P1467822637od_a_a: $tType). 21.10/10.51 thf(list_a_type, type, list_a: $tType). 21.10/10.51 thf(nat_type, type, nat: $tType). 21.10/10.51 thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))). 21.10/10.51 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 21.10/10.51 thf(produc1055075589od_a_a_type, type, produc1055075589od_a_a: (list_P1467822637od_a_a > (list_P1467822637od_a_a > list_P1891567085od_a_a))). 21.10/10.51 thf(produc778776796_a_a_a_type, type, produc778776796_a_a_a: (list_P1467822637od_a_a > (list_a > list_P319927492_a_a_a))). 21.10/10.51 thf(produc16441326od_a_a_type, type, produc16441326od_a_a: (list_a > (list_P1467822637od_a_a > list_P1458844246od_a_a))). 21.10/10.51 thf(product_a_a_type, type, product_a_a: (list_a > (list_a > list_P1467822637od_a_a))). 21.10/10.51 thf(suc_type, type, suc: (nat > nat)). 21.10/10.51 thf(size_s1052379225od_a_a_type, type, size_s1052379225od_a_a: (list_P1891567085od_a_a > nat)). 21.10/10.51 thf(size_s736232240_a_a_a_type, type, size_s736232240_a_a_a: (list_P319927492_a_a_a > nat)). 21.10/10.51 thf(size_s1875148994od_a_a_type, type, size_s1875148994od_a_a: (list_P1458844246od_a_a > nat)). 21.10/10.51 thf(size_s642698393od_a_a_type, type, size_s642698393od_a_a: (list_P1467822637od_a_a > nat)). 21.10/10.51 thf(size_size_list_a_type, type, size_size_list_a: (list_a > nat)). 21.10/10.51 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 21.10/10.51 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 21.10/10.51 thf(divide_divide_nat_type, type, divide_divide_nat: (nat > (nat > nat))). 21.10/10.51 thf(k_type, type, k: nat). 21.10/10.51 thf(n_type, type, n: nat). 21.10/10.51 thf(xs_type, type, xs: list_a). 21.10/10.51 thf(35,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) <= (A = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_nat_OdiscI)). 21.10/10.51 thf(320,plain,((! [A:nat,B:nat]: (~ (A = zero_zero_nat) | ~ (A = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 21.10/10.51 thf(181,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (? [D:nat]: ((ord_less_nat @ B @ (times_times_nat @ C @ (suc @ D))) & (A @ D) & (ord_less_eq_nat @ (times_times_nat @ C @ D) @ B)) | ((A @ zero_zero_nat) & (C = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_split__div_H)). 21.10/10.51 thf(809,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (? [D:nat]: ((ord_less_nat @ B @ (times_times_nat @ C @ (suc @ D))) & (A @ D) & (ord_less_eq_nat @ (times_times_nat @ C @ D) @ B)) | ((A @ zero_zero_nat) & (C = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 21.10/10.51 thf(79,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ A @ B)) = ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ B) & (ord_less_eq_nat @ (suc @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_one__le__mult__iff)). 21.10/10.51 thf(468,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ A @ B)) = ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ B) & (ord_less_eq_nat @ (suc @ zero_zero_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 21.10/10.51 thf(13,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Zero__neq__Suc)). 21.10/10.51 thf(234,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 21.10/10.51 thf(172,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_mult__cancel2)). 21.10/10.51 thf(777,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 21.10/10.51 thf(135,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_mult__right__cancel)). 21.10/10.51 thf(666,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 21.10/10.51 thf(43,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((A = B) <= (~ (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__SucE)). 21.10/10.51 thf(352,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 21.10/10.51 thf(38,axiom,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_le__numeral__extra_I3_J)). 21.10/10.51 thf(333,plain,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 21.10/10.51 thf(17,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_le__zero__eq)). 21.10/10.51 thf(249,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 21.10/10.51 thf(157,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((ord_less_eq_nat @ (times_times_nat @ B @ A) @ C) & (ord_less_nat @ C @ (times_times_nat @ (suc @ B) @ A))) = ((divide_divide_nat @ C @ A) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_le__less__div__conv)). 21.10/10.51 thf(730,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((ord_less_eq_nat @ (times_times_nat @ B @ A) @ C) & (ord_less_nat @ C @ (times_times_nat @ (suc @ B) @ A))) = ((divide_divide_nat @ C @ A) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 21.10/10.51 thf(23,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C))) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_diff__induct)). 21.10/10.51 thf(269,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 21.10/10.51 thf(152,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_mult__eq__0__iff)). 21.10/10.51 thf(715,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 21.10/10.51 thf(41,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_div__mult__self1__is__m)). 21.10/10.51 thf(340,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 21.10/10.51 thf(136,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_nat__mult__eq__cancel__disj)). 21.10/10.51 thf(670,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 21.10/10.51 thf(155,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (times_times_nat @ (suc @ (divide_divide_nat @ B @ A)) @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_less__div__Suc__mult)). 21.10/10.51 thf(724,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (times_times_nat @ (suc @ (divide_divide_nat @ B @ A)) @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 21.10/10.51 thf(42,axiom,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) <= (A = zero_zero_nat)) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)) <= (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_div__mult__mult1__if)). 21.10/10.51 thf(344,plain,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) | ~ (A = zero_zero_nat)) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 21.10/10.51 thf(107,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_mult__nonpos__nonneg)). 21.10/10.51 thf(559,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 21.10/10.51 thf(128,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__not__refl)). 21.10/10.51 thf(638,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 21.10/10.51 thf(3,axiom,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_div__by__0)). 21.10/10.51 thf(189,plain,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 21.10/10.51 thf(65,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_mult__right__mono)). 21.10/10.51 thf(421,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 21.10/10.51 thf(36,axiom,((! [A:list_P1467822637od_a_a,B:list_P1467822637od_a_a]: (((size_s642698393od_a_a @ A) != (size_s642698393od_a_a @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_neq__if__length__neq)). 21.10/10.51 thf(325,plain,((! [A:list_P1467822637od_a_a,B:list_P1467822637od_a_a]: ((~ ((size_s642698393od_a_a @ A) = (size_s642698393od_a_a @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 21.10/10.51 thf(11,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Suc__le__mono)). 21.10/10.51 thf(228,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 21.10/10.51 thf(72,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (times_times_nat @ A @ B)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_one__eq__mult__iff)). 21.10/10.51 thf(448,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (times_times_nat @ A @ B)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 21.10/10.51 thf(34,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Suc__neq__Zero)). 21.10/10.51 thf(316,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 21.10/10.51 thf(113,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = ((B @ A) | ? [C:nat]: ((B @ C) & (ord_less_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Ex__less__Suc)). 21.10/10.51 thf(591,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = ((B @ A) | ? [C:nat]: ((B @ C) & (ord_less_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 21.10/10.51 thf(14,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_nat_Odistinct_I1_J)). 21.10/10.51 thf(238,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 21.10/10.51 thf(180,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_mult__strict__right__mono)). 21.10/10.51 thf(806,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 21.10/10.51 thf(185,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_nat @ B @ A) <= (~ (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_linorder__neqE__nat)). 21.10/10.51 thf(821,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 21.10/10.51 thf(83,axiom,((! [A:list_a,B:list_a]: ((size_s642698393od_a_a @ (product_a_a @ A @ B)) = (times_times_nat @ (size_size_list_a @ A) @ (size_size_list_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_length__product)). 21.10/10.51 thf(480,plain,((! [A:list_a,B:list_a]: ((size_s642698393od_a_a @ (product_a_a @ A @ B)) = (times_times_nat @ (size_size_list_a @ A) @ (size_size_list_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 21.10/10.51 thf(8,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((A @ zero_zero_nat) <= (! [C:nat]: ((A @ C) <= (A @ (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zero__induct)). 21.10/10.51 thf(211,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((A @ zero_zero_nat) | ~ (! [C:nat]: ((A @ C) | ~ (A @ (suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 21.10/10.51 thf(131,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_gr0__implies__Suc)). 21.10/10.51 thf(646,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 21.10/10.51 thf(57,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_bot__nat__0_Onot__eq__extremum)). 21.10/10.51 thf(397,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 21.10/10.51 thf(27,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_zero__reorient)). 21.10/10.51 thf(280,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 21.10/10.51 thf(29,axiom,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_div__by__Suc__0)). 21.10/10.51 thf(293,plain,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 21.10/10.51 thf(133,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_mult__pos__neg2)). 21.10/10.51 thf(660,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 21.10/10.51 thf(62,axiom,((! [A:nat]: ? [B:list_a]: ((size_size_list_a @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Ex__list__of__length)). 21.10/10.51 thf(411,plain,((! [A:nat]: ? [B:list_a]: ((size_size_list_a @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 21.10/10.51 thf(67,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) != zero_zero_nat) => ((B != zero_zero_nat) & (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_mult__not__zero)). 21.10/10.51 thf(428,plain,((! [A:nat,B:nat]: ((~ ((times_times_nat @ A @ B) = zero_zero_nat)) => (~ (B = zero_zero_nat) & ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 21.10/10.51 thf(97,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_nonzero__mult__div__cancel__right)). 21.10/10.51 thf(527,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 21.10/10.51 thf(158,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_gr0__conv__Suc)). 21.10/10.51 thf(734,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 21.10/10.51 thf(9,axiom,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_div__0)). 21.10/10.51 thf(221,plain,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 21.10/10.51 thf(52,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_less__nat__zero__code)). 21.10/10.51 thf(380,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 21.10/10.51 thf(69,axiom,((! [A:list_P1467822637od_a_a,B:list_P1467822637od_a_a]: ((size_s1052379225od_a_a @ (produc1055075589od_a_a @ A @ B)) = (times_times_nat @ (size_s642698393od_a_a @ A) @ (size_s642698393od_a_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_length__product)). 21.10/10.51 thf(439,plain,((! [A:list_P1467822637od_a_a,B:list_P1467822637od_a_a]: ((size_s1052379225od_a_a @ (produc1055075589od_a_a @ A @ B)) = (times_times_nat @ (size_s642698393od_a_a @ A) @ (size_s642698393od_a_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 21.10/10.51 thf(5,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Zero__not__Suc)). 21.10/10.51 thf(201,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 21.10/10.51 thf(167,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) = ((ord_less_nat @ A @ B) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Euclidean__Division_Odiv__eq__0__iff)). 21.10/10.51 thf(761,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) = ((ord_less_nat @ A @ B) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 21.10/10.51 thf(99,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ (suc @ C))) | (B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Ex__less__Suc2)). 21.10/10.51 thf(534,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ (suc @ C))) | (B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 21.10/10.51 thf(103,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_mult__0__right)). 21.10/10.51 thf(546,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 21.10/10.51 thf(177,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((((C @ A @ B) <= (! [D:nat,E:nat,F:nat]: ((ord_less_nat @ D @ E) => ((((C @ E @ F) => (C @ D @ F)) <= (C @ D @ E)) <= (ord_less_nat @ E @ F))))) <= (! [D:nat]: (C @ D @ (suc @ D)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_less__Suc__induct)). 21.10/10.51 thf(793,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((C @ A @ B) | ~ (! [D:nat,E:nat,F:nat]: ((ord_less_nat @ D @ E) => (((C @ E @ F) => (C @ D @ F)) | ~ (C @ D @ E) | ~ (ord_less_nat @ E @ F)))) | ~ (! [D:nat]: (C @ D @ (suc @ D))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 21.10/10.51 thf(39,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) & (B = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_mult__eq__1__iff)). 21.10/10.51 thf(334,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) & (B = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 21.10/10.51 thf(162,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ (suc @ A)))) = ((B @ A) & ! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_All__less__Suc)). 21.10/10.51 thf(746,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ (suc @ A)))) = ((B @ A) & ! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 21.10/10.51 thf(20,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_old_Onat_Oexhaust)). 21.10/10.51 thf(260,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 21.10/10.51 thf(66,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((divide_divide_nat @ B @ A) = zero_zero_nat) = (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_div__eq__0__conv_H)). 21.10/10.51 thf(424,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((divide_divide_nat @ B @ A) = zero_zero_nat) = (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 21.10/10.51 thf(4,axiom,((! [A:(nat > $o)]: ((~ (A @ zero_zero_nat)) => ((? [B:nat]: ((A @ (suc @ B)) & ~ (A @ B))) <= (? [B:nat]: (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_exists__least__lemma)). 21.10/10.51 thf(192,plain,((! [A:(nat > $o)]: ((~ (A @ zero_zero_nat)) => (? [B:nat]: ((A @ (suc @ B)) & ~ (A @ B)) | ~ (? [B:nat]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 21.10/10.51 thf(25,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_bot__nat__0_Oextremum)). 21.10/10.51 thf(275,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 21.10/10.51 thf(109,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_mult_Ocommute)). 21.10/10.51 thf(566,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 21.10/10.51 thf(18,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_old_Onat_Odistinct_I1_J)). 21.10/10.51 thf(252,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 21.10/10.51 thf(46,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ A @ (times_times_nat @ B @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_n__less__m__mult__n)). 21.10/10.51 thf(361,plain,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ A @ (times_times_nat @ B @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 21.10/10.51 thf(68,axiom,((! [A:(list_a > $o),B:list_a]: ((A @ B) <= (! [C:list_a]: ((A @ C) <= (! [D:list_a]: ((ord_less_nat @ (size_size_list_a @ D) @ (size_size_list_a @ C)) => (A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_length__induct)). 21.10/10.51 thf(435,plain,((! [A:(list_a > $o),B:list_a]: ((A @ B) | ~ (! [C:list_a]: ((A @ C) | ~ (! [D:list_a]: ((ord_less_nat @ (size_size_list_a @ D) @ (size_size_list_a @ C)) => (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 21.10/10.51 thf(37,axiom,((! [A:nat,B:nat]: ((A = B) <= ((suc @ A) = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Suc__inject)). 21.10/10.51 thf(329,plain,((! [A:nat,B:nat]: ((A = B) | ~ ((suc @ A) = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 21.10/10.51 thf(87,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_not__less0)). 21.10/10.51 thf(493,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 21.10/10.51 thf(140,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_mult__neg__pos)). 21.10/10.51 thf(682,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 21.10/10.51 thf(150,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__antisym)). 21.10/10.51 thf(710,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 21.10/10.51 thf(10,axiom,((! [A:nat]: ((~ (! [B:nat]: (A != (suc @ B)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_list__decode_Ocases)). 21.10/10.51 thf(224,plain,((! [A:nat]: (~ (! [B:nat]: ~ (A = (suc @ B))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 21.10/10.51 thf(121,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_ab__semigroup__mult__class_Omult__ac_I1_J)). 21.10/10.51 thf(615,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 21.10/10.51 thf(59,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_zero__less__iff__neq__zero)). 21.10/10.51 thf(403,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 21.10/10.51 thf(1,conjecture,((ord_less_nat @ (times_times_nat @ n @ k) @ (size_size_list_a @ xs))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)). 21.10/10.51 thf(2,negated_conjecture,((~ (ord_less_nat @ (times_times_nat @ n @ k) @ (size_size_list_a @ xs)))),inference(neg_conjecture,[status(cth)],[1])). 21.10/10.51 thf(188,plain,((~ (ord_less_nat @ (times_times_nat @ n @ k) @ (size_size_list_a @ xs)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 21.10/10.51 thf(119,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_gr__implies__gr0)). 21.10/10.51 thf(610,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 21.10/10.51 thf(174,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ (times_times_nat @ C @ A)) <= (ord_less_nat @ (divide_divide_nat @ B @ A) @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_div__less__imp__less__mult)). 21.10/10.51 thf(783,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (times_times_nat @ C @ A)) | ~ (ord_less_nat @ (divide_divide_nat @ B @ A) @ C) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 21.10/10.51 thf(100,axiom,((! [A:list_P1467822637od_a_a,B:list_a]: ((size_s736232240_a_a_a @ (produc778776796_a_a_a @ A @ B)) = (times_times_nat @ (size_s642698393od_a_a @ A) @ (size_size_list_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_length__product)). 21.10/10.51 thf(537,plain,((! [A:list_P1467822637od_a_a,B:list_a]: ((size_s736232240_a_a_a @ (produc778776796_a_a_a @ A @ B)) = (times_times_nat @ (size_s642698393od_a_a @ A) @ (size_size_list_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 21.10/10.51 thf(82,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_nat__mult__less__cancel1)). 21.10/10.51 thf(476,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 21.10/10.51 thf(86,axiom,((! [A:list_a,B:list_a]: (((size_size_list_a @ A) != (size_size_list_a @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_neq__if__length__neq)). 21.10/10.51 thf(489,plain,((! [A:list_a,B:list_a]: ((~ ((size_size_list_a @ A) = (size_size_list_a @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 21.10/10.51 thf(139,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_gr__zeroI)). 21.10/10.51 thf(679,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 21.10/10.51 thf(149,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_gr__implies__not__zero)). 21.10/10.51 thf(706,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 21.10/10.51 thf(80,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Suc__mono)). 21.10/10.51 thf(471,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 21.10/10.51 thf(19,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_old_Onat_Odistinct_I2_J)). 21.10/10.51 thf(256,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 21.10/10.51 thf(147,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (divide_divide_nat @ A @ C) @ B) <= (ord_less_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Util__Div_Oless__mult__imp__div__less)). 21.10/10.51 thf(701,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (divide_divide_nat @ A @ C) @ B) | ~ (ord_less_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 21.10/10.51 thf(75,axiom,(((divide_divide_nat @ (size_size_list_a @ xs) @ k) = (suc @ n))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 21.10/10.51 thf(457,plain,(((divide_divide_nat @ (size_size_list_a @ xs) @ k) = (suc @ n))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 21.10/10.51 thf(154,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 21.10/10.51 thf(721,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 21.10/10.51 thf(49,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 21.10/10.51 thf(371,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 21.10/10.51 thf(6,axiom,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_bits__div__0)). 21.10/10.51 thf(205,plain,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 21.10/10.51 thf(91,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_zero__less__mult__pos2)). 21.10/10.51 thf(508,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ A)) | ~ (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 21.10/10.51 thf(153,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mult__is__0)). 21.10/10.51 thf(718,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 21.10/10.51 thf(122,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_eq_nat @ B @ C) <= (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_nat__mult__le__cancel__disj)). 21.10/10.51 thf(618,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_eq_nat @ B @ C) | ~ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 21.10/10.51 thf(93,axiom,((! [A:list_a,B:list_P1467822637od_a_a]: ((size_s1875148994od_a_a @ (produc16441326od_a_a @ A @ B)) = (times_times_nat @ (size_size_list_a @ A) @ (size_s642698393od_a_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_length__product)). 21.10/10.51 thf(513,plain,((! [A:list_a,B:list_P1467822637od_a_a]: ((size_s1875148994od_a_a @ (produc16441326od_a_a @ A @ B)) = (times_times_nat @ (size_size_list_a @ A) @ (size_s642698393od_a_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 21.10/10.51 thf(186,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_less__not__refl3)). 21.10/10.51 thf(824,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 21.10/10.51 thf(21,axiom,((! [A:nat]: ((ord_less_eq_nat @ (suc @ (suc @ zero_zero_nat)) @ A) = ((A != (suc @ zero_zero_nat)) & (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_nat__geSucSuc0__conv)). 21.10/10.51 thf(264,plain,((! [A:nat]: ((ord_less_eq_nat @ (suc @ (suc @ zero_zero_nat)) @ A) = (~ (A = (suc @ zero_zero_nat)) & ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 21.10/10.51 thf(30,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_nat__leSuc0__conv)). 21.10/10.51 thf(296,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 21.10/10.51 thf(108,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_nonzero__mult__div__cancel__left)). 21.10/10.51 thf(562,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 21.10/10.51 thf(144,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_zero__less__mult__pos)). 21.10/10.51 thf(694,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ B)) | ~ (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 21.10/10.51 thf(161,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_div__eq__0__conv)). 21.10/10.51 thf(743,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 21.10/10.51 thf(129,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (A != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_less__ge__neq__conv)). 21.10/10.51 thf(641,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 21.10/10.51 thf(71,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__trans__Suc)). 21.10/10.51 thf(445,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 21.10/10.51 thf(111,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: (((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)))) <= (ord_less_nat @ zero_zero_nat @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_infinite__descent0)). 21.10/10.51 thf(572,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: (((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)))) | ~ (ord_less_nat @ zero_zero_nat @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 21.10/10.51 thf(101,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_nat__0__less__mult__iff)). 21.10/10.51 thf(540,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 21.10/10.51 thf(151,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Suc__less__SucD)). 21.10/10.51 thf(713,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 21.10/10.51 thf(89,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (((ord_less_eq_nat @ B @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ A)) | ((ord_less_eq_nat @ A @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_split__mult__neg__le)). 21.10/10.51 thf(498,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (((ord_less_eq_nat @ B @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ A)) | ((ord_less_eq_nat @ A @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 21.10/10.51 thf(168,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__not__refl2)). 21.10/10.51 thf(764,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 21.10/10.51 thf(60,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_mult__le__cancel2)). 21.10/10.51 thf(406,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 21.10/10.51 thf(51,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_mult__strict__left__mono)). 21.10/10.51 thf(377,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 21.10/10.51 thf(73,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => (((times_times_nat @ A @ B) != zero_zero_nat) <= (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_no__zero__divisors)). 21.10/10.51 thf(451,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => (~ ((times_times_nat @ A @ B) = zero_zero_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 21.10/10.51 thf(16,axiom,((! [A:list_P1467822637od_a_a,B:list_P1467822637od_a_a]: (((size_s642698393od_a_a @ A) != (size_s642698393od_a_a @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_size__neq__size__imp__neq)). 21.10/10.51 thf(245,plain,((! [A:list_P1467822637od_a_a,B:list_P1467822637od_a_a]: ((~ ((size_s642698393od_a_a @ A) = (size_s642698393od_a_a @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 21.10/10.51 thf(159,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = zero_zero_nat) | ? [C:nat]: ((ord_less_nat @ C @ B) & (A = (suc @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_less__Suc__eq__0__disj)). 21.10/10.51 thf(737,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = zero_zero_nat) | ? [C:nat]: ((ord_less_nat @ C @ B) & (A = (suc @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 21.10/10.51 thf(132,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((((C @ A) <= (! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ D) <= (C @ (suc @ D)))))) <= (! [D:nat]: ((B = (suc @ D)) => (C @ D)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_strict__inc__induct)). 21.10/10.51 thf(649,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((C @ A) | ~ (! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ D) | ~ (C @ (suc @ D))))) | ~ (! [D:nat]: ((B = (suc @ D)) => (C @ D))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 21.10/10.51 thf(32,axiom,((! [A:nat]: ? [B:list_P1467822637od_a_a]: ((size_s642698393od_a_a @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Ex__list__of__length)). 21.10/10.51 thf(303,plain,((! [A:nat]: ? [B:list_P1467822637od_a_a]: ((size_s642698393od_a_a @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 21.10/10.51 thf(7,axiom,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_bits__div__by__0)). 21.10/10.51 thf(208,plain,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 21.10/10.51 thf(126,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: ((B != (suc @ C)) <= (ord_less_nat @ A @ C)))) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Suc__lessE)). 21.10/10.51 thf(631,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: (~ (B = (suc @ C)) | ~ (ord_less_nat @ A @ C))) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 21.10/10.51 thf(166,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ B @ C) & (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_nat__mult__less__cancel__disj)). 21.10/10.51 thf(758,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ B @ C) & (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 21.10/10.51 thf(183,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (B != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_ge__less__neq__conv)). 21.10/10.51 thf(816,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 21.10/10.51 thf(114,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (A != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_le__greater__neq__conv)). 21.10/10.51 thf(594,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 21.10/10.51 thf(123,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ B @ C)) = (divide_divide_nat @ (divide_divide_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_div__mult2__eq)). 21.10/10.51 thf(621,plain,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ B @ C)) = (divide_divide_nat @ (divide_divide_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 21.10/10.51 thf(84,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((A = C) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_mult__cancel__right)). 21.10/10.51 thf(483,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((A = C) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 21.10/10.51 thf(77,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__Suc__eq)). 21.10/10.51 thf(462,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 21.10/10.51 thf(48,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_mult__cancel2__gr0)). 21.10/10.51 thf(367,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 21.10/10.51 thf(105,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_infinite__descent)). 21.10/10.51 thf(552,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 21.10/10.51 thf(169,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_mult_Oleft__commute)). 21.10/10.51 thf(768,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 21.10/10.51 thf(173,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => ((ord_less_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ B @ A)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_one__less__mult)). 21.10/10.51 thf(780,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => ((ord_less_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ B @ A)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 21.10/10.51 thf(74,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__SucI)). 21.10/10.51 thf(455,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 21.10/10.51 thf(33,axiom,((! [A:(nat > $o),B:nat]: (((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B)) <= (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_old_Onat_Oinducts)). 21.10/10.51 thf(306,plain,((! [A:(nat > $o),B:nat]: (((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B)) | ~ (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 21.10/10.51 thf(31,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_n__not__Suc__n)). 21.10/10.51 thf(299,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 21.10/10.51 thf(22,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_zero__le)). 21.10/10.51 thf(267,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 21.10/10.51 thf(141,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_mult__less__cancel2)). 21.10/10.51 thf(685,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 21.10/10.51 thf(95,axiom,((! [A:nat]: ((ord_less_nat @ A @ (suc @ (suc @ zero_zero_nat))) = ((A = (suc @ zero_zero_nat)) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_nat__lessSucSuc0__conv)). 21.10/10.51 thf(521,plain,((! [A:nat]: ((ord_less_nat @ A @ (suc @ (suc @ zero_zero_nat))) = ((A = (suc @ zero_zero_nat)) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 21.10/10.51 thf(81,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_not__less__zero)). 21.10/10.51 thf(473,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 21.10/10.51 thf(138,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_lift__Suc__mono__less__iff)). 21.10/10.51 thf(675,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 21.10/10.51 thf(98,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_mult__nonneg__nonneg)). 21.10/10.51 thf(531,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 21.10/10.51 thf(134,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_mult_Oassoc)). 21.10/10.51 thf(663,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 21.10/10.51 thf(50,axiom,((! [A:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) = ((A != zero_zero_nat) & (A != (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_nat__grSuc0__conv)). 21.10/10.51 thf(374,plain,((! [A:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) = (~ (A = zero_zero_nat) & ~ (A = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 21.10/10.51 thf(182,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_div__mult__self__is__m)). 21.10/10.51 thf(812,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 21.10/10.51 thf(163,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = zero_zero_nat)) <= ((times_times_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_divisors__zero)). 21.10/10.51 thf(749,plain,((! [A:nat,B:nat]: ((A = zero_zero_nat) | (B = zero_zero_nat) | ~ ((times_times_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 21.10/10.51 thf(94,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((A @ D) <= (ord_less_nat @ D @ C))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_nat__less__induct)). 21.10/10.51 thf(516,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((A @ D) | ~ (ord_less_nat @ D @ C))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 21.10/10.51 thf(44,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mult__0)). 21.10/10.51 thf(355,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 21.10/10.51 thf(63,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_gr__implies__not0)). 21.10/10.51 thf(414,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 21.10/10.51 thf(61,axiom,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_less__numeral__extra_I3_J)). 21.10/10.51 thf(409,plain,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 21.10/10.51 thf(137,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) => (B != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_greater__le__neq__conv)). 21.10/10.51 thf(673,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) => (~ (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 21.10/10.51 thf(130,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_mult__zero__right)). 21.10/10.51 thf(643,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 21.10/10.51 thf(148,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (suc @ B)) = (A = B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_not__less__less__Suc__eq)). 21.10/10.51 thf(703,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (suc @ B)) = (A = B)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 21.10/10.51 thf(116,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_mult__cancel__left)). 21.10/10.51 thf(600,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 21.10/10.51 thf(156,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_mult__mono)). 21.10/10.51 thf(727,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 21.10/10.51 thf(54,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_nat__mult__div__cancel1)). 21.10/10.51 thf(386,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 21.10/10.51 thf(120,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_mult__nonneg__nonpos)). 21.10/10.51 thf(612,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 21.10/10.51 thf(125,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_div__mult__mult1)). 21.10/10.51 thf(627,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 21.10/10.51 thf(106,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_mult__mono_H)). 21.10/10.51 thf(556,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 21.10/10.51 thf(142,axiom,((k != zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)). 21.10/10.51 thf(688,plain,((~ (k = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 21.10/10.51 thf(96,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__zeroE)). 21.10/10.51 thf(524,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 21.10/10.51 thf(170,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (divide_divide_nat @ B @ A) @ C) = (ord_less_nat @ B @ (times_times_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_div__less__conv)). 21.10/10.51 thf(771,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (divide_divide_nat @ B @ A) @ C) = (ord_less_nat @ B @ (times_times_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 21.10/10.51 thf(78,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__irrefl__nat)). 21.10/10.51 thf(465,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 21.10/10.51 thf(12,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_old_Onat_Oinject)). 21.10/10.51 thf(231,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 21.10/10.51 thf(55,axiom,((! [A:(list_P1467822637od_a_a > $o),B:list_P1467822637od_a_a]: ((! [C:list_P1467822637od_a_a]: ((A @ C) <= (! [D:list_P1467822637od_a_a]: ((ord_less_nat @ (size_s642698393od_a_a @ D) @ (size_s642698393od_a_a @ C)) => (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_length__induct)). 21.10/10.51 thf(390,plain,((! [A:(list_P1467822637od_a_a > $o),B:list_P1467822637od_a_a]: ((! [C:list_P1467822637od_a_a]: ((A @ C) | ~ (! [D:list_P1467822637od_a_a]: ((ord_less_nat @ (size_s642698393od_a_a @ D) @ (size_s642698393od_a_a @ C)) => (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 21.10/10.51 thf(112,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((ord_less_nat @ A @ C) & (B = (suc @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Suc__less__eq2)). 21.10/10.51 thf(588,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((ord_less_nat @ A @ C) & (B = (suc @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 21.10/10.51 thf(146,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Suc__lessD)). 21.10/10.51 thf(699,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 21.10/10.51 thf(64,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_nat__neq__iff)). 21.10/10.51 thf(418,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 21.10/10.51 thf(175,axiom,((! [A:list_a,B:list_a]: ((A != B) <= ((size_size_list_a @ A) != (size_size_list_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_size__neq__size__imp__neq)). 21.10/10.51 thf(786,plain,((! [A:list_a,B:list_a]: (~ (A = B) | ((size_size_list_a @ A) = (size_size_list_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 21.10/10.51 thf(110,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_nat__mult__eq__cancel1)). 21.10/10.51 thf(568,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 21.10/10.51 thf(92,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult__less__mono1)). 21.10/10.51 thf(510,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 21.10/10.51 thf(53,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (((suc @ A) != B) => (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Suc__lessI)). 21.10/10.51 thf(383,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((~ ((suc @ A) = B)) => (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 21.10/10.51 thf(104,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ (suc @ A)))) = (! [C:nat]: ((B @ (suc @ C)) <= (ord_less_nat @ C @ A)) & (B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_All__less__Suc2)). 21.10/10.51 thf(549,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ (suc @ A)))) = (! [C:nat]: ((B @ (suc @ C)) | ~ (ord_less_nat @ C @ A)) & (B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 21.10/10.51 thf(178,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_not__gr0)). 21.10/10.51 thf(800,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 21.10/10.51 thf(164,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_mult__zero__left)). 21.10/10.51 thf(752,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 21.10/10.51 thf(184,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_bot__nat__0_Oextremum__strict)). 21.10/10.51 thf(818,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 21.10/10.51 thf(176,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_neq0__conv)). 21.10/10.51 thf(790,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 21.10/10.51 thf(24,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_le0)). 21.10/10.51 thf(273,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 21.10/10.51 thf(117,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_mult__left__cancel)). 21.10/10.51 thf(603,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 21.10/10.51 thf(15,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_nat_Oinject)). 21.10/10.51 thf(242,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 21.10/10.51 thf(45,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_not__gr__zero)). 21.10/10.51 thf(358,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 21.10/10.51 thf(58,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_gr0I)). 21.10/10.51 thf(400,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 21.10/10.51 thf(187,axiom,((! [A:nat,B:nat]: (((B != (suc @ A)) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C)))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Nat_OlessE)). 21.10/10.51 thf(828,plain,((! [A:nat,B:nat]: (((~ (B = (suc @ A))) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (~ (B = (suc @ C))))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 21.10/10.51 thf(127,axiom,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_less__Suc0)). 21.10/10.51 thf(635,plain,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 21.10/10.51 thf(145,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ (suc @ A) @ B) @ (times_times_nat @ (suc @ A) @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Suc__mult__less__cancel1)). 21.10/10.51 thf(696,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ (suc @ A) @ B) @ (times_times_nat @ (suc @ A) @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 21.10/10.51 thf(28,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_nat__induct)). 21.10/10.51 thf(283,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 21.10/10.51 thf(160,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_mult__pos__pos)). 21.10/10.51 thf(740,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 21.10/10.51 thf(115,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (divide_divide_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_div__mult__mult2)). 21.10/10.51 thf(596,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (divide_divide_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 21.10/10.51 thf(76,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_mult__nonneg__nonpos2)). 21.10/10.51 thf(459,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 21.10/10.51 thf(70,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ (times_times_nat @ A @ B)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_n__less__n__mult__m)). 21.10/10.51 thf(442,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ (times_times_nat @ A @ B)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 21.10/10.51 thf(90,axiom,((! [A:nat,B:nat,C:nat]: (((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_nat__mult__div__cancel__disj)). 21.10/10.51 thf(501,plain,((! [A:nat,B:nat,C:nat]: (((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 21.10/10.51 thf(118,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mult__less__mono2)). 21.10/10.51 thf(607,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 21.10/10.51 thf(56,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__Suc)). 21.10/10.51 thf(395,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 21.10/10.51 thf(124,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Suc__less__eq)). 21.10/10.51 thf(624,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 21.10/10.51 thf(26,axiom,((! [A:nat]: ((A != zero_zero_nat) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_not0__implies__Suc)). 21.10/10.51 thf(277,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 21.10/10.51 thf(143,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_not__less__eq)). 21.10/10.51 thf(691,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 21.10/10.51 thf(85,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_div__less)). 21.10/10.51 thf(486,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 21.10/10.51 thf(179,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_mult__left__mono)). 21.10/10.51 thf(803,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 21.10/10.51 thf(40,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_mult__cancel1)). 21.10/10.51 thf(337,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 21.10/10.51 thf(102,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (suc @ A) @ B) = (times_times_nat @ (suc @ A) @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Suc__mult__cancel1)). 21.10/10.51 thf(543,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (suc @ A) @ B) = (times_times_nat @ (suc @ A) @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 21.10/10.51 thf(171,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_lessI)). 21.10/10.51 thf(775,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 21.10/10.51 thf(165,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_mult__pos__neg)). 21.10/10.51 thf(755,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 21.10/10.51 thf(88,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (divide_divide_nat @ A @ C) @ B) <= (ord_less_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Euclidean__Division_Oless__mult__imp__div__less)). 21.10/10.51 thf(496,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (divide_divide_nat @ A @ C) @ B) | ~ (ord_less_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 21.10/10.51 thf(47,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_lift__Suc__mono__less)). 21.10/10.51 thf(364,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 21.10/10.51 thf(1792,plain,($false),inference(e,[status(thm)],[320,809,468,234,777,666,352,333,249,730,269,715,340,670,724,344,559,638,189,421,325,228,448,316,591,238,806,821,480,211,646,397,280,293,660,411,428,527,734,221,380,439,201,761,534,546,793,334,746,260,424,192,275,566,252,361,435,329,493,682,710,224,615,403,188,610,783,537,476,489,679,706,471,256,701,457,721,371,205,508,718,618,513,824,264,296,562,694,743,641,445,572,540,713,498,764,406,377,451,245,737,649,303,208,631,758,816,594,621,483,462,367,552,768,780,455,306,299,267,685,521,473,675,531,663,374,812,749,516,355,414,409,673,643,703,600,727,386,612,627,556,688,524,771,465,231,390,588,699,418,786,568,510,383,549,800,752,818,790,273,603,242,358,400,828,635,696,283,740,596,459,442,501,607,395,624,277,691,486,803,337,543,775,755,496,364])). 21.10/10.51 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 21.10/10.51 % [INFO] Killing All external provers ... 21.10/10.51 FINAL WATCH: 19.8 CPU 5.4 WC 21.10/10.51 Killed 3 orphans 21.10/10.51 Killed 2 orphans 21.10/10.51 EOF