0.00/0.00 % Leo-III: Strategy 1 (for '60') 97.67/24.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 97.67/24.34 % [INFO] Parsing done (212ms). 97.67/24.34 % [INFO] Running in sequential loop mode. 97.67/24.34 % [CONFIG] Using configuration: timeout(60) with strategy 97.67/24.34 % [INFO] eprover registered as external prover. 97.67/24.34 % [INFO] cvc4 registered as external prover. 97.67/24.34 % [INFO] Parsing finished. Scanning for conjecture ... 97.67/24.34 % [INFO] Found a conjecture and 328 axioms. Running axiom selection ... 97.67/24.34 % [INFO] Axiom selection finished. Selected 325 axioms (removed 3 axioms). 97.67/24.34 % [INFO] Problem is higher-order (TPTP THF). 97.67/24.34 % [INFO] Type checking passed. Searching for refutation ... 97.67/24.34 % External prover 'cvc4' found a proof! 97.67/24.34 % [INFO] Killing All external provers ... 97.67/24.34 % Time passed: 21825ms (effective reasoning time: 21265ms) 97.67/24.34 % Solved by strategy 97.67/24.34 % Axioms used in derivation (325): fact_41_not0__implies__Suc, fact_24_n__not__Suc__n, fact_241_add__mono__thms__linordered__field_I5_J, fact_260_add_Ocommute, fact_220_add__Suc, fact_213_trans__less__add2, fact_200_of__nat__0__eq__iff, fact_319_add__0__iff, fact_304_zless__iff__Suc__zadd, fact_238_add__mono__thms__linordered__field_I2_J, fact_248_ab__semigroup__add__class_Oadd__ac_I1_J, fact_91_option_Oinducts, fact_285_one__is__add, fact_175_add_Oleft__neutral, fact_252_group__cancel_Oadd1, fact_299_zero__less__imp__eq__int, fact_107_Ex__less__Suc2, fact_40_Ex__list__of__length, fact_281_pos__add__strict, fact_35_size__neq__size__imp__neq, fact_298_pos__int__cases, fact_20_option_Oinject, fact_198_of__nat__0, fact_169_add__cancel__left__left, fact_88_split__option__all, fact_292_gen__length__def, fact_96_option_OdiscI, fact_251_group__cancel_Oadd1, fact_314_verit__sum__simplify, fact_0_nth__Cons__Suc, fact_127_find__Some__iff, fact_141_less__numeral__extra_I3_J, fact_263_add__left__imp__eq, fact_243_add_Ocomm__neutral, fact_82_length__induct, fact_280_pos__add__strict, fact_43_old_Onat_Oexhaust, fact_23_not__Cons__self2, fact_250_add__mono__thms__linordered__semiring_I4_J, fact_182_add__Suc__right, fact_149_Cons__nth__drop__Suc, fact_77_Suc__lessI, fact_257_add_Oleft__cancel, fact_114_Skolem__list__nth, fact_216_not__add__less2, fact_191_add__less__same__cancel2, fact_36_size__neq__size__imp__neq, fact_293_gen__length__def, fact_27_infinite__descent, fact_133_find_Osimps_I2_J, fact_38_neq__if__length__neq, fact_315_int__ops_I5_J, fact_180_add__is__0, fact_124_option_Osize_I4_J, fact_159_of__nat__eq__iff, fact_258_add_Oright__cancel, fact_186_list__ex__simps_I1_J, fact_14_less__nat__zero__code, fact_168_add__cancel__left__left, fact_295_list_Osize_I4_J, fact_172_add_Oright__neutral, fact_21_option_Oinject, fact_271_less__imp__of__nat__less, fact_273_of__nat__less__imp__less, fact_183_nat__add__left__cancel__less, fact_255_add_Oassoc, fact_123_fvi__Suc, fact_161_add__eq__0__iff__both__eq__0, fact_112_list__eq__iff__nth__eq, fact_312_int__if, fact_100_lift__Suc__mono__less__iff, fact_300_zadd__int__left, fact_89_split__option__ex, fact_204_of__nat__less__iff, fact_228_add__less__imp__less__left, fact_81_length__induct, fact_132_zero__reorient, fact_287_less__natE, fact_131_zero__reorient, fact_117_nth__equalityI, fact_153_of__nat__0__less__iff, fact_119_fvi__Suc__bound, fact_307_nat__int__comparison_I2_J, fact_242_add_Ogroup__left__neutral, fact_102_lift__Suc__mono__less, fact_163_add__cancel__right__right, fact_120_length__Cons, fact_267_of__nat__less__0__iff, fact_93_option_Oexhaust, fact_302_plus__int__code_I2_J, fact_157_add__right__cancel, fact_118_not__gr__zero, fact_104_gr0__implies__Suc, fact_289_less__add__Suc2, fact_52_Collect__cong, fact_28_nat__less__induct, fact_224_plus__nat_Oadd__0, fact_239_add__mono__thms__linordered__field_I2_J, fact_33_nat__neq__iff, fact_75_less__SucI, fact_146_option_Osize__gen_I2_J, fact_189_add__less__same__cancel1, fact_98_option_Odistinct_I1_J, fact_306_linorder__neqE__linordered__idom, fact_210_drop__Suc__Cons, fact_156_add__right__cancel, fact_30_less__not__refl3, fact_140_less__numeral__extra_I3_J, fact_61_not__less0, fact_29_less__irrefl__nat, fact_106_gr0__conv__Suc, fact_282_nth__via__drop, fact_37_neq__if__length__neq, fact_1_nth__Cons__Suc, fact_116_nth__equalityI, fact_165_add__cancel__right__left, fact_74_Ex__less__Suc, fact_83_combine__options__cases, fact_46_Suc__neq__Zero, fact_15_bot__nat__0_Onot__eq__extremum, fact_158_of__nat__eq__iff, fact_193_less__add__same__cancel1, fact_234_add__strict__mono, fact_223_add__eq__self__zero, fact_70_Suc__less__eq2, fact_109_length__Suc__conv, fact_296_add__less__zeroD, fact_13_neq0__conv, fact_290_less__iff__Suc__add, fact_286_less__imp__add__positive, fact_137_gr__implies__not__zero, fact_22_not__Cons__self2, fact_174_add_Oleft__neutral, fact_229_add__less__imp__less__left, fact_58_infinite__descent0, fact_125_option_Osize_I4_J, fact_218_add__less__mono, fact_130_option_Osize__neq, fact_317_triangle__Suc, fact_7_not__None__eq, fact_73_less__Suc__eq, fact_34_size__neq__size__imp__neq, fact_259_add_Ocommute, fact_143_length__code, fact_166_add__cancel__left__right, fact_113_list__eq__iff__nth__eq, fact_176_add__less__cancel__right, fact_80_Nat_OlessE, fact_222_add__Suc__shift, fact_253_group__cancel_Oadd2, fact_284_add__is__1, fact_177_add__less__cancel__right, fact_5_zero__less__Suc, fact_154_add__left__cancel, fact_194_less__add__same__cancel2, fact_160_zero__eq__add__iff__both__eq__0, fact_185_drop__drop, fact_121_length__Cons, fact_207_of__nat__add, fact_105_All__less__Suc2, fact_309_verit__comp__simplify1_I1_J, fact_2_nth__Cons__0, fact_128_find__Some__iff, fact_215_add__less__mono1, fact_311_nat__int__comparison_I1_J, fact_308_int__ops_I1_J, fact_97_option_Odistinct_I1_J, fact_237_add__mono__thms__linordered__field_I1_J, fact_19_nat_Oinject, fact_62_not__gr0, fact_111_Suc__length__conv, fact_264_add__left__imp__eq, fact_26_linorder__neqE__nat, fact_99_lift__Suc__mono__less__iff, fact_178_add__less__cancel__left, fact_254_group__cancel_Oadd2, fact_49_nat__induct, fact_57_bot__nat__0_Oextremum__strict, fact_240_add__mono__thms__linordered__field_I5_J, fact_66_less__Suc__induct, fact_69_less__antisym, fact_235_add__strict__mono, fact_197_zero__less__double__add__iff__zero__less__single__add, fact_268_of__nat__less__0__iff, fact_11_Suc__mono, fact_63_gr0I, fact_272_less__imp__of__nat__less, fact_275_add__neg__neg, fact_245_comm__monoid__add__class_Oadd__0, fact_261_add_Oleft__commute, fact_64_not__less__less__Suc__eq, fact_72_not__less__eq, fact_249_add__mono__thms__linordered__semiring_I4_J, fact_266_add__right__imp__eq, fact_170_double__zero__sym, fact_244_add_Ocomm__neutral, fact_31_less__not__refl2, fact_10_lessI, fact_110_Suc__length__conv, fact_313_verit__sum__simplify, fact_226_add__less__imp__less__right, fact_279_canonically__ordered__monoid__add__class_OlessE, fact_79_Suc__lessD, fact_9_not__Some__eq, fact_135_gr__zeroI, fact_92_option_Oinducts, fact_209_drop__Suc__Cons, fact_303_plus__int__code_I1_J, fact_212_less__add__eq__less, fact_199_of__nat__0, fact_202_of__nat__eq__0__iff, fact_262_add_Oleft__commute, fact_195_less__add__same__cancel2, fact_42_old_Onat_Oinducts, fact_151_list__ex__length, fact_206_of__nat__add, fact_187_list__ex__simps_I1_J, fact_86_combine__options__cases, fact_305_less__int__code_I1_J, fact_108_length__Suc__conv, fact_294_list_Osize_I4_J, fact_147_option_Osize__gen_I2_J, fact_188_add__less__same__cancel1, fact_12_Suc__less__eq, fact_95_option_OdiscI, fact_65_strict__inc__induct, fact_16_list_Oinject, fact_318_add__0__iff, fact_78_Suc__lessE, conj_1, fact_44_Zero__not__Suc, fact_71_All__less__Suc, fact_301_int__int__eq, fact_201_of__nat__0__eq__iff, fact_265_add__right__imp__eq, fact_214_trans__less__add1, fact_76_less__SucE, fact_164_add__cancel__right__left, fact_4_less__Suc0, fact_232_add__strict__left__mono, fact_269_of__nat__neq__0, fact_231_add__strict__right__mono, fact_17_list_Oinject, fact_181_Nat_Oadd__0__right, fact_236_add__mono__thms__linordered__field_I1_J, fact_321_nth__drop, fact_205_of__nat__less__iff, fact_45_Zero__neq__Suc, fact_288_less__add__Suc1, fact_256_add_Oassoc, fact_152_of__nat__0__less__iff, fact_310_verit__comp__simplify1_I1_J, fact_3_nth__Cons__0, fact_221_nat__arith_Osuc1, fact_87_split__option__all, fact_184_drop0, fact_217_not__add__less1, fact_48_diff__induct, fact_246_comm__monoid__add__class_Oadd__0, fact_139_list__decode_Ocases, fact_39_Ex__list__of__length, fact_6_not__None__eq, fact_208_add__gr__0, fact_162_add__cancel__right__right, fact_54_old_Onat_Odistinct_I1_J, fact_316_int__plus, fact_283_nth__via__drop, fact_247_ab__semigroup__add__class_Oadd__ac_I1_J, fact_136_not__less__zero, fact_85_combine__options__cases, fact_56_nat_Odistinct_I1_J, fact_8_not__Some__eq, fact_276_add__neg__neg, fact_230_add__strict__right__mono, fact_25_Suc__inject, fact_274_of__nat__less__imp__less, fact_103_less__Suc__eq__0__disj, fact_227_add__less__imp__less__right, fact_190_add__less__same__cancel2, fact_101_lift__Suc__mono__less, fact_278_add__pos__pos, fact_297_Euclid__induct, fact_68_Suc__less__SucD, fact_53_nat_OdiscI, fact_60_less__zeroE, fact_179_add__less__cancel__left, fact_129_exists__least__lemma, fact_203_of__nat__eq__0__iff, fact_322_nth__drop, fact_142_length__code, fact_18_old_Onat_Oinject, fact_211_is__num__normalize_I1_J, fact_148_Cons__nth__drop__Suc, fact_192_less__add__same__cancel1, fact_320_triangle__0, fact_270_of__nat__neq__0, conj_0, fact_59_gr__implies__not0, fact_50_mem__Collect__eq, fact_155_add__left__cancel, fact_167_add__cancel__left__right, fact_90_split__option__ex, fact_145_gen__length__code_I2_J, fact_225_drop__0, fact_55_old_Onat_Odistinct_I2_J, fact_233_add__strict__left__mono, fact_32_less__not__refl, fact_173_add_Oright__neutral, fact_219_add__lessD1, fact_51_Collect__mem__eq, fact_94_option_Oexhaust, fact_196_double__add__less__zero__iff__single__add__less__zero, fact_138_zero__less__iff__neq__zero, fact_134_find_Osimps_I2_J, fact_126_option_Osize_I3_J, fact_277_add__pos__pos, fact_150_list__ex__length, fact_144_gen__length__code_I2_J, fact_115_Skolem__list__nth, fact_171_double__zero, fact_122_option_Osize__gen_I1_J, fact_67_less__trans__Suc, fact_47_zero__induct, fact_291_less__imp__Suc__add, fact_84_combine__options__cases 97.67/24.34 % No. of inferences in proof: 654 97.67/24.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21825 ms resp. 21265 ms w/o parsing 97.67/24.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 97.67/24.34 thf(option_option_b_type, type, option_option_b: $tType). 97.67/24.34 thf(list_option_b_type, type, list_option_b: $tType). 97.67/24.34 thf(set_nat_type, type, set_nat: $tType). 97.67/24.34 thf(option_b_type, type, option_b: $tType). 97.67/24.34 thf(formula_a_type, type, formula_a: $tType). 97.67/24.34 thf(list_b_type, type, list_b: $tType). 97.67/24.34 thf(nat_type, type, nat: $tType). 97.67/24.34 thf(int_type, type, int: $tType). 97.67/24.34 thf(b_type, type, b: $tType). 97.67/24.34 thf(plus_plus_int_type, type, plus_plus_int: (int > (int > int))). 97.67/24.34 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 97.67/24.34 thf(zero_zero_int_type, type, zero_zero_int: int). 97.67/24.34 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 97.67/24.34 thf(if_nat_type, type, if_nat: ($o > (nat > (nat > nat)))). 97.67/24.34 thf(drop_option_b_type, type, drop_option_b: (nat > (list_option_b > list_option_b))). 97.67/24.34 thf(drop_b_type, type, drop_b: (nat > (list_b > list_b))). 97.67/24.34 thf(find_option_b_type, type, find_option_b: ((option_b > $o) > (list_option_b > option_option_b))). 97.67/24.34 thf(find_b_type, type, find_b: ((b > $o) > (list_b > option_b))). 97.67/24.34 thf(gen_length_option_b_type, type, gen_length_option_b: (nat > (list_option_b > nat))). 97.67/24.34 thf(gen_length_b_type, type, gen_length_b: (nat > (list_b > nat))). 97.67/24.34 thf(cons_option_b_type, type, cons_option_b: (option_b > (list_option_b > list_option_b))). 97.67/24.34 thf(cons_b_type, type, cons_b: (b > (list_b > list_b))). 97.67/24.34 thf(list_ex_option_b_type, type, list_ex_option_b: ((option_b > $o) > (list_option_b > $o))). 97.67/24.34 thf(list_ex_b_type, type, list_ex_b: ((b > $o) > (list_b > $o))). 97.67/24.34 thf(nth_option_b_type, type, nth_option_b: (list_option_b > (nat > option_b))). 97.67/24.34 thf(nth_b_type, type, nth_b: (list_b > (nat > b))). 97.67/24.34 thf(fvi_a_type, type, fvi_a: (nat > (formula_a > set_nat))). 97.67/24.34 thf(suc_type, type, suc: (nat > nat)). 97.67/24.34 thf(semiri2019852685at_int_type, type, semiri2019852685at_int: (nat > int)). 97.67/24.34 thf(semiri1382578993at_nat_type, type, semiri1382578993at_nat: (nat > nat)). 97.67/24.34 thf(size_s1671393719tion_b_type, type, size_s1671393719tion_b: (list_option_b > nat)). 97.67/24.34 thf(size_size_list_b_type, type, size_size_list_b: (list_b > nat)). 97.67/24.34 thf(size_s684879735tion_b_type, type, size_s684879735tion_b: (option_option_b > nat)). 97.67/24.34 thf(size_size_option_b_type, type, size_size_option_b: (option_b > nat)). 97.67/24.34 thf(nat_triangle_type, type, nat_triangle: (nat > nat)). 97.67/24.34 thf(none_option_b_type, type, none_option_b: option_option_b). 97.67/24.34 thf(none_b_type, type, none_b: option_b). 97.67/24.34 thf(some_option_b_type, type, some_option_b: (option_b > option_option_b)). 97.67/24.34 thf(some_b_type, type, some_b: (b > option_b)). 97.67/24.34 thf(size_option_option_b_type, type, size_option_option_b: ((option_b > nat) > (option_option_b > nat))). 97.67/24.34 thf(size_option_b_type, type, size_option_b: ((b > nat) > (option_b > nat))). 97.67/24.34 thf(ord_less_int_type, type, ord_less_int: (int > (int > $o))). 97.67/24.34 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 97.67/24.34 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 97.67/24.34 thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)). 97.67/24.34 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 97.67/24.34 thf(phi_type, type, phi: formula_a). 97.67/24.34 thf(b2_type, type, b2: nat). 97.67/24.34 thf(n_type, type, n: nat). 97.67/24.34 thf(v_type, type, v: list_option_b). 97.67/24.34 thf(x_type, type, x: b). 97.67/24.34 thf(218,axiom,(((size_size_option_b @ none_b) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_option_Osize_I3_J)). 97.67/24.34 thf(1036,plain,(((size_size_option_b @ none_b) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 97.67/24.34 thf(45,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => (((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ D @ (plus_plus_nat @ D @ E)) <= (A @ D @ E)))) <= (! [D:nat]: (A @ D @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_Euclid__induct)). 97.67/24.34 thf(479,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ D @ (plus_plus_nat @ D @ E)) | ~ (A @ D @ E))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 97.67/24.34 thf(191,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C))) <= (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_lift__Suc__mono__less)). 97.67/24.34 thf(941,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C))) | ~ (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 97.67/24.34 thf(256,axiom,((! [A:list_option_b,B:list_option_b]: (((size_s1671393719tion_b @ A) != (size_s1671393719tion_b @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_size__neq__size__imp__neq)). 97.67/24.34 thf(1179,plain,((! [A:list_option_b,B:list_option_b]: ((~ ((size_s1671393719tion_b @ A) = (size_s1671393719tion_b @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 97.67/24.34 thf(239,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_not__gr0)). 97.67/24.34 thf(1110,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 97.67/24.34 thf(97,axiom,((! [A:(nat > $o),B:(nat > $o)]: (((collect_nat @ A) = (collect_nat @ B)) <= (! [C:nat]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Collect__cong)). 97.67/24.34 thf(645,plain,((! [A:(nat > $o),B:(nat > $o)]: (((collect_nat @ (A)) = (collect_nat @ (B))) | ~ (! [C:nat]: ((A @ C) = (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 97.67/24.34 thf(175,axiom,((! [A:nat,B:option_b,C:list_option_b]: ((drop_option_b @ (suc @ A) @ (cons_option_b @ B @ C)) = (drop_option_b @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_drop__Suc__Cons)). 97.67/24.34 thf(892,plain,((! [A:nat,B:option_b,C:list_option_b]: ((drop_option_b @ (suc @ A) @ (cons_option_b @ B @ C)) = (drop_option_b @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 97.67/24.34 thf(9,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_add_Oleft__commute)). 97.67/24.34 thf(365,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 97.67/24.34 thf(259,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__less__Suc)). 97.67/24.34 thf(1190,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 97.67/24.34 thf(180,axiom,((! [A:b]: (none_b != (some_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_option_Odistinct_I1_J)). 97.67/24.34 thf(909,plain,((! [A:b]: ~ (none_b = (some_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 97.67/24.34 thf(3,axiom,((! [A:option_option_b]: ((A != none_option_b) = (? [B:option_b]: (A = (some_option_b @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_not__None__eq)). 97.67/24.34 thf(333,plain,((! [A:option_option_b]: ((~ (A = none_option_b)) = (? [B:option_b]: (A = (some_option_b @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 97.67/24.34 thf(292,axiom,((! [A:option_option_b,B:(option_option_b > (option_b > $o)),C:option_b]: (((B @ A @ C) <= (A = none_option_b)) => (((! [D:option_b,E:b]: ((A = (some_option_b @ D)) => ((C = (some_b @ E)) => (B @ A @ C)))) => (B @ A @ C)) <= ((B @ A @ C) <= (C = none_b)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_combine__options__cases)). 97.67/24.34 thf(1315,plain,((! [A:option_option_b,B:(option_option_b > (option_b > $o)),C:option_b]: (((B @ A @ C) | ~ (A = none_option_b)) => (((! [D:option_b,E:b]: ((A = (some_option_b @ D)) => ((C = (some_b @ E)) => (B @ A @ C)))) => (B @ A @ C)) | ~ ((B @ A @ C) | ~ (C = none_b)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 97.67/24.34 thf(56,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_nat__int__comparison_I1_J)). 97.67/24.34 thf(518,plain,(((= @ nat) = (^ [A:nat,B:nat]: ((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 97.67/24.34 thf(211,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_not__less__eq)). 97.67/24.34 thf(1005,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 97.67/24.34 thf(310,axiom,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_int @ (A @ B) @ (A @ C)) <= (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_lift__Suc__mono__less)). 97.67/24.34 thf(1401,plain,((! [A:(nat > int),B:nat,C:nat]: ((ord_less_int @ (A @ B) @ (A @ C)) | ~ (ord_less_nat @ B @ C) | ~ (! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 97.67/24.34 thf(317,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__not__refl3)). 97.67/24.34 thf(1422,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 97.67/24.34 thf(169,axiom,((! [A:nat]: ? [B:list_option_b]: ((size_s1671393719tion_b @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Ex__list__of__length)). 97.67/24.34 thf(873,plain,((! [A:nat]: ? [B:list_option_b]: ((size_s1671393719tion_b @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 97.67/24.34 thf(106,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_group__cancel_Oadd2)). 97.67/24.34 thf(677,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C))) | ~ (A = (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 97.67/24.34 thf(321,axiom,((! [A:(nat > $o),B:nat]: (((A @ B) <= (! [C:nat]: ((A @ C) => (A @ (suc @ C))))) <= (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__induct)). 97.67/24.34 thf(1437,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ C) => (A @ (suc @ C)))) | ~ (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 97.67/24.34 thf(220,axiom,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus_nat @ B @ C)) => ((suc @ A) = (plus_plus_nat @ B @ (suc @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_nat__arith_Osuc1)). 97.67/24.34 thf(1041,plain,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus_nat @ B @ C)) => ((suc @ A) = (plus_plus_nat @ B @ (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 97.67/24.34 thf(58,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_zero__eq__add__iff__both__eq__0)). 97.67/24.34 thf(523,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 97.67/24.34 thf(77,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_group__cancel_Oadd1)). 97.67/24.34 thf(582,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 97.67/24.34 thf(318,axiom,((((size_s1671393719tion_b @ v) = n) & ! [A:nat]: ((ord_less_nat @ A @ n) => (((nth_option_b @ v @ A) = none_b) = (~ (member_nat @ A @ (fvi_a @ (suc @ b2) @ phi))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)). 97.67/24.34 thf(1426,plain,((((size_s1671393719tion_b @ v) = n) & ! [A:nat]: ((ord_less_nat @ A @ n) => (((nth_option_b @ v @ A) = none_b) = (~ (member_nat @ A @ (fvi_a @ (suc @ b2) @ phi))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 97.67/24.34 thf(248,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_11_Suc__mono)). 97.67/24.34 thf(1137,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)],[248])). 97.67/24.34 thf(291,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((A @ C) <= (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_nat__less__induct)). 97.67/24.34 thf(1310,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 97.67/24.34 thf(144,axiom,(((= @ list_option_b) = (^ [A:list_option_b,B:list_option_b]: (! [C:nat]: ((ord_less_nat @ C @ (size_s1671393719tion_b @ A)) => ((nth_option_b @ A @ C) = (nth_option_b @ B @ C))) & ((size_s1671393719tion_b @ A) = (size_s1671393719tion_b @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_list__eq__iff__nth__eq)). 97.67/24.34 thf(797,plain,(((= @ list_option_b) = (^ [A:list_option_b,B:list_option_b]: (! [C:nat]: ((ord_less_nat @ C @ (size_s1671393719tion_b @ A)) => ((nth_option_b @ A @ C) = (nth_option_b @ B @ C))) & ((size_s1671393719tion_b @ A) = (size_s1671393719tion_b @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 97.67/24.34 thf(43,axiom,((gen_length_b = (^ [A:nat,B:list_b]: (plus_plus_nat @ A @ (size_size_list_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_gen__length__def)). 97.67/24.34 thf(472,plain,(((gen_length_b) = (^ [A:nat,B:list_b]: (plus_plus_nat @ A @ (size_size_list_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 97.67/24.34 thf(150,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_less__imp__Suc__add)). 97.67/24.34 thf(814,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 97.67/24.34 thf(227,axiom,((! [A:(option_b > $o),B:option_b,C:list_option_b]: (((~ (A @ B)) => ((find_option_b @ A @ (cons_option_b @ B @ C)) = (find_option_b @ A @ C))) & (((find_option_b @ A @ (cons_option_b @ B @ C)) = (some_option_b @ B)) <= (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_find_Osimps_I2_J)). 97.67/24.34 thf(1063,plain,((! [A:(option_b > $o),B:option_b,C:list_option_b]: (((~ (A @ B)) => ((find_option_b @ (A) @ (cons_option_b @ B @ C)) = (find_option_b @ (A) @ C))) & (((find_option_b @ (A) @ (cons_option_b @ B @ C)) = (some_option_b @ B)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 97.67/24.34 thf(299,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_pos__add__strict)). 97.67/24.34 thf(1354,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 97.67/24.34 thf(187,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_add__less__cancel__left)). 97.67/24.34 thf(930,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 97.67/24.34 thf(296,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_old_Onat_Odistinct_I1_J)). 97.67/24.34 thf(1342,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 97.67/24.34 thf(181,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_add__Suc__right)). 97.67/24.34 thf(913,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 97.67/24.34 thf(261,axiom,((! [A:b,B:list_b]: ((size_size_list_b @ (cons_b @ A @ B)) = (suc @ (size_size_list_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_length__Cons)). 97.67/24.34 thf(1196,plain,((! [A:b,B:list_b]: ((size_size_list_b @ (cons_b @ A @ B)) = (suc @ (size_size_list_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 97.67/24.34 thf(177,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ A) @ B) <= ((suc @ A) != B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Suc__lessI)). 97.67/24.34 thf(898,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) | ((suc @ A) = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 97.67/24.34 thf(244,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (ord_less_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_nat__int__comparison_I2_J)). 97.67/24.34 thf(1127,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (ord_less_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 97.67/24.34 thf(116,axiom,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_of__nat__add)). 97.67/24.34 thf(709,plain,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 97.67/24.34 thf(159,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_add__less__imp__less__left)). 97.67/24.34 thf(841,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 97.67/24.34 thf(301,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((A @ zero_zero_nat) <= (! [C:nat]: ((A @ (suc @ C)) => (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__induct)). 97.67/24.34 thf(1366,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((A @ zero_zero_nat) | ~ (! [C:nat]: ((A @ (suc @ C)) => (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 97.67/24.34 thf(99,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) => (ord_less_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add__less__imp__less__right)). 97.67/24.34 thf(651,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) => (ord_less_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 97.67/24.34 thf(51,axiom,(((drop_option_b @ zero_zero_nat) = (^ [A:list_option_b]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_drop0)). 97.67/24.34 thf(504,plain,(((drop_option_b @ zero_zero_nat) = (^ [A:list_option_b]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 97.67/24.34 thf(277,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_n__not__Suc__n)). 97.67/24.34 thf(1264,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 97.67/24.34 thf(114,axiom,((! [A:option_b]: (none_option_b != (some_option_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_option_Odistinct_I1_J)). 97.67/24.34 thf(702,plain,((! [A:option_b]: ~ (none_option_b = (some_option_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 97.67/24.34 thf(146,axiom,((! [A:nat,B:b,C:list_b]: ((drop_b @ (suc @ A) @ (cons_b @ B @ C)) = (drop_b @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_drop__Suc__Cons)). 97.67/24.34 thf(802,plain,((! [A:nat,B:b,C:list_b]: ((drop_b @ (suc @ A) @ (cons_b @ B @ C)) = (drop_b @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 97.67/24.34 thf(327,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_less__imp__of__nat__less)). 97.67/24.34 thf(1462,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 97.67/24.34 thf(194,axiom,((! [A:nat,B:nat,C:formula_a]: ((member_nat @ A @ (fvi_a @ (suc @ B) @ C)) = (member_nat @ (suc @ A) @ (fvi_a @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_fvi__Suc)). 97.67/24.34 thf(949,plain,((! [A:nat,B:nat,C:formula_a]: ((member_nat @ A @ (fvi_a @ (suc @ B) @ C)) = (member_nat @ (suc @ A) @ (fvi_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 97.67/24.34 thf(39,axiom,((! [A:nat]: ~ (ord_less_int @ (semiri2019852685at_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_of__nat__less__0__iff)). 97.67/24.34 thf(460,plain,((! [A:nat]: ~ (ord_less_int @ (semiri2019852685at_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 97.67/24.34 thf(78,axiom,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ A) = (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_add__less__same__cancel1)). 97.67/24.34 thf(587,plain,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ A) = (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 97.67/24.34 thf(89,axiom,((! [A:nat]: (((semiri2019852685at_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_of__nat__eq__0__iff)). 97.67/24.34 thf(619,plain,((! [A:nat]: (((semiri2019852685at_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 97.67/24.34 thf(151,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_73_less__Suc__eq)). 97.67/24.34 thf(817,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)],[151])). 97.67/24.34 thf(163,axiom,((list_ex_b = (^ [A:(b > $o),B:list_b]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_b @ B)) & (A @ (nth_b @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_list__ex__length)). 97.67/24.34 thf(853,plain,(((list_ex_b) = (^ [A:(b > $o),B:list_b]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_b @ B)) & (A @ (nth_b @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 97.67/24.34 thf(303,axiom,((! [A:(option_b > $o),B:option_b,C:list_option_b]: ((list_ex_option_b @ A @ (cons_option_b @ B @ C)) = ((A @ B) | (list_ex_option_b @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_list__ex__simps_I1_J)). 97.67/24.34 thf(1379,plain,((! [A:(option_b > $o),B:option_b,C:list_option_b]: ((list_ex_option_b @ (A) @ (cons_option_b @ B @ C)) = ((A @ B) | (list_ex_option_b @ (A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 97.67/24.34 thf(168,axiom,((! [A:nat,B:list_option_b]: (((suc @ A) = (size_s1671393719tion_b @ B)) = (? [C:option_b,D:list_option_b]: (((size_s1671393719tion_b @ D) = A) & (B = (cons_option_b @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Suc__length__conv)). 97.67/24.34 thf(870,plain,((! [A:nat,B:list_option_b]: (((suc @ A) = (size_s1671393719tion_b @ B)) = (? [C:option_b,D:list_option_b]: (((size_s1671393719tion_b @ D) = A) & (B = (cons_option_b @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 97.67/24.34 thf(200,axiom,((! [A:(option_b > $o),B:option_b]: ((A @ none_b) => ((! [C:b]: (A @ (some_b @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_option_Oinducts)). 97.67/24.34 thf(969,plain,((! [A:(option_b > $o),B:option_b]: ((A @ none_b) => ((! [C:b]: (A @ (some_b @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 97.67/24.34 thf(25,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_add_Oright__cancel)). 97.67/24.34 thf(416,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 97.67/24.34 thf(35,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= (ord_less_int @ C @ D)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__strict__mono)). 97.67/24.34 thf(448,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ (ord_less_int @ C @ D) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 97.67/24.34 thf(236,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_add__less__cancel__right)). 97.67/24.34 thf(1100,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 97.67/24.34 thf(214,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_less__irrefl__nat)). 97.67/24.34 thf(1013,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 97.67/24.34 thf(137,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_less__SucI)). 97.67/24.34 thf(770,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 97.67/24.34 thf(48,axiom,((! [A:b,B:list_b]: ((cons_b @ A @ B) != B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_not__Cons__self2)). 97.67/24.34 thf(492,plain,((! [A:b,B:list_b]: ~ ((cons_b @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 97.67/24.34 thf(323,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_bot__nat__0_Onot__eq__extremum)). 97.67/24.34 thf(1450,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 97.67/24.34 thf(46,axiom,((! [A:option_b,B:option_b]: (((size_size_option_b @ A) != (size_size_option_b @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_size__neq__size__imp__neq)). 97.67/24.34 thf(485,plain,((! [A:option_b,B:option_b]: ((~ ((size_size_option_b @ A) = (size_size_option_b @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 97.67/24.34 thf(216,axiom,((! [A:nat,B:b,C:list_b]: ((gen_length_b @ A @ (cons_b @ B @ C)) = (gen_length_b @ (suc @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_gen__length__code_I2_J)). 97.67/24.34 thf(1020,plain,((! [A:nat,B:b,C:list_b]: ((gen_length_b @ A @ (cons_b @ B @ C)) = (gen_length_b @ (suc @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 97.67/24.34 thf(257,axiom,((! [A:(option_b > $o),B:list_option_b,C:option_b]: (((find_option_b @ A @ B) = (some_option_b @ C)) = (? [D:nat]: ((A @ (nth_option_b @ B @ D)) & ! [E:nat]: ((~ (A @ (nth_option_b @ B @ E))) <= (ord_less_nat @ E @ D)) & (C = (nth_option_b @ B @ D)) & (ord_less_nat @ D @ (size_s1671393719tion_b @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_find__Some__iff)). 97.67/24.34 thf(1183,plain,((! [A:(option_b > $o),B:list_option_b,C:option_b]: (((find_option_b @ (A) @ B) = (some_option_b @ C)) = (? [D:nat]: ((A @ (nth_option_b @ B @ D)) & ! [E:nat]: (~ (A @ (nth_option_b @ B @ E)) | ~ (ord_less_nat @ E @ D)) & (C = (nth_option_b @ B @ D)) & (ord_less_nat @ D @ (size_s1671393719tion_b @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 97.67/24.34 thf(223,axiom,((! [A:option_b,B:list_option_b,C:nat]: ((nth_option_b @ (cons_option_b @ A @ B) @ (suc @ C)) = (nth_option_b @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_nth__Cons__Suc)). 97.67/24.34 thf(1051,plain,((! [A:option_b,B:list_option_b,C:nat]: ((nth_option_b @ (cons_option_b @ A @ B) @ (suc @ C)) = (nth_option_b @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 97.67/24.34 thf(124,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ A @ B) & (ord_less_int @ C @ D)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_add__mono__thms__linordered__field_I5_J)). 97.67/24.34 thf(734,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ A @ B) & (ord_less_int @ C @ D)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 97.67/24.34 thf(322,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__not__refl)). 97.67/24.34 thf(1447,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 97.67/24.34 thf(167,axiom,((! [A:option_b]: ((~ (! [B:b]: (A != (some_b @ B)))) <= (A != none_b)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_option_Oexhaust)). 97.67/24.34 thf(866,plain,((! [A:option_b]: (~ (! [B:b]: ~ (A = (some_b @ B))) | (A = none_b)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 97.67/24.34 thf(308,axiom,((! [A:option_b,B:b]: ((A != none_b) <= (A = (some_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_option_OdiscI)). 97.67/24.34 thf(1394,plain,((! [A:option_b,B:b]: (~ (A = none_b) | ~ (A = (some_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 97.67/24.34 thf(29,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ab__semigroup__add__class_Oadd__ac_I1_J)). 97.67/24.34 thf(428,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 97.67/24.34 thf(273,axiom,((! [A:nat]: ((? [B:nat]: (A = (suc @ B))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_not0__implies__Suc)). 97.67/24.34 thf(1242,plain,((! [A:nat]: (? [B:nat]: (A = (suc @ B)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 97.67/24.34 thf(83,axiom,(((nat_triangle @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_triangle__0)). 97.67/24.34 thf(602,plain,(((nat_triangle @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 97.67/24.34 thf(203,axiom,((member_nat @ zero_zero_nat @ (fvi_a @ b2 @ phi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 97.67/24.34 thf(981,plain,((member_nat @ zero_zero_nat @ (fvi_a @ b2 @ phi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 97.67/24.34 thf(136,axiom,((! [A:(nat > int),B:nat,C:nat]: ((! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_int @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_lift__Suc__mono__less__iff)). 97.67/24.34 thf(766,plain,((! [A:(nat > int),B:nat,C:nat]: ((! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_int @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 97.67/24.34 thf(229,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => (((C @ A) <= (! [D:nat]: (((C @ (suc @ D)) => (C @ D)) <= (ord_less_nat @ D @ B)))) <= (! [D:nat]: ((B = (suc @ D)) => (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_strict__inc__induct)). 97.67/24.34 thf(1074,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((C @ A) | ~ (! [D:nat]: (((C @ (suc @ D)) => (C @ D)) | ~ (ord_less_nat @ D @ B))) | ~ (! [D:nat]: ((B = (suc @ D)) => (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 97.67/24.34 thf(264,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_nat @ A @ B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_add__mono__thms__linordered__field_I1_J)). 97.67/24.34 thf(1206,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_nat @ A @ B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 97.67/24.34 thf(14,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_add_Oright__neutral)). 97.67/24.34 thf(380,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 97.67/24.34 thf(54,axiom,((! [A:nat,B:list_b,C:b,D:list_b]: (((drop_b @ A @ B) = (cons_b @ C @ D)) => ((nth_b @ B @ A) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_nth__via__drop)). 97.67/24.34 thf(512,plain,((! [A:nat,B:list_b,C:b,D:list_b]: (((drop_b @ A @ B) = (cons_b @ C @ D)) => ((nth_b @ B @ A) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 97.67/24.34 thf(60,axiom,((! [A:nat,B:nat]: ((B = zero_zero_nat) <= ((plus_plus_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_add__eq__self__zero)). 97.67/24.34 thf(529,plain,((! [A:nat,B:nat]: ((B = zero_zero_nat) | ~ ((plus_plus_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 97.67/24.34 thf(66,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_group__cancel_Oadd2)). 97.67/24.34 thf(546,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 97.67/24.34 thf(185,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_zero__less__iff__neq__zero)). 97.67/24.34 thf(925,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 97.67/24.34 thf(262,axiom,((! [A:nat,B:list_option_b,C:option_b,D:list_option_b]: (((drop_option_b @ A @ B) = (cons_option_b @ C @ D)) => ((nth_option_b @ B @ A) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_nth__via__drop)). 97.67/24.34 thf(1199,plain,((! [A:nat,B:list_option_b,C:option_b,D:list_option_b]: (((drop_option_b @ A @ B) = (cons_option_b @ C @ D)) => ((nth_option_b @ B @ A) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 97.67/24.34 thf(134,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_linorder__neqE__nat)). 97.67/24.34 thf(761,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 97.67/24.34 thf(62,axiom,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ B) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add__less__same__cancel2)). 97.67/24.34 thf(534,plain,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ B) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 97.67/24.34 thf(225,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_76_less__SucE)). 97.67/24.34 thf(1057,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)],[225])). 97.67/24.34 thf(280,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Zero__not__Suc)). 97.67/24.34 thf(1274,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 97.67/24.34 thf(306,axiom,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_triangle__Suc)). 97.67/24.34 thf(1387,plain,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 97.67/24.34 thf(269,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_verit__comp__simplify1_I1_J)). 97.67/24.34 thf(1223,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 97.67/24.34 thf(233,axiom,((! [A:option_b,B:list_option_b]: ((size_s1671393719tion_b @ (cons_option_b @ A @ B)) = (suc @ (size_s1671393719tion_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_length__Cons)). 97.67/24.34 thf(1091,plain,((! [A:option_b,B:list_option_b]: ((size_s1671393719tion_b @ (cons_option_b @ A @ B)) = (suc @ (size_s1671393719tion_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 97.67/24.34 thf(154,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_infinite__descent)). 97.67/24.34 thf(825,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 97.67/24.34 thf(195,axiom,((! [A:option_b,B:list_option_b]: ((nth_option_b @ (cons_option_b @ A @ B) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nth__Cons__0)). 97.67/24.34 thf(952,plain,((! [A:option_b,B:list_option_b]: ((nth_option_b @ (cons_option_b @ A @ B) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 97.67/24.34 thf(267,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = (? [C:nat]: ((B @ C) & (ord_less_nat @ C @ A)) | (B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Ex__less__Suc)). 97.67/24.34 thf(1217,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = (? [C:nat]: ((B @ C) & (ord_less_nat @ C @ A)) | (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 97.67/24.34 thf(152,axiom,(((= @ list_b) = (^ [A:list_b,B:list_b]: (((size_size_list_b @ A) = (size_size_list_b @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_b @ A)) => ((nth_b @ A @ C) = (nth_b @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_list__eq__iff__nth__eq)). 97.67/24.34 thf(820,plain,(((= @ list_b) = (^ [A:list_b,B:list_b]: (((size_size_list_b @ A) = (size_size_list_b @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_b @ A)) => ((nth_b @ A @ C) = (nth_b @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 97.67/24.34 thf(18,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add_Oleft__neutral)). 97.67/24.34 thf(392,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 97.67/24.34 thf(122,axiom,(((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_int__ops_I1_J)). 97.67/24.34 thf(729,plain,(((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 97.67/24.34 thf(111,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add__right__cancel)). 97.67/24.34 thf(693,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 97.67/24.34 thf(92,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_add__cancel__left__right)). 97.67/24.34 thf(630,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 97.67/24.34 thf(182,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = ((B @ zero_zero_nat) & ! [C:nat]: ((B @ (suc @ C)) <= (ord_less_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_All__less__Suc2)). 97.67/24.34 thf(916,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = ((B @ zero_zero_nat) & ! [C:nat]: ((B @ (suc @ C)) | ~ (ord_less_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 97.67/24.34 thf(72,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_add__cancel__left__right)). 97.67/24.34 thf(566,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 97.67/24.34 thf(171,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) => (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_less__add__eq__less)). 97.67/24.34 thf(879,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) => (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 97.67/24.34 thf(31,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_add__cancel__left__left)). 97.67/24.34 thf(435,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 97.67/24.34 thf(155,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_69_less__antisym)). 97.67/24.34 thf(830,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)],[155])). 97.67/24.34 thf(174,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = ((B @ A) & ! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_All__less__Suc)). 97.67/24.34 thf(889,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = ((B @ A) & ! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 97.67/24.34 thf(254,axiom,((! [A:option_b,B:(option_b > (option_b > $o)),C:option_b]: (((A = none_b) => (B @ A @ C)) => (((C = none_b) => (B @ A @ C)) => ((! [D:b,E:b]: ((A = (some_b @ D)) => ((C = (some_b @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_combine__options__cases)). 97.67/24.34 thf(1159,plain,((! [A:option_b,B:(option_b > (option_b > $o)),C:option_b]: (((A = none_b) => (B @ A @ C)) => (((C = none_b) => (B @ A @ C)) => ((! [D:b,E:b]: ((A = (some_b @ D)) => ((C = (some_b @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 97.67/24.34 thf(265,axiom,((! [A:nat,B:list_option_b,C:nat]: (((nth_option_b @ (drop_option_b @ A @ B) @ C) = (nth_option_b @ B @ (plus_plus_nat @ A @ C))) <= (ord_less_eq_nat @ A @ (size_s1671393719tion_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_nth__drop)). 97.67/24.34 thf(1210,plain,((! [A:nat,B:list_option_b,C:nat]: (((nth_option_b @ (drop_option_b @ A @ B) @ C) = (nth_option_b @ B @ (plus_plus_nat @ A @ C))) | ~ (ord_less_eq_nat @ A @ (size_s1671393719tion_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 97.67/24.34 thf(67,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add_Oleft__cancel)). 97.67/24.34 thf(551,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 97.67/24.34 thf(282,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E))))) <= (! [D:nat]: (A @ zero_zero_nat @ (suc @ D)))) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_diff__induct)). 97.67/24.34 thf(1281,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) | ~ (! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 97.67/24.34 thf(285,axiom,((('?' @ option_b) = (^ [A:(option_b > $o)]: (? [B:b]: (A @ (some_b @ B)) | (A @ none_b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_split__option__ex)). 97.67/24.34 thf(1291,plain,((('?' @ option_b) = (^ [A:(option_b > $o)]: (? [B:b]: (A @ (some_b @ B)) | (A @ none_b))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 97.67/24.34 thf(238,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: (B != (suc @ (plus_plus_nat @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_less__natE)). 97.67/24.34 thf(1106,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: ~ (B = (suc @ (plus_plus_nat @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 97.67/24.34 thf(287,axiom,((! [A:option_b,B:list_option_b]: ((size_s1671393719tion_b @ (cons_option_b @ A @ B)) = (plus_plus_nat @ (size_s1671393719tion_b @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_list_Osize_I4_J)). 97.67/24.34 thf(1296,plain,((! [A:option_b,B:list_option_b]: ((size_s1671393719tion_b @ (cons_option_b @ A @ B)) = (plus_plus_nat @ (size_s1671393719tion_b @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 97.67/24.34 thf(104,axiom,((! [A:$o,B:nat,C:nat]: (((~ (A)) => ((semiri2019852685at_int @ (if_nat @ A @ B @ C)) = (semiri2019852685at_int @ C))) & (((semiri2019852685at_int @ (if_nat @ A @ B @ C)) = (semiri2019852685at_int @ B)) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_int__if)). 97.67/24.34 thf(665,plain,((! [A:$o,B:nat,C:nat]: (((~ (A)) => ((semiri2019852685at_int @ (if_nat @ A @ B @ C)) = (semiri2019852685at_int @ C))) & (((semiri2019852685at_int @ (if_nat @ A @ B @ C)) = (semiri2019852685at_int @ B)) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 97.67/24.34 thf(107,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_add__left__imp__eq)). 97.67/24.34 thf(682,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 97.67/24.34 thf(312,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_bot__nat__0_Oextremum__strict)). 97.67/24.34 thf(1407,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 97.67/24.34 thf(298,axiom,((! [A:option_b,B:list_option_b]: ((cons_option_b @ A @ B) != B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_not__Cons__self2)). 97.67/24.34 thf(1350,plain,((! [A:option_b,B:list_option_b]: ~ ((cons_option_b @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 97.67/24.34 thf(127,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_add__left__cancel)). 97.67/24.34 thf(742,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 97.67/24.34 thf(250,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_70_Suc__less__eq2)). 97.67/24.34 thf(1143,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)],[250])). 97.67/24.34 thf(275,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_nat @ B @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_add__less__same__cancel1)). 97.67/24.34 thf(1259,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_nat @ B @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 97.67/24.34 thf(88,axiom,((! [A:nat,B:nat,C:nat]: ((A = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_add__right__imp__eq)). 97.67/24.34 thf(615,plain,((! [A:nat,B:nat,C:nat]: ((A = C) | ~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 97.67/24.34 thf(121,axiom,((! [A:list_b,B:list_b]: (((size_size_list_b @ A) != (size_size_list_b @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_neq__if__length__neq)). 97.67/24.34 thf(725,plain,((! [A:list_b,B:list_b]: ((~ ((size_size_list_b @ A) = (size_size_list_b @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 97.67/24.34 thf(80,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_add__pos__pos)). 97.67/24.34 thf(593,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 97.67/24.34 thf(86,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_plus__nat_Oadd__0)). 97.67/24.34 thf(610,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 97.67/24.34 thf(241,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Suc__neq__Zero)). 97.67/24.34 thf(1118,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 97.67/24.34 thf(1,conjecture,((! [A:nat]: (~ (ord_less_nat @ A @ (suc @ n)) | (((nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ A) = none_b) = (~ (member_nat @ A @ (fvi_a @ b2 @ phi))))) & ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) = (suc @ n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)). 97.67/24.34 thf(2,negated_conjecture,((~ (! [A:nat]: (~ (ord_less_nat @ A @ (suc @ n)) | (((nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ A) = none_b) = (~ (member_nat @ A @ (fvi_a @ b2 @ phi))))) & ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) = (suc @ n))))),inference(neg_conjecture,[status(cth)],[1])). 97.67/24.34 thf(328,plain,((~ (! [A:nat]: (~ (ord_less_nat @ A @ (suc @ n)) | (((nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ A) = none_b) = (~ (member_nat @ A @ (fvi_a @ b2 @ phi))))) & ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) = (suc @ n))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 97.67/24.34 thf(230,axiom,((! [A:option_b,B:list_option_b,C:option_b,D:list_option_b]: (((cons_option_b @ A @ B) = (cons_option_b @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_list_Oinject)). 97.67/24.34 thf(1082,plain,((! [A:option_b,B:list_option_b,C:option_b,D:list_option_b]: (((cons_option_b @ A @ B) = (cons_option_b @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 97.67/24.34 thf(5,axiom,((! [A:int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_double__zero__sym)). 97.67/24.34 thf(339,plain,((! [A:int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 97.67/24.34 thf(188,axiom,((! [A:option_b]: ((A != none_b) = (? [B:b]: (A = (some_b @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__None__eq)). 97.67/24.34 thf(933,plain,((! [A:option_b]: ((~ (A = none_b)) = (? [B:b]: (A = (some_b @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 97.67/24.34 thf(63,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ A @ B)) = (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__add__same__cancel1)). 97.67/24.34 thf(537,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ A @ B)) = (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 97.67/24.34 thf(96,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_add_Ogroup__left__neutral)). 97.67/24.34 thf(642,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 97.67/24.34 thf(47,axiom,((! [A:nat,B:nat,C:int]: ((plus_plus_int @ (semiri2019852685at_int @ A) @ (plus_plus_int @ (semiri2019852685at_int @ B) @ C)) = (plus_plus_int @ (semiri2019852685at_int @ (plus_plus_nat @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_zadd__int__left)). 97.67/24.34 thf(489,plain,((! [A:nat,B:nat,C:int]: ((plus_plus_int @ (semiri2019852685at_int @ A) @ (plus_plus_int @ (semiri2019852685at_int @ B) @ C)) = (plus_plus_int @ (semiri2019852685at_int @ (plus_plus_nat @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 97.67/24.34 thf(266,axiom,((! [A:b]: ((size_size_option_b @ (some_b @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_option_Osize_I4_J)). 97.67/24.34 thf(1214,plain,((! [A:b]: ((size_size_option_b @ (some_b @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 97.67/24.34 thf(115,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_of__nat__add)). 97.67/24.34 thf(706,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 97.67/24.34 thf(316,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_old_Onat_Oinject)). 97.67/24.34 thf(1419,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 97.67/24.34 thf(68,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_add_Oleft__neutral)). 97.67/24.34 thf(554,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 97.67/24.34 thf(131,axiom,((('?' @ option_option_b) = (^ [A:(option_option_b > $o)]: ((A @ none_option_b) | ? [B:option_b]: (A @ (some_option_b @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_split__option__ex)). 97.67/24.34 thf(753,plain,((('?' @ option_option_b) = (^ [A:(option_option_b > $o)]: ((A @ none_option_b) | ? [B:option_b]: (A @ (some_option_b @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 97.67/24.34 thf(178,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_not__less__less__Suc__eq)). 97.67/24.34 thf(901,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 97.67/24.34 thf(108,axiom,((('!' @ option_option_b) = (^ [A:(option_option_b > $o)]: (! [B:option_b]: (A @ (some_option_b @ B)) & (A @ none_option_b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_split__option__all)). 97.67/24.34 thf(686,plain,((('!' @ option_option_b) = (^ [A:(option_option_b > $o)]: (! [B:option_b]: (A @ (some_option_b @ B)) & (A @ none_option_b))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 97.67/24.34 thf(314,axiom,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_less__Suc0)). 97.67/24.34 thf(1414,plain,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 97.67/24.34 thf(59,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_ab__semigroup__add__class_Oadd__ac_I1_J)). 97.67/24.34 thf(526,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 97.67/24.34 thf(215,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Suc__inject)). 97.67/24.34 thf(1016,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 97.67/24.34 thf(79,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_comm__monoid__add__class_Oadd__0)). 97.67/24.34 thf(590,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 97.67/24.34 thf(90,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_group__cancel_Oadd1)). 97.67/24.34 thf(622,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 97.67/24.34 thf(252,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (? [B:nat]: ((A = (semiri2019852685at_int @ B)) & (ord_less_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_zero__less__imp__eq__int)). 97.67/24.34 thf(1150,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (? [B:nat]: ((A = (semiri2019852685at_int @ B)) & (ord_less_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 97.67/24.34 thf(246,axiom,((! [A:nat,B:formula_a,C:nat]: ((! [D:nat]: ((member_nat @ D @ (fvi_a @ A @ B)) => (ord_less_nat @ D @ (suc @ C)))) <= (! [D:nat]: ((ord_less_nat @ D @ C) <= (member_nat @ D @ (fvi_a @ (suc @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_fvi__Suc__bound)). 97.67/24.34 thf(1131,plain,((! [A:nat,B:formula_a,C:nat]: (! [D:nat]: ((member_nat @ D @ (fvi_a @ A @ B)) => (ord_less_nat @ D @ (suc @ C))) | ~ (! [D:nat]: ((ord_less_nat @ D @ C) | ~ (member_nat @ D @ (fvi_a @ (suc @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 97.67/24.34 thf(260,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_99_lift__Suc__mono__less__iff)). 97.67/24.34 thf(1192,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)],[260])). 97.67/24.34 thf(205,axiom,((list_ex_option_b = (^ [A:(option_b > $o),B:list_option_b]: ? [C:nat]: ((A @ (nth_option_b @ B @ C)) & (ord_less_nat @ C @ (size_s1671393719tion_b @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_list__ex__length)). 97.67/24.34 thf(984,plain,(((list_ex_option_b) = (^ [A:(option_b > $o),B:list_option_b]: ? [C:nat]: ((A @ (nth_option_b @ B @ C)) & (ord_less_nat @ C @ (size_s1671393719tion_b @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 97.67/24.34 thf(73,axiom,((! [A:list_option_b]: ((drop_option_b @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_drop__0)). 97.67/24.34 thf(569,plain,((! [A:list_option_b]: ((drop_option_b @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 97.67/24.34 thf(139,axiom,((! [A:nat,B:nat]: ((A = (suc @ B)) => (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_nat_OdiscI)). 97.67/24.34 thf(779,plain,((! [A:nat,B:nat]: ((A = (suc @ B)) => (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 97.67/24.34 thf(11,axiom,((! [A:int]: ~ (ord_less_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_verit__comp__simplify1_I1_J)). 97.67/24.34 thf(371,plain,((! [A:int]: ~ (ord_less_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 97.67/24.34 thf(325,axiom,((! [A:b,B:list_b]: ((size_size_list_b @ (cons_b @ A @ B)) = (plus_plus_nat @ (size_size_list_b @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_list_Osize_I4_J)). 97.67/24.34 thf(1456,plain,((! [A:b,B:list_b]: ((size_size_list_b @ (cons_b @ A @ B)) = (plus_plus_nat @ (size_size_list_b @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 97.67/24.34 thf(304,axiom,((gen_length_option_b = (^ [A:nat,B:list_option_b]: (plus_plus_nat @ A @ (size_s1671393719tion_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_gen__length__def)). 97.67/24.34 thf(1382,plain,(((gen_length_option_b) = (^ [A:nat,B:list_option_b]: (plus_plus_nat @ A @ (size_s1671393719tion_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 97.67/24.34 thf(226,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_add__is__1)). 97.67/24.34 thf(1060,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 97.67/24.34 thf(38,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_add__cancel__right__left)). 97.67/24.34 thf(457,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 97.67/24.34 thf(320,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_nat @ C @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__less__mono)). 97.67/24.34 thf(1434,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_nat @ C @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 97.67/24.34 thf(93,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_int__plus)). 97.67/24.34 thf(633,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 97.67/24.34 thf(147,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_gr0__conv__Suc)). 97.67/24.34 thf(805,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 97.67/24.34 thf(224,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_nat__add__left__cancel__less)). 97.67/24.34 thf(1054,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 97.67/24.34 thf(105,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ A)) = (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_less__add__same__cancel2)). 97.67/24.34 thf(674,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ A)) = (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 97.67/24.34 thf(143,axiom,((! [A:(option_b > nat),B:option_b]: ((size_option_option_b @ A @ (some_option_b @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_option_Osize__gen_I2_J)). 97.67/24.34 thf(794,plain,((! [A:(option_b > nat),B:option_b]: ((size_option_option_b @ (A) @ (some_option_b @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 97.67/24.34 thf(103,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_add_Ocomm__neutral)). 97.67/24.34 thf(662,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 97.67/24.34 thf(281,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_nat_Oinject)). 97.67/24.34 thf(1278,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 97.67/24.34 thf(28,axiom,((! [A:int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_double__zero)). 97.67/24.34 thf(425,plain,((! [A:int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 97.67/24.34 thf(251,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (~ (! [C:nat]: ((B != (suc @ C)) <= (ord_less_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Suc__lessE)). 97.67/24.34 thf(1146,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (~ (! [C:nat]: (~ (B = (suc @ C)) | ~ (ord_less_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 97.67/24.34 thf(237,axiom,((! [A:nat,B:list_option_b]: ((ord_less_nat @ A @ (size_s1671393719tion_b @ B)) => ((cons_option_b @ (nth_option_b @ B @ A) @ (drop_option_b @ (suc @ A) @ B)) = (drop_option_b @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Cons__nth__drop__Suc)). 97.67/24.34 thf(1103,plain,((! [A:nat,B:list_option_b]: ((ord_less_nat @ A @ (size_s1671393719tion_b @ B)) => ((cons_option_b @ (nth_option_b @ B @ A) @ (drop_option_b @ (suc @ A) @ B)) = (drop_option_b @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 97.67/24.34 thf(128,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_add__is__0)). 97.67/24.34 thf(745,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 97.67/24.34 thf(34,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_add__left__imp__eq)). 97.67/24.34 thf(444,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 97.67/24.34 thf(199,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_list__decode_Ocases)). 97.67/24.34 thf(965,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 97.67/24.34 thf(130,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__less__cancel__left)). 97.67/24.34 thf(750,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 97.67/24.34 thf(253,axiom,((! [A:(list_option_b > $o),B:list_option_b]: ((! [C:list_option_b]: ((A @ C) <= (! [D:list_option_b]: ((A @ D) <= (ord_less_nat @ (size_s1671393719tion_b @ D) @ (size_s1671393719tion_b @ C)))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_length__induct)). 97.67/24.34 thf(1154,plain,((! [A:(list_option_b > $o),B:list_option_b]: ((! [C:list_option_b]: ((A @ C) | ~ (! [D:list_option_b]: ((A @ D) | ~ (ord_less_nat @ (size_s1671393719tion_b @ D) @ (size_s1671393719tion_b @ C)))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 97.67/24.34 thf(21,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D)) <= ((A = B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__mono__thms__linordered__semiring_I4_J)). 97.67/24.34 thf(402,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D)) | ~ ((A = B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 97.67/24.34 thf(160,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_lessI)). 97.67/24.34 thf(843,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 97.67/24.34 thf(138,axiom,((! [A:(b > $o),B:b,C:list_b]: ((((find_b @ A @ (cons_b @ B @ C)) = (find_b @ A @ C)) <= (~ (A @ B))) & (((find_b @ A @ (cons_b @ B @ C)) = (some_b @ B)) <= (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_find_Osimps_I2_J)). 97.67/24.34 thf(772,plain,((! [A:(b > $o),B:b,C:list_b]: ((((find_b @ (A) @ (cons_b @ B @ C)) = (find_b @ (A) @ C)) | (A @ B)) & (((find_b @ (A) @ (cons_b @ B @ C)) = (some_b @ B)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 97.67/24.34 thf(76,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_add__cancel__right__left)). 97.67/24.34 thf(579,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 97.67/24.34 thf(243,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__zeroE)). 97.67/24.34 thf(1124,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 97.67/24.34 thf(270,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((A @ (suc @ C)) <= (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_old_Onat_Oinducts)). 97.67/24.34 thf(1226,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ (suc @ C)) | ~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 97.67/24.34 thf(24,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_add_Oleft__commute)). 97.67/24.34 thf(413,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 97.67/24.34 thf(179,axiom,((! [A:list_option_b,B:list_option_b]: (((size_s1671393719tion_b @ A) = (size_s1671393719tion_b @ B)) => ((! [C:nat]: (((nth_option_b @ A @ C) = (nth_option_b @ B @ C)) <= (ord_less_nat @ C @ (size_s1671393719tion_b @ A)))) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_nth__equalityI)). 97.67/24.34 thf(904,plain,((! [A:list_option_b,B:list_option_b]: (((size_s1671393719tion_b @ A) = (size_s1671393719tion_b @ B)) => ((! [C:nat]: (((nth_option_b @ A @ C) = (nth_option_b @ B @ C)) | ~ (ord_less_nat @ C @ (size_s1671393719tion_b @ A)))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 97.67/24.34 thf(201,axiom,((! [A:nat]: ((ord_less_int @ zero_zero_int @ (semiri2019852685at_int @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_of__nat__0__less__iff)). 97.67/24.34 thf(975,plain,((! [A:nat]: ((ord_less_int @ zero_zero_int @ (semiri2019852685at_int @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 97.67/24.34 thf(249,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_add__mono__thms__linordered__field_I2_J)). 97.67/24.34 thf(1139,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 97.67/24.34 thf(189,axiom,((! [A:nat,B:list_b]: (((suc @ A) = (size_size_list_b @ B)) = (? [C:b,D:list_b]: (((size_size_list_b @ D) = A) & (B = (cons_b @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Suc__length__conv)). 97.67/24.34 thf(936,plain,((! [A:nat,B:list_b]: (((suc @ A) = (size_size_list_b @ B)) = (? [C:b,D:list_b]: (((size_size_list_b @ D) = A) & (B = (cons_b @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 97.67/24.34 thf(74,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_plus__int__code_I2_J)). 97.67/24.34 thf(572,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 97.67/24.34 thf(279,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_not__less__zero)). 97.67/24.34 thf(1271,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 97.67/24.34 thf(141,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))) | ((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_one__is__add)). 97.67/24.34 thf(787,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))) | ((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 97.67/24.34 thf(50,axiom,((! [A:(option_option_b > $o),B:option_option_b]: ((A @ none_option_b) => ((! [C:option_b]: (A @ (some_option_b @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_option_Oinducts)). 97.67/24.34 thf(498,plain,((! [A:(option_option_b > $o),B:option_option_b]: ((A @ none_option_b) => ((! [C:option_b]: (A @ (some_option_b @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 97.67/24.34 thf(272,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_12_Suc__less__eq)). 97.67/24.34 thf(1239,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)],[272])). 97.67/24.34 thf(293,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_old_Onat_Odistinct_I2_J)). 97.67/24.34 thf(1332,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 97.67/24.34 thf(41,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__strict__right__mono)). 97.67/24.34 thf(466,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 97.67/24.34 thf(183,axiom,((! [A:nat,B:(nat > (option_b > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:option_b]: (B @ C @ D)))) = (? [C:list_option_b]: (((size_s1671393719tion_b @ C) = A) & ! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_option_b @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Skolem__list__nth)). 97.67/24.34 thf(919,plain,((! [A:nat,B:(nat > (option_b > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:option_b]: (B @ C @ D)))) = (? [C:list_option_b]: (((size_s1671393719tion_b @ C) = A) & ! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_option_b @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 97.67/24.34 thf(193,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_less__add__Suc1)). 97.67/24.34 thf(947,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 97.67/24.34 thf(64,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (ord_less_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_add__less__cancel__right)). 97.67/24.34 thf(540,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (ord_less_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 97.67/24.34 thf(22,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((ord_less_int @ A @ B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add__mono__thms__linordered__field_I1_J)). 97.67/24.34 thf(406,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ ((ord_less_int @ A @ B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 97.67/24.34 thf(140,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_add__strict__left__mono)). 97.67/24.34 thf(784,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 97.67/24.34 thf(26,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_zero__reorient)). 97.67/24.34 thf(419,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 97.67/24.34 thf(53,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_verit__sum__simplify)). 97.67/24.34 thf(509,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 97.67/24.34 thf(242,axiom,((! [A:nat,B:nat]: ((ord_less_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_of__nat__less__imp__less)). 97.67/24.34 thf(1122,plain,((! [A:nat,B:nat]: ((ord_less_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B)) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 97.67/24.34 thf(290,axiom,((! [A:list_b,B:nat]: (((size_size_list_b @ A) = (suc @ B)) = (? [C:b,D:list_b]: ((A = (cons_b @ C @ D)) & ((size_size_list_b @ D) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_length__Suc__conv)). 97.67/24.34 thf(1307,plain,((! [A:list_b,B:nat]: (((size_size_list_b @ A) = (suc @ B)) = (? [C:b,D:list_b]: ((A = (cons_b @ C @ D)) & ((size_size_list_b @ D) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 97.67/24.34 thf(166,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_gr0__implies__Suc)). 97.67/24.34 thf(863,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 97.67/24.34 thf(135,axiom,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_less__numeral__extra_I3_J)). 97.67/24.34 thf(764,plain,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 97.67/24.34 thf(84,axiom,((! [A:nat]: ? [B:list_b]: ((size_size_list_b @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Ex__list__of__length)). 97.67/24.34 thf(604,plain,((! [A:nat]: ? [B:list_b]: ((size_size_list_b @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 97.67/24.34 thf(222,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_add__pos__pos)). 97.67/24.34 thf(1048,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 97.67/24.34 thf(125,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add_Oassoc)). 97.67/24.34 thf(736,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 97.67/24.34 thf(13,axiom,((! [A:option_option_b]: ((! [B:option_b]: (A != (some_option_b @ B))) = (A = none_option_b)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_not__Some__eq)). 97.67/24.34 thf(377,plain,((! [A:option_option_b]: ((! [B:option_b]: ~ (A = (some_option_b @ B))) = (A = none_option_b)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 97.67/24.34 thf(207,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_not__less0)). 97.67/24.34 thf(990,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 97.67/24.34 thf(209,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((((! [D:nat,E:nat,F:nat]: ((((C @ D @ E) => ((C @ E @ F) => (C @ D @ F))) <= (ord_less_nat @ E @ F)) <= (ord_less_nat @ D @ E))) => (C @ A @ B)) <= (! [D:nat]: (C @ D @ (suc @ D)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__Suc__induct)). 97.67/24.34 thf(996,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((! [D:nat,E:nat,F:nat]: (((C @ D @ E) => ((C @ E @ F) => (C @ D @ F))) | ~ (ord_less_nat @ E @ F) | ~ (ord_less_nat @ D @ E))) => (C @ A @ B)) | ~ (! [D:nat]: (C @ D @ (suc @ D))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 97.67/24.34 thf(8,axiom,((! [A:int]: ((ord_less_int @ (plus_plus_int @ A @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_double__add__less__zero__iff__single__add__less__zero)). 97.67/24.34 thf(362,plain,((! [A:int]: ((ord_less_int @ (plus_plus_int @ A @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 97.67/24.34 thf(36,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_is__num__normalize_I1_J)). 97.67/24.34 thf(451,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 97.67/24.34 thf(82,axiom,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_int__int__eq)). 97.67/24.34 thf(599,plain,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 97.67/24.34 thf(302,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_trans__less__add2)). 97.67/24.34 thf(1376,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 97.67/24.34 thf(133,axiom,((! [A:list_option_b,B:nat]: (((size_s1671393719tion_b @ A) = (suc @ B)) = (? [C:option_b,D:list_option_b]: (((size_s1671393719tion_b @ D) = B) & (A = (cons_option_b @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_length__Suc__conv)). 97.67/24.34 thf(758,plain,((! [A:list_option_b,B:nat]: (((size_s1671393719tion_b @ A) = (suc @ B)) = (? [C:option_b,D:list_option_b]: (((size_s1671393719tion_b @ D) = B) & (A = (cons_option_b @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 97.67/24.34 thf(165,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: ((B = (plus_plus_nat @ A @ C)) => (C = zero_zero_nat)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_canonically__ordered__monoid__add__class_OlessE)). 97.67/24.34 thf(858,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ((B = (plus_plus_nat @ A @ C)) => (C = zero_zero_nat))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 97.67/24.34 thf(145,axiom,((! [A:nat,B:list_b]: (((cons_b @ (nth_b @ B @ A) @ (drop_b @ (suc @ A) @ B)) = (drop_b @ A @ B)) <= (ord_less_nat @ A @ (size_size_list_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Cons__nth__drop__Suc)). 97.67/24.34 thf(799,plain,((! [A:nat,B:list_b]: (((cons_b @ (nth_b @ B @ A) @ (drop_b @ (suc @ A) @ B)) = (drop_b @ A @ B)) | ~ (ord_less_nat @ A @ (size_size_list_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 97.67/24.34 thf(176,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1382578993at_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_of__nat__0__less__iff)). 97.67/24.34 thf(895,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1382578993at_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 97.67/24.34 thf(286,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_add__less__mono1)). 97.67/24.34 thf(1293,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 97.67/24.34 thf(149,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_of__nat__less__iff)). 97.67/24.34 thf(811,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 97.67/24.34 thf(16,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = B) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_add__cancel__left__left)). 97.67/24.34 thf(387,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = B) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 97.67/24.34 thf(162,axiom,((! [A:nat,B:nat]: (((~ (! [C:nat]: ((B != (suc @ C)) <= (ord_less_nat @ A @ C)))) <= (B != (suc @ A))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Nat_OlessE)). 97.67/24.34 thf(848,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: (~ (B = (suc @ C)) | ~ (ord_less_nat @ A @ C))) | (B = (suc @ A)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 97.67/24.34 thf(57,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_add__cancel__right__right)). 97.67/24.34 thf(520,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 97.67/24.34 thf(20,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_add_Oright__neutral)). 97.67/24.34 thf(399,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 97.67/24.34 thf(197,axiom,((('!' @ option_b) = (^ [A:(option_b > $o)]: (! [B:b]: (A @ (some_b @ B)) & (A @ none_b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_split__option__all)). 97.67/24.34 thf(959,plain,((('!' @ option_b) = (^ [A:(option_b > $o)]: (! [B:b]: (A @ (some_b @ B)) & (A @ none_b))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 97.67/24.34 thf(172,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_not__gr__zero)). 97.67/24.34 thf(883,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 97.67/24.34 thf(255,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_gr__zeroI)). 97.67/24.34 thf(1176,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 97.67/24.34 thf(206,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat_Odistinct_I1_J)). 97.67/24.34 thf(986,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 97.67/24.34 thf(32,axiom,((! [A:option_option_b]: ((~ (! [B:option_b]: (A != (some_option_b @ B)))) <= (A != none_option_b)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_option_Oexhaust)). 97.67/24.34 thf(438,plain,((! [A:option_option_b]: (~ (! [B:option_b]: ~ (A = (some_option_b @ B))) | (A = none_option_b)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 97.67/24.34 thf(30,axiom,((! [A:int,B:int,C:int]: ((A = C) <= ((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_add__right__imp__eq)). 97.67/24.34 thf(431,plain,((! [A:int,B:int,C:int]: ((A = C) | ~ ((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 97.67/24.34 thf(100,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Nat_Oadd__0__right)). 97.67/24.34 thf(653,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 97.67/24.34 thf(184,axiom,((! [A:nat,B:option_b,C:list_option_b]: ((gen_length_option_b @ A @ (cons_option_b @ B @ C)) = (gen_length_option_b @ (suc @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_gen__length__code_I2_J)). 97.67/24.34 thf(922,plain,((! [A:nat,B:option_b,C:list_option_b]: ((gen_length_option_b @ A @ (cons_option_b @ B @ C)) = (gen_length_option_b @ (suc @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 97.67/24.34 thf(94,axiom,((! [A:int,B:int]: (((ord_less_int @ B @ A) <= (~ (ord_less_int @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_linorder__neqE__linordered__idom)). 97.67/24.34 thf(636,plain,((! [A:int,B:int]: ((ord_less_int @ B @ A) | (ord_less_int @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 97.67/24.34 thf(274,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_infinite__descent0)). 97.67/24.34 thf(1245,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 97.67/24.34 thf(240,axiom,((! [A:list_b,B:list_b]: (((! [C:nat]: (((nth_b @ A @ C) = (nth_b @ B @ C)) <= (ord_less_nat @ C @ (size_size_list_b @ A)))) => (A = B)) <= ((size_size_list_b @ A) = (size_size_list_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_nth__equalityI)). 97.67/24.34 thf(1113,plain,((! [A:list_b,B:list_b]: (((! [C:nat]: (((nth_b @ A @ C) = (nth_b @ B @ C)) | ~ (ord_less_nat @ C @ (size_size_list_b @ A)))) => (A = B)) | ~ ((size_size_list_b @ A) = (size_size_list_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 97.67/24.34 thf(71,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_add__0__iff)). 97.67/24.34 thf(563,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 97.67/24.34 thf(263,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_add__strict__right__mono)). 97.67/24.34 thf(1203,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 97.67/24.34 thf(192,axiom,((! [A:nat]: ((A != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_gr0I)). 97.67/24.34 thf(944,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 97.67/24.34 thf(12,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (plus_plus_int @ A @ C)) <= (ord_less_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_pos__add__strict)). 97.67/24.34 thf(374,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ (plus_plus_int @ A @ C)) | ~ (ord_less_int @ B @ C) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 97.67/24.34 thf(55,axiom,((size_size_list_b = (gen_length_b @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_length__code)). 97.67/24.34 thf(516,plain,(((size_size_list_b) = (gen_length_b @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 97.67/24.34 thf(6,axiom,((! [A:option_option_b,B:(option_option_b > (option_option_b > $o)),C:option_option_b]: (((A = none_option_b) => (B @ A @ C)) => (((B @ A @ C) <= (! [D:option_b,E:option_b]: ((A = (some_option_b @ D)) => ((C = (some_option_b @ E)) => (B @ A @ C))))) <= ((B @ A @ C) <= (C = none_option_b)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_combine__options__cases)). 97.67/24.34 thf(342,plain,((! [A:option_option_b,B:(option_option_b > (option_option_b > $o)),C:option_option_b]: (((A = none_option_b) => (B @ A @ C)) => ((B @ A @ C) | ~ (! [D:option_b,E:option_b]: ((A = (some_option_b @ D)) => ((C = (some_option_b @ E)) => (B @ A @ C)))) | ~ ((B @ A @ C) | ~ (C = none_option_b)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 97.67/24.34 thf(157,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_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_208_add__gr__0)). 97.67/24.34 thf(836,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_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)],[157])). 97.67/24.34 thf(247,axiom,((! [A:option_b]: ((size_s684879735tion_b @ (some_option_b @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_option_Osize_I4_J)). 97.67/24.34 thf(1134,plain,((! [A:option_b]: ((size_s684879735tion_b @ (some_option_b @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 97.67/24.34 thf(98,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ A)) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_zero__less__double__add__iff__zero__less__single__add)). 97.67/24.34 thf(648,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ A)) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 97.67/24.34 thf(190,axiom,((ord_less_int = (^ [A:int,B:int]: ? [C:nat]: (B = (plus_plus_int @ A @ (semiri2019852685at_int @ (suc @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_zless__iff__Suc__zadd)). 97.67/24.34 thf(939,plain,(((ord_less_int) = (^ [A:int,B:int]: ? [C:nat]: (B = (plus_plus_int @ A @ (semiri2019852685at_int @ (suc @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 97.67/24.34 thf(295,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Suc__lessD)). 97.67/24.34 thf(1340,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 97.67/24.34 thf(164,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_not__add__less2)). 97.67/24.34 thf(855,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 97.67/24.34 thf(228,axiom,((! [A:int]: ((~ (! [B:nat]: ((A = (semiri2019852685at_int @ B)) => (~ (ord_less_nat @ zero_zero_nat @ B))))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_pos__int__cases)). 97.67/24.34 thf(1070,plain,((! [A:int]: (~ (! [B:nat]: ((A = (semiri2019852685at_int @ B)) => (~ (ord_less_nat @ zero_zero_nat @ B)))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 97.67/24.34 thf(126,axiom,((! [A:nat]: ((zero_zero_int = (semiri2019852685at_int @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_of__nat__0__eq__iff)). 97.67/24.34 thf(739,plain,((! [A:nat]: ((zero_zero_int = (semiri2019852685at_int @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 97.67/24.34 thf(208,axiom,((! [A:option_b]: ((! [B:b]: (A != (some_b @ B))) = (A = none_b)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_not__Some__eq)). 97.67/24.34 thf(993,plain,((! [A:option_b]: ((! [B:b]: ~ (A = (some_b @ B))) = (A = none_b)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 97.67/24.34 thf(117,axiom,((! [A:option_b]: ((size_size_option_b @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_option_Osize__neq)). 97.67/24.34 thf(712,plain,((! [A:option_b]: ~ ((size_size_option_b @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 97.67/24.34 thf(69,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_add__0__iff)). 97.67/24.34 thf(557,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 97.67/24.34 thf(210,axiom,((size_s1671393719tion_b = (gen_length_option_b @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_length__code)). 97.67/24.34 thf(1003,plain,(((size_s1671393719tion_b) = (gen_length_option_b @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 97.67/24.34 thf(258,axiom,((! [A:list_option_b,B:list_option_b]: (((size_s1671393719tion_b @ A) != (size_s1671393719tion_b @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_neq__if__length__neq)). 97.67/24.34 thf(1186,plain,((! [A:list_option_b,B:list_option_b]: ((~ ((size_s1671393719tion_b @ A) = (size_s1671393719tion_b @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 97.67/24.34 thf(219,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_less__add__same__cancel2)). 97.67/24.34 thf(1038,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 97.67/24.34 thf(276,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_less__iff__Suc__add)). 97.67/24.34 thf(1262,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 97.67/24.34 thf(40,axiom,((! [A:int]: ((zero_zero_int = A) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zero__reorient)). 97.67/24.34 thf(463,plain,((! [A:int]: ((zero_zero_int = A) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 97.67/24.34 thf(231,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_mem__Collect__eq)). 97.67/24.34 thf(1085,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 97.67/24.34 thf(148,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Collect__mem__eq)). 97.67/24.34 thf(808,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 97.67/24.34 thf(7,axiom,((! [A:(b > $o),B:b,C:list_b]: ((list_ex_b @ A @ (cons_b @ B @ C)) = ((list_ex_b @ A @ C) | (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_list__ex__simps_I1_J)). 97.67/24.34 thf(359,plain,((! [A:(b > $o),B:b,C:list_b]: ((list_ex_b @ (A) @ (cons_b @ B @ C)) = ((list_ex_b @ (A) @ C) | (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 97.67/24.34 thf(283,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__strict__mono)). 97.67/24.34 thf(1285,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 97.67/24.34 thf(294,axiom,((! [A:nat,B:nat]: ((B != zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_gr__implies__not0)). 97.67/24.34 thf(1336,plain,((! [A:nat,B:nat]: (~ (B = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 97.67/24.34 thf(268,axiom,((! [A:b,B:list_b,C:nat]: ((nth_b @ (cons_b @ A @ B) @ (suc @ C)) = (nth_b @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_nth__Cons__Suc)). 97.67/24.34 thf(1220,plain,((! [A:b,B:list_b,C:nat]: ((nth_b @ (cons_b @ A @ B) @ (suc @ C)) = (nth_b @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 97.67/24.34 thf(311,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_add__Suc)). 97.67/24.34 thf(1404,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 97.67/24.34 thf(4,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_comm__monoid__add__class_Oadd__0)). 97.67/24.34 thf(336,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 97.67/24.34 thf(87,axiom,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_less__numeral__extra_I3_J)). 97.67/24.34 thf(613,plain,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 97.67/24.34 thf(212,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_68_Suc__less__SucD)). 97.67/24.34 thf(1008,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)],[212])). 97.67/24.34 thf(170,axiom,((! [A:nat,B:nat]: ((ord_less_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_of__nat__less__iff)). 97.67/24.34 thf(876,plain,((! [A:nat,B:nat]: ((ord_less_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 97.67/24.34 thf(101,axiom,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_of__nat__eq__iff)). 97.67/24.34 thf(656,plain,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 97.67/24.34 thf(217,axiom,((! [A:option_b,B:(option_b > (option_option_b > $o)),C:option_option_b]: ((((B @ A @ C) <= (C = none_option_b)) => ((B @ A @ C) <= (! [D:b,E:option_b]: (((C = (some_option_b @ E)) => (B @ A @ C)) <= (A = (some_b @ D)))))) <= ((A = none_b) => (B @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_combine__options__cases)). 97.67/24.34 thf(1023,plain,((! [A:option_b,B:(option_b > (option_option_b > $o)),C:option_option_b]: ((((B @ A @ C) | ~ (C = none_option_b)) => ((B @ A @ C) | ~ (! [D:b,E:option_b]: (((C = (some_option_b @ E)) => (B @ A @ C)) | ~ (A = (some_b @ D)))))) | ~ ((A = none_b) => (B @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 97.67/24.34 thf(234,axiom,((! [A:b,B:b]: (((some_b @ A) = (some_b @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_option_Oinject)). 97.67/24.34 thf(1094,plain,((! [A:b,B:b]: (((some_b @ A) = (some_b @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 97.67/24.34 thf(202,axiom,((! [A:(b > nat)]: ((size_option_b @ A @ none_b) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_option_Osize__gen_I1_J)). 97.67/24.34 thf(978,plain,((! [A:(b > nat)]: ((size_option_b @ (A) @ none_b) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 97.67/24.34 thf(161,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add__Suc__shift)). 97.67/24.34 thf(845,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 97.67/24.34 thf(91,axiom,((! [A:b,B:list_b,C:b,D:list_b]: (((cons_b @ A @ B) = (cons_b @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_list_Oinject)). 97.67/24.34 thf(627,plain,((! [A:b,B:list_b,C:b,D:list_b]: (((cons_b @ A @ B) = (cons_b @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 97.67/24.34 thf(326,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_less__nat__zero__code)). 97.67/24.34 thf(1459,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 97.67/24.34 thf(109,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_add__right__cancel)). 97.67/24.34 thf(688,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 97.67/24.34 thf(213,axiom,((! [A:nat]: ~ (ord_less_nat @ (semiri1382578993at_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_of__nat__less__0__iff)). 97.67/24.34 thf(1010,plain,((! [A:nat]: ~ (ord_less_nat @ (semiri1382578993at_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 97.67/24.34 thf(307,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_less__not__refl2)). 97.67/24.34 thf(1390,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 97.67/24.34 thf(10,axiom,((! [A:nat,B:nat]: (((semiri1382578993at_nat @ A) = (semiri1382578993at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_of__nat__eq__iff)). 97.67/24.34 thf(368,plain,((! [A:nat,B:nat]: (((semiri1382578993at_nat @ A) = (semiri1382578993at_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 97.67/24.34 thf(324,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_add__neg__neg)). 97.67/24.34 thf(1453,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 97.67/24.34 thf(113,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_verit__sum__simplify)). 97.67/24.34 thf(699,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 97.67/24.34 thf(198,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Zero__neq__Suc)). 97.67/24.34 thf(961,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 97.67/24.34 thf(129,axiom,(((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_of__nat__0)). 97.67/24.34 thf(748,plain,(((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 97.67/24.34 thf(17,axiom,(((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_of__nat__0)). 97.67/24.34 thf(390,plain,(((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 97.67/24.34 thf(123,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_add__left__cancel)). 97.67/24.34 thf(731,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 97.67/24.34 thf(15,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) & (A = B)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_add__mono__thms__linordered__field_I2_J)). 97.67/24.34 thf(383,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) & (A = B)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 97.67/24.34 thf(221,axiom,((! [A:nat,B:(nat > (b > $o))]: ((! [C:nat]: ((? [D:b]: (B @ C @ D)) <= (ord_less_nat @ C @ A))) = (? [C:list_b]: (((size_size_list_b @ C) = A) & ! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_b @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_Skolem__list__nth)). 97.67/24.34 thf(1045,plain,((! [A:nat,B:(nat > (b > $o))]: ((! [C:nat]: (? [D:b]: (B @ C @ D) | ~ (ord_less_nat @ C @ A))) = (? [C:list_b]: (((size_size_list_b @ C) = A) & ! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_b @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 97.67/24.34 thf(118,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D)) <= ((C = D) & (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_add__mono__thms__linordered__semiring_I4_J)). 97.67/24.34 thf(716,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D)) | ~ ((C = D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 97.67/24.34 thf(235,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_33_nat__neq__iff)). 97.67/24.34 thf(1097,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)],[235])). 97.67/24.34 thf(289,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)). 97.67/24.34 thf(1303,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 97.67/24.34 thf(156,axiom,((! [A:(b > nat),B:b]: ((size_option_b @ A @ (some_b @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_option_Osize__gen_I2_J)). 97.67/24.34 thf(833,plain,((! [A:(b > nat),B:b]: ((size_option_b @ (A) @ (some_b @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 97.67/24.34 thf(23,axiom,((! [A:b,B:list_b]: ((nth_b @ (cons_b @ A @ B) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_nth__Cons__0)). 97.67/24.34 thf(410,plain,((! [A:b,B:list_b]: ((nth_b @ (cons_b @ A @ B) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 97.67/24.34 thf(27,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_add__strict__left__mono)). 97.67/24.34 thf(422,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 97.67/24.34 thf(142,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_old_Onat_Oexhaust)). 97.67/24.34 thf(790,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 97.67/24.34 thf(52,axiom,((! [A:nat]: (((semiri1382578993at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_of__nat__eq__0__iff)). 97.67/24.34 thf(506,plain,((! [A:nat]: (((semiri1382578993at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 97.67/24.34 thf(284,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_not__add__less1)). 97.67/24.34 thf(1288,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 97.67/24.34 thf(61,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_add_Ocommute)). 97.67/24.34 thf(532,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 97.67/24.34 thf(112,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_plus__int__code_I1_J)). 97.67/24.34 thf(696,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 97.67/24.34 thf(119,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_add_Ocomm__neutral)). 97.67/24.34 thf(720,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 97.67/24.34 thf(196,axiom,((! [A:nat]: ((semiri1382578993at_nat @ (suc @ A)) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_of__nat__neq__0)). 97.67/24.34 thf(955,plain,((! [A:nat]: ~ ((semiri1382578993at_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 97.67/24.34 thf(297,axiom,((! [A:nat,B:nat]: ((? [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) & ((plus_plus_nat @ A @ C) = B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_less__imp__add__positive)). 97.67/24.34 thf(1346,plain,((! [A:nat,B:nat]: (? [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) & ((plus_plus_nat @ A @ C) = B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 97.67/24.34 thf(44,axiom,((! [A:option_option_b,B:option_b]: ((A = (some_option_b @ B)) => (A != none_option_b)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_option_OdiscI)). 97.67/24.34 thf(474,plain,((! [A:option_option_b,B:option_b]: ((A = (some_option_b @ B)) => (~ (A = none_option_b))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 97.67/24.34 thf(313,axiom,((! [A:(list_b > $o),B:list_b]: ((A @ B) <= (! [C:list_b]: ((A @ C) <= (! [D:list_b]: ((A @ D) <= (ord_less_nat @ (size_size_list_b @ D) @ (size_size_list_b @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_length__induct)). 97.67/24.34 thf(1410,plain,((! [A:(list_b > $o),B:list_b]: ((A @ B) | ~ (! [C:list_b]: ((A @ C) | ~ (! [D:list_b]: ((A @ D) | ~ (ord_less_nat @ (size_size_list_b @ D) @ (size_size_list_b @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 97.67/24.34 thf(173,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_103_less__Suc__eq__0__disj)). 97.67/24.34 thf(886,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)],[173])). 97.67/24.34 thf(186,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_less__add__Suc2)). 97.67/24.34 thf(928,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 97.67/24.34 thf(271,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__trans__Suc)). 97.67/24.34 thf(1236,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 97.67/24.34 thf(245,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_less__imp__of__nat__less)). 97.67/24.34 thf(1129,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 97.67/24.34 thf(305,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_less__add__same__cancel1)). 97.67/24.34 thf(1384,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 97.67/24.34 thf(81,axiom,((! [A:nat]: ((zero_zero_nat = (semiri1382578993at_nat @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_of__nat__0__eq__iff)). 97.67/24.34 thf(596,plain,((! [A:nat]: ((zero_zero_nat = (semiri1382578993at_nat @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 97.67/24.34 thf(300,axiom,((! [A:(nat > $o)]: (((? [B:nat]: (A @ B)) => (? [B:nat]: (~ (A @ B) & (A @ (suc @ B))))) <= (~ (A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_exists__least__lemma)). 97.67/24.34 thf(1357,plain,((! [A:(nat > $o)]: (((? [B:nat]: (A @ B)) => (? [B:nat]: (~ (A @ B) & (A @ (suc @ B))))) | (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 97.67/24.34 thf(120,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) <= (ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_add__less__imp__less__left)). 97.67/24.34 thf(723,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) | ~ (ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 97.67/24.34 thf(153,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = (? [C:nat]: ((B @ (suc @ C)) & (ord_less_nat @ C @ A)) | (B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_Ex__less__Suc2)). 97.67/24.34 thf(822,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = (? [C:nat]: ((B @ (suc @ C)) & (ord_less_nat @ C @ A)) | (B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 97.67/24.34 thf(288,axiom,((! [A:nat]: ((semiri2019852685at_int @ (suc @ A)) != zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_of__nat__neq__0)). 97.67/24.34 thf(1299,plain,((! [A:nat]: ~ ((semiri2019852685at_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 97.67/24.34 thf(110,axiom,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int) => ((ord_less_int @ B @ zero_zero_int) | (ord_less_int @ A @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_add__less__zeroD)). 97.67/24.34 thf(691,plain,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int) => ((ord_less_int @ B @ zero_zero_int) | (ord_less_int @ A @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 97.67/24.34 thf(33,axiom,((plus_plus_int = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_add_Ocommute)). 97.67/24.34 thf(442,plain,(((plus_plus_int) = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 97.67/24.34 thf(309,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_add__lessD1)). 97.67/24.34 thf(1399,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 97.67/24.34 thf(85,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_add__cancel__right__right)). 97.67/24.34 thf(607,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 97.67/24.34 thf(19,axiom,((! [A:list_b,B:list_b]: (((size_size_list_b @ A) != (size_size_list_b @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_size__neq__size__imp__neq)). 97.67/24.34 thf(395,plain,((! [A:list_b,B:list_b]: ((~ ((size_size_list_b @ A) = (size_size_list_b @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 97.67/24.34 thf(158,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_nat @ C @ D) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_add__mono__thms__linordered__field_I5_J)). 97.67/24.34 thf(839,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_nat @ C @ D) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 97.67/24.34 thf(278,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_add__less__same__cancel2)). 97.67/24.34 thf(1268,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 97.67/24.34 thf(75,axiom,((! [A:nat,B:list_b,C:nat]: ((ord_less_eq_nat @ A @ (size_size_list_b @ B)) => ((nth_b @ (drop_b @ A @ B) @ C) = (nth_b @ B @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_nth__drop)). 97.67/24.34 thf(575,plain,((! [A:nat,B:list_b,C:nat]: ((ord_less_eq_nat @ A @ (size_size_list_b @ B)) => ((nth_b @ (drop_b @ A @ B) @ C) = (nth_b @ B @ (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 97.67/24.34 thf(204,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add__less__imp__less__right)). 97.67/24.34 thf(982,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 97.67/24.34 thf(319,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_trans__less__add1)). 97.67/24.34 thf(1431,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 97.67/24.34 thf(42,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_int__ops_I5_J)). 97.67/24.34 thf(469,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 97.67/24.34 thf(102,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_add__eq__0__iff__both__eq__0)). 97.67/24.34 thf(659,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 97.67/24.34 thf(65,axiom,((! [A:int,B:int]: (((ord_less_int @ B @ zero_zero_int) => (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_add__neg__neg)). 97.67/24.34 thf(543,plain,((! [A:int,B:int]: (((ord_less_int @ B @ zero_zero_int) => (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int)) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 97.67/24.34 thf(70,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add_Oassoc)). 97.67/24.34 thf(560,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 97.67/24.34 thf(95,axiom,((! [A:option_b,B:option_b]: (((some_option_b @ A) = (some_option_b @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_option_Oinject)). 97.67/24.34 thf(639,plain,((! [A:option_b,B:option_b]: (((some_option_b @ A) = (some_option_b @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 97.67/24.34 thf(132,axiom,((! [A:(b > $o),B:list_b,C:b]: (((find_b @ A @ B) = (some_b @ C)) = (? [D:nat]: ((ord_less_nat @ D @ (size_size_list_b @ B)) & (C = (nth_b @ B @ D)) & ! [E:nat]: ((~ (A @ (nth_b @ B @ E))) <= (ord_less_nat @ E @ D)) & (A @ (nth_b @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_find__Some__iff)). 97.67/24.34 thf(755,plain,((! [A:(b > $o),B:list_b,C:b]: (((find_b @ (A) @ B) = (some_b @ C)) = (? [D:nat]: ((ord_less_nat @ D @ (size_size_list_b @ B)) & (C = (nth_b @ B @ D)) & ! [E:nat]: (~ (A @ (nth_b @ B @ E)) | ~ (ord_less_nat @ E @ D)) & (A @ (nth_b @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 97.67/24.34 thf(232,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_neq0__conv)). 97.67/24.34 thf(1088,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 97.67/24.34 thf(315,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_of__nat__less__imp__less)). 97.67/24.34 thf(1417,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 97.67/24.34 thf(49,axiom,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_less__int__code_I1_J)). 97.67/24.34 thf(496,plain,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 97.67/24.34 thf(37,axiom,((! [A:nat,B:nat,C:list_option_b]: ((drop_option_b @ A @ (drop_option_b @ B @ C)) = (drop_option_b @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_drop__drop)). 97.67/24.34 thf(454,plain,((! [A:nat,B:nat,C:list_option_b]: ((drop_option_b @ A @ (drop_option_b @ B @ C)) = (drop_option_b @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 97.67/24.34 thf(22975,plain,($false),inference(cvc4,[status(thm)],[1036,479,941,1179,1110,645,892,365,1190,909,333,1315,518,1005,1401,1422,873,677,1437,1041,523,582,1426,1137,1310,797,472,814,1063,1354,930,1342,913,1196,898,1127,709,841,1366,651,504,1264,702,802,1462,949,460,587,619,817,853,1379,870,969,416,448,1100,1013,770,492,1450,485,1020,1183,1051,734,1447,866,1394,428,1242,602,981,766,1074,1206,380,512,529,546,925,1199,761,534,1057,1274,1387,1223,1091,825,952,1217,820,392,729,693,630,916,566,879,435,830,889,1159,1210,551,1281,1291,1106,1296,665,682,1407,1350,742,1143,1259,615,725,593,610,1118,328,1082,339,933,537,642,489,1214,706,1419,554,753,901,686,1414,526,1016,590,622,1150,1131,1192,984,569,779,371,1456,1382,1060,457,1434,633,805,1054,674,794,662,1278,425,1146,1103,745,444,965,750,1154,402,843,772,579,1124,1226,413,904,975,1139,936,572,1271,787,498,1239,1332,466,919,947,540,406,784,419,509,1122,1307,863,764,604,1048,736,377,990,996,362,451,599,1376,758,858,799,895,1293,811,387,848,520,399,959,883,1176,986,438,431,653,922,636,1245,1113,563,1203,944,374,516,342,836,1134,648,939,1340,855,1070,739,993,712,557,1003,1186,1038,1262,463,1085,808,359,1285,1336,1220,1404,336,613,1008,876,656,1023,1094,978,845,627,1459,688,1010,1390,368,1453,699,961,748,390,731,383,1045,716,1097,1303,833,410,422,790,506,1288,532,696,720,955,1346,474,1410,886,928,1236,1129,1384,596,1357,723,822,1299,691,442,1399,607,395,839,1268,575,982,1431,469,659,543,560,639,755,1088,1417,496,454])). 97.67/24.34 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 97.67/24.34 % [INFO] Killing All external provers ... 97.67/24.34 WARNING: TreeLimitedRun lost 30.17s, total lost is 30.17s 97.67/24.34 FINAL WATCH: 91.5 CPU 22.2 WC 97.67/24.34 Killed 1 orphans 97.67/24.34 Killed 1 orphans 97.67/24.34 EOF