0.00/0.00 % Leo-III: Strategy 1 (for '60') 29.34/14.62 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 29.34/14.62 % [INFO] Parsing done (446ms). 29.34/14.62 % [INFO] Running in sequential loop mode. 29.34/14.62 % [CONFIG] Using configuration: timeout(60) with strategy 29.34/14.62 % [INFO] eprover registered as external prover. 29.34/14.62 % [INFO] cvc4 registered as external prover. 29.34/14.62 % [INFO] Parsing finished. Scanning for conjecture ... 29.34/14.62 % [INFO] Found a conjecture and 352 axioms. Running axiom selection ... 29.34/14.62 % [INFO] Axiom selection finished. Selected 352 axioms (removed 0 axioms). 29.34/14.62 % [INFO] Problem is higher-order (TPTP THF). 29.34/14.62 % [INFO] Type checking passed. Searching for refutation ... 29.34/14.62 % External prover 'cvc4' found a proof! 29.34/14.62 % [INFO] Killing All external provers ... 29.34/14.62 % Time passed: 10649ms (effective reasoning time: 9644ms) 29.34/14.62 % Solved by strategy 29.34/14.62 % Axioms used in derivation (352): fact_67_le__add__diff__inverse2, fact_34_abs__abs, fact_299_eq__refl, fact_320_left__add__mult__distrib, fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_213_left__diff__distrib_H, fact_41_mult_Oleft__neutral, fact_9_Eq2, fact_196_one__le__numeral, fact_27_numeral__eq__iff, fact_252_order__subst1, fact_301_le__cases, fact_316_nat__le__add__iff1, fact_210_right__diff__distrib_H, fact_93_one__reorient, fact_126_add__mono, fact_65_semiring__norm_I68_J, fact_106_add_Oleft__commute, fact_245_nat__1__add__1, fact_154_diff__eq__eq, fact_193_eq__add__iff1, fact_1_rb1, fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_161_square__diff__one__factored, fact_42_mult_Oleft__neutral, fact_335_diff__le__mono2, fact_62_semiring__norm_I11_J, fact_292_antisym, fact_4_Eq4, fact_223_mult__2__right, fact_109_add__right__imp__eq, fact_311_complete__real, fact_240_order__refl, fact_302_le__cases, fact_287_ord__le__eq__subst, fact_242_semiring__norm_I6_J, fact_347_diff__mult__distrib2, fact_338_mult__le__mono2, fact_231_sin__bound__lemma, fact_189_le__diff__eq, fact_110_add__right__imp__eq, fact_334_le__diff__iff_H, fact_194_numeral__Bit0, fact_100_add_Oassoc, fact_253_order__subst1, fact_308_le__cases3, fact_235_mult__diff__mult, fact_163_mult_Oleft__commute, fact_119_le__iff__add, fact_184_add__le__add__imp__diff__le, fact_201_ordered__ring__class_Ole__add__iff2, fact_350_Nat_Ole__imp__diff__is__add, fact_206_diff__eq__diff__less__eq, fact_198_abs__triangle__ineq, fact_328_Nat_Oadd__diff__assoc, fact_349_diff__commute, fact_243_semiring__norm_I2_J, fact_150_diff__add__eq, fact_183_le__add__diff, fact_22_numeral__le__iff, fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_227_mult__numeral__1__right, fact_38_add__le__cancel__left, fact_122_less__eqE, fact_17_mult__numeral__left__semiring__numeral, fact_218_abs__mult, fact_89_ab__semigroup__add__class_Oadd__ac_I1_J, fact_8_corr__p, fact_113_one__plus__numeral__commute, fact_111_le__num__One__iff, fact_120_add__right__mono, fact_33_abs__idempotent, fact_55_diff__add__cancel, fact_271_ord__eq__le__subst, fact_78_num__double, fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_214_right__diff__distrib, fact_281_ord__le__eq__subst, fact_76_numeral__eq__one__iff, fact_155_group__cancel_Osub1, fact_283_ord__le__eq__subst, fact_112_one__plus__numeral__commute, fact_69_le__add__diff__inverse, fact_244_dbl__simps_I5_J, fact_160_abs__one, fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_291_antisym, fact_32_semiring__norm_I87_J, fact_247_numerals_I1_J, fact_262_order__subst2, fact_229_mult__numeral__1, fact_294_linear, fact_132_add__mono__thms__linordered__semiring_I3_J, fact_323_nat__add__left__cancel__le, fact_307_le__cases3, fact_135_distrib__right, fact_344_le__trans, fact_40_mult_Oright__neutral, fact_59_mem__Collect__eq, fact_268_verit__la__disequality, fact_195_numeral__Bit0, fact_212_left__diff__distrib_H, fact_43_numeral__plus__numeral, fact_174_rho__bound2__def, fact_149_diff__add__eq__diff__diff__swap, fact_16_semiring__norm_I83_J, fact_60_Collect__mem__eq, fact_204_abs__triangle__ineq4, fact_233_rate__2, fact_286_ord__le__eq__subst, fact_277_ord__eq__le__subst, fact_107_add__left__imp__eq, fact_300_le__cases, fact_141_ring__class_Oring__distribs_I1_J, fact_251_order__subst1, fact_5_Eq3, fact_18_mult__numeral__left__semiring__numeral, fact_104_add_Ocommute, fact_191_square__diff__square__factored, fact_288_eq__iff, fact_125_add__mono, fact_73_distrib__left__numeral, fact_158_comm__monoid__mult__class_Omult__1, fact_146_add__implies__diff, fact_332_diff__le__mono, fact_68_le__add__diff__inverse, fact_312_PC__monotone, fact_257_order__subst1, fact_58_abs__1, fact_310_antisym__conv, fact_203_abs__diff__triangle__ineq, fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_254_order__subst1, fact_133_combine__common__factor, fact_232_rate__1, fact_256_order__subst1, fact_219_abs__minus__commute, fact_305_order_Otrans, fact_152_add__diff__eq, fact_57_abs__add__abs, fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062, fact_86_numeral__le__one__iff, fact_147_diff__diff__add, fact_84_one__add__one, fact_282_ord__le__eq__subst, fact_134_combine__common__factor, fact_88_ab__semigroup__add__class_Oadd__ac_I1_J, fact_138_distrib__left, fact_315_nat__eq__add__iff2, fact_64_semiring__norm_I71_J, fact_230_abs__triangle__ineq2__sym, fact_280_ord__le__eq__subst, fact_37_add__le__cancel__left, fact_148_diff__diff__add, fact_317_nat__le__add__iff2, fact_72_distrib__left__numeral, fact_156_mult_Ocomm__neutral, fact_340_mult__le__mono, fact_216_abs__ge__self, fact_313_verit__eq__simplify_I10_J, fact_82_numeral__plus__one, fact_101_add_Oleft__cancel, fact_269_verit__la__disequality, fact_25_abs__triangle__ineq3, fact_75_one__eq__numeral__iff, fact_0_rb2, fact_153_eq__diff__eq, fact_85_one__add__one, fact_49_add__diff__cancel__right, fact_190_diff__le__eq, fact_172_diff__right__commute, fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, fact_348_diff__mult__distrib, fact_205_abs__diff__le__iff, fact_202_ordered__ring__class_Ole__add__iff1, fact_11_left__diff__distrib__numeral, fact_322_nat__mult__eq__1__iff, fact_143_le__numeral__extra_I4_J, fact_258_order__subst2, fact_24_abs__triangle__ineq2, fact_215_left__diff__distrib, fact_327_Nat_Oadd__diff__assoc2, fact_26_numeral__eq__iff, fact_209_diff__mono, fact_274_ord__eq__le__subst, fact_165_mult_Ocommute, fact_289_eq__iff, fact_87_numeral__le__one__iff, fact_246_add__One__commute, fact_115_add__le__imp__le__right, fact_168_mult_Oassoc, fact_309_antisym__conv, fact_234_dbl__simps_I3_J, fact_159_comm__monoid__mult__class_Omult__1, fact_6_corr__q, fact_171_diff__right__commute, fact_61_semiring__norm_I13_J, fact_98_group__cancel_Oadd2, fact_285_ord__le__eq__subst, fact_114_correct__closed, fact_255_order__subst1, fact_295_linear, fact_35_add__le__cancel__right, fact_20_numeral__times__numeral, fact_241_eq__diff__eq_H, fact_318_nat__diff__add__eq1, fact_186_diff__add, fact_63_semiring__norm_I12_J, fact_144_le__numeral__extra_I4_J, fact_326_Nat_Odiff__diff__right, fact_173_diff__eq__diff__eq, fact_331_Nat_Odiff__diff__eq, fact_44_numeral__plus__numeral, fact_30_add__right__cancel, fact_53_add__diff__cancel__left, fact_324_diff__diff__cancel, fact_102_add_Oright__cancel, fact_217_abs__le__D1, fact_129_add__mono__thms__linordered__semiring_I2_J, fact_239_order__refl, fact_336_Nat_Oex__has__greatest__nat, fact_97_group__cancel_Oadd2, fact_71_distrib__right__numeral, fact_50_add__diff__cancel__right, fact_226_mult__numeral__1__right, fact_15_semiring__norm_I85_J, fact_341_le__antisym, fact_279_ord__le__eq__subst, fact_237_okRead1__def, fact_140_comm__semiring__class_Odistrib, fact_80_one__plus__numeral, fact_105_add_Oleft__commute, fact_21_numeral__le__iff, fact_121_add__right__mono, fact_54_add__diff__cancel__left, fact_337_nat__le__linear, fact_108_add__left__imp__eq, fact_66_le__add__diff__inverse2, fact_304_order_Otrans, fact_23_okRead2__def, fact_52_add__diff__cancel__left_H, fact_225_mult__2, fact_275_ord__eq__le__subst, fact_199_numeral__One, fact_192_eq__add__iff2, fact_128_add__mono__thms__linordered__semiring_I1_J, fact_170_ab__semigroup__mult__class_Omult__ac_I1_J, fact_303_order_Otrans, fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_197_one__le__numeral, fact_130_add__mono__thms__linordered__semiring_I2_J, fact_3_Eq1, fact_123_add__left__mono, fact_200_numeral__One, fact_272_ord__eq__le__subst, fact_259_order__subst2, fact_103_add_Ocommute, fact_325_diff__diff__left, fact_345_le__refl, fact_261_order__subst2, fact_263_order__subst2, fact_314_nat__eq__add__iff1, fact_187_add__le__imp__le__diff, fact_330_le__diff__iff, fact_260_order__subst2, fact_164_mult_Oleft__commute, fact_95_group__cancel_Oadd1, fact_139_comm__semiring__class_Odistrib, fact_124_add__left__mono, fact_45_add__numeral__left, fact_248_dbl__def, fact_28_add__left__cancel, fact_7_PC__ie, fact_14_abs__mult__self__eq, fact_116_add__le__imp__le__right, fact_136_distrib__right, fact_151_diff__diff__eq2, fact_346_le__cube, fact_296_linear, fact_298_eq__refl, fact_51_add__diff__cancel__left_H, fact_249_order__subst1, fact_290_eq__iff, fact_238_order__refl, fact_70_distrib__right__numeral, fact_31_add__right__cancel, fact_92_add__mono__thms__linordered__semiring_I4_J, fact_166_mult_Ocommute, fact_264_order__subst2, fact_145_add__implies__diff, fact_81_one__plus__numeral, fact_266_order__subst2, fact_236_verit__eq__simplify_I8_J, fact_12_right__diff__distrib__numeral, fact_118_add__le__imp__le__left, fact_29_add__left__cancel, fact_351_diff__add__inverse2, fact_157_mult_Ocomm__neutral, fact_339_mult__le__mono1, fact_270_ord__eq__le__subst, fact_96_group__cancel_Oadd1, fact_56_add__diff__cancel, fact_39_mult_Oright__neutral, fact_220_left__add__twice, fact_46_add__numeral__left, fact_321_nat__1__eq__mult__iff, fact_83_numeral__plus__one, fact_142_ring__class_Oring__distribs_I2_J, fact_342_le__square, fact_137_distrib__left, fact_273_ord__eq__le__subst, fact_188_add__le__imp__le__diff, fact_319_nat__diff__add__eq2, fact_306_le__cases3, fact_224_mult__2, fact_297_eq__refl, fact_265_order__subst2, fact_13_abs__numeral, fact_222_mult__2__right, fact_221_left__add__twice, fact_167_mult_Oassoc, fact_79_semiring__norm_I69_J, fact_207_diff__right__mono, fact_91_add__mono__thms__linordered__semiring_I4_J, fact_90_is__num__normalize_I1_J, fact_162_rho__bound1__def, fact_2_ie, fact_267_verit__la__disequality, fact_211_right__diff__distrib_H, fact_117_add__le__imp__le__left, fact_36_add__le__cancel__right, fact_48_add__diff__cancel__right_H, fact_99_add_Oassoc, fact_293_antisym, fact_208_diff__left__mono, fact_276_ord__eq__le__subst, fact_343_eq__imp__le, fact_329_eq__diff__iff, fact_333_diff__le__self, fact_185_add__le__add__imp__diff__le, fact_250_order__subst1, fact_19_numeral__times__numeral, fact_127_add__mono__thms__linordered__semiring_I1_J, fact_169_ab__semigroup__mult__class_Omult__ac_I1_J, fact_94_one__reorient, fact_278_ord__eq__le__subst, fact_228_mult__numeral__1, fact_47_add__diff__cancel__right_H, fact_77_numeral__eq__one__iff, fact_74_one__eq__numeral__iff, fact_131_add__mono__thms__linordered__semiring_I3_J, fact_284_ord__le__eq__subst 29.34/14.62 % No. of inferences in proof: 708 29.34/14.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10649 ms resp. 9644 ms w/o parsing 29.34/14.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 29.34/14.62 thf(set_real_type, type, set_real: $tType). 29.34/14.62 thf(real_type, type, real: $tType). 29.34/14.62 thf(num_type, type, num: $tType). 29.34/14.62 thf(nat_type, type, nat: $tType). 29.34/14.62 thf(genClo1161277105lle_PC_type, type, genClo1161277105lle_PC: (nat > (real > real))). 29.34/14.62 thf(genClo1144207539le_rho_type, type, genClo1144207539le_rho: real). 29.34/14.62 thf(genClo1015804716orrect_type, type, genClo1015804716orrect: (nat > (real > $o))). 29.34/14.62 thf(genClo293725281kRead1_type, type, genClo293725281kRead1: ((nat > real) > (real > ((nat > $o) > $o)))). 29.34/14.62 thf(genClo293725282kRead2_type, type, genClo293725282kRead2: ((nat > real) > ((nat > real) > (real > ((nat > $o) > $o))))). 29.34/14.62 thf(genClo2108747022bound1_type, type, genClo2108747022bound1: ((nat > (real > real)) > $o)). 29.34/14.62 thf(genClo2108747023bound2_type, type, genClo2108747023bound2: ((nat > (real > real)) > $o)). 29.34/14.62 thf(abs_abs_real_type, type, abs_abs_real: (real > real)). 29.34/14.62 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 29.34/14.62 thf(minus_minus_real_type, type, minus_minus_real: (real > (real > real))). 29.34/14.62 thf(one_one_nat_type, type, one_one_nat: nat). 29.34/14.62 thf(one_one_real_type, type, one_one_real: real). 29.34/14.62 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 29.34/14.62 thf(plus_plus_num_type, type, plus_plus_num: (num > (num > num))). 29.34/14.62 thf(plus_plus_real_type, type, plus_plus_real: (real > (real > real))). 29.34/14.62 thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))). 29.34/14.62 thf(times_times_num_type, type, times_times_num: (num > (num > num))). 29.34/14.62 thf(times_times_real_type, type, times_times_real: (real > (real > real))). 29.34/14.62 thf(neg_numeral_dbl_real_type, type, neg_numeral_dbl_real: (real > real)). 29.34/14.62 thf(bit0_type, type, bit0: (num > num)). 29.34/14.62 thf(one_type, type, one: num). 29.34/14.62 thf(numeral_numeral_nat_type, type, numeral_numeral_nat: (num > nat)). 29.34/14.62 thf(numeral_numeral_real_type, type, numeral_numeral_real: (num > real)). 29.34/14.62 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 29.34/14.62 thf(ord_less_eq_num_type, type, ord_less_eq_num: (num > (num > $o))). 29.34/14.62 thf(ord_less_eq_real_type, type, ord_less_eq_real: (real > (real > $o))). 29.34/14.62 thf(collect_real_type, type, collect_real: ((real > $o) > set_real)). 29.34/14.62 thf(member_real_type, type, member_real: (real > (set_real > $o))). 29.34/14.62 thf(c_type, type, c: (nat > (real > real))). 29.34/14.62 thf(d_type, type, d: (nat > (real > real))). 29.34/14.62 thf(p_type, type, p: nat). 29.34/14.62 thf(q_type, type, q: nat). 29.34/14.62 thf(s_type, type, s: real). 29.34/14.62 thf(t_type, type, t: real). 29.34/14.62 thf(203,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_add__le__cancel__right)). 29.34/14.62 thf(1036,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 29.34/14.62 thf(289,axiom,((! [A:num,B:num,C:(num > real),D:real]: ((((C @ B) = D) => ((ord_less_eq_real @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_ord__le__eq__subst)). 29.34/14.62 thf(1337,plain,((! [A:num,B:num,C:(num > real),D:real]: ((((C @ B) = D) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 29.34/14.62 thf(334,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_add__le__imp__le__right)). 29.34/14.62 thf(1469,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 29.34/14.62 thf(241,axiom,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_mult__numeral__1__right)). 29.34/14.62 thf(1168,plain,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 29.34/14.62 thf(168,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ C) @ B)) @ D) <= (ord_less_eq_real @ (abs_abs_real @ C) @ D)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_sin__bound__lemma)). 29.34/14.62 thf(941,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ C) @ B)) @ D) | ~ (ord_less_eq_real @ (abs_abs_real @ C) @ D) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 29.34/14.62 thf(90,axiom,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_le__numeral__extra_I4_J)). 29.34/14.62 thf(666,plain,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 29.34/14.62 thf(42,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: ((A = (B @ C)) => ((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_ord__eq__le__subst)). 29.34/14.62 thf(481,plain,((! [A:nat,B:(num > nat),C:num,D:num]: ((A = (B @ C)) => ((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 29.34/14.62 thf(6,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_diff__le__self)). 29.34/14.62 thf(365,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 29.34/14.62 thf(298,axiom,((! [A:real,B:real]: ((A = B) | ~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_verit__la__disequality)). 29.34/14.62 thf(1369,plain,((! [A:real,B:real]: ((A = B) | ~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 29.34/14.62 thf(217,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ B @ C) & (genClo1015804716orrect @ A @ C)) => (ord_less_eq_real @ (times_times_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (genClo1161277105lle_PC @ A @ C) @ (genClo1161277105lle_PC @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_rate__2)). 29.34/14.62 thf(1083,plain,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ B @ C) & (genClo1015804716orrect @ A @ C)) => (ord_less_eq_real @ (times_times_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (genClo1161277105lle_PC @ A @ C) @ (genClo1161277105lle_PC @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 29.34/14.62 thf(176,axiom,((ord_less_eq_real @ one_one_real @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_le__numeral__extra_I4_J)). 29.34/14.62 thf(962,plain,((ord_less_eq_real @ one_one_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 29.34/14.62 thf(38,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: ((((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))) <= (ord_less_eq_num @ C @ D)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_order__subst1)). 29.34/14.62 thf(468,plain,((! [A:nat,B:(num > nat),C:num,D:num]: (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))) | ~ (ord_less_eq_num @ C @ D) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 29.34/14.62 thf(122,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_le__trans)). 29.34/14.62 thf(777,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 29.34/14.62 thf(59,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_nat__le__linear)). 29.34/14.62 thf(555,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 29.34/14.62 thf(53,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_add__left__mono)). 29.34/14.62 thf(523,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 29.34/14.62 thf(191,axiom,((! [A:num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_one__le__numeral)). 29.34/14.62 thf(1005,plain,((! [A:num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 29.34/14.62 thf(109,axiom,((! [A:real,B:(real > $o)]: ((member_real @ A @ (collect_real @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_mem__Collect__eq)). 29.34/14.62 thf(730,plain,((! [A:real,B:(real > $o)]: ((member_real @ A @ (collect_real @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 29.34/14.62 thf(214,axiom,((! [A:num]: ((bit0 @ A) != one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_semiring__norm_I85_J)). 29.34/14.62 thf(1068,plain,((! [A:num]: ~ ((bit0 @ A) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 29.34/14.62 thf(315,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_add__le__imp__le__left)). 29.34/14.62 thf(1422,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 29.34/14.62 thf(152,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Nat_Oadd__diff__assoc2)). 29.34/14.62 thf(878,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 29.34/14.62 thf(75,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_le__add__diff)). 29.34/14.62 thf(614,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 29.34/14.62 thf(151,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_group__cancel_Oadd1)). 29.34/14.62 thf(873,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 29.34/14.62 thf(32,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2)). 29.34/14.62 thf(449,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 29.34/14.62 thf(344,axiom,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_abs__idempotent)). 29.34/14.62 thf(1497,plain,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 29.34/14.62 thf(12,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_diff__right__commute)). 29.34/14.62 thf(384,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 29.34/14.62 thf(46,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add__left__imp__eq)). 29.34/14.62 thf(500,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 29.34/14.62 thf(275,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_order__subst1)). 29.34/14.62 thf(1275,plain,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 29.34/14.62 thf(39,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_le__antisym)). 29.34/14.62 thf(472,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 29.34/14.62 thf(124,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_group__cancel_Oadd1)). 29.34/14.62 thf(782,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 29.34/14.62 thf(103,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D)) <= ((A = B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__mono__thms__linordered__semiring_I4_J)). 29.34/14.62 thf(709,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D)) | ~ ((A = B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 29.34/14.62 thf(22,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_diff__le__mono2)). 29.34/14.62 thf(417,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 29.34/14.62 thf(297,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_mult_Ocomm__neutral)). 29.34/14.62 thf(1366,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 29.34/14.62 thf(29,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_164_mult_Oleft__commute)). 29.34/14.62 thf(436,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)],[29])). 29.34/14.62 thf(339,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_left__diff__distrib)). 29.34/14.62 thf(1482,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 29.34/14.62 thf(85,axiom,((! [A:num,B:num]: (((ord_less_eq_num @ B @ A) = (B = A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_antisym__conv)). 29.34/14.62 thf(651,plain,((! [A:num,B:num]: (((ord_less_eq_num @ B @ A) = (B = A)) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 29.34/14.62 thf(138,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))))) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_order__subst1)). 29.34/14.62 thf(829,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))))) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 29.34/14.62 thf(18,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__diff__cancel__left_H)). 29.34/14.62 thf(404,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 29.34/14.62 thf(107,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => (((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_order__subst2)). 29.34/14.62 thf(724,plain,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 29.34/14.62 thf(318,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) => (A = B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_antisym)). 29.34/14.62 thf(1430,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) => (A = B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 29.34/14.62 thf(47,axiom,((! [A:num,B:num,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (times_times_nat @ (numeral_numeral_nat @ B) @ C)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_mult__numeral__left__semiring__numeral)). 29.34/14.62 thf(504,plain,((! [A:num,B:num,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (times_times_nat @ (numeral_numeral_nat @ B) @ C)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 29.34/14.62 thf(271,axiom,((! [A:num]: ((plus_plus_num @ one @ A) = (plus_plus_num @ A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__One__commute)). 29.34/14.62 thf(1264,plain,((! [A:num]: ((plus_plus_num @ one @ A) = (plus_plus_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 29.34/14.62 thf(347,axiom,((genClo293725281kRead1 = (^ [A:(nat > real),B:real,C:(nat > $o)]: ! [D:nat,E:nat]: (((C @ D) & (C @ E)) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_okRead1__def)). 29.34/14.62 thf(1511,plain,(((genClo293725281kRead1) = (^ [A:(nat > real),B:real,C:(nat > $o)]: ! [D:nat,E:nat]: (((C @ D) & (C @ E)) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 29.34/14.62 thf(130,axiom,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_order_Otrans)). 29.34/14.62 thf(802,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 29.34/14.62 thf(276,axiom,((! [A:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_numeral__plus__one)). 29.34/14.62 thf(1279,plain,((! [A:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 29.34/14.62 thf(165,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ B @ C) & (genClo1015804716orrect @ A @ C)) => (ord_less_eq_real @ (genClo1161277105lle_PC @ A @ B) @ (genClo1161277105lle_PC @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_PC__monotone)). 29.34/14.62 thf(934,plain,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ B @ C) & (genClo1015804716orrect @ A @ C)) => (ord_less_eq_real @ (genClo1161277105lle_PC @ A @ B) @ (genClo1161277105lle_PC @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 29.34/14.62 thf(330,axiom,((ord_less_eq_real @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)) @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_PC__ie)). 29.34/14.62 thf(1462,plain,((ord_less_eq_real @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)) @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 29.34/14.62 thf(56,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_is__num__normalize_I1_J)). 29.34/14.62 thf(542,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 29.34/14.62 thf(301,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ordered__ring__class_Ole__add__iff1)). 29.34/14.62 thf(1379,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 29.34/14.62 thf(265,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_left__diff__distrib_H)). 29.34/14.62 thf(1247,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 29.34/14.62 thf(150,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_mult__le__mono)). 29.34/14.62 thf(870,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 29.34/14.62 thf(338,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_le__add__diff__inverse)). 29.34/14.62 thf(1479,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 29.34/14.62 thf(179,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_mult__numeral__1)). 29.34/14.62 thf(969,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 29.34/14.62 thf(222,axiom,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_eq__refl)). 29.34/14.62 thf(1115,plain,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 29.34/14.62 thf(343,axiom,((! [A:num]: ((times_times_num @ one @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_semiring__norm_I12_J)). 29.34/14.62 thf(1494,plain,((! [A:num]: ((times_times_num @ one @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 29.34/14.62 thf(259,axiom,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_abs__abs)). 29.34/14.62 thf(1232,plain,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 29.34/14.62 thf(194,axiom,(((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_dbl__simps_I3_J)). 29.34/14.62 thf(1013,plain,(((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 29.34/14.62 thf(120,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_eq__refl)). 29.34/14.62 thf(770,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 29.34/14.62 thf(312,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_mult_Oassoc)). 29.34/14.62 thf(1415,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 29.34/14.62 thf(40,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_antisym__conv)). 29.34/14.62 thf(475,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 29.34/14.62 thf(325,axiom,((! [A:num,B:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_numeral__le__iff)). 29.34/14.62 thf(1450,plain,((! [A:num,B:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 29.34/14.62 thf(229,axiom,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_one__add__one)). 29.34/14.62 thf(1136,plain,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 29.34/14.62 thf(197,axiom,((genClo293725282kRead2 = (^ [A:(nat > real),B:(nat > real),C:real,D:(nat > $o)]: ! [E:nat]: ((D @ E) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ E) @ (B @ E))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_okRead2__def)). 29.34/14.62 thf(1020,plain,(((genClo293725282kRead2) = (^ [A:(nat > real),B:(nat > real),C:real,D:(nat > $o)]: ! [E:nat]: ((D @ E) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ E) @ (B @ E))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 29.34/14.62 thf(178,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_diff__diff__add)). 29.34/14.62 thf(966,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 29.34/14.62 thf(136,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_order__subst2)). 29.34/14.62 thf(821,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 29.34/14.62 thf(44,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_Nat_Oadd__diff__assoc)). 29.34/14.62 thf(492,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 29.34/14.62 thf(332,axiom,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_mult__numeral__1__right)). 29.34/14.62 thf(1465,plain,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 29.34/14.62 thf(313,axiom,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_right__diff__distrib__numeral)). 29.34/14.62 thf(1418,plain,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 29.34/14.62 thf(78,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_nat__add__left__cancel__le)). 29.34/14.62 thf(623,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 29.34/14.62 thf(351,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_abs__one)). 29.34/14.62 thf(1526,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 29.34/14.62 thf(290,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)) <= (ord_less_eq_real @ C @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_diff__mono)). 29.34/14.62 thf(1345,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)) | ~ (ord_less_eq_real @ C @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 29.34/14.62 thf(319,axiom,((! [A:num,B:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_numeral__plus__numeral)). 29.34/14.62 thf(1433,plain,((! [A:num,B:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 29.34/14.62 thf(26,axiom,((! [A:num,B:(nat > num),C:nat,D:nat]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_order__subst1)). 29.34/14.62 thf(428,plain,((! [A:num,B:(nat > num),C:nat,D:nat]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 29.34/14.62 thf(349,axiom,((! [A:num]: ((abs_abs_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_abs__numeral)). 29.34/14.62 thf(1521,plain,((! [A:num]: ((abs_abs_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 29.34/14.62 thf(48,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_mult_Ocomm__neutral)). 29.34/14.62 thf(507,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 29.34/14.62 thf(71,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_98_group__cancel_Oadd2)). 29.34/14.62 thf(602,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)],[71])). 29.34/14.62 thf(183,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ B @ C)) = (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_le__diff__eq)). 29.34/14.62 thf(981,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ B @ C)) = (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 29.34/14.62 thf(324,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = (B = (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_eq__diff__eq_H)). 29.34/14.62 thf(1447,plain,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = (B = (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 29.34/14.62 thf(174,axiom,((! [A:num]: ((times_times_num @ (bit0 @ one) @ A) = (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_num__double)). 29.34/14.62 thf(956,plain,((! [A:num]: ((times_times_num @ (bit0 @ one) @ A) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 29.34/14.62 thf(215,axiom,((! [A:real,B:real,C:(real > num),D:num]: ((((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_ord__le__eq__subst)). 29.34/14.62 thf(1072,plain,((! [A:real,B:real,C:(real > num),D:num]: ((((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 29.34/14.62 thf(33,axiom,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_one__plus__numeral__commute)). 29.34/14.62 thf(453,plain,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 29.34/14.62 thf(223,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_semiring__norm_I83_J)). 29.34/14.62 thf(1119,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 29.34/14.62 thf(121,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_mult_Oassoc)). 29.34/14.62 thf(774,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 29.34/14.62 thf(30,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_ord__le__eq__subst)). 29.34/14.62 thf(439,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 29.34/14.62 thf(94,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_mult__le__mono2)). 29.34/14.62 thf(678,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 29.34/14.62 thf(127,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_linear)). 29.34/14.62 thf(793,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 29.34/14.62 thf(251,axiom,((! [A:real,B:(num > real),C:num,D:num]: ((A = (B @ C)) => (((ord_less_eq_real @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_eq_num @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_ord__eq__le__subst)). 29.34/14.62 thf(1199,plain,((! [A:real,B:(num > real),C:num,D:num]: ((A = (B @ C)) => ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 29.34/14.62 thf(236,axiom,((! [A:num]: ((one_one_nat = (numeral_numeral_nat @ A)) = (one = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_one__eq__numeral__iff)). 29.34/14.62 thf(1153,plain,((! [A:num]: ((one_one_nat = (numeral_numeral_nat @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 29.34/14.62 thf(11,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_diff__mult__distrib2)). 29.34/14.62 thf(381,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 29.34/14.62 thf(210,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ C) <= (ord_less_eq_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_order_Otrans)). 29.34/14.62 thf(1057,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ B @ C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 29.34/14.62 thf(282,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_add__mono)). 29.34/14.62 thf(1311,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 29.34/14.62 thf(55,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: ((((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F)))) <= ((C @ B) = D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_ord__le__eq__subst)). 29.34/14.62 thf(534,plain,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 29.34/14.62 thf(304,axiom,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) = (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Eq1)). 29.34/14.62 thf(1387,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) = (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 29.34/14.62 thf(137,axiom,((! [A:num,B:(num > num),C:num,D:num]: ((ord_less_eq_num @ A @ (B @ C)) => (((ord_less_eq_num @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_eq_num @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_order__subst1)). 29.34/14.62 thf(825,plain,((! [A:num,B:(num > num),C:num,D:num]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 29.34/14.62 thf(268,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_add__diff__eq)). 29.34/14.62 thf(1255,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 29.34/14.62 thf(243,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)) <= (ord_less_eq_real @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_order__subst2)). 29.34/14.62 thf(1174,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)) | ~ (ord_less_eq_real @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 29.34/14.62 thf(134,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ B @ (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_add_Oleft__commute)). 29.34/14.62 thf(815,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ B @ (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 29.34/14.62 thf(261,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_nat__1__add__1)). 29.34/14.62 thf(1238,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 29.34/14.62 thf(256,axiom,((! [A:num,B:num]: ((times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_numeral__times__numeral)). 29.34/14.62 thf(1223,plain,((! [A:num,B:num]: ((times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 29.34/14.62 thf(157,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)) => (((~ (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ B @ A)) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => ((~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B)))) <= ((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_le__cases3)). 29.34/14.62 thf(894,plain,((! [A:nat,B:nat,C:nat]: ((~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)) => ((~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ A)) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))) | ~ ((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 29.34/14.62 thf(205,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_diff__le__eq)). 29.34/14.62 thf(1042,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 29.34/14.62 thf(172,axiom,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_mult__2__right)). 29.34/14.62 thf(952,plain,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 29.34/14.62 thf(224,axiom,((! [A:real,B:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = (times_times_real @ (plus_plus_real @ A @ B) @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_square__diff__square__factored)). 29.34/14.62 thf(1123,plain,((! [A:real,B:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = (times_times_real @ (plus_plus_real @ A @ B) @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 29.34/14.62 thf(148,axiom,((! [A:set_real]: ((collect_real @ (^ [B:real]: (member_real @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Collect__mem__eq)). 29.34/14.62 thf(862,plain,((! [A:set_real]: ((collect_real @ (^ [B:real]: (member_real @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 29.34/14.62 thf(19,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_left__diff__distrib_H)). 29.34/14.62 thf(407,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 29.34/14.62 thf(80,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_add__mono__thms__linordered__semiring_I1_J)). 29.34/14.62 thf(630,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 29.34/14.62 thf(202,axiom,((! [A:real,B:real,C:real,D:real]: ((((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => ((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (ord_less_eq_real @ (minus_minus_real @ C @ B) @ D))) <= (ord_less_eq_real @ C @ (plus_plus_real @ D @ B))) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_add__le__add__imp__diff__le)). 29.34/14.62 thf(1032,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => ((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (ord_less_eq_real @ (minus_minus_real @ C @ B) @ D))) | ~ (ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 29.34/14.62 thf(145,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_108_add__left__imp__eq)). 29.34/14.62 thf(852,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)],[145])). 29.34/14.62 thf(244,axiom,((! [A:num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_dbl__simps_I5_J)). 29.34/14.62 thf(1178,plain,((! [A:num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 29.34/14.62 thf(65,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_140_comm__semiring__class_Odistrib)). 29.34/14.62 thf(583,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)],[65])). 29.34/14.62 thf(253,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_ord__le__eq__subst)). 29.34/14.62 thf(1210,plain,((! [A:real,B:real,C:(real > nat),D:nat]: (((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 29.34/14.62 thf(200,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_comm__semiring__class_Odistrib)). 29.34/14.62 thf(1027,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 29.34/14.62 thf(226,axiom,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ C)) @ (abs_abs_real @ (minus_minus_real @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_abs__diff__triangle__ineq)). 29.34/14.62 thf(1128,plain,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ C)) @ (abs_abs_real @ (minus_minus_real @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 29.34/14.62 thf(306,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((((! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_ord__le__eq__subst)). 29.34/14.62 thf(1392,plain,((! [A:real,B:real,C:(real > real),D:real]: (((! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 29.34/14.62 thf(238,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_semiring__norm_I87_J)). 29.34/14.62 thf(1159,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 29.34/14.62 thf(36,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_320_left__add__mult__distrib)). 29.34/14.62 thf(461,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)],[36])). 29.34/14.62 thf(249,axiom,(((numeral_numeral_real @ one) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_numeral__One)). 29.34/14.62 thf(1195,plain,(((numeral_numeral_real @ one) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 29.34/14.62 thf(310,axiom,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_group__cancel_Osub1)). 29.34/14.62 thf(1407,plain,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 29.34/14.62 thf(34,axiom,((! [A:num,B:num]: (((A = B) <= (ord_less_eq_num @ B @ A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_antisym)). 29.34/14.62 thf(456,plain,((! [A:num,B:num]: ((A = B) | ~ (ord_less_eq_num @ B @ A) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 29.34/14.62 thf(142,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_antisym)). 29.34/14.62 thf(842,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 29.34/14.62 thf(308,axiom,((times_times_real = (^ [A:real,B:real]: (times_times_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_mult_Ocommute)). 29.34/14.62 thf(1402,plain,(((times_times_real) = (^ [A:real,B:real]: (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 29.34/14.62 thf(295,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = ((plus_plus_real @ A @ C) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_eq__diff__eq)). 29.34/14.62 thf(1360,plain,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = ((plus_plus_real @ A @ C) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 29.34/14.62 thf(233,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_mult_Oright__neutral)). 29.34/14.62 thf(1143,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 29.34/14.62 thf(273,axiom,((! [A:real,B:real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_abs__add__abs)). 29.34/14.62 thf(1270,plain,((! [A:real,B:real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 29.34/14.62 thf(170,axiom,((! [A:nat,B:real,C:real]: ((genClo1015804716orrect @ A @ B) <= ((ord_less_eq_real @ B @ C) & (genClo1015804716orrect @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_correct__closed)). 29.34/14.62 thf(948,plain,((! [A:nat,B:real,C:real]: ((genClo1015804716orrect @ A @ B) | ~ ((ord_less_eq_real @ B @ C) & (genClo1015804716orrect @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 29.34/14.62 thf(73,axiom,((! [A:num]: (ord_less_eq_num @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_order__refl)). 29.34/14.62 thf(610,plain,((! [A:num]: (ord_less_eq_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 29.34/14.62 thf(23,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_diff__diff__cancel)). 29.34/14.62 thf(420,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 29.34/14.62 thf(113,axiom,((! [A:num,B:num]: (((numeral_numeral_nat @ A) = (numeral_numeral_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_numeral__eq__iff)). 29.34/14.62 thf(742,plain,((! [A:num,B:num]: (((numeral_numeral_nat @ A) = (numeral_numeral_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 29.34/14.62 thf(63,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) <= (~ (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_le__cases)). 29.34/14.62 thf(578,plain,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) | (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 29.34/14.62 thf(99,axiom,((! [A:real]: ((one_one_real = A) = (A = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_one__reorient)). 29.34/14.62 thf(697,plain,((! [A:real]: ((one_one_real = A) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 29.34/14.62 thf(219,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_ord__eq__le__subst)). 29.34/14.62 thf(1089,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 29.34/14.62 thf(354,axiom,((! [A:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_numeral__plus__one)). 29.34/14.62 thf(1534,plain,((! [A:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 29.34/14.62 thf(196,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_add__diff__cancel__right_H)). 29.34/14.62 thf(1017,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 29.34/14.62 thf(230,axiom,((ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Eq3)). 29.34/14.62 thf(1138,plain,((ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 29.34/14.62 thf(3,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_diff__commute)). 29.34/14.62 thf(356,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 29.34/14.62 thf(154,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_29_add__left__cancel)). 29.34/14.62 thf(884,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)],[154])). 29.34/14.62 thf(329,axiom,((genClo1015804716orrect @ p @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_corr__p)). 29.34/14.62 thf(1461,plain,((genClo1015804716orrect @ p @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 29.34/14.62 thf(97,axiom,((! [A:num,B:num]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_numeral__times__numeral)). 29.34/14.62 thf(686,plain,((! [A:num,B:num]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 29.34/14.62 thf(316,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_left__add__twice)). 29.34/14.62 thf(1424,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 29.34/14.62 thf(54,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_ord__eq__le__subst)). 29.34/14.62 thf(526,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 29.34/14.62 thf(43,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_322_nat__mult__eq__1__iff)). 29.34/14.62 thf(489,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)],[43])). 29.34/14.62 thf(252,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_mult__2)). 29.34/14.62 thf(1207,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 29.34/14.62 thf(204,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_ring__class_Oring__distribs_I1_J)). 29.34/14.62 thf(1039,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 29.34/14.62 thf(58,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_ord__le__eq__subst)). 29.34/14.62 thf(547,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 29.34/14.62 thf(102,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_add_Oassoc)). 29.34/14.62 thf(706,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 29.34/14.62 thf(286,axiom,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_ord__eq__le__subst)). 29.34/14.62 thf(1324,plain,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 29.34/14.62 thf(112,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_eq_nat @ C @ D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_add__mono__thms__linordered__semiring_I2_J)). 29.34/14.62 thf(738,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_eq_nat @ C @ D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 29.34/14.62 thf(86,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_add__le__imp__le__left)). 29.34/14.62 thf(654,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 29.34/14.62 thf(248,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_eq_real @ A @ (plus_plus_real @ B @ C)) & (ord_less_eq_real @ (minus_minus_real @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_abs__diff__le__iff)). 29.34/14.62 thf(1192,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_eq_real @ A @ (plus_plus_real @ B @ C)) & (ord_less_eq_real @ (minus_minus_real @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 29.34/14.62 thf(211,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_one__add__one)). 29.34/14.62 thf(1060,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 29.34/14.62 thf(106,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_ab__semigroup__add__class_Oadd__ac_I1_J)). 29.34/14.62 thf(721,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 29.34/14.62 thf(190,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_mult__2)). 29.34/14.62 thf(1002,plain,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 29.34/14.62 thf(327,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_semiring__norm_I71_J)). 29.34/14.62 thf(1456,plain,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 29.34/14.62 thf(302,axiom,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (bit0 @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_semiring__norm_I13_J)). 29.34/14.62 thf(1382,plain,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (bit0 @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 29.34/14.62 thf(184,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_right__diff__distrib)). 29.34/14.62 thf(984,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 29.34/14.62 thf(159,axiom,((! [A:nat,B:nat,C:num]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ C)) = (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ C)) @ (times_times_nat @ B @ (numeral_numeral_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_distrib__right__numeral)). 29.34/14.62 thf(911,plain,((! [A:nat,B:nat,C:num]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ C)) = (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ C)) @ (times_times_nat @ B @ (numeral_numeral_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 29.34/14.62 thf(167,axiom,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_one__plus__numeral__commute)). 29.34/14.62 thf(938,plain,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 29.34/14.62 thf(263,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_diff__add__eq__diff__diff__swap)). 29.34/14.62 thf(1241,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 29.34/14.62 thf(131,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_89_ab__semigroup__add__class_Oadd__ac_I1_J)). 29.34/14.62 thf(805,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)],[131])). 29.34/14.62 thf(209,axiom,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (plus_plus_real @ (times_times_real @ C @ B) @ D)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_combine__common__factor)). 29.34/14.62 thf(1054,plain,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (plus_plus_real @ (times_times_real @ C @ B) @ D)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 29.34/14.62 thf(16,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_add__diff__cancel__left)). 29.34/14.62 thf(398,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 29.34/14.62 thf(246,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) & (A = B)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_add__mono__thms__linordered__semiring_I2_J)). 29.34/14.62 thf(1185,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) & (A = B)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 29.34/14.62 thf(66,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_linear)). 29.34/14.62 thf(586,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 29.34/14.62 thf(89,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_110_add__right__imp__eq)). 29.34/14.62 thf(662,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)],[89])). 29.34/14.62 thf(274,axiom,((! [A:num]: (ord_less_eq_num @ one @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_semiring__norm_I68_J)). 29.34/14.62 thf(1273,plain,((! [A:num]: (ord_less_eq_num @ one @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 29.34/14.62 thf(146,axiom,((! [A:num,B:nat,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ A) @ B) @ (times_times_nat @ (numeral_numeral_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_distrib__left__numeral)). 29.34/14.62 thf(856,plain,((! [A:num,B:nat,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ A) @ B) @ (times_times_nat @ (numeral_numeral_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 29.34/14.62 thf(114,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_add_Oright__cancel)). 29.34/14.62 thf(745,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 29.34/14.62 thf(98,axiom,((! [A:num,B:(num > num),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_ord__eq__le__subst)). 29.34/14.62 thf(689,plain,((! [A:num,B:(num > num),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 29.34/14.62 thf(110,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_mult_Ocommute)). 29.34/14.62 thf(733,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 29.34/14.62 thf(50,axiom,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) <= (ord_less_eq_num @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_order__subst2)). 29.34/14.62 thf(513,plain,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ (ord_less_eq_num @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 29.34/14.62 thf(234,axiom,((! [A:num]: ((one_one_real = (numeral_numeral_real @ A)) = (one = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_one__eq__numeral__iff)). 29.34/14.62 thf(1146,plain,((! [A:num]: ((one_one_real = (numeral_numeral_real @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 29.34/14.62 thf(181,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = ((plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) = E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_eq__add__iff1)). 29.34/14.62 thf(975,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = ((plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 29.34/14.62 thf(24,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_diff__diff__left)). 29.34/14.62 thf(423,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 29.34/14.62 thf(192,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add__left__mono)). 29.34/14.62 thf(1007,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 29.34/14.62 thf(305,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_diff__add__eq)). 29.34/14.62 thf(1389,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 29.34/14.62 thf(257,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_mult__numeral__1)). 29.34/14.62 thf(1226,plain,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 29.34/14.62 thf(57,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_add_Ocommute)). 29.34/14.62 thf(545,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 29.34/14.62 thf(341,axiom,((! [A:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ one_one_real) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_numeral__le__one__iff)). 29.34/14.62 thf(1488,plain,((! [A:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ one_one_real) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 29.34/14.62 thf(166,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_abs__triangle__ineq)). 29.34/14.62 thf(936,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 29.34/14.62 thf(125,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_100_add_Oassoc)). 29.34/14.62 thf(787,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)],[125])). 29.34/14.62 thf(104,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_Nat_Ole__imp__diff__is__add)). 29.34/14.62 thf(713,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 29.34/14.62 thf(287,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_verit__eq__simplify_I8_J)). 29.34/14.62 thf(1332,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 29.34/14.62 thf(161,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_nat__le__add__iff1)). 29.34/14.62 thf(919,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 29.34/14.62 thf(294,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F)))) <= (ord_less_eq_nat @ (C @ B) @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_order__subst2)). 29.34/14.62 thf(1356,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) | ~ (ord_less_eq_nat @ (C @ B) @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 29.34/14.62 thf(231,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) & (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_add__mono__thms__linordered__semiring_I1_J)). 29.34/14.62 thf(1139,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) & (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 29.34/14.62 thf(346,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_real @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_ord__le__eq__subst)). 29.34/14.62 thf(1503,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])). 29.34/14.62 thf(269,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (minus_minus_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__diff__cancel__left)). 29.34/14.62 thf(1258,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (minus_minus_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 29.34/14.62 thf(101,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_eq__iff)). 29.34/14.62 thf(704,plain,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 29.34/14.62 thf(95,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_170_ab__semigroup__mult__class_Omult__ac_I1_J)). 29.34/14.62 thf(681,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)],[95])). 29.34/14.62 thf(277,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_diff__eq__diff__eq)). 29.34/14.62 thf(1282,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 29.34/14.62 thf(350,axiom,(((numeral_numeral_nat @ one) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_numeral__One)). 29.34/14.62 thf(1524,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 29.34/14.62 thf(5,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_add__diff__cancel__right_H)). 29.34/14.62 thf(362,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 29.34/14.62 thf(28,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_le__refl)). 29.34/14.62 thf(434,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 29.34/14.62 thf(281,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_verit__eq__simplify_I10_J)). 29.34/14.62 thf(1307,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 29.34/14.62 thf(10,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_le__diff__iff)). 29.34/14.62 thf(377,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 29.34/14.62 thf(186,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_distrib__right)). 29.34/14.62 thf(990,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 29.34/14.62 thf(188,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_distrib__left)). 29.34/14.62 thf(996,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 29.34/14.62 thf(300,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_diff__right__commute)). 29.34/14.62 thf(1376,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 29.34/14.62 thf(321,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_add__diff__cancel__right)). 29.34/14.62 thf(1439,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 29.34/14.62 thf(335,axiom,((! [A:real,B:real,C:real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_diff__eq__eq)). 29.34/14.62 thf(1471,plain,((! [A:real,B:real,C:real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 29.34/14.62 thf(216,axiom,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_one__plus__numeral)). 29.34/14.62 thf(1080,plain,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 29.34/14.62 thf(7,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__diff__cancel__right)). 29.34/14.62 thf(367,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 29.34/14.62 thf(235,axiom,((! [A:num,B:(real > num),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))))) <= (ord_less_eq_num @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_order__subst1)). 29.34/14.62 thf(1149,plain,((! [A:num,B:(real > num),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))))) | ~ (ord_less_eq_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 29.34/14.62 thf(79,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Nat_Odiff__diff__right)). 29.34/14.62 thf(626,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 29.34/14.62 thf(198,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_diff__eq__diff__less__eq)). 29.34/14.62 thf(1022,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 29.34/14.62 thf(279,axiom,((! [A:set_real]: (((? [B:real]: (! [C:real]: ((ord_less_eq_real @ B @ C) <= (! [D:real]: ((ord_less_eq_real @ D @ C) <= (member_real @ D @ A)))) & ! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B)))) <= (? [B:real]: ! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B)))) <= (? [B:real]: (member_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_complete__real)). 29.34/14.62 thf(1293,plain,((! [A:set_real]: (? [B:real]: (! [C:real]: ((ord_less_eq_real @ B @ C) | ~ (! [D:real]: ((ord_less_eq_real @ D @ C) | ~ (member_real @ D @ A)))) & ! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B))) | ~ (? [B:real]: ! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B))) | ~ (? [B:real]: (member_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 29.34/14.62 thf(164,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_le__square)). 29.34/14.62 thf(932,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 29.34/14.62 thf(133,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))) => (ord_less_eq_num @ (C @ A) @ D)) <= (ord_less_eq_num @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_order__subst2)). 29.34/14.62 thf(811,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ (ord_less_eq_num @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 29.34/14.62 thf(13,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_right__diff__distrib_H)). 29.34/14.62 thf(387,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 29.34/14.62 thf(129,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_mult_Oright__neutral)). 29.34/14.62 thf(799,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 29.34/14.62 thf(239,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_order__subst1)). 29.34/14.62 thf(1162,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 29.34/14.62 thf(144,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2)). 29.34/14.62 thf(848,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 29.34/14.62 thf(100,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc)). 29.34/14.62 thf(700,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 29.34/14.62 thf(52,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_136_distrib__right)). 29.34/14.62 thf(520,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)],[52])). 29.34/14.62 thf(242,axiom,((! [A:real,B:real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_abs__minus__commute)). 29.34/14.62 thf(1171,plain,((! [A:real,B:real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 29.34/14.62 thf(336,axiom,(((numeral_numeral_nat @ one) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_numerals_I1_J)). 29.34/14.62 thf(1474,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 29.34/14.62 thf(175,axiom,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_diff__add__cancel)). 29.34/14.62 thf(959,plain,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 29.34/14.62 thf(82,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: (B != (plus_plus_nat @ A @ C)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_less__eqE)). 29.34/14.62 thf(636,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ~ (B = (plus_plus_nat @ A @ C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 29.34/14.62 thf(123,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_le__cases)). 29.34/14.62 thf(780,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 29.34/14.62 thf(195,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_abs__triangle__ineq4)). 29.34/14.62 thf(1015,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 29.34/14.62 thf(15,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_le__diff__iff_H)). 29.34/14.62 thf(394,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 29.34/14.62 thf(266,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add__le__cancel__left)). 29.34/14.62 thf(1250,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 29.34/14.62 thf(323,axiom,((genClo2108747023bound2 = (^ [A:(nat > (real > real))]: ! [B:nat,C:real,D:real]: ((ord_less_eq_real @ (times_times_real @ (minus_minus_real @ D @ C) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (A @ B @ D) @ (A @ B @ C))) <= ((genClo1015804716orrect @ B @ D) & (ord_less_eq_real @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_rho__bound2__def)). 29.34/14.62 thf(1445,plain,(((genClo2108747023bound2) = (^ [A:(nat > (real > real))]: ! [B:nat,C:real,D:real]: ((ord_less_eq_real @ (times_times_real @ (minus_minus_real @ D @ C) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (A @ B @ D) @ (A @ B @ C))) | ~ ((genClo1015804716orrect @ B @ D) & (ord_less_eq_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 29.34/14.62 thf(352,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_mult_Oleft__neutral)). 29.34/14.62 thf(1528,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 29.34/14.62 thf(93,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_add__right__cancel)). 29.34/14.62 thf(675,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 29.34/14.62 thf(280,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_diff__left__mono)). 29.34/14.62 thf(1304,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 29.34/14.62 thf(128,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (minus_minus_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_nat__diff__add__eq2)). 29.34/14.62 thf(795,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (minus_minus_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 29.34/14.62 thf(9,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_diff__diff__add)). 29.34/14.62 thf(374,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 29.34/14.62 thf(76,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mult_Oleft__neutral)). 29.34/14.62 thf(617,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 29.34/14.62 thf(1,conjecture,((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 29.34/14.62 thf(2,negated_conjecture,((~ (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(neg_conjecture,[status(cth)],[1])). 29.34/14.62 thf(355,plain,((~ (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 29.34/14.62 thf(245,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_order__subst1)). 29.34/14.62 thf(1181,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 29.34/14.62 thf(140,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_add__right__mono)). 29.34/14.62 thf(836,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 29.34/14.62 thf(207,axiom,((! [A:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_numeral__le__one__iff)). 29.34/14.62 thf(1049,plain,((! [A:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 29.34/14.62 thf(25,axiom,(((= @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (ord_less_eq_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_eq__iff)). 29.34/14.62 thf(426,plain,(((= @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (ord_less_eq_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 29.34/14.62 thf(240,axiom,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_eq__iff)). 29.34/14.62 thf(1166,plain,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 29.34/14.62 thf(60,axiom,((! [A:num,B:num,C:num]: ((((~ (ord_less_eq_num @ A @ C)) <= (ord_less_eq_num @ B @ A)) => (((~ (ord_less_eq_num @ C @ B)) <= (ord_less_eq_num @ A @ C)) => (((ord_less_eq_num @ C @ B) => (~ (ord_less_eq_num @ B @ A))) => ((~ ((~ (ord_less_eq_num @ A @ B)) <= (ord_less_eq_num @ C @ A))) <= ((~ (ord_less_eq_num @ C @ A)) <= (ord_less_eq_num @ B @ C)))))) <= ((ord_less_eq_num @ A @ B) => (~ (ord_less_eq_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_le__cases3)). 29.34/14.62 thf(557,plain,((! [A:num,B:num,C:num]: (((~ (ord_less_eq_num @ A @ C) | ~ (ord_less_eq_num @ B @ A)) => ((~ (ord_less_eq_num @ C @ B) | ~ (ord_less_eq_num @ A @ C)) => (((ord_less_eq_num @ C @ B) => (~ (ord_less_eq_num @ B @ A))) => (~ (~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ C @ A)) | ~ (~ (ord_less_eq_num @ C @ A) | ~ (ord_less_eq_num @ B @ C)))))) | ~ ((ord_less_eq_num @ A @ B) => (~ (ord_less_eq_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 29.34/14.62 thf(64,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_add__mono)). 29.34/14.62 thf(580,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 29.34/14.62 thf(83,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_134_combine__common__factor)). 29.34/14.62 thf(640,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)],[83])). 29.34/14.62 thf(199,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_abs__le__D1)). 29.34/14.62 thf(1025,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 29.34/14.62 thf(237,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_diff__right__mono)). 29.34/14.62 thf(1156,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 29.34/14.62 thf(307,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_abs__triangle__ineq2)). 29.34/14.62 thf(1400,plain,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 29.34/14.62 thf(155,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (A = B)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add__mono__thms__linordered__semiring_I4_J)). 29.34/14.62 thf(887,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (A = B)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 29.34/14.62 thf(21,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_diff__add__inverse2)). 29.34/14.62 thf(414,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 29.34/14.62 thf(272,axiom,((! [A:real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_abs__mult__self__eq)). 29.34/14.62 thf(1267,plain,((! [A:real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 29.34/14.62 thf(353,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((plus_plus_real @ (minus_minus_real @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__add__diff__inverse2)). 29.34/14.62 thf(1531,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((plus_plus_real @ (minus_minus_real @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 29.34/14.62 thf(187,axiom,((! [A:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ one_one_real) = (times_times_real @ (plus_plus_real @ A @ one_one_real) @ (minus_minus_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_square__diff__one__factored)). 29.34/14.62 thf(993,plain,((! [A:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ one_one_real) = (times_times_real @ (plus_plus_real @ A @ one_one_real) @ (minus_minus_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 29.34/14.62 thf(8,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_add__implies__diff)). 29.34/14.62 thf(370,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 29.34/14.62 thf(105,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((plus_plus_nat @ (times_times_nat @ A @ C) @ D) = (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (D = (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_nat__eq__add__iff2)). 29.34/14.62 thf(717,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((plus_plus_nat @ (times_times_nat @ A @ C) @ D) = (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (D = (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 29.34/14.62 thf(260,axiom,((! [A:num]: ((ord_less_eq_num @ A @ one) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_le__num__One__iff)). 29.34/14.62 thf(1235,plain,((! [A:num]: ((ord_less_eq_num @ A @ one) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 29.34/14.62 thf(284,axiom,((! [A:num,B:num]: (((numeral_numeral_real @ A) = (numeral_numeral_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_numeral__eq__iff)). 29.34/14.62 thf(1317,plain,((! [A:num,B:num]: (((numeral_numeral_real @ A) = (numeral_numeral_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 29.34/14.62 thf(218,axiom,((! [A:real,B:(num > real),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))))) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_order__subst1)). 29.34/14.62 thf(1085,plain,((! [A:real,B:(num > real),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))))) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 29.34/14.62 thf(4,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_diff__mult__distrib)). 29.34/14.62 thf(359,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 29.34/14.62 thf(227,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_semiring__norm_I6_J)). 29.34/14.62 thf(1130,plain,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 29.34/14.62 thf(84,axiom,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => (((C @ B) = D) => ((! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_ord__le__eq__subst)). 29.34/14.62 thf(643,plain,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => (((C @ B) = D) => ((! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 29.34/14.62 thf(255,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_numeral__Bit0)). 29.34/14.62 thf(1220,plain,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 29.34/14.62 thf(171,axiom,((genClo2108747022bound1 @ c)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_rb1)). 29.34/14.62 thf(951,plain,((genClo2108747022bound1 @ (c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 29.34/14.62 thf(132,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__le__cancel__right)). 29.34/14.62 thf(808,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 29.34/14.62 thf(278,axiom,((! [A:num,B:(real > num),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_num @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_ord__eq__le__subst)). 29.34/14.62 thf(1285,plain,((! [A:num,B:(real > num),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_num @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 29.34/14.62 thf(254,axiom,((! [A:nat,B:real,C:real]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C)) => (ord_less_eq_real @ (minus_minus_real @ (genClo1161277105lle_PC @ A @ C) @ (genClo1161277105lle_PC @ A @ B)) @ (times_times_real @ (minus_minus_real @ C @ B) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_rate__1)). 29.34/14.62 thf(1218,plain,((! [A:nat,B:real,C:real]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C)) => (ord_less_eq_real @ (minus_minus_real @ (genClo1161277105lle_PC @ A @ C) @ (genClo1161277105lle_PC @ A @ B)) @ (times_times_real @ (minus_minus_real @ C @ B) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 29.34/14.62 thf(309,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_diff__diff__eq2)). 29.34/14.62 thf(1404,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 29.34/14.62 thf(232,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_abs__1)). 29.34/14.62 thf(1141,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 29.34/14.62 thf(87,axiom,((! [A:nat,B:nat]: (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A) | (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_verit__la__disequality)). 29.34/14.62 thf(656,plain,((! [A:nat,B:nat]: (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 29.34/14.62 thf(317,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_comm__monoid__mult__class_Omult__1)). 29.34/14.62 thf(1427,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 29.34/14.62 thf(182,axiom,((! [A:num,B:num,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_mult__numeral__left__semiring__numeral)). 29.34/14.62 thf(978,plain,((! [A:num,B:num,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 29.34/14.62 thf(61,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_eq_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_nat__le__add__iff2)). 29.34/14.62 thf(571,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_eq_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 29.34/14.62 thf(299,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_eq_real @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_order__subst2)). 29.34/14.62 thf(1372,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 29.34/14.62 thf(74,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_add__le__imp__le__right)). 29.34/14.62 thf(612,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 29.34/14.62 thf(147,axiom,((! [A:num,B:num,C:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ (numeral_numeral_nat @ B) @ C)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__numeral__left)). 29.34/14.62 thf(859,plain,((! [A:num,B:num,C:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ (numeral_numeral_nat @ B) @ C)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 29.34/14.62 thf(262,axiom,((ord_less_eq_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062)). 29.34/14.62 thf(1240,plain,((ord_less_eq_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 29.34/14.62 thf(293,axiom,((! [A:num]: ~ (ord_less_eq_num @ (bit0 @ A) @ one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_semiring__norm_I69_J)). 29.34/14.62 thf(1353,plain,((! [A:num]: ~ (ord_less_eq_num @ (bit0 @ A) @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 29.34/14.62 thf(70,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_add__le__imp__le__diff)). 29.34/14.62 thf(600,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 29.34/14.62 thf(340,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_add__right__mono)). 29.34/14.62 thf(1485,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 29.34/14.62 thf(208,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) <= (~ (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_le__cases)). 29.34/14.62 thf(1052,plain,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 29.34/14.62 thf(143,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add__le__cancel__left)). 29.34/14.62 thf(845,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 29.34/14.62 thf(314,axiom,((ord_less_eq_real @ s @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ie)). 29.34/14.62 thf(1421,plain,((ord_less_eq_real @ s @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 29.34/14.62 thf(328,axiom,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_abs__ge__self)). 29.34/14.62 thf(1459,plain,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 29.34/14.62 thf(92,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc)). 29.34/14.62 thf(671,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 29.34/14.62 thf(311,axiom,((! [A:real,B:real]: ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_abs__mult)). 29.34/14.62 thf(1412,plain,((! [A:real,B:real]: ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 29.34/14.62 thf(156,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_comm__monoid__mult__class_Omult__1)). 29.34/14.62 thf(891,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 29.34/14.62 thf(225,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_order__refl)). 29.34/14.62 thf(1126,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 29.34/14.62 thf(247,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_right__diff__distrib_H)). 29.34/14.62 thf(1189,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 29.34/14.62 thf(193,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__diff__cancel__left_H)). 29.34/14.62 thf(1010,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 29.34/14.62 thf(326,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_add__diff__cancel)). 29.34/14.62 thf(1453,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 29.34/14.62 thf(303,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_abs__triangle__ineq3)). 29.34/14.62 thf(1385,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 29.34/14.62 thf(337,axiom,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_distrib__left__numeral)). 29.34/14.62 thf(1476,plain,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 29.34/14.62 thf(115,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2)). 29.34/14.62 thf(748,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 29.34/14.62 thf(212,axiom,((! [A:real,B:real,C:num]: ((times_times_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ C)) = (plus_plus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_distrib__right__numeral)). 29.34/14.62 thf(1062,plain,((! [A:real,B:real,C:num]: ((times_times_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ C)) = (plus_plus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 29.34/14.62 thf(14,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_Nat_Odiff__diff__eq)). 29.34/14.62 thf(390,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 29.34/14.62 thf(81,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((plus_plus_nat @ (times_times_nat @ B @ C) @ D) = (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) = E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_nat__eq__add__iff1)). 29.34/14.62 thf(632,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((plus_plus_nat @ (times_times_nat @ B @ C) @ D) = (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 29.34/14.62 thf(17,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_diff__le__mono)). 29.34/14.62 thf(401,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 29.34/14.62 thf(264,axiom,((! [A:num]: ((times_times_num @ A @ one) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_semiring__norm_I11_J)). 29.34/14.62 thf(1244,plain,((! [A:num]: ((times_times_num @ A @ one) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 29.34/14.62 thf(67,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_nat__diff__add__eq1)). 29.34/14.62 thf(588,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 29.34/14.62 thf(267,axiom,(((plus_plus_num @ one @ one) = (bit0 @ one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_semiring__norm_I2_J)). 29.34/14.62 thf(1253,plain,(((plus_plus_num @ one @ one) = (bit0 @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 29.34/14.62 thf(177,axiom,((! [A:num,B:num,C:real]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ (numeral_numeral_real @ B) @ C)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__numeral__left)). 29.34/14.62 thf(963,plain,((! [A:num,B:num,C:real]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ (numeral_numeral_real @ B) @ C)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 29.34/14.62 thf(51,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__left__cancel)). 29.34/14.62 thf(517,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 29.34/14.62 thf(169,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_abs__triangle__ineq2__sym)). 29.34/14.62 thf(946,plain,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 29.34/14.62 thf(221,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ B) => (~ (ord_less_eq_real @ B @ C))) => ((((~ (ord_less_eq_real @ C @ B)) <= (ord_less_eq_real @ A @ C)) => (((~ (ord_less_eq_real @ B @ A)) <= (ord_less_eq_real @ C @ B)) => (((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))) => (~ ((ord_less_eq_real @ C @ A) => (~ (ord_less_eq_real @ A @ B))))))) <= ((~ (ord_less_eq_real @ A @ C)) <= (ord_less_eq_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_le__cases3)). 29.34/14.62 thf(1101,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ B) => (~ (ord_less_eq_real @ B @ C))) => (((~ (ord_less_eq_real @ C @ B) | ~ (ord_less_eq_real @ A @ C)) => ((~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ C @ B)) => (((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))) => (~ ((ord_less_eq_real @ C @ A) => (~ (ord_less_eq_real @ A @ B))))))) | ~ (~ (ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 29.34/14.62 thf(160,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add)). 29.34/14.62 thf(914,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 29.34/14.62 thf(49,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_106_add_Oleft__commute)). 29.34/14.62 thf(510,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)],[49])). 29.34/14.62 thf(91,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_eq__imp__le)). 29.34/14.62 thf(667,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 29.34/14.62 thf(163,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add_Oleft__cancel)). 29.34/14.62 thf(929,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 29.34/14.62 thf(41,axiom,((! [A:num,B:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_numeral__le__iff)). 29.34/14.62 thf(478,plain,((! [A:num,B:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 29.34/14.62 thf(118,axiom,((! [A:num,B:num]: ((A = B) => (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_eq__refl)). 29.34/14.62 thf(763,plain,((! [A:num,B:num]: ((A = B) => (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 29.34/14.62 thf(348,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_ord__eq__le__subst)). 29.34/14.62 thf(1513,plain,((! [A:nat,B:(real > nat),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 29.34/14.62 thf(96,axiom,((neg_numeral_dbl_real = (^ [A:real]: (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_dbl__def)). 29.34/14.62 thf(684,plain,(((neg_numeral_dbl_real) = (^ [A:real]: (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 29.34/14.62 thf(322,axiom,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_numeral__Bit0)). 29.34/14.62 thf(1442,plain,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 29.34/14.62 thf(206,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = C) => (A = (minus_minus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_add__implies__diff)). 29.34/14.62 thf(1045,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = C) => (A = (minus_minus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 29.34/14.62 thf(201,axiom,(((minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Eq4)). 29.34/14.62 thf(1030,plain,(((minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 29.34/14.62 thf(342,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (C = (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_eq__add__iff2)). 29.34/14.62 thf(1491,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (C = (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 29.34/14.62 thf(228,axiom,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ (bit0 @ one))) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_mult__2__right)). 29.34/14.62 thf(1133,plain,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ (bit0 @ one))) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 29.34/14.62 thf(291,axiom,((! [A:real,B:real,C:(real > num),D:num]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_order__subst2)). 29.34/14.62 thf(1348,plain,((! [A:real,B:real,C:(real > num),D:num]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 29.34/14.62 thf(116,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_le__add__diff__inverse)). 29.34/14.62 thf(752,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 29.34/14.62 thf(31,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_le__cube)). 29.34/14.62 thf(447,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 29.34/14.62 thf(27,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_le__iff__add)). 29.34/14.62 thf(432,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 29.34/14.62 thf(220,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= ((C = D) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_add__mono__thms__linordered__semiring_I3_J)). 29.34/14.62 thf(1097,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ ((C = D) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 29.34/14.62 thf(258,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_mult_Oleft__commute)). 29.34/14.62 thf(1229,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 29.34/14.62 thf(135,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_one__reorient)). 29.34/14.62 thf(818,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 29.34/14.62 thf(126,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_mult__le__mono1)). 29.34/14.62 thf(790,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 29.34/14.62 thf(149,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ D @ A) = (plus_plus_real @ B @ (plus_plus_real @ D @ C))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_group__cancel_Oadd2)). 29.34/14.62 thf(865,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ D @ A) = (plus_plus_real @ B @ (plus_plus_real @ D @ C))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 29.34/14.62 thf(111,axiom,((! [A:num,B:num]: ((A = B) | ~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_verit__la__disequality)). 29.34/14.62 thf(735,plain,((! [A:num,B:num]: ((A = B) | ~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 29.34/14.62 thf(189,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_ring__class_Oring__distribs_I2_J)). 29.34/14.62 thf(999,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 29.34/14.62 thf(77,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_138_distrib__left)). 29.34/14.62 thf(620,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)],[77])). 29.34/14.62 thf(139,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((B = one_one_nat) & (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_nat__1__eq__mult__iff)). 29.34/14.62 thf(833,plain,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((B = one_one_nat) & (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 29.34/14.62 thf(20,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_eq__diff__iff)). 29.34/14.62 thf(410,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 29.34/14.62 thf(320,axiom,((! [A:num]: (((numeral_numeral_nat @ A) = one_one_nat) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_numeral__eq__one__iff)). 29.34/14.62 thf(1436,plain,((! [A:num]: (((numeral_numeral_nat @ A) = one_one_nat) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 29.34/14.62 thf(288,axiom,((genClo2108747022bound1 = (^ [A:(nat > (real > real))]: ! [B:nat,C:real,D:real]: (((genClo1015804716orrect @ B @ D) & (ord_less_eq_real @ C @ D)) => (ord_less_eq_real @ (minus_minus_real @ (A @ B @ D) @ (A @ B @ C)) @ (times_times_real @ (minus_minus_real @ D @ C) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_rho__bound1__def)). 29.34/14.62 thf(1335,plain,(((genClo2108747022bound1) = (^ [A:(nat > (real > real))]: ! [B:nat,C:real,D:real]: (((genClo1015804716orrect @ B @ D) & (ord_less_eq_real @ C @ D)) => (ord_less_eq_real @ (minus_minus_real @ (A @ B @ D) @ (A @ B @ C)) @ (times_times_real @ (minus_minus_real @ D @ C) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 29.34/14.62 thf(119,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_diff__add)). 29.34/14.62 thf(767,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 29.34/14.62 thf(250,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => (ord_less_eq_real @ A @ (minus_minus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_add__le__imp__le__diff)). 29.34/14.62 thf(1197,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => (ord_less_eq_real @ A @ (minus_minus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 29.34/14.62 thf(213,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ C @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ordered__ring__class_Ole__add__iff2)). 29.34/14.62 thf(1065,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ C @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 29.34/14.62 thf(173,axiom,((ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Eq2)). 29.34/14.62 thf(955,plain,((ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 29.34/14.62 thf(296,axiom,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_left__add__twice)). 29.34/14.62 thf(1363,plain,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 29.34/14.62 thf(283,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_ab__semigroup__mult__class_Omult__ac_I1_J)). 29.34/14.62 thf(1314,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 29.34/14.62 thf(141,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse)). 29.34/14.62 thf(839,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 29.34/14.62 thf(108,axiom,((plus_plus_real = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Ocommute)). 29.34/14.62 thf(728,plain,(((plus_plus_real) = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 29.34/14.62 thf(185,axiom,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ (minus_minus_real @ B @ D)) @ (times_times_real @ (minus_minus_real @ A @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_mult__diff__mult)). 29.34/14.62 thf(987,plain,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ (minus_minus_real @ B @ D)) @ (times_times_real @ (minus_minus_real @ A @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 29.34/14.62 thf(270,axiom,((! [A:real,B:real,C:num]: ((times_times_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ C)) = (minus_minus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_left__diff__distrib__numeral)). 29.34/14.62 thf(1261,plain,((! [A:real,B:real,C:num]: ((times_times_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ C)) = (minus_minus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 29.34/14.62 thf(62,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_order_Otrans)). 29.34/14.62 thf(575,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 29.34/14.62 thf(69,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ A @ B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_add__mono__thms__linordered__semiring_I3_J)). 29.34/14.62 thf(596,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ A @ B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 29.34/14.62 thf(35,axiom,((! [A:num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_one__le__numeral)). 29.34/14.62 thf(459,plain,((! [A:num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 29.34/14.62 thf(158,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_31_add__right__cancel)). 29.34/14.62 thf(908,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)],[158])). 29.34/14.62 thf(345,axiom,((! [A:num]: (((numeral_numeral_real @ A) = one_one_real) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_numeral__eq__one__iff)). 29.34/14.62 thf(1500,plain,((! [A:num]: (((numeral_numeral_real @ A) = one_one_real) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 29.34/14.62 thf(72,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__add__diff__inverse2)). 29.34/14.62 thf(607,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 29.34/14.62 thf(292,axiom,((genClo1015804716orrect @ q @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_corr__q)). 29.34/14.62 thf(1352,plain,((genClo1015804716orrect @ q @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 29.34/14.62 thf(37,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) => (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_add__right__imp__eq)). 29.34/14.62 thf(464,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) => (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 29.34/14.62 thf(285,axiom,((! [A:num,B:num,C:(num > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_order__subst2)). 29.34/14.62 thf(1320,plain,((! [A:num,B:num,C:(num > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 29.34/14.62 thf(162,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_Nat_Oex__has__greatest__nat)). 29.34/14.62 thf(923,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 29.34/14.62 thf(117,axiom,((! [A:num,B:(nat > num),C:nat,D:nat]: ((A = (B @ C)) => (((ord_less_eq_num @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F))))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_ord__eq__le__subst)). 29.34/14.62 thf(755,plain,((! [A:num,B:(nat > num),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 29.34/14.62 thf(45,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right)). 29.34/14.62 thf(496,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 29.34/14.62 thf(153,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_order__refl)). 29.34/14.62 thf(882,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 29.34/14.62 thf(180,axiom,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_one__plus__numeral)). 29.34/14.62 thf(972,plain,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 29.34/14.62 thf(331,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_linear)). 29.34/14.62 thf(1463,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 29.34/14.62 thf(88,axiom,((! [A:num,B:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_numeral__plus__numeral)). 29.34/14.62 thf(659,plain,((! [A:num,B:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 29.34/14.62 thf(68,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => (((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D) <= (ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B))) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_add__le__add__imp__diff__le)). 29.34/14.62 thf(592,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D) | ~ (ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 29.34/14.62 thf(333,axiom,((genClo2108747023bound2 @ d)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_rb2)). 29.34/14.62 thf(1468,plain,((genClo2108747023bound2 @ (d))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 29.34/14.62 thf(1576,plain,($false),inference(cvc4,[status(thm)],[1036,1337,1469,1168,941,666,481,365,1369,1083,962,468,777,555,523,1005,730,1068,1422,878,614,873,449,1497,384,500,1275,472,782,709,417,1366,436,1482,651,829,404,724,1430,504,1264,1511,802,1279,934,1462,542,1379,1247,870,1479,969,1115,1494,1232,1013,770,1415,475,1450,1136,1020,966,821,492,1465,1418,623,1526,1345,1433,428,1521,507,602,981,1447,956,1072,453,1119,774,439,678,793,1199,1153,381,1057,1311,534,1387,825,1255,1174,815,1238,1223,894,1042,952,1123,862,407,630,1032,852,1178,583,1210,1027,1128,1392,1159,461,1195,1407,456,842,1402,1360,1143,1270,948,610,420,742,578,697,1089,1534,1017,1138,356,884,1461,686,1424,526,489,1207,1039,547,706,1324,738,654,1192,1060,721,1002,1456,1382,984,911,938,1241,805,1054,398,1185,586,662,1273,856,745,689,733,513,1146,975,423,1007,1389,1226,545,1488,936,787,713,1332,919,1356,1139,1503,1258,704,681,1282,1524,362,434,1307,377,990,996,1376,1439,1471,1080,367,1149,626,1022,1293,932,811,387,799,1162,848,700,520,1171,1474,959,636,780,1015,394,1250,1445,1528,675,1304,795,374,617,355,1181,836,1049,426,1166,557,580,640,1025,1156,1400,887,414,1267,1531,993,370,717,1235,1317,1085,359,1130,643,1220,951,808,1285,1218,1404,1141,656,1427,978,571,1372,612,859,1240,1353,600,1485,1052,845,1421,1459,671,1412,891,1126,1189,1010,1453,1385,1476,748,1062,390,632,401,1244,588,1253,963,517,946,1101,914,510,667,929,478,763,1513,684,1442,1045,1030,1491,1133,1348,752,447,432,1097,1229,818,790,865,735,999,620,833,410,1436,1335,767,1197,1065,955,1363,1314,839,728,987,1261,575,596,459,908,1500,607,1352,464,1320,923,755,496,882,972,1463,659,592,1468])). 29.34/14.62 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 29.34/14.62 % [INFO] Killing All external provers ... 29.34/14.62 FINAL WATCH: 26.9 CPU 11.4 WC 29.34/14.62 Killed 1 orphans 29.34/14.62 Killed 1 orphans 29.34/14.62 Killed 1 orphans 29.34/14.62 EOF