0.00/0.00 % Leo-III: Strategy 1 (for '60') 85.82/25.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 85.82/25.02 % [INFO] Parsing done (232ms). 85.82/25.02 % [INFO] Running in sequential loop mode. 85.82/25.02 % [CONFIG] Using configuration: timeout(60) with strategy 85.82/25.02 % [INFO] eprover registered as external prover. 85.82/25.02 % [INFO] cvc4 registered as external prover. 85.82/25.02 % [INFO] Parsing finished. Scanning for conjecture ... 85.82/25.02 % [INFO] Found a conjecture and 312 axioms. Running axiom selection ... 85.82/25.02 % [INFO] Axiom selection finished. Selected 312 axioms (removed 0 axioms). 85.82/25.02 % [INFO] Problem is higher-order (TPTP THF). 85.82/25.02 % [INFO] Type checking passed. Searching for refutation ... 85.82/25.02 % External prover 'cvc4' found a proof! 85.82/25.02 % [INFO] Killing All external provers ... 85.82/25.02 % Time passed: 19615ms (effective reasoning time: 19023ms) 85.82/25.02 % Solved by strategy 85.82/25.02 % Axioms used in derivation (312): fact_53_add__right__cancel, fact_69_mult_Oassoc, fact_120_of__nat__1__eq__iff, fact_19_of__nat__eq__iff, fact_18_of__nat__eq__iff, fact_66_ab__semigroup__mult__class_Omult__ac_I1_J, fact_182_div__by__0, fact_198_nat__mult__eq__1__iff, fact_307_div__add__self2, fact_24_add__mult__distrib2, fact_243_int__ops_I1_J, fact_241_zero__reorient, fact_114_div__by__1, fact_295_plus__1__eq__Suc, fact_55_add__left__cancel, fact_62_crossproduct__noteq, fact_180_bits__div__0, fact_63_fixed__root_Op, fact_43_mult__of__nat__commute, fact_140_distrib__right__NO__MATCH, fact_91_add__left__imp__eq, fact_95_int__if, fact_106_distrib__right, fact_169_add__cancel__left__left, fact_247_mult__right__cancel, fact_14_power__Suc, fact_46_unique__euclidean__semiring__with__nat__class_Oof__nat__div, fact_274_nat_OdiscI, fact_189_of__nat__0__eq__iff, fact_232_div__mult__self1, fact_30_nat__arith_Osuc1, fact_239_One__nat__def, fact_218_div__mult__mult2, fact_255_mult__not__zero, fact_299_of__nat__neq__0, help_If_2_1_If_001t__Nat__Onat_T, fact_93_add__right__imp__eq, fact_225_div__self, fact_13_power__Suc, fact_209_gbinomial__1, fact_298_power__0, fact_123_of__nat__1, fact_188_of__nat__0__eq__iff, fact_231_div__mult__self1, fact_212_mult__cancel__left2, fact_284_add__eq__self__zero, fact_211_mult__cancel__left1, fact_44_mult__of__nat__commute, fact_48_power__Suc2, fact_168_add__cancel__left__left, fact_143_distrib__left__NO__MATCH, fact_61_crossproduct__noteq, fact_193_power__Suc0__right, fact_68_mult_Oassoc, fact_34_power__add, fact_224_nonzero__mult__div__cancel__right, fact_105_distrib__right, fact_157_mult__eq__0__iff, fact_222_nonzero__mult__div__cancel__left, fact_2_of__nat__power, fact_23_add__mult__distrib, fact_122_of__nat__1, fact_103_distrib__left, fact_264_add__0__iff, fact_70_mult_Ocommute, fact_109__092_060open_062_092_060And_062n_O_Ax_A_L_Ax_A_K_An_A_061_Ax_A_K_A_I1_A_L_An_J_092_060close_062, fact_131_comm__monoid__mult__class_Omult__1, fact_268_power__not__zero, fact_5_of__nat__power__eq__of__nat__cancel__iff, fact_98_crossproduct__eq, fact_11_div__mult2__eq_H, fact_249_mult__left__cancel, fact_186_of__nat__0, fact_215_div__mult__mult1, fact_124_of__nat__Suc, fact_230_gbinomial__0_I2_J, fact_80_group__cancel_Oadd2, fact_58_int__distrib_I1_J, fact_42_power__commutes, fact_21_add__Suc__right, fact_79_group__cancel_Oadd1, fact_72_mult_Oleft__commute, fact_116_power__one, fact_38_power__commuting__commutes, fact_52_int__ops_I5_J, fact_77_add__mono__thms__linordered__semiring_I4_J, fact_201_gbinomial__0_I1_J, fact_237_div__mult__self4, fact_115_div__by__1, fact_29_add__Suc, fact_279_Zero__neq__Suc, fact_183_div__by__0, fact_163_add_Oleft__neutral, fact_96_int__int__eq, fact_214_mult__cancel__right2, fact_178_bits__div__by__0, fact_132_left__right__inverse__power, fact_208_gbinomial__1, fact_138_distrib__right__NO__MATCH, fact_204_power__Suc__0, fact_113_mult_Oleft__neutral, fact_15_fixed__root__axioms, fact_81_group__cancel_Oadd2, fact_22_mult__Suc__right, fact_223_nonzero__mult__div__cancel__right, fact_125_of__nat__Suc, fact_10_of__nat__mult, fact_127_one__reorient, fact_263_add__0__iff, fact_153_mult__cancel__right, fact_207_gbinomial__Suc0, fact_119_of__nat__eq__1__iff, fact_219_div__mult__mult1__if, fact_252_divisors__zero, fact_297_power__0, fact_251_no__zero__divisors, fact_262_add_Ogroup__left__neutral, fact_97_crossproduct__eq, fact_242_zero__reorient, fact_121_of__nat__1__eq__iff, fact_175_add__cancel__right__right, fact_154_mult__cancel__left, fact_300_of__nat__neq__0, fact_83_add_Oassoc, fact_102_comm__semiring__class_Odistrib, help_If_3_1_If_001t__Nat__Onat_T, fact_301_one__is__add, fact_290_plus__int__code_I2_J, fact_258_comm__monoid__add__class_Oadd__0, fact_41_power__commutes, fact_259_comm__monoid__add__class_Oadd__0, fact_51_int__plus, fact_302_add__is__1, fact_306_div__add__self1, fact_33_power__add, fact_285_plus__nat_Oadd__0, fact_152_mult__cancel__right, fact_287_mult__0, fact_67_ab__semigroup__mult__class_Omult__ac_I1_J, fact_89_add_Oleft__commute, fact_136_bits__div__by__1, fact_272_old_Onat_Odistinct_I2_J, help_If_1_1_If_001t__Nat__Onat_T, fact_135_int__ops_I4_J, fact_203_nat__power__eq__Suc__0__iff, fact_184_div__0, fact_294_Suc__eq__plus1__left, fact_172_add__cancel__right__left, fact_158_mult__zero__right, fact_85_add_Oright__cancel, fact_117_power__one, fact_73_mult_Oleft__commute, fact_9_of__nat__mult, fact_111_mult_Oright__neutral, fact_200_div__by__Suc__0, fact_126_one__reorient, fact_227_power__0__Suc, fact_27_power__mult, fact_266_zero__neq__one, fact_59_int__distrib_I2_J, fact_256_verit__sum__simplify, fact_112_mult_Oleft__neutral, fact_151_mult__is__0, fact_35_n__not__Suc__n, fact_181_bits__div__0, fact_276_diff__induct, fact_12_div__mult2__eq_H, fact_304_odd__nonzero, fact_238_div__mult__self4, fact_3_of__nat__eq__of__nat__power__cancel__iff, fact_104_distrib__left, fact_170_add__cancel__left__right, fact_234_div__mult__self2, fact_185_div__0, fact_303_int__ops_I2_J, fact_57_zdiv__int, fact_110_mult_Oright__neutral, fact_64_fixed__root__def, fact_292_add__scale__eq__noteq, fact_40_power__mult__distrib, fact_137_bits__div__by__1, fact_32_Suc__mult__cancel1, fact_195_mult__eq__1__iff, fact_155_mult__cancel__left, fact_229_gbinomial__0_I2_J, fact_47_power__Suc2, fact_277_zero__induct, fact_206_gbinomial__Suc0, fact_101_comm__semiring__class_Odistrib, fact_176_add__eq__0__iff__both__eq__0, fact_244_power__0__left, fact_164_add_Oright__neutral, fact_139_distrib__right__NO__MATCH, fact_286_nat__mult__eq__cancel__disj, fact_190_of__nat__eq__0__iff, fact_199_nat__1__eq__mult__iff, fact_71_mult_Ocommute, fact_16_old_Onat_Oinject, fact_128_mult_Ocomm__neutral, fact_74_ab__semigroup__add__class_Oadd__ac_I1_J, fact_162_add_Oleft__neutral, fact_75_ab__semigroup__add__class_Oadd__ac_I1_J, fact_159_mult__zero__right, fact_36_Suc__inject, fact_141_distrib__right__NO__MATCH, fact_288_times__int__code_I2_J, fact_54_add__right__cancel, fact_260_add_Ocomm__neutral, fact_107_combine__common__factor, fact_250_no__zero__divisors, fact_281_old_Onat_Oexhaust, fact_202_gbinomial__0_I1_J, fact_192_power__Suc0__right, fact_261_add_Ocomm__neutral, fact_216_div__mult__mult1, fact_133_left__right__inverse__power, fact_99_ring__class_Oring__distribs_I2_J, fact_56_add__left__cancel, fact_254_mult__not__zero, fact_8_of__nat__add, fact_39_power__mult__distrib, fact_269_nat__mult__1__right, fact_296_Suc__eq__plus1, fact_246_mult__right__cancel, fact_134_int__Suc, fact_278_Suc__neq__Zero, fact_273_old_Onat_Odistinct_I1_J, fact_194_one__eq__mult__iff, fact_82_add_Oassoc, fact_257_verit__sum__simplify, fact_187_of__nat__0, fact_60_left__add__mult__distrib, fact_145_distrib__left__NO__MATCH, fact_17_nat_Oinject, fact_270_nat__mult__1, fact_228_power__0__Suc, fact_217_div__mult__mult2, fact_149_mult__cancel1, fact_167_double__zero__sym, fact_50_zadd__int__left, fact_28_power__mult, fact_166_double__zero, fact_197_power__one__right, fact_25_mult__Suc, fact_26_div__mult2__eq, fact_220_div__mult__mult1__if, fact_161_mult__zero__left, fact_31_add__Suc__shift, fact_144_distrib__left__NO__MATCH, fact_221_nonzero__mult__div__cancel__left, fact_179_bits__div__by__0, fact_165_add_Oright__neutral, fact_78_group__cancel_Oadd1, fact_4_of__nat__eq__of__nat__power__cancel__iff, fact_305_div__add__self1, fact_86_add_Ocommute, fact_248_mult__left__cancel, fact_171_add__cancel__left__right, fact_49_int__ops_I7_J, fact_118_of__nat__eq__1__iff, fact_84_add_Oleft__cancel, fact_174_add__cancel__right__right, fact_90_add__left__imp__eq, fact_129_mult_Ocomm__neutral, fact_76_add__mono__thms__linordered__semiring_I4_J, fact_148_mult__cancel2, fact_88_add_Oleft__commute, fact_265_zero__neq__one, fact_94_nat__int__comparison_I1_J, fact_291_plus__int__code_I1_J, fact_45_unique__euclidean__semiring__with__nat__class_Oof__nat__div, fact_226_div__self, fact_210_sum__squares__eq__zero__iff, fact_293_add__scale__eq__noteq, fact_213_mult__cancel__right1, fact_87_add_Ocommute, fact_146_Nat_Oadd__0__right, fact_245_power__0__left, fact_191_of__nat__eq__0__iff, fact_236_div__mult__self3, fact_205_nat__mult__div__cancel__disj, fact_240_mult__eq__self__implies__10, fact_6_of__nat__power__eq__of__nat__cancel__iff, fact_289_times__int__code_I1_J, fact_1_of__nat__power, fact_282_old_Onat_Oinducts, fact_142_distrib__left__NO__MATCH, fact_160_mult__zero__left, fact_280_Zero__not__Suc, fact_0_xn, fact_108_combine__common__factor, fact_20_p, fact_177_zero__eq__add__iff__both__eq__0, fact_173_add__cancel__right__left, fact_147_add__is__0, fact_308_div__add__self2, fact_275_nat__induct, fact_233_div__mult__self2, fact_92_add__right__imp__eq, fact_283_not0__implies__Suc, fact_267_power__not__zero, fact_150_mult__0__right, fact_196_power__one__right, fact_65_fixed__root_Ointro, fact_100_ring__class_Oring__distribs_I1_J, fact_7_of__nat__add, fact_37_power__commuting__commutes, fact_253_divisors__zero, fact_271_nat_Odistinct_I1_J, fact_130_comm__monoid__mult__class_Omult__1, fact_156_mult__eq__0__iff, fact_235_div__mult__self3 85.82/25.02 % No. of inferences in proof: 628 85.82/25.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19615 ms resp. 19023 ms w/o parsing 85.82/25.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 85.82/25.02 thf(nat_type, type, nat: $tType). 85.82/25.02 thf(int_type, type, int: $tType). 85.82/25.02 thf(gbinomial_int_type, type, gbinomial_int: (int > (nat > int))). 85.82/25.02 thf(gbinomial_nat_type, type, gbinomial_nat: (nat > (nat > nat))). 85.82/25.02 thf(one_one_int_type, type, one_one_int: int). 85.82/25.02 thf(one_one_nat_type, type, one_one_nat: nat). 85.82/25.02 thf(plus_plus_int_type, type, plus_plus_int: (int > (int > int))). 85.82/25.02 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 85.82/25.02 thf(times_times_int_type, type, times_times_int: (int > (int > int))). 85.82/25.02 thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))). 85.82/25.02 thf(zero_zero_int_type, type, zero_zero_int: int). 85.82/25.02 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 85.82/25.02 thf(nO_MATCH_int_int_type, type, nO_MATCH_int_int: (int > (int > $o))). 85.82/25.02 thf(nO_MATCH_int_nat_type, type, nO_MATCH_int_nat: (int > (nat > $o))). 85.82/25.02 thf(nO_MATCH_nat_int_type, type, nO_MATCH_nat_int: (nat > (int > $o))). 85.82/25.02 thf(nO_MATCH_nat_nat_type, type, nO_MATCH_nat_nat: (nat > (nat > $o))). 85.82/25.02 thf(if_nat_type, type, if_nat: ($o > (nat > (nat > nat)))). 85.82/25.02 thf(suc_type, type, suc: (nat > nat)). 85.82/25.02 thf(semiri2019852685at_int_type, type, semiri2019852685at_int: (nat > int)). 85.82/25.02 thf(semiri1382578993at_nat_type, type, semiri1382578993at_nat: (nat > nat)). 85.82/25.02 thf(nthRoo1352626670d_root_type, type, nthRoo1352626670d_root: (nat > (nat > $o))). 85.82/25.02 thf(power_power_int_type, type, power_power_int: (int > (nat > int))). 85.82/25.02 thf(power_power_nat_type, type, power_power_nat: (nat > (nat > nat))). 85.82/25.02 thf(divide_divide_int_type, type, divide_divide_int: (int > (int > int))). 85.82/25.02 thf(divide_divide_nat_type, type, divide_divide_nat: (nat > (nat > nat))). 85.82/25.02 thf(n_type, type, n: int). 85.82/25.02 thf(p_type, type, p: nat). 85.82/25.02 thf(pm_type, type, pm: nat). 85.82/25.02 thf(x_type, type, x: int). 85.82/25.02 thf(306,axiom,((! [A:nat]: ((semiri2019852685at_int @ (suc @ A)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_int__Suc)). 85.82/25.02 thf(1337,plain,((! [A:nat]: ((semiri2019852685at_int @ (suc @ A)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 85.82/25.02 thf(19,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__left__imp__eq)). 85.82/25.02 thf(365,plain,((! [A:nat,B:nat,C:nat]: ((B = C) | ~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 85.82/25.02 thf(137,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_old_Onat_Odistinct_I1_J)). 85.82/25.02 thf(760,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 85.82/25.02 thf(238,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_Zero__neq__Suc)). 85.82/25.02 thf(1105,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 85.82/25.02 thf(13,axiom,((zero_zero_int != one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_zero__neq__one)). 85.82/25.02 thf(347,plain,((~ (zero_zero_int = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 85.82/25.02 thf(162,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (suc @ A) @ B) = (times_times_nat @ (suc @ A) @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Suc__mult__cancel1)). 85.82/25.02 thf(846,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (suc @ A) @ B) = (times_times_nat @ (suc @ A) @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 85.82/25.02 thf(197,axiom,(((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_int__ops_I1_J)). 85.82/25.02 thf(962,plain,(((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 85.82/25.02 thf(258,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_82_add_Oassoc)). 85.82/25.02 thf(1179,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)],[258])). 85.82/25.02 thf(109,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_add_Ocomm__neutral)). 85.82/25.02 thf(666,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 85.82/25.02 thf(52,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((nO_MATCH_nat_nat @ (divide_divide_nat @ A @ B) @ C) => ((times_times_nat @ (plus_plus_nat @ D @ E) @ C) = (plus_plus_nat @ (times_times_nat @ D @ C) @ (times_times_nat @ E @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_distrib__right__NO__MATCH)). 85.82/25.02 thf(481,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((nO_MATCH_nat_nat @ (divide_divide_nat @ A @ B) @ C) => ((times_times_nat @ (plus_plus_nat @ D @ E) @ C) = (plus_plus_nat @ (times_times_nat @ D @ C) @ (times_times_nat @ E @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 85.82/25.02 thf(97,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ B @ A)) => ((times_times_nat @ (power_power_nat @ A @ C) @ B) = (times_times_nat @ B @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_power__commuting__commutes)). 85.82/25.02 thf(628,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ B @ A)) => ((times_times_nat @ (power_power_nat @ A @ C) @ B) = (times_times_nat @ B @ (power_power_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 85.82/25.02 thf(215,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_old_Onat_Oexhaust)). 85.82/25.02 thf(1031,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 85.82/25.02 thf(202,axiom,((! [A:int,B:int,C:int]: ((((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = zero_zero_int) <= (A = zero_zero_int)) & (((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (divide_divide_int @ B @ C)) <= (A != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_div__mult__mult1__if)). 85.82/25.02 thf(977,plain,((! [A:int,B:int,C:int]: ((((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = zero_zero_int) | ~ (A = zero_zero_int)) & (((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (divide_divide_int @ B @ C)) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 85.82/25.02 thf(268,axiom,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_div__0)). 85.82/25.02 thf(1211,plain,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 85.82/25.02 thf(65,axiom,((! [A:nat,B:nat]: ((if_nat @ $true @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Nat__Onat_T)). 85.82/25.02 thf(523,plain,((! [A:nat,B:nat]: ((if_nat @ $true @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 85.82/25.02 thf(293,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_275_nat__induct)). 85.82/25.02 thf(1290,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)],[293])). 85.82/25.02 thf(131,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_add__0__iff)). 85.82/25.02 thf(741,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 85.82/25.02 thf(23,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (times_times_nat @ B @ C)) = (power_power_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_power__mult)). 85.82/25.02 thf(379,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (times_times_nat @ B @ C)) = (power_power_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 85.82/25.02 thf(61,axiom,((! [A:nat]: ((power_power_nat @ one_one_nat @ A) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_power__one)). 85.82/25.02 thf(511,plain,((! [A:nat]: ((power_power_nat @ one_one_nat @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 85.82/25.02 thf(93,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_56_add__left__cancel)). 85.82/25.02 thf(614,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)],[93])). 85.82/25.02 thf(296,axiom,((! [A:int]: ((A != zero_zero_int) => ((divide_divide_int @ A @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_div__self)). 85.82/25.02 thf(1305,plain,((! [A:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ A @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 85.82/25.02 thf(218,axiom,(((plus_plus_nat @ one_one_nat) = suc)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_plus__1__eq__Suc)). 85.82/25.02 thf(1041,plain,(((plus_plus_nat @ one_one_nat) = (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 85.82/25.02 thf(25,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (divide_divide_nat @ B @ C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_div__mult__mult2)). 85.82/25.02 thf(385,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (divide_divide_nat @ B @ C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 85.82/25.02 thf(247,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (times_times_nat @ A @ B)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_one__eq__mult__iff)). 85.82/25.02 thf(1137,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (times_times_nat @ A @ B)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 85.82/25.02 thf(124,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_zero__neq__one)). 85.82/25.02 thf(715,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 85.82/25.02 thf(119,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_group__cancel_Oadd1)). 85.82/25.02 thf(698,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 85.82/25.02 thf(188,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((A @ C) => (A @ (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_old_Onat_Oinducts)). 85.82/25.02 thf(930,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ C) => (A @ (suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 85.82/25.02 thf(253,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_85_add_Oright__cancel)). 85.82/25.02 thf(1164,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)],[253])). 85.82/25.02 thf(147,axiom,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_power__one__right)). 85.82/25.02 thf(797,plain,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 85.82/25.02 thf(133,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_84_add_Oleft__cancel)). 85.82/25.02 thf(747,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)],[133])). 85.82/25.02 thf(183,axiom,((! [A:int,B:int]: ((A = (times_times_int @ A @ B)) = ((B = one_one_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_mult__cancel__left1)). 85.82/25.02 thf(913,plain,((! [A:int,B:int]: ((A = (times_times_int @ A @ B)) = ((B = one_one_int) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 85.82/25.02 thf(225,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_add_Ogroup__left__neutral)). 85.82/25.02 thf(1063,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 85.82/25.02 thf(11,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = one_one_nat) <= ((times_times_nat @ A @ B) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_left__right__inverse__power)). 85.82/25.02 thf(340,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = one_one_nat) | ~ ((times_times_nat @ A @ B) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 85.82/25.02 thf(244,axiom,((! [A:nat]: ((semiri1382578993at_nat @ (suc @ A)) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_of__nat__neq__0)). 85.82/25.02 thf(1127,plain,((! [A:nat]: ~ ((semiri1382578993at_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 85.82/25.02 thf(122,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_distrib__left)). 85.82/25.02 thf(709,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 85.82/25.02 thf(34,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_add__mult__distrib2)). 85.82/25.02 thf(417,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 85.82/25.02 thf(174,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_Zero__not__Suc)). 85.82/25.02 thf(885,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 85.82/25.02 thf(313,axiom,((suc = (plus_plus_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Suc__eq__plus1__left)). 85.82/25.02 thf(1359,plain,(((suc) = (plus_plus_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 85.82/25.02 thf(40,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_add__cancel__right__left)). 85.82/25.02 thf(436,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 85.82/25.02 thf(285,axiom,((! [A:nat]: ((one_one_int = (semiri2019852685at_int @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_of__nat__1__eq__iff)). 85.82/25.02 thf(1265,plain,((! [A:nat]: ((one_one_int = (semiri2019852685at_int @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 85.82/25.02 thf(26,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_mult_Oleft__neutral)). 85.82/25.02 thf(389,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 85.82/25.02 thf(79,axiom,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (power_power_nat @ A @ B)) = (power_power_nat @ (semiri1382578993at_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_of__nat__power)). 85.82/25.02 thf(570,plain,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (power_power_nat @ A @ B)) = (power_power_nat @ (semiri1382578993at_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 85.82/25.02 thf(21,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_zero__eq__add__iff__both__eq__0)). 85.82/25.02 thf(372,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 85.82/25.02 thf(12,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ C @ B))) = ((A = C) | (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_crossproduct__eq)). 85.82/25.02 thf(344,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ C @ B))) = ((A = C) | (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 85.82/25.02 thf(290,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_Suc__neq__Zero)). 85.82/25.02 thf(1279,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 85.82/25.02 thf(224,axiom,((! [A:int,B:nat]: ((A != zero_zero_int) => ((power_power_int @ A @ B) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_power__not__zero)). 85.82/25.02 thf(1059,plain,((! [A:int,B:nat]: ((~ (A = zero_zero_int)) => (~ ((power_power_int @ A @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 85.82/25.02 thf(192,axiom,((p = (suc @ pm))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_p)). 85.82/25.02 thf(949,plain,((p = (suc @ pm))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 85.82/25.02 thf(84,axiom,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (divide_divide_nat @ A @ B)) = (divide_divide_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_unique__euclidean__semiring__with__nat__class_Oof__nat__div)). 85.82/25.02 thf(587,plain,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (divide_divide_nat @ A @ B)) = (divide_divide_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 85.82/25.02 thf(302,axiom,((! [A:nat,B:int]: ((times_times_int @ (semiri2019852685at_int @ A) @ B) = (times_times_int @ B @ (semiri2019852685at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_mult__of__nat__commute)). 85.82/25.02 thf(1323,plain,((! [A:nat,B:int]: ((times_times_int @ (semiri2019852685at_int @ A) @ B) = (times_times_int @ B @ (semiri2019852685at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 85.82/25.02 thf(70,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C != D) & (A != B)) = ((plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) != (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_crossproduct__noteq)). 85.82/25.02 thf(542,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((~ (C = D) & ~ (A = B)) = (~ ((plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 85.82/25.02 thf(47,axiom,((! [A:int]: ((gbinomial_int @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_gbinomial__1)). 85.82/25.02 thf(460,plain,((! [A:int]: ((gbinomial_int @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 85.82/25.02 thf(180,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_50_zadd__int__left)). 85.82/25.02 thf(902,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)],[180])). 85.82/25.02 thf(100,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_add__mult__distrib)). 85.82/25.02 thf(638,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 85.82/25.02 thf(233,axiom,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_mult__zero__left)). 85.82/25.02 thf(1087,plain,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 85.82/25.02 thf(279,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_88_add_Oleft__commute)). 85.82/25.02 thf(1247,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)],[279])). 85.82/25.02 thf(309,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add__cancel__right__right)). 85.82/25.02 thf(1347,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 85.82/25.02 thf(173,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_30_nat__arith_Osuc1)). 85.82/25.02 thf(881,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)],[173])). 85.82/25.02 thf(186,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = A) = ((B = one_one_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_mult__cancel__left2)). 85.82/25.02 thf(924,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = A) = ((B = one_one_int) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 85.82/25.02 thf(55,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (semiri1382578993at_nat @ A) @ B) = (times_times_nat @ B @ (semiri1382578993at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mult__of__nat__commute)). 85.82/25.02 thf(492,plain,((! [A:nat,B:nat]: ((times_times_nat @ (semiri1382578993at_nat @ A) @ B) = (times_times_nat @ B @ (semiri1382578993at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 85.82/25.02 thf(295,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_add__cancel__right__left)). 85.82/25.02 thf(1302,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 85.82/25.02 thf(305,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_int__ops_I7_J)). 85.82/25.02 thf(1334,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 85.82/25.02 thf(62,axiom,((! [A:nat]: (((semiri1382578993at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_of__nat__eq__0__iff)). 85.82/25.02 thf(514,plain,((! [A:nat]: (((semiri1382578993at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 85.82/25.02 thf(15,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_89_add_Oleft__commute)). 85.82/25.02 thf(353,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)],[15])). 85.82/25.02 thf(291,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_74_ab__semigroup__add__class_Oadd__ac_I1_J)). 85.82/25.02 thf(1283,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)],[291])). 85.82/25.02 thf(181,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_78_group__cancel_Oadd1)). 85.82/25.02 thf(905,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)],[181])). 85.82/25.02 thf(239,axiom,((! [A:nat]: ((semiri2019852685at_int @ (suc @ A)) != zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_of__nat__neq__0)). 85.82/25.02 thf(1109,plain,((! [A:nat]: ~ ((semiri2019852685at_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 85.82/25.02 thf(5,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_nat__mult__eq__cancel__disj)). 85.82/25.02 thf(321,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 85.82/25.02 thf(53,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_nonzero__mult__div__cancel__left)). 85.82/25.02 thf(485,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 85.82/25.02 thf(158,axiom,((! [A:nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_power__Suc0__right)). 85.82/25.02 thf(834,plain,((! [A:nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 85.82/25.02 thf(89,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mult_Oassoc)). 85.82/25.02 thf(602,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 85.82/25.02 thf(117,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_7_of__nat__add)). 85.82/25.02 thf(692,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)],[117])). 85.82/25.02 thf(140,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_nat_Odistinct_I1_J)). 85.82/25.02 thf(774,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 85.82/25.02 thf(265,axiom,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_div__by__1)). 85.82/25.02 thf(1201,plain,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 85.82/25.02 thf(163,axiom,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_mult_Ocomm__neutral)). 85.82/25.02 thf(849,plain,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 85.82/25.02 thf(229,axiom,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_int__int__eq)). 85.82/25.02 thf(1074,plain,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 85.82/25.02 thf(185,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_92_add__right__imp__eq)). 85.82/25.02 thf(920,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)],[185])). 85.82/25.02 thf(41,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_add__0__iff)). 85.82/25.02 thf(439,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 85.82/25.02 thf(108,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_81_group__cancel_Oadd2)). 85.82/25.02 thf(661,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)],[108])). 85.82/25.02 thf(227,axiom,((! [A:int,B:int]: (((plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_sum__squares__eq__zero__iff)). 85.82/25.02 thf(1067,plain,((! [A:int,B:int]: (((plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 85.82/25.02 thf(220,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_51_int__plus)). 85.82/25.02 thf(1047,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)],[220])). 85.82/25.02 thf(298,axiom,((! [A:nat]: ((? [B:nat]: (A = (suc @ B))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_not0__implies__Suc)). 85.82/25.02 thf(1311,plain,((! [A:nat]: (? [B:nat]: (A = (suc @ B)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 85.82/25.02 thf(67,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ (semiri1382578993at_nat @ B) @ (semiri1382578993at_nat @ C))) = (divide_divide_nat @ (divide_divide_nat @ A @ (semiri1382578993at_nat @ B)) @ (semiri1382578993at_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_div__mult2__eq_H)). 85.82/25.02 thf(534,plain,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ (semiri1382578993at_nat @ B) @ (semiri1382578993at_nat @ C))) = (divide_divide_nat @ (divide_divide_nat @ A @ (semiri1382578993at_nat @ B)) @ (semiri1382578993at_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 85.82/25.02 thf(288,axiom,(((power_power_int @ x @ p) = n)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_xn)). 85.82/25.02 thf(1274,plain,(((power_power_int @ x @ p) = n)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 85.82/25.02 thf(9,axiom,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_power__one__right)). 85.82/25.02 thf(334,plain,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 85.82/25.02 thf(182,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_old_Onat_Oinject)). 85.82/25.02 thf(910,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 85.82/25.02 thf(141,axiom,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_bits__div__0)). 85.82/25.02 thf(778,plain,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 85.82/25.02 thf(282,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_old_Onat_Odistinct_I2_J)). 85.82/25.02 thf(1255,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 85.82/25.02 thf(256,axiom,((times_times_int = (^ [A:int,B:int]: (times_times_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mult_Ocommute)). 85.82/25.02 thf(1174,plain,(((times_times_int) = (^ [A:int,B:int]: (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 85.82/25.02 thf(270,axiom,((! [A:int]: ((gbinomial_int @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_gbinomial__Suc0)). 85.82/25.02 thf(1217,plain,((! [A:int]: ((gbinomial_int @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 85.82/25.02 thf(27,axiom,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_div__by__1)). 85.82/25.02 thf(392,plain,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 85.82/25.02 thf(36,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_nat__mult__1)). 85.82/25.02 thf(424,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 85.82/25.02 thf(31,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_combine__common__factor)). 85.82/25.02 thf(407,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 85.82/25.02 thf(153,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((power_power_int @ zero_zero_int @ A) = zero_zero_int)) & ((A = zero_zero_nat) => ((power_power_int @ zero_zero_int @ A) = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_power__0__left)). 85.82/25.02 thf(815,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((power_power_int @ zero_zero_int @ A) = zero_zero_int)) & ((A = zero_zero_nat) => ((power_power_int @ zero_zero_int @ A) = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 85.82/25.02 thf(276,axiom,((! [A:nat]: ((semiri1382578993at_nat @ (suc @ A)) = (plus_plus_nat @ one_one_nat @ (semiri1382578993at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_of__nat__Suc)). 85.82/25.02 thf(1238,plain,((! [A:nat]: ((semiri1382578993at_nat @ (suc @ A)) = (plus_plus_nat @ one_one_nat @ (semiri1382578993at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 85.82/25.02 thf(195,axiom,(((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_of__nat__0)). 85.82/25.02 thf(957,plain,(((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 85.82/25.02 thf(177,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ (power_power_nat @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_power__Suc2)). 85.82/25.02 thf(894,plain,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ (power_power_nat @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 85.82/25.02 thf(155,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (power_power_nat @ A @ B)) = (power_power_int @ (semiri2019852685at_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_of__nat__power)). 85.82/25.02 thf(825,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (power_power_nat @ A @ B)) = (power_power_int @ (semiri2019852685at_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 85.82/25.02 thf(308,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ A) = (plus_plus_int @ B @ (divide_divide_int @ C @ A))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_div__mult__self4)). 85.82/25.02 thf(1343,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ A) = (plus_plus_int @ B @ (divide_divide_int @ C @ A))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 85.82/25.02 thf(184,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_76_add__mono__thms__linordered__semiring_I4_J)). 85.82/25.02 thf(916,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)],[184])). 85.82/25.02 thf(78,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_mult__right__cancel)). 85.82/25.02 thf(566,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 85.82/25.02 thf(96,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_comm__monoid__mult__class_Omult__1)). 85.82/25.02 thf(625,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 85.82/25.02 thf(164,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_distrib__right)). 85.82/25.02 thf(852,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 85.82/25.02 thf(83,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ A) @ C) @ A) = (plus_plus_nat @ B @ (divide_divide_nat @ C @ A))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_div__mult__self3)). 85.82/25.02 thf(583,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ A) @ C) @ A) = (plus_plus_nat @ B @ (divide_divide_nat @ C @ A))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 85.82/25.02 thf(175,axiom,((one_one_nat = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_One__nat__def)). 85.82/25.02 thf(889,plain,((one_one_nat = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 85.82/25.02 thf(136,axiom,((! [A:nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ A) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_power__Suc__0)). 85.82/25.02 thf(757,plain,((! [A:nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ A) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 85.82/25.02 thf(73,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_plus__nat_Oadd__0)). 85.82/25.02 thf(551,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 85.82/25.02 thf(209,axiom,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_mult_Oright__neutral)). 85.82/25.02 thf(1012,plain,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 85.82/25.02 thf(114,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ (times_times_nat @ C @ A)) @ A) = (plus_plus_nat @ C @ (divide_divide_nat @ B @ A))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_div__mult__self1)). 85.82/25.02 thf(682,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ (times_times_nat @ C @ A)) @ A) = (plus_plus_nat @ C @ (divide_divide_nat @ B @ A))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 85.82/25.02 thf(263,axiom,((! [A:int,B:int,C:int,D:int]: (((A != B) & (C != D)) = ((plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) != (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_crossproduct__noteq)). 85.82/25.02 thf(1195,plain,((! [A:int,B:int,C:int,D:int]: ((~ (A = B) & ~ (C = D)) = (~ ((plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) = (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 85.82/25.02 thf(6,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((nO_MATCH_nat_nat @ (divide_divide_nat @ A @ B) @ C) => ((times_times_nat @ C @ (plus_plus_nat @ D @ E)) = (plus_plus_nat @ (times_times_nat @ C @ D) @ (times_times_nat @ C @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_distrib__left__NO__MATCH)). 85.82/25.02 thf(324,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((nO_MATCH_nat_nat @ (divide_divide_nat @ A @ B) @ C) => ((times_times_nat @ C @ (plus_plus_nat @ D @ E)) = (plus_plus_nat @ (times_times_nat @ C @ D) @ (times_times_nat @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 85.82/25.02 thf(201,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_one__is__add)). 85.82/25.02 thf(974,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 85.82/25.02 thf(310,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_plus__int__code_I1_J)). 85.82/25.02 thf(1350,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 85.82/25.02 thf(275,axiom,((! [A:nat,B:nat]: ((nthRoo1352626670d_root @ A @ B) <= (A = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_fixed__root_Ointro)). 85.82/25.02 thf(1234,plain,((! [A:nat,B:nat]: ((nthRoo1352626670d_root @ A @ B) | ~ (A = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 85.82/25.02 thf(104,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_75_ab__semigroup__add__class_Oadd__ac_I1_J)). 85.82/25.02 thf(650,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)],[104])). 85.82/25.02 thf(242,axiom,((! [A:nat]: ((gbinomial_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_gbinomial__Suc0)). 85.82/25.02 thf(1121,plain,((! [A:nat]: ((gbinomial_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 85.82/25.02 thf(273,axiom,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = ((A = zero_zero_int) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_mult__cancel__left)). 85.82/25.02 thf(1227,plain,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = ((A = zero_zero_int) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 85.82/25.02 thf(16,axiom,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (times_times_nat @ A @ B)) = (times_times_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_of__nat__mult)). 85.82/25.02 thf(356,plain,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (times_times_nat @ A @ B)) = (times_times_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 85.82/25.02 thf(86,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_verit__sum__simplify)). 85.82/25.02 thf(593,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 85.82/25.02 thf(170,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ B) = (plus_plus_nat @ B @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_mult__Suc)). 85.82/25.02 thf(869,plain,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ B) = (plus_plus_nat @ B @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 85.82/25.02 thf(35,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ (plus_plus_nat @ A @ B) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_div__add__self1)). 85.82/25.02 thf(420,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ (plus_plus_nat @ A @ B) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 85.82/25.02 thf(204,axiom,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_mult__zero__right)). 85.82/25.02 thf(989,plain,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 85.82/25.02 thf(283,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (times_times_nat @ B @ C)) = (power_power_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_power__mult)). 85.82/25.02 thf(1259,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (times_times_nat @ B @ C)) = (power_power_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 85.82/25.02 thf(3,axiom,((! [A:$o]: ((A = $true) | (A = $false)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Nat__Onat_T)). 85.82/25.02 thf(317,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 85.82/25.02 thf(7,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_power__mult__distrib)). 85.82/25.02 thf(328,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 85.82/25.02 thf(252,axiom,((! [A:int,B:int,C:int]: ((((times_times_int @ B @ A) = (times_times_int @ C @ A)) = (B = C)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_mult__right__cancel)). 85.82/25.02 thf(1160,plain,((! [A:int,B:int,C:int]: ((((times_times_int @ B @ A) = (times_times_int @ C @ A)) = (B = C)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 85.82/25.02 thf(214,axiom,((! [A:nat,B:nat]: ((times_times_nat @ A @ (suc @ B)) = (plus_plus_nat @ A @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_mult__Suc__right)). 85.82/25.02 thf(1028,plain,((! [A:nat,B:nat]: ((times_times_nat @ A @ (suc @ B)) = (plus_plus_nat @ A @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 85.82/25.02 thf(314,axiom,((! [A:nat,B:nat,C:int,D:int,E:int]: (((times_times_int @ (plus_plus_int @ D @ E) @ C) = (plus_plus_int @ (times_times_int @ D @ C) @ (times_times_int @ E @ C))) <= (nO_MATCH_nat_int @ (divide_divide_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_distrib__right__NO__MATCH)). 85.82/25.02 thf(1361,plain,((! [A:nat,B:nat,C:int,D:int,E:int]: (((times_times_int @ (plus_plus_int @ D @ E) @ C) = (plus_plus_int @ (times_times_int @ D @ C) @ (times_times_int @ E @ C))) | ~ (nO_MATCH_nat_int @ (divide_divide_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 85.82/25.02 thf(259,axiom,((! [A:nat]: (((semiri2019852685at_int @ A) = one_one_int) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_of__nat__eq__1__iff)). 85.82/25.02 thf(1182,plain,((! [A:nat]: (((semiri2019852685at_int @ A) = one_one_int) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 85.82/25.02 thf(68,axiom,((! [A:nat]: ((zero_zero_nat = (semiri1382578993at_nat @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_of__nat__0__eq__iff)). 85.82/25.02 thf(537,plain,((! [A:nat]: ((zero_zero_nat = (semiri1382578993at_nat @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 85.82/25.02 thf(110,axiom,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_bits__div__by__0)). 85.82/25.02 thf(669,plain,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 85.82/25.02 thf(115,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_mult__zero__left)). 85.82/25.02 thf(686,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 85.82/25.02 thf(66,axiom,((! [A:nat]: ((((power_power_nat @ zero_zero_nat @ A) = one_one_nat) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_power__0__left)). 85.82/25.02 thf(526,plain,((! [A:nat]: ((((power_power_nat @ zero_zero_nat @ A) = one_one_nat) | ~ (A = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 85.82/25.02 thf(54,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_mult__cancel2)). 85.82/25.02 thf(489,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 85.82/25.02 thf(269,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_55_add__left__cancel)). 85.82/25.02 thf(1214,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)],[269])). 85.82/25.02 thf(85,axiom,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_power__0)). 85.82/25.02 thf(590,plain,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 85.82/25.02 thf(113,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = one_one_nat)) <= (A = (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_mult__eq__self__implies__10)). 85.82/25.02 thf(679,plain,((! [A:nat,B:nat]: ((A = zero_zero_nat) | (B = one_one_nat) | ~ (A = (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 85.82/25.02 thf(121,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_mult__cancel__left)). 85.82/25.02 thf(706,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 85.82/25.02 thf(74,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_mult_Ocomm__neutral)). 85.82/25.02 thf(554,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 85.82/25.02 thf(135,axiom,((! [A:nat,B:nat,C:int,D:int,E:int]: ((nO_MATCH_nat_int @ (divide_divide_nat @ A @ B) @ C) => ((times_times_int @ C @ (plus_plus_int @ D @ E)) = (plus_plus_int @ (times_times_int @ C @ D) @ (times_times_int @ C @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_distrib__left__NO__MATCH)). 85.82/25.02 thf(753,plain,((! [A:nat,B:nat,C:int,D:int,E:int]: ((nO_MATCH_nat_int @ (divide_divide_nat @ A @ B) @ C) => ((times_times_int @ C @ (plus_plus_int @ D @ E)) = (plus_plus_int @ (times_times_int @ C @ D) @ (times_times_int @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 85.82/25.02 thf(159,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_power__add)). 85.82/25.02 thf(837,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 85.82/25.02 thf(103,axiom,((! [A:nat]: ((gbinomial_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_gbinomial__1)). 85.82/25.02 thf(647,plain,((! [A:nat]: ((gbinomial_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 85.82/25.02 thf(249,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((divide_divide_int @ (plus_plus_int @ A @ B) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_div__add__self1)). 85.82/25.02 thf(1150,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (plus_plus_int @ A @ B) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 85.82/25.02 thf(130,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_53_add__right__cancel)). 85.82/25.02 thf(738,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)],[130])). 85.82/25.02 thf(245,axiom,((! [A:int,B:int,C:int,D:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ (plus_plus_int @ (times_times_int @ C @ B) @ D)) = (plus_plus_int @ (times_times_int @ (plus_plus_int @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_combine__common__factor)). 85.82/25.02 thf(1131,plain,((! [A:int,B:int,C:int,D:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ (plus_plus_int @ (times_times_int @ C @ B) @ D)) = (plus_plus_int @ (times_times_int @ (plus_plus_int @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 85.82/25.02 thf(262,axiom,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_power__0)). 85.82/25.02 thf(1192,plain,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 85.82/25.02 thf(90,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_mult__zero__right)). 85.82/25.02 thf(605,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 85.82/25.02 thf(236,axiom,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_bits__div__by__1)). 85.82/25.02 thf(1099,plain,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 85.82/25.02 thf(203,axiom,((! [A:int,B:int,C:nat,D:nat,E:nat]: (((times_times_nat @ C @ (plus_plus_nat @ D @ E)) = (plus_plus_nat @ (times_times_nat @ C @ D) @ (times_times_nat @ C @ E))) <= (nO_MATCH_int_nat @ (divide_divide_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_distrib__left__NO__MATCH)). 85.82/25.02 thf(985,plain,((! [A:int,B:int,C:nat,D:nat,E:nat]: (((times_times_nat @ C @ (plus_plus_nat @ D @ E)) = (plus_plus_nat @ (times_times_nat @ C @ D) @ (times_times_nat @ C @ E))) | ~ (nO_MATCH_int_nat @ (divide_divide_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 85.82/25.02 thf(221,axiom,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_div__by__0)). 85.82/25.02 thf(1050,plain,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 85.82/25.02 thf(46,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_add__cancel__right__right)). 85.82/25.02 thf(457,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 85.82/25.02 thf(277,axiom,((! [A:int,B:int]: ((A = (times_times_int @ B @ A)) = ((B = one_one_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_mult__cancel__right1)). 85.82/25.02 thf(1241,plain,((! [A:int,B:int]: ((A = (times_times_int @ B @ A)) = ((B = one_one_int) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 85.82/25.02 thf(150,axiom,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_mult_Oleft__neutral)). 85.82/25.02 thf(805,plain,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 85.82/25.02 thf(60,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_mult__eq__0__iff)). 85.82/25.02 thf(508,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 85.82/25.02 thf(254,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((divide_divide_int @ (times_times_int @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_nonzero__mult__div__cancel__right)). 85.82/25.02 thf(1167,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (times_times_int @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 85.82/25.02 thf(260,axiom,((! [A:int,B:int,C:nat]: (((times_times_int @ A @ B) = one_one_int) => ((times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_left__right__inverse__power)). 85.82/25.02 thf(1185,plain,((! [A:int,B:int,C:nat]: (((times_times_int @ A @ B) = one_one_int) => ((times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 85.82/25.02 thf(146,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_int__distrib_I1_J)). 85.82/25.02 thf(794,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 85.82/25.02 thf(125,axiom,(((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_of__nat__0)). 85.82/25.02 thf(718,plain,(((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 85.82/25.02 thf(292,axiom,((! [A:int,B:int,C:int]: ((B = C) <= ((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__left__imp__eq)). 85.82/25.02 thf(1286,plain,((! [A:int,B:int,C:int]: ((B = C) | ~ ((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 85.82/25.02 thf(216,axiom,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_times__int__code_I2_J)). 85.82/25.02 thf(1035,plain,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 85.82/25.02 thf(134,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_add_Ocomm__neutral)). 85.82/25.02 thf(750,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 85.82/25.02 thf(38,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_mult__0)). 85.82/25.02 thf(430,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 85.82/25.02 thf(80,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_add_Oright__neutral)). 85.82/25.02 thf(573,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 85.82/25.02 thf(116,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ B @ C)) = (divide_divide_nat @ (divide_divide_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_div__mult2__eq)). 85.82/25.02 thf(689,plain,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ B @ C)) = (divide_divide_nat @ (divide_divide_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 85.82/25.02 thf(43,axiom,((! [A:nat,B:nat]: (((B != zero_zero_nat) & (A != zero_zero_nat)) <= ((times_times_nat @ A @ B) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_mult__not__zero)). 85.82/25.02 thf(444,plain,((! [A:nat,B:nat]: ((~ (B = zero_zero_nat) & ~ (A = zero_zero_nat)) | ((times_times_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 85.82/25.02 thf(22,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (plus_plus_nat @ B @ A) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_div__add__self2)). 85.82/25.02 thf(375,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (plus_plus_nat @ B @ A) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 85.82/25.02 thf(250,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ B @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mult_Oleft__commute)). 85.82/25.02 thf(1154,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ B @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 85.82/25.02 thf(30,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((A != zero_zero_nat) => (((B = C) & (D != E)) => ((plus_plus_nat @ B @ (times_times_nat @ A @ D)) != (plus_plus_nat @ C @ (times_times_nat @ A @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_add__scale__eq__noteq)). 85.82/25.02 thf(402,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((~ (A = zero_zero_nat)) => (((B = C) & ~ (D = E)) => (~ ((plus_plus_nat @ B @ (times_times_nat @ A @ D)) = (plus_plus_nat @ C @ (times_times_nat @ A @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 85.82/25.02 thf(128,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_power__commutes)). 85.82/25.02 thf(732,plain,((! [A:nat,B:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 85.82/25.02 thf(161,axiom,((! [A:int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_double__zero)). 85.82/25.02 thf(843,plain,((! [A:int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 85.82/25.02 thf(82,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_mult__left__cancel)). 85.82/25.02 thf(579,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 85.82/25.02 thf(243,axiom,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_div__by__Suc__0)). 85.82/25.02 thf(1124,plain,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 85.82/25.02 thf(71,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_add__is__0)). 85.82/25.02 thf(545,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 85.82/25.02 thf(33,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__mono__thms__linordered__semiring_I4_J)). 85.82/25.02 thf(413,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 85.82/25.02 thf(101,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mult_Oleft__commute)). 85.82/25.02 thf(641,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 85.82/25.02 thf(24,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_distrib__right)). 85.82/25.02 thf(382,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 85.82/25.02 thf(287,axiom,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_of__nat__eq__iff)). 85.82/25.02 thf(1271,plain,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 85.82/25.02 thf(57,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((power_power_nat @ A @ B) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_power__not__zero)). 85.82/25.02 thf(498,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => (~ ((power_power_nat @ A @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 85.82/25.02 thf(49,axiom,((! [A:nat,B:nat]: ((((times_times_nat @ A @ B) != zero_zero_nat) <= (B != zero_zero_nat)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_no__zero__divisors)). 85.82/25.02 thf(466,plain,((! [A:nat,B:nat]: (~ ((times_times_nat @ A @ B) = zero_zero_nat) | (B = zero_zero_nat) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 85.82/25.02 thf(234,axiom,((! [A:int,B:int]: (((divide_divide_int @ (times_times_int @ A @ B) @ A) = B) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_nonzero__mult__div__cancel__left)). 85.82/25.02 thf(1090,plain,((! [A:int,B:int]: (((divide_divide_int @ (times_times_int @ A @ B) @ A) = B) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 85.82/25.02 thf(272,axiom,((! [A:nat]: ((semiri2019852685at_int @ (suc @ A)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_int__ops_I4_J)). 85.82/25.02 thf(1224,plain,((! [A:nat]: ((semiri2019852685at_int @ (suc @ A)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 85.82/25.02 thf(312,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_nat__power__eq__Suc__0__iff)). 85.82/25.02 thf(1356,plain,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 85.82/25.02 thf(14,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_mult__0__right)). 85.82/25.02 thf(350,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 85.82/25.02 thf(69,axiom,(((semiri1382578993at_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_of__nat__1)). 85.82/25.02 thf(540,plain,(((semiri1382578993at_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 85.82/25.02 thf(111,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (plus_plus_nat @ B @ (times_times_nat @ A @ C)) @ A) = (plus_plus_nat @ C @ (divide_divide_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_div__mult__self2)). 85.82/25.02 thf(672,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (plus_plus_nat @ B @ (times_times_nat @ A @ C)) @ A) = (plus_plus_nat @ C @ (divide_divide_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 85.82/25.02 thf(92,axiom,((! [A:nat,B:nat]: ((if_nat @ $false @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Nat__Onat_T)). 85.82/25.02 thf(611,plain,((! [A:nat,B:nat]: ((if_nat @ $false @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 85.82/25.02 thf(144,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((nO_MATCH_int_int @ (divide_divide_int @ A @ B) @ C) => ((times_times_int @ C @ (plus_plus_int @ D @ E)) = (plus_plus_int @ (times_times_int @ C @ D) @ (times_times_int @ C @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_distrib__left__NO__MATCH)). 85.82/25.02 thf(787,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((nO_MATCH_int_int @ (divide_divide_int @ A @ B) @ C) => ((times_times_int @ C @ (plus_plus_int @ D @ E)) = (plus_plus_int @ (times_times_int @ C @ D) @ (times_times_int @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 85.82/25.02 thf(138,axiom,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_power__mult__distrib)). 85.82/25.02 thf(764,plain,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 85.82/25.02 thf(157,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_distrib__left)). 85.82/25.02 thf(831,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 85.82/25.02 thf(206,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ C @ A)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_div__mult__self1)). 85.82/25.02 thf(996,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ C @ A)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 85.82/25.02 thf(4,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Nat_Oadd__0__right)). 85.82/25.02 thf(318,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 85.82/25.02 thf(219,axiom,((! [A:int,B:int]: ((((times_times_int @ A @ B) != zero_zero_int) <= (B != zero_zero_int)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_no__zero__divisors)). 85.82/25.02 thf(1043,plain,((! [A:int,B:int]: (~ ((times_times_int @ A @ B) = zero_zero_int) | (B = zero_zero_int) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 85.82/25.02 thf(88,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_zero__reorient)). 85.82/25.02 thf(599,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 85.82/25.02 thf(168,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ (suc @ D) @ (suc @ E)) <= (A @ D @ E)))) <= (! [D:nat]: (A @ zero_zero_nat @ (suc @ D)))) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_diff__induct)). 85.82/25.02 thf(863,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ (suc @ D) @ (suc @ E)) | ~ (A @ D @ E))) | ~ (! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 85.82/25.02 thf(143,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_unique__euclidean__semiring__with__nat__class_Oof__nat__div)). 85.82/25.02 thf(784,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 85.82/25.02 thf(241,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (divide_divide_int @ B @ C)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_div__mult__mult2)). 85.82/25.02 thf(1117,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (divide_divide_int @ B @ C)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 85.82/25.02 thf(18,axiom,((! [A:nat,B:nat]: ((B = zero_zero_nat) <= ((plus_plus_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_add__eq__self__zero)). 85.82/25.02 thf(362,plain,((! [A:nat,B:nat]: ((B = zero_zero_nat) | ~ ((plus_plus_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 85.82/25.02 thf(44,axiom,((! [A:nat,B:nat,C:nat]: (((semiri1382578993at_nat @ A) = (power_power_nat @ (semiri1382578993at_nat @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_of__nat__power__eq__of__nat__cancel__iff)). 85.82/25.02 thf(451,plain,((! [A:nat,B:nat,C:nat]: (((semiri1382578993at_nat @ A) = (power_power_nat @ (semiri1382578993at_nat @ B) @ C)) = (A = (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 85.82/25.02 thf(231,axiom,((! [A:int,B:int,C:nat]: (((times_times_int @ (power_power_int @ A @ C) @ B) = (times_times_int @ B @ (power_power_int @ A @ C))) <= ((times_times_int @ A @ B) = (times_times_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_power__commuting__commutes)). 85.82/25.02 thf(1080,plain,((! [A:int,B:int,C:nat]: (((times_times_int @ (power_power_int @ A @ C) @ B) = (times_times_int @ B @ (power_power_int @ A @ C))) | ~ ((times_times_int @ A @ B) = (times_times_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 85.82/25.02 thf(166,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_nat__int__comparison_I1_J)). 85.82/25.02 thf(858,plain,(((= @ nat) = (^ [A:nat,B:nat]: ((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 85.82/25.02 thf(95,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ A) = (plus_plus_nat @ B @ (divide_divide_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_div__mult__self4)). 85.82/25.02 thf(621,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ A) = (plus_plus_nat @ B @ (divide_divide_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 85.82/25.02 thf(64,axiom,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_div__by__0)). 85.82/25.02 thf(520,plain,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 85.82/25.02 thf(198,axiom,((! [A:int,B:int]: (((B = zero_zero_int) | (A = zero_zero_int)) <= ((times_times_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_divisors__zero)). 85.82/25.02 thf(964,plain,((! [A:int,B:int]: ((B = zero_zero_int) | (A = zero_zero_int) | ~ ((times_times_int @ A @ B) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 85.82/25.02 thf(190,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_int @ (semiri2019852685at_int @ A) @ B) = (semiri2019852685at_int @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_of__nat__eq__of__nat__power__cancel__iff)). 85.82/25.02 thf(943,plain,((! [A:nat,B:nat,C:nat]: (((power_power_int @ (semiri2019852685at_int @ A) @ B) = (semiri2019852685at_int @ C)) = ((power_power_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 85.82/25.02 thf(212,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_zdiv__int)). 85.82/25.02 thf(1022,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 85.82/25.02 thf(255,axiom,((! [A:nat,B:nat,C:nat]: (((semiri2019852685at_int @ A) = (power_power_int @ (semiri2019852685at_int @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_of__nat__power__eq__of__nat__cancel__iff)). 85.82/25.02 thf(1171,plain,((! [A:nat,B:nat,C:nat]: (((semiri2019852685at_int @ A) = (power_power_int @ (semiri2019852685at_int @ B) @ C)) = (A = (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 85.82/25.02 thf(264,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_int__distrib_I2_J)). 85.82/25.02 thf(1198,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 85.82/25.02 thf(29,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_comm__semiring__class_Odistrib)). 85.82/25.02 thf(399,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 85.82/25.02 thf(196,axiom,((! [A:int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_double__zero__sym)). 85.82/25.02 thf(959,plain,((! [A:int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 85.82/25.02 thf(118,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_add_Oleft__neutral)). 85.82/25.02 thf(695,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 85.82/25.02 thf(226,axiom,((nthRoo1352626670d_root @ p @ pm)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_fixed__root__axioms)). 85.82/25.02 thf(1066,plain,((nthRoo1352626670d_root @ p @ pm)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 85.82/25.02 thf(210,axiom,((! [A:int,B:int,C:int]: ((((times_times_int @ A @ B) = (times_times_int @ A @ C)) = (B = C)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_mult__left__cancel)). 85.82/25.02 thf(1015,plain,((! [A:int,B:int,C:int]: ((((times_times_int @ A @ B) = (times_times_int @ A @ C)) = (B = C)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 85.82/25.02 thf(207,axiom,((! [A:$o,B:nat,C:nat]: ((((semiri2019852685at_int @ (if_nat @ A @ B @ C)) = (semiri2019852685at_int @ B)) <= (A)) & ((~ (A)) => ((semiri2019852685at_int @ (if_nat @ A @ B @ C)) = (semiri2019852685at_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_int__if)). 85.82/25.02 thf(1000,plain,((! [A:$o,B:nat,C:nat]: ((((semiri2019852685at_int @ (if_nat @ A @ B @ C)) = (semiri2019852685at_int @ B)) | ~ (A)) & ((~ (A)) => ((semiri2019852685at_int @ (if_nat @ A @ B @ C)) = (semiri2019852685at_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 85.82/25.02 thf(280,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ (power_power_int @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_power__Suc2)). 85.82/25.02 thf(1250,plain,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ (power_power_int @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 85.82/25.02 thf(237,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_comm__semiring__class_Odistrib)). 85.82/25.02 thf(1102,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 85.82/25.02 thf(59,axiom,((! [A:int]: ((gbinomial_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_gbinomial__0_I1_J)). 85.82/25.02 thf(505,plain,((! [A:int]: ((gbinomial_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 85.82/25.02 thf(105,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_nat__mult__1__right)). 85.82/25.02 thf(653,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 85.82/25.02 thf(107,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_add__cancel__left__right)). 85.82/25.02 thf(658,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 85.82/25.02 thf(257,axiom,((! [A:nat]: ((power_power_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_power__0__Suc)). 85.82/25.02 thf(1176,plain,((! [A:nat]: ((power_power_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 85.82/25.02 thf(91,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = zero_zero_nat)) <= ((times_times_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_divisors__zero)). 85.82/25.02 thf(608,plain,((! [A:nat,B:nat]: ((A = zero_zero_nat) | (B = zero_zero_nat) | ~ ((times_times_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 85.82/25.02 thf(240,axiom,((! [A:int,B:int]: (((divide_divide_int @ (plus_plus_int @ B @ A) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ one_one_int)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_div__add__self2)). 85.82/25.02 thf(1113,plain,((! [A:int,B:int]: (((divide_divide_int @ (plus_plus_int @ B @ A) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ one_one_int)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 85.82/25.02 thf(77,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_comm__monoid__add__class_Oadd__0)). 85.82/25.02 thf(563,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 85.82/25.02 thf(51,axiom,((! [A:nat,B:nat,C:nat]: (((A = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat)) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)) <= (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_nat__mult__div__cancel__disj)). 85.82/25.02 thf(473,plain,((! [A:nat,B:nat,C:nat]: (((A = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat)) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 85.82/25.02 thf(267,axiom,((! [A:int]: ((plus_plus_int @ x @ (times_times_int @ x @ A)) = (times_times_int @ x @ (plus_plus_int @ one_one_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109__092_060open_062_092_060And_062n_O_Ax_A_L_Ax_A_K_An_A_061_Ax_A_K_A_I1_A_L_An_J_092_060close_062)). 85.82/25.02 thf(1208,plain,((! [A:int]: ((plus_plus_int @ x @ (times_times_int @ x @ A)) = (times_times_int @ x @ (plus_plus_int @ one_one_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 85.82/25.02 thf(72,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_add__eq__0__iff__both__eq__0)). 85.82/25.02 thf(548,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 85.82/25.02 thf(187,axiom,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_times__int__code_I1_J)). 85.82/25.02 thf(927,plain,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 85.82/25.02 thf(246,axiom,((! [A:nat]: ((gbinomial_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_gbinomial__0_I2_J)). 85.82/25.02 thf(1134,plain,((! [A:nat]: ((gbinomial_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 85.82/25.02 thf(152,axiom,((! [A:nat,B:nat]: ((A = (suc @ B)) <= (nthRoo1352626670d_root @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_fixed__root_Op)). 85.82/25.02 thf(812,plain,((! [A:nat,B:nat]: ((A = (suc @ B)) | ~ (nthRoo1352626670d_root @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 85.82/25.02 thf(94,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_93_add__right__imp__eq)). 85.82/25.02 thf(617,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)],[94])). 85.82/25.02 thf(307,axiom,((! [A:int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_power__Suc0__right)). 85.82/25.02 thf(1340,plain,((! [A:int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 85.82/25.02 thf(165,axiom,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_bits__div__by__0)). 85.82/25.02 thf(855,plain,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 85.82/25.02 thf(213,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_comm__monoid__add__class_Oadd__0)). 85.82/25.02 thf(1025,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 85.82/25.02 thf(200,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_ab__semigroup__mult__class_Omult__ac_I1_J)). 85.82/25.02 thf(971,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 85.82/25.02 thf(194,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = B) = ((B = zero_zero_int) | (A = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_mult__cancel__right2)). 85.82/25.02 thf(954,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = B) = ((B = zero_zero_int) | (A = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 85.82/25.02 thf(274,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Suc__inject)). 85.82/25.02 thf(1230,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 85.82/25.02 thf(123,axiom,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_bits__div__0)). 85.82/25.02 thf(712,plain,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 85.82/25.02 thf(75,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_one__reorient)). 85.82/25.02 thf(557,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 85.82/25.02 thf(228,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((divide_divide_int @ (plus_plus_int @ (times_times_int @ B @ A) @ C) @ A) = (plus_plus_int @ B @ (divide_divide_int @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_div__mult__self3)). 85.82/25.02 thf(1070,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (plus_plus_int @ (times_times_int @ B @ A) @ C) @ A) = (plus_plus_int @ B @ (divide_divide_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 85.82/25.02 thf(171,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_n__not__Suc__n)). 85.82/25.02 thf(872,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 85.82/25.02 thf(222,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power__Suc)). 85.82/25.02 thf(1053,plain,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 85.82/25.02 thf(294,axiom,(((semiri2019852685at_int @ one_one_nat) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_int__ops_I2_J)). 85.82/25.02 thf(1300,plain,(((semiri2019852685at_int @ one_one_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 85.82/25.02 thf(145,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_add_Oright__neutral)). 85.82/25.02 thf(791,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 85.82/25.02 thf(8,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)). 85.82/25.02 thf(331,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 85.82/25.02 thf(217,axiom,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ C @ B)) = ((B = zero_zero_int) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_mult__cancel__right)). 85.82/25.02 thf(1038,plain,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ C @ B)) = ((B = zero_zero_int) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 85.82/25.02 thf(58,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_left__add__mult__distrib)). 85.82/25.02 thf(502,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 85.82/25.02 thf(160,axiom,((! [A:nat]: ((power_power_int @ one_one_int @ A) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_power__one)). 85.82/25.02 thf(840,plain,((! [A:nat]: ((power_power_int @ one_one_int @ A) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 85.82/25.02 thf(284,axiom,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_comm__monoid__mult__class_Omult__1)). 85.82/25.02 thf(1262,plain,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 85.82/25.02 thf(48,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_ab__semigroup__mult__class_Omult__ac_I1_J)). 85.82/25.02 thf(463,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 85.82/25.02 thf(300,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_power__Suc)). 85.82/25.02 thf(1317,plain,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ A @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 85.82/25.02 thf(17,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_54_add__right__cancel)). 85.82/25.02 thf(359,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)],[17])). 85.82/25.02 thf(271,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ A @ C)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_div__mult__self2)). 85.82/25.02 thf(1220,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ A @ C)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 85.82/25.02 thf(50,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_mult__is__0)). 85.82/25.02 thf(470,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 85.82/25.02 thf(81,axiom,((! [A:nat]: (((divide_divide_nat @ A @ A) = one_one_nat) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_div__self)). 85.82/25.02 thf(576,plain,((! [A:nat]: (((divide_divide_nat @ A @ A) = one_one_nat) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 85.82/25.02 thf(193,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_52_int__ops_I5_J)). 85.82/25.02 thf(951,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)],[193])). 85.82/25.02 thf(151,axiom,((! [A:int]: ((plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) != zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_odd__nonzero)). 85.82/25.02 thf(808,plain,((! [A:int]: ~ ((plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 85.82/25.02 thf(132,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_add__cancel__left__right)). 85.82/25.02 thf(744,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 85.82/25.02 thf(120,axiom,((! [A:int]: ((zero_zero_int = A) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_zero__reorient)). 85.82/25.02 thf(703,plain,((! [A:int]: ((zero_zero_int = A) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 85.82/25.02 thf(106,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add_Ocommute)). 85.82/25.02 thf(656,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 85.82/25.02 thf(311,axiom,((! [A:nat]: ((zero_zero_int = (semiri2019852685at_int @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_of__nat__0__eq__iff)). 85.82/25.02 thf(1353,plain,((! [A:nat]: ((zero_zero_int = (semiri2019852685at_int @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 85.82/25.02 thf(172,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_group__cancel_Oadd2)). 85.82/25.02 thf(876,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 85.82/25.02 thf(235,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((A != zero_zero_int) => (((plus_plus_int @ B @ (times_times_int @ A @ D)) != (plus_plus_int @ C @ (times_times_int @ A @ E))) <= ((B = C) & (D != E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_add__scale__eq__noteq)). 85.82/25.02 thf(1094,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((~ (A = zero_zero_int)) => (~ ((plus_plus_int @ B @ (times_times_int @ A @ D)) = (plus_plus_int @ C @ (times_times_int @ A @ E))) | ~ ((B = C) & ~ (D = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 85.82/25.02 thf(248,axiom,((! [A:(nat > $o),B:nat]: (((A @ zero_zero_nat) <= (! [C:nat]: ((A @ C) <= (A @ (suc @ C))))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_zero__induct)). 85.82/25.02 thf(1140,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) | ~ (! [C:nat]: ((A @ C) | ~ (A @ (suc @ C)))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 85.82/25.02 thf(232,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_ring__class_Oring__distribs_I2_J)). 85.82/25.02 thf(1084,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 85.82/25.02 thf(251,axiom,((! [A:nat]: ((power_power_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_power__0__Suc)). 85.82/25.02 thf(1157,plain,((! [A:nat]: ((power_power_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 85.82/25.03 thf(56,axiom,((! [A:nat]: (((semiri1382578993at_nat @ A) = one_one_nat) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_of__nat__eq__1__iff)). 85.82/25.03 thf(495,plain,((! [A:nat]: (((semiri1382578993at_nat @ A) = one_one_nat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 85.82/25.03 thf(176,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_8_of__nat__add)). 85.82/25.03 thf(891,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)],[176])). 85.82/25.03 thf(261,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_31_add__Suc__shift)). 85.82/25.03 thf(1189,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)],[261])). 85.82/25.03 thf(289,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)). 85.82/25.03 thf(1276,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = B) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 85.82/25.03 thf(303,axiom,((! [A:nat,B:nat]: ((A = (suc @ B)) => (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_nat_OdiscI)). 85.82/25.03 thf(1326,plain,((! [A:nat,B:nat]: ((A = (suc @ B)) => (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 85.82/25.03 thf(281,axiom,((nthRoo1352626670d_root = (^ [A:nat,B:nat]: (A = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_fixed__root__def)). 85.82/25.03 thf(1253,plain,(((nthRoo1352626670d_root) = (^ [A:nat,B:nat]: (A = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 85.82/25.03 thf(63,axiom,((! [A:int]: ((one_one_int = A) = (A = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_one__reorient)). 85.82/25.03 thf(517,plain,((! [A:int]: ((one_one_int = A) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 85.82/25.03 thf(191,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_add_Oleft__neutral)). 85.82/25.03 thf(946,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 85.82/25.03 thf(98,axiom,((! [A:nat]: ((one_one_nat = (semiri1382578993at_nat @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_of__nat__1__eq__iff)). 85.82/25.03 thf(632,plain,((! [A:nat]: ((one_one_nat = (semiri1382578993at_nat @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 85.82/25.03 thf(278,axiom,((! [A:nat]: ((gbinomial_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_gbinomial__0_I2_J)). 85.82/25.03 thf(1244,plain,((! [A:nat]: ((gbinomial_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 85.82/25.03 thf(142,axiom,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ A @ B) @ A) = (times_times_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_power__commutes)). 85.82/25.03 thf(781,plain,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ A @ B) @ A) = (times_times_int @ A @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 85.82/25.03 thf(39,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) & (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_nat__mult__eq__1__iff)). 85.82/25.03 thf(433,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) & (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 85.82/25.03 thf(297,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_21_add__Suc__right)). 85.82/25.03 thf(1308,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)],[297])). 85.82/25.03 thf(230,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_plus__int__code_I2_J)). 85.82/25.03 thf(1077,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 85.82/25.03 thf(179,axiom,((! [A:int,B:nat,C:nat]: ((divide_divide_int @ A @ (times_times_int @ (semiri2019852685at_int @ B) @ (semiri2019852685at_int @ C))) = (divide_divide_int @ (divide_divide_int @ A @ (semiri2019852685at_int @ B)) @ (semiri2019852685at_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_div__mult2__eq_H)). 85.82/25.03 thf(899,plain,((! [A:int,B:nat,C:nat]: ((divide_divide_int @ A @ (times_times_int @ (semiri2019852685at_int @ B) @ (semiri2019852685at_int @ C))) = (divide_divide_int @ (divide_divide_int @ A @ (semiri2019852685at_int @ B)) @ (semiri2019852685at_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 85.82/25.03 thf(148,axiom,((! [A:nat]: ((semiri2019852685at_int @ (suc @ A)) = (plus_plus_int @ one_one_int @ (semiri2019852685at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_of__nat__Suc)). 85.82/25.03 thf(800,plain,((! [A:nat]: ((semiri2019852685at_int @ (suc @ A)) = (plus_plus_int @ one_one_int @ (semiri2019852685at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 85.82/25.03 thf(1,conjecture,(((divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (suc @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (suc @ pm))) = x)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 85.82/25.03 thf(2,negated_conjecture,((~ ((divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (suc @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (suc @ pm))) = x))),inference(neg_conjecture,[status(cth)],[1])). 85.82/25.03 thf(315,plain,((~ ((divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (suc @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (suc @ pm))) = x))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 85.82/25.03 thf(169,axiom,(((semiri2019852685at_int @ one_one_nat) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_of__nat__1)). 85.82/25.03 thf(867,plain,(((semiri2019852685at_int @ one_one_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 85.82/25.03 thf(129,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_mult_Oright__neutral)). 85.82/25.03 thf(735,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 85.82/25.03 thf(32,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_mult__cancel__right)). 85.82/25.03 thf(410,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 85.82/25.03 thf(199,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (divide_divide_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_div__mult__mult1)). 85.82/25.03 thf(967,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (divide_divide_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 85.82/25.03 thf(299,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_nat_Oinject)). 85.82/25.03 thf(1314,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 85.82/25.03 thf(223,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_add__is__1)). 85.82/25.03 thf(1056,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 85.82/25.03 thf(156,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_verit__sum__simplify)). 85.82/25.03 thf(828,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 85.82/25.03 thf(99,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_mult__cancel1)). 85.82/25.03 thf(635,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 85.82/25.03 thf(126,axiom,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) <= (A = zero_zero_nat)) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)) <= (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_div__mult__mult1__if)). 85.82/25.03 thf(720,plain,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) | ~ (A = zero_zero_nat)) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 85.82/25.03 thf(178,axiom,((suc = (^ [A:nat]: (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Suc__eq__plus1)). 85.82/25.03 thf(897,plain,(((suc) = (^ [A:nat]: (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 85.82/25.03 thf(139,axiom,((! [A:int,B:int]: (((B != zero_zero_int) & (A != zero_zero_int)) <= ((times_times_int @ A @ B) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_mult__not__zero)). 85.82/25.03 thf(767,plain,((! [A:int,B:int]: ((~ (B = zero_zero_int) & ~ (A = zero_zero_int)) | ((times_times_int @ A @ B) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 85.82/25.03 thf(28,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_div__mult__mult1)). 85.82/25.03 thf(395,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 85.82/25.03 thf(127,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_nonzero__mult__div__cancel__right)). 85.82/25.03 thf(728,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 85.82/25.03 thf(286,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = (suc @ zero_zero_nat)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_mult__eq__1__iff)). 85.82/25.03 thf(1268,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = (suc @ zero_zero_nat)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 85.82/25.03 thf(37,axiom,((! [A:nat,B:nat]: (((semiri1382578993at_nat @ A) = (semiri1382578993at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_of__nat__eq__iff)). 85.82/25.03 thf(427,plain,((! [A:nat,B:nat]: (((semiri1382578993at_nat @ A) = (semiri1382578993at_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 85.82/25.03 thf(167,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ C @ B))) = ((B = D) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_crossproduct__eq)). 85.82/25.03 thf(860,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ C @ B))) = ((B = D) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 85.82/25.03 thf(87,axiom,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_div__0)). 85.82/25.03 thf(596,plain,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 85.82/25.03 thf(211,axiom,((! [A:nat]: (((semiri2019852685at_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_of__nat__eq__0__iff)). 85.82/25.03 thf(1019,plain,((! [A:nat]: (((semiri2019852685at_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 85.82/25.03 thf(102,axiom,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_bits__div__by__1)). 85.82/25.03 thf(644,plain,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 85.82/25.03 thf(205,axiom,((! [A:int,B:int,C:nat,D:nat,E:nat]: (((times_times_nat @ (plus_plus_nat @ D @ E) @ C) = (plus_plus_nat @ (times_times_nat @ D @ C) @ (times_times_nat @ E @ C))) <= (nO_MATCH_int_nat @ (divide_divide_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_distrib__right__NO__MATCH)). 85.82/25.03 thf(992,plain,((! [A:int,B:int,C:nat,D:nat,E:nat]: (((times_times_nat @ (plus_plus_nat @ D @ E) @ C) = (plus_plus_nat @ (times_times_nat @ D @ C) @ (times_times_nat @ E @ C))) | ~ (nO_MATCH_int_nat @ (divide_divide_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 85.82/25.03 thf(154,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mult_Oassoc)). 85.82/25.03 thf(822,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 85.82/25.03 thf(42,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_mult_Ocommute)). 85.82/25.03 thf(442,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 85.82/25.03 thf(20,axiom,((! [A:nat]: ((gbinomial_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_gbinomial__0_I1_J)). 85.82/25.03 thf(369,plain,((! [A:nat]: ((gbinomial_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 85.82/25.03 thf(304,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_mult__eq__0__iff)). 85.82/25.03 thf(1331,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 85.82/25.03 thf(149,axiom,((plus_plus_int = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add_Ocommute)). 85.82/25.03 thf(803,plain,(((plus_plus_int) = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 85.82/25.03 thf(301,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_29_add__Suc)). 85.82/25.03 thf(1320,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)],[301])). 85.82/25.03 thf(10,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_nat__1__eq__mult__iff)). 85.82/25.03 thf(337,plain,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 85.82/25.03 thf(189,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_ring__class_Oring__distribs_I1_J)). 85.82/25.03 thf(940,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 85.82/25.03 thf(208,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_of__nat__mult)). 85.82/25.03 thf(1009,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 85.82/25.03 thf(76,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ (semiri1382578993at_nat @ A) @ B) = (semiri1382578993at_nat @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_of__nat__eq__of__nat__power__cancel__iff)). 85.82/25.03 thf(560,plain,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ (semiri1382578993at_nat @ A) @ B) = (semiri1382578993at_nat @ C)) = ((power_power_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 85.82/25.03 thf(112,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_power__add)). 85.82/25.03 thf(676,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 85.82/25.03 thf(266,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((times_times_int @ (plus_plus_int @ D @ E) @ C) = (plus_plus_int @ (times_times_int @ D @ C) @ (times_times_int @ E @ C))) <= (nO_MATCH_int_int @ (divide_divide_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_distrib__right__NO__MATCH)). 85.82/25.03 thf(1204,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((times_times_int @ (plus_plus_int @ D @ E) @ C) = (plus_plus_int @ (times_times_int @ D @ C) @ (times_times_int @ E @ C))) | ~ (nO_MATCH_int_int @ (divide_divide_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 85.82/25.03 thf(45,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_83_add_Oassoc)). 85.82/25.03 thf(454,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)],[45])). 85.82/25.03 thf(42661,plain,($false),inference(cvc4,[status(thm)],[1337,365,760,1105,347,846,962,1179,666,481,628,1031,977,1211,523,1290,741,379,511,614,1305,1041,385,1137,715,698,930,1164,797,747,913,1063,340,1127,709,417,885,1359,436,1265,389,570,372,344,1279,1059,949,587,1323,542,460,902,638,1087,1247,1347,881,924,492,1302,1334,514,353,1283,905,1109,321,485,834,602,692,774,1201,849,1074,920,439,661,1067,1047,1311,534,1274,334,910,778,1255,1174,1217,392,424,407,815,1238,957,894,825,1343,916,566,625,852,583,889,757,551,1012,682,1195,324,974,1350,1234,650,1121,1227,356,593,869,420,989,1259,317,328,1160,1028,1361,1182,537,669,686,526,489,1214,590,679,706,554,753,837,647,1150,738,1131,1192,605,1099,985,1050,457,1241,805,508,1167,1185,794,718,1286,1035,750,430,573,689,444,375,1154,402,732,843,579,1124,545,413,641,382,1271,498,466,1090,1224,1356,350,540,672,611,787,764,831,996,318,1043,599,863,784,1117,362,451,1080,858,621,520,964,943,1022,1171,1198,399,959,695,1066,1015,1000,1250,1102,505,653,658,1176,608,1113,563,473,1208,548,927,1134,812,617,1340,855,1025,971,954,1230,712,557,1070,872,1053,1300,791,331,1038,502,840,1262,463,1317,359,1220,470,576,951,808,744,703,656,1353,876,1094,1140,1084,1157,495,891,1189,1276,1326,1253,517,946,632,1244,781,433,1308,1077,899,800,315,867,735,410,967,1314,1056,828,635,720,897,767,395,728,1268,427,860,596,1019,644,992,822,442,369,1331,803,1320,337,940,1009,560,676,1204,454])). 85.82/25.03 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 85.82/25.03 % [INFO] Killing All external provers ... 85.82/25.03 FINAL WATCH: 52.4 CPU 19.9 WC 85.82/25.03 Killed 3 orphans 85.82/25.03 Killed 1 orphans 85.82/25.03 Killed 1 orphans 85.82/25.03 EOF