0.00/0.02 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39 0.11/0.38 % Computer : n002.cluster.edu 0.11/0.38 % Model : x86_64 x86_64 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.38 % Memory : 8046.5625MB 0.11/0.38 % OS : Linux 6.8.0-71-generic 0.11/0.38 % CPULimit : 1440 0.11/0.38 % WCLimit : 180 0.11/0.38 % DateTime : Mon Jul 27 12:34:43 UTC 2026 0.11/0.38 % CPUTime : 0.11/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39 0.61/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 1.50/0.95 % [INFO] Parsing done (259ms). 1.50/0.95 % [INFO] Running in sequential loop mode. 2.48/1.16 % [INFO] eprover registered as external prover. 2.48/1.17 % [INFO] Scanning for conjecture ... 2.73/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ... 3.04/1.33 % [INFO] Axiom selection finished. Selected 213 axioms (removed 142 axioms). 3.50/1.48 % [INFO] Problem is higher-order (TPTP THF). 3.87/1.50 % [INFO] Type checking passed. 3.87/1.50 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 84.22/18.16 % External prover 'e' found a proof! 84.22/18.16 % [INFO] Killing All external provers ... 84.22/18.17 % Time passed: 17693ms (effective reasoning time: 17208ms) 84.22/18.17 % Solved by strategy 84.22/18.17 % Axioms used in derivation (213): fact_17_polymul_Osimps_I14_J, fact_288_combine__common__factor, fact_29_Ipoly_Osimps_I6_J, fact_341_poly__cmul_Osimps_I5_J, fact_279_add__mono__thms__linordered__semiring_I4_J, fact_207_poly__deriv_Osimps_I3_J, fact_33_poly_Odistinct_I35_J, fact_198_headconst_Osimps_I2_J, fact_256_poly__deriv__aux_Osimps_I6_J, fact_262_add__is__0, fact_126_zero__reorient, fact_32_poly_Odistinct_I49_J, fact_44_polymul_Osimps_I24_J, fact_166_shift1__nz, fact_275_isnpolyh_Osimps_I8_J, fact_170_shift1__def, fact_290_distrib__right, help_If_2_1_If_001t__Nat__Onat_T, fact_249_degreen_Osimps_I3_J, fact_144_mult__left__cancel, fact_332_crossproduct__eq, fact_65_polymul__eq0__iff, fact_62_polymul__1_I2_J, fact_50_isnpolyh_Osimps_I4_J, fact_206_degree__npolyhCN, fact_284_add_Oleft__commute, fact_36_poly_Odistinct_I29_J, fact_110_mult__cancel__right2, fact_246_degreen_Osimps_I6_J, fact_150_comm__monoid__mult__class_Omult__1, fact_104_polymul_Osimps_I23_J, fact_52_isnpolyh_Osimps_I1_J, fact_57_polymul_Osimps_I6_J, fact_83_poly_Odistinct_I15_J, fact_169_shift1__isnpoly, fact_324_behead_Osimps_I8_J, fact_348_poly__deriv_Osimps_I7_J, fact_333_Euclid__induct, fact_322_behead_Osimps_I3_J, fact_7_polymul_Osimps_I20_J, fact_72_poly_Oinject_I2_J, fact_30_Ipoly_Osimps_I1_J, fact_107_mult__cancel__left1, fact_138_mult__not__zero, fact_124_mult__eq__0__iff, fact_147_zero__neq__one, fact_176_headconst__zero, fact_300_poly_Odistinct_I11_J, fact_92_polymul_Osimps_I5_J, fact_77_poly_Odistinct_I25_J, fact_261_add__right__cancel, fact_216_degree_Osimps_I3_J, fact_310_polymul_Osimps_I28_J, fact_267_add__cancel__right__left, fact_316_behead_Osimps_I2_J, fact_179_polysubst0_Osimps_I8_J, fact_90_polymul_Osimps_I17_J, fact_292_distrib__left, fact_70_polymul_Osimps_I3_J, fact_5_wf__bs__polyul, fact_15_polymul_Osimps_I26_J, fact_230_funpow__isnpolyh, fact_303_polymul_Osimps_I22_J, fact_213_degree_Osimps_I6_J, fact_306_Ipoly_Osimps_I4_J, fact_58_isnpolyh__zero__iff, fact_75_poly__cmul_Osimps_I3_J, fact_100_isnpoly__def, fact_264_zero__eq__add__iff__both__eq__0, fact_140_divisors__zero, fact_61_polymul__0_I1_J, fact_20_poly_Oinject_I8_J, fact_180_polysubst0_Osimps_I1_J, fact_26_poly_Oinject_I3_J, fact_280_group__cancel_Oadd1, fact_98_zero__normh, fact_152_mult_Ocomm__neutral, fact_2_nq, fact_260_add__left__cancel, fact_251_head_Osimps_I1_J, fact_12_polymul_Osimps_I1_J, fact_258_funpow__shift1__isnpoly, fact_136_one__reorient, fact_25_poly_Oinject_I5_J, fact_305_polymul_Osimps_I10_J, fact_335_polypow_Osimps_I1_J, fact_320_behead_Osimps_I4_J, fact_54_polynate__norm, fact_274_add__eq__self__zero, fact_351_polymul_Osimps_I7_J, fact_343_behead_Osimps_I7_J, fact_281_group__cancel_Oadd2, help_If_3_1_If_001t__Nat__Onat_T, fact_130_mult_Oassoc, fact_132_mult_Ocommute, fact_134_mult_Oleft__commute, fact_311_poly__cmul_Osimps_I8_J, fact_253_head__eq__headn0, fact_200_polysubst0_Osimps_I2_J, fact_116_mult__cancel__right, fact_259_funpow__shift1, fact_192_headn_Osimps_I3_J, fact_74_polynate_Osimps_I1_J, fact_294_comm__semiring__class_Odistrib, help_If_1_1_If_001t__Nat__Onat_T, fact_308_polymul_Osimps_I16_J, fact_339_behead_Osimps_I5_J, fact_69_poly__cmul_Osimps_I6_J, fact_105_polymul_Osimps_I2_J, fact_295_ring__class_Oring__distribs_I1_J, fact_214_degree_Osimps_I4_J, fact_159_shift1__isnpolyh, fact_55_isnpolyh__unique, fact_108_mult__cancel__left2, fact_142_no__zero__divisors, fact_194_wf__bs__polysub, fact_285_add__left__imp__eq, fact_109_mult__cancel__right1, fact_283_add_Ocommute, fact_190_headn_Osimps_I4_J, fact_28_polynate, fact_146_mult__right__cancel, fact_263_Nat_Oadd__0__right, fact_86_isnpolyh_Osimps_I3_J, fact_328_add__0__iff, fact_219_poly__deriv_Osimps_I1_J, fact_266_add__cancel__right__right, fact_298_add_Ocomm__neutral, fact_225_funpow__0, fact_114_mult_Oleft__neutral, fact_184_polysubst0_Osimps_I4_J, fact_1_np, fact_334_verit__sum__simplify, fact_210_degree_Osimps_I2_J, fact_195_polysub__norm, fact_79_poly_Odistinct_I1_J, fact_239_head_Osimps_I3_J, fact_53_polynate_Osimps_I8_J, fact_327_add__scale__eq__noteq, fact_222_head__nz, fact_3_polymul__norm, fact_66_poly__cmul_Osimps_I4_J, fact_202_polysub__0, fact_338_degreen_Oelims, fact_347_poly__deriv_Osimps_I5_J, fact_242_head__isnpolyh, fact_330_crossproduct__noteq, fact_269_add__cancel__left__left, fact_148_zero__neq__one, fact_296_ring__class_Oring__distribs_I2_J, fact_218_poly__deriv_Osimps_I2_J, fact_60_polymul__0_I2_J, fact_174_headn__nz, fact_93_poly__cmul_Osimps_I1_J, fact_10_polymul, fact_59_poly__cmul, fact_189_headn_Osimps_I6_J, fact_40_poly_Odistinct_I7_J, fact_314_behead, fact_64_polynate_Osimps_I7_J, fact_22_poly_Oinject_I1_J, fact_122_mult__zero__right, fact_349_polypow__normh, fact_278_ab__semigroup__add__class_Oadd__ac_I1_J, fact_282_add_Oassoc, fact_345_poly__cmul_Osimps_I7_J, fact_118_mult__cancel__left, fact_299_comm__monoid__add__class_Oadd__0, fact_37_poly_Odistinct_I13_J, fact_227_funpow__swap1, fact_243_degreen_Osimps_I2_J, fact_237_head_Osimps_I4_J, fact_128_ab__semigroup__mult__class_Omult__ac_I1_J, fact_9_polymul_Osimps_I8_J, fact_41_poly_Odistinct_I3_J, fact_13_polynate_Osimps_I4_J, fact_48_isnpolyh_Osimps_I6_J, fact_247_degreen_Osimps_I4_J, fact_96_one__normh, fact_63_polymul__1_I1_J, fact_233_head_Osimps_I2_J, fact_271_add_Oleft__neutral, fact_220_funpow__shift1__1, fact_135_one__reorient, fact_265_add__eq__0__iff__both__eq__0, fact_19_polymul_Osimps_I18_J, fact_102_polymul_Osimps_I11_J, fact_112_mult_Oright__neutral, fact_236_head_Osimps_I6_J, fact_255_poly__deriv__aux_Osimps_I2_J, fact_268_add__cancel__left__right, fact_286_add__right__imp__eq, fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062, fact_125_zero__reorient, fact_224_degreen__npolyhCN, fact_209_poly__deriv_Osimps_I6_J, fact_82_poly_Odistinct_I19_J, fact_315_behead__isnpolyh, fact_87_poly__cmul_Osimps_I2_J, fact_208_poly__deriv_Osimps_I4_J, fact_319_behead_Osimps_I6_J, fact_183_polysubst0_Osimps_I6_J, fact_186_headn_Osimps_I2_J, fact_297_poly_Odistinct_I47_J, fact_120_mult__zero__left, fact_157_shift1, fact_313_poly__deriv_Osimps_I8_J, fact_270_add_Oright__neutral, fact_177_polysub__same__0, fact_204_headnz, fact_196_headconst_Osimps_I1_J, fact_46_polymul_Osimps_I12_J, fact_273_plus__nat_Oadd__0 84.22/18.17 % No. of inferences in proof: 430 84.22/18.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17693 ms resp. 17208 ms w/o parsing 85.07/18.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 85.07/18.34 thf(polyno1532895200ly_nat_type, type, polyno1532895200ly_nat: $tType). 85.07/18.34 thf(polyno727731844poly_a_type, type, polyno727731844poly_a: $tType). 85.07/18.34 thf(list_nat_type, type, list_nat: $tType). 85.07/18.34 thf(list_a_type, type, list_a: $tType). 85.07/18.34 thf(nat_type, type, nat: $tType). 85.07/18.34 thf(a_type, type, a: $tType). 85.07/18.34 thf(one_one_nat_decl, type, one_one_nat: nat). 85.07/18.34 thf(one_one_a_decl, type, one_one_a: a). 85.07/18.34 thf(plus_plus_nat_decl, type, plus_plus_nat: (nat > (nat > nat))). 85.07/18.34 thf(plus_plus_a_decl, type, plus_plus_a: (a > (a > a))). 85.07/18.34 thf(times_times_a_decl, type, times_times_a: (a > (a > a))). 85.07/18.34 thf(zero_zero_nat_decl, type, zero_zero_nat: nat). 85.07/18.34 thf(zero_zero_a_decl, type, zero_zero_a: a). 85.07/18.34 thf(if_nat_decl, type, if_nat: ($o > (nat > (nat > nat)))). 85.07/18.34 thf(compow1114216044poly_a_decl, type, compow1114216044poly_a: (nat > ((polyno727731844poly_a > polyno727731844poly_a) > (polyno727731844poly_a > polyno727731844poly_a)))). 85.07/18.34 thf(polyno422358502poly_a_decl, type, polyno422358502poly_a: (list_a > (polyno727731844poly_a > a))). 85.07/18.34 thf(polyno1465139388head_a_decl, type, polyno1465139388head_a: (polyno727731844poly_a > polyno727731844poly_a)). 85.07/18.34 thf(polyno578545843gree_a_decl, type, polyno578545843gree_a: (polyno727731844poly_a > nat)). 85.07/18.34 thf(polyno1674775833reen_a_decl, type, polyno1674775833reen_a: (polyno727731844poly_a > (nat > nat))). 85.07/18.34 thf(polyno1884029055head_a_decl, type, polyno1884029055head_a: (polyno727731844poly_a > polyno727731844poly_a)). 85.07/18.34 thf(polyno2115742616onst_a_decl, type, polyno2115742616onst_a: (polyno727731844poly_a > a)). 85.07/18.34 thf(polyno567601229eadn_a_decl, type, polyno567601229eadn_a: (polyno727731844poly_a > (nat > polyno727731844poly_a))). 85.07/18.34 thf(polyno190918219poly_a_decl, type, polyno190918219poly_a: (polyno727731844poly_a > $o)). 85.07/18.34 thf(polyno1372495879olyh_a_decl, type, polyno1372495879olyh_a: (polyno727731844poly_a > (nat > $o))). 85.07/18.34 thf(polyno1623170614_Add_a_decl, type, polyno1623170614_Add_a: (polyno727731844poly_a > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno2024845497ound_a_decl, type, polyno2024845497ound_a: (nat > polyno727731844poly_a)). 85.07/18.34 thf(polyno1057396216e_CN_a_decl, type, polyno1057396216e_CN_a: (polyno727731844poly_a > (nat > (polyno727731844poly_a > polyno727731844poly_a)))). 85.07/18.34 thf(polyno439679028le_C_a_decl, type, polyno439679028le_C_a: (a > polyno727731844poly_a)). 85.07/18.34 thf(polyno1491482291_Mul_a_decl, type, polyno1491482291_Mul_a: (polyno727731844poly_a > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno96675367_Neg_a_decl, type, polyno96675367_Neg_a: (polyno727731844poly_a > polyno727731844poly_a)). 85.07/18.34 thf(polyno1538138524e_Pw_a_decl, type, polyno1538138524e_Pw_a: (polyno727731844poly_a > (nat > polyno727731844poly_a))). 85.07/18.34 thf(polyno975704247_Sub_a_decl, type, polyno975704247_Sub_a: (polyno727731844poly_a > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno562434098cmul_a_decl, type, polyno562434098cmul_a: (a > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno212464073eriv_a_decl, type, polyno212464073eriv_a: (polyno727731844poly_a > polyno727731844poly_a)). 85.07/18.34 thf(polyno1006823949_aux_a_decl, type, polyno1006823949_aux_a: (a > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno1934269411ymul_a_decl, type, polyno1934269411ymul_a: (polyno727731844poly_a > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno955999183nate_a_decl, type, polyno955999183nate_a: (polyno727731844poly_a > polyno727731844poly_a)). 85.07/18.34 thf(polyno1371724751ypow_a_decl, type, polyno1371724751ypow_a: (nat > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno1418491367ysub_a_decl, type, polyno1418491367ysub_a: (polyno727731844poly_a > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno1397854436bst0_a_decl, type, polyno1397854436bst0_a: (polyno727731844poly_a > (polyno727731844poly_a > polyno727731844poly_a))). 85.07/18.34 thf(polyno784948432ift1_a_decl, type, polyno784948432ift1_a: (polyno727731844poly_a > polyno727731844poly_a)). 85.07/18.34 thf(polyno896877631f_bs_a_decl, type, polyno896877631f_bs_a: (list_a > (polyno727731844poly_a > $o))). 85.07/18.34 thf(n0_decl, type, n0: nat). 85.07/18.34 thf(n1_decl, type, n1: nat). 85.07/18.34 thf(p_decl, type, p: polyno727731844poly_a). 85.07/18.34 thf(q_decl, type, q: polyno727731844poly_a). 85.07/18.34 thf(189,axiom,((polyno1372495879olyh_a @ p @ n0)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_np)). 85.07/18.34 thf(878,plain,((polyno1372495879olyh_a @ p @ n0)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 85.07/18.34 thf(82,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat]: ((polyno1491482291_Mul_a @ A @ B) != (polyno1538138524e_Pw_a @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_poly_Odistinct_I47_J)). 85.07/18.34 thf(479,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat]: ~ ((polyno1491482291_Mul_a @ A @ B) = (polyno1538138524e_Pw_a @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 85.07/18.34 thf(43,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_add_Ocomm__neutral)). 85.07/18.34 thf(347,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 85.07/18.34 thf(179,axiom,((! [A:polyno727731844poly_a,B:nat]: (((polyno1934269411ymul_a @ A @ (polyno439679028le_C_a @ one_one_a)) = A) <= (polyno1372495879olyh_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_polymul__1_I1_J)). 85.07/18.34 thf(846,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1934269411ymul_a @ A @ (polyno439679028le_C_a @ one_one_a)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 85.07/18.34 thf(8,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_plus__nat_Oadd__0)). 85.07/18.34 thf(234,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 85.07/18.34 thf(123,axiom,((! [A:a]: ((times_times_a @ zero_zero_a @ A) = zero_zero_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mult__zero__left)). 85.07/18.34 thf(666,plain,((! [A:a]: ((times_times_a @ zero_zero_a @ A) = zero_zero_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 85.07/18.34 thf(13,axiom,((! [A:nat]: ((polyno578545843gree_a @ (polyno2024845497ound_a @ A)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_degree_Osimps_I3_J)). 85.07/18.34 thf(249,plain,((! [A:nat]: ((polyno578545843gree_a @ (polyno2024845497ound_a @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 85.07/18.34 thf(39,axiom,((! [A:a,B:a,C:a]: ((times_times_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_comm__semiring__class_Odistrib)). 85.07/18.34 thf(333,plain,((! [A:a,B:a,C:a]: ((times_times_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 85.07/18.34 thf(113,axiom,((polyno190918219poly_a = (^ [A:polyno727731844poly_a]: (polyno1372495879olyh_a @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_isnpoly__def)). 85.07/18.34 thf(628,plain,(((polyno190918219poly_a) = (^ [A:polyno727731844poly_a]: (polyno1372495879olyh_a @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 85.07/18.34 thf(55,axiom,((! [A:a,B:a,C:a,D:a]: ((plus_plus_a @ (times_times_a @ A @ B) @ (plus_plus_a @ (times_times_a @ C @ B) @ D)) = (plus_plus_a @ (times_times_a @ (plus_plus_a @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_combine__common__factor)). 85.07/18.34 thf(385,plain,((! [A:a,B:a,C:a,D:a]: ((plus_plus_a @ (times_times_a @ A @ B) @ (plus_plus_a @ (times_times_a @ C @ B) @ D)) = (plus_plus_a @ (times_times_a @ (plus_plus_a @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 85.07/18.34 thf(163,axiom,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno1623170614_Add_a @ B @ C)) = (plus_plus_a @ (polyno422358502poly_a @ A @ B) @ (polyno422358502poly_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_Ipoly_Osimps_I4_J)). 85.07/18.35 thf(797,plain,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno1623170614_Add_a @ B @ C)) = (plus_plus_a @ (polyno422358502poly_a @ A @ B) @ (polyno422358502poly_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 85.07/18.35 thf(138,axiom,(((polyno1371724751ypow_a @ zero_zero_nat) = (^ [A:polyno727731844poly_a]: (polyno439679028le_C_a @ one_one_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_polypow_Osimps_I1_J)). 85.07/18.35 thf(715,plain,(((polyno1371724751ypow_a @ zero_zero_nat) = (^ [A:polyno727731844poly_a]: (polyno439679028le_C_a @ one_one_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 85.07/18.35 thf(133,axiom,((! [A:polyno727731844poly_a,B:nat,C:nat]: ((polyno1372495879olyh_a @ A @ B) => (polyno1372495879olyh_a @ (polyno1371724751ypow_a @ C @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_polypow__normh)). 85.07/18.35 thf(698,plain,((! [A:polyno727731844poly_a,B:nat,C:nat]: ((polyno1372495879olyh_a @ A @ B) => (polyno1372495879olyh_a @ (polyno1371724751ypow_a @ C @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 85.07/18.35 thf(209,axiom,((! [A:a,B:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno96675367_Neg_a @ B)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno96675367_Neg_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_poly__cmul_Osimps_I7_J)). 85.07/18.35 thf(945,plain,((! [A:a,B:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno96675367_Neg_a @ B)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno96675367_Neg_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 85.07/18.35 thf(99,axiom,((polyno784948432ift1_a = (polyno1057396216e_CN_a @ (polyno439679028le_C_a @ zero_zero_a) @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_shift1__def)). 85.07/18.35 thf(538,plain,(((polyno784948432ift1_a) = (polyno1057396216e_CN_a @ (polyno439679028le_C_a @ zero_zero_a) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 85.07/18.35 thf(61,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_zero__reorient)). 85.07/18.35 thf(404,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 85.07/18.35 thf(197,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:nat]: ((polyno1934269411ymul_a @ A @ (polyno1538138524e_Pw_a @ B @ C)) = (polyno1491482291_Mul_a @ A @ (polyno1538138524e_Pw_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_polymul_Osimps_I22_J)). 85.07/18.35 thf(898,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:nat]: ((polyno1934269411ymul_a @ A @ (polyno1538138524e_Pw_a @ B @ C)) = (polyno1491482291_Mul_a @ A @ (polyno1538138524e_Pw_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 85.07/18.35 thf(136,axiom,((! [A:a,B:a]: ((polyno562434098cmul_a @ A @ (polyno439679028le_C_a @ B)) = (polyno439679028le_C_a @ (times_times_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_poly__cmul_Osimps_I1_J)). 85.07/18.35 thf(709,plain,((! [A:a,B:a]: ((polyno562434098cmul_a @ A @ (polyno439679028le_C_a @ B)) = (polyno439679028le_C_a @ (times_times_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 85.07/18.35 thf(192,axiom,((! [A:a,B:nat]: ((polyno562434098cmul_a @ A @ (polyno2024845497ound_a @ B)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno2024845497ound_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_poly__cmul_Osimps_I3_J)). 85.07/18.35 thf(885,plain,((! [A:a,B:nat]: ((polyno562434098cmul_a @ A @ (polyno2024845497ound_a @ B)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno2024845497ound_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 85.07/18.35 thf(26,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_add__eq__0__iff__both__eq__0)). 85.07/18.35 thf(288,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 85.07/18.35 thf(108,axiom,((! [A:a]: ((zero_zero_a = A) = (A = zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__reorient)). 85.07/18.35 thf(565,plain,((! [A:a]: ((zero_zero_a = A) = (A = zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 85.07/18.35 thf(57,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_add_Ocommute)). 85.07/18.35 thf(389,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 85.07/18.35 thf(140,axiom,((! [A:a,B:a,C:a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_mult_Oassoc)). 85.07/18.35 thf(719,plain,((! [A:a,B:a,C:a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 85.07/18.35 thf(159,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno212464073eriv_a @ (polyno1538138524e_Pw_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_poly__deriv_Osimps_I8_J)). 85.07/18.35 thf(785,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno212464073eriv_a @ (polyno1538138524e_Pw_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 85.07/18.35 thf(42,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/sandbox/benchmark/theBenchmark.p',fact_284_add_Oleft__commute)). 85.07/18.35 thf(344,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)],[42])). 85.07/18.35 thf(207,axiom,((! [A:a,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: (((A != zero_zero_a) => ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ B @ C @ D) @ (polyno439679028le_C_a @ A)) = (polyno1057396216e_CN_a @ (polyno1934269411ymul_a @ B @ (polyno439679028le_C_a @ A)) @ C @ (polyno1934269411ymul_a @ D @ (polyno439679028le_C_a @ A))))) & ((A = zero_zero_a) => ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ B @ C @ D) @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_polymul_Osimps_I3_J)). 85.07/18.35 thf(934,plain,((! [A:a,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: (((~ (A = zero_zero_a)) => ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ B @ C @ D) @ (polyno439679028le_C_a @ A)) = (polyno1057396216e_CN_a @ (polyno1934269411ymul_a @ B @ (polyno439679028le_C_a @ A)) @ C @ (polyno1934269411ymul_a @ D @ (polyno439679028le_C_a @ A))))) & ((A = zero_zero_a) => ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ B @ C @ D) @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 85.07/18.35 thf(106,axiom,((! [A:a,B:a]: ((A = (times_times_a @ A @ B)) = ((A = zero_zero_a) | (B = one_one_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_mult__cancel__left1)). 85.07/18.35 thf(559,plain,((! [A:a,B:a]: ((A = (times_times_a @ A @ B)) = ((A = zero_zero_a) | (B = one_one_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 85.07/18.35 thf(181,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1934269411ymul_a @ (polyno439679028le_C_a @ zero_zero_a) @ A) = (polyno439679028le_C_a @ zero_zero_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_polymul__0_I2_J)). 85.07/18.35 thf(853,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1934269411ymul_a @ (polyno439679028le_C_a @ zero_zero_a) @ A) = (polyno439679028le_C_a @ zero_zero_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 85.07/18.35 thf(156,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:polyno727731844poly_a]: ((polyno1623170614_Add_a @ A @ B) != (polyno1491482291_Mul_a @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_poly_Odistinct_I29_J)). 85.07/18.35 thf(770,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:polyno727731844poly_a]: ~ ((polyno1623170614_Add_a @ A @ B) = (polyno1491482291_Mul_a @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 85.07/18.35 thf(6,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1674775833reen_a @ (polyno1623170614_Add_a @ A @ B)) = (^ [C:nat]: (zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_degreen_Osimps_I4_J)). 85.07/18.35 thf(228,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1674775833reen_a @ (polyno1623170614_Add_a @ A @ B)) = (^ [C:nat]: (zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 85.07/18.35 thf(74,axiom,((! [A:nat]: ((polyno955999183nate_a @ (polyno2024845497ound_a @ A)) = (polyno1057396216e_CN_a @ (polyno439679028le_C_a @ zero_zero_a) @ A @ (polyno439679028le_C_a @ one_one_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_polynate_Osimps_I1_J)). 85.07/18.35 thf(448,plain,((! [A:nat]: ((polyno955999183nate_a @ (polyno2024845497ound_a @ A)) = (polyno1057396216e_CN_a @ (polyno439679028le_C_a @ zero_zero_a) @ A @ (polyno439679028le_C_a @ one_one_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 85.07/18.35 thf(17,axiom,((! [A:a]: ((polyno1674775833reen_a @ (polyno439679028le_C_a @ A)) = (^ [B:nat]: (zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_degreen_Osimps_I2_J)). 85.07/18.35 thf(261,plain,((! [A:a]: ((polyno1674775833reen_a @ (polyno439679028le_C_a @ A)) = (^ [B:nat]: (zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 85.07/18.35 thf(1,conjecture,(((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 85.07/18.35 thf(2,negated_conjecture,((~ ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p)))),inference(neg_conjecture,[status(cth)],[1])). 85.07/18.35 thf(216,plain,((~ ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 85.07/18.35 thf(86,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:polyno727731844poly_a]: (((polyno1491482291_Mul_a @ A @ B) = (polyno1491482291_Mul_a @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_poly_Oinject_I5_J)). 85.07/18.35 thf(492,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:polyno727731844poly_a]: (((polyno1491482291_Mul_a @ A @ B) = (polyno1491482291_Mul_a @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 85.07/18.35 thf(35,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_add__cancel__left__left)). 85.07/18.35 thf(321,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 85.07/18.35 thf(52,axiom,((polyno1884029055head_a = (^ [A:polyno727731844poly_a]: (polyno567601229eadn_a @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_head__eq__headn0)). 85.07/18.35 thf(376,plain,(((polyno1884029055head_a) = (^ [A:polyno727731844poly_a]: (polyno567601229eadn_a @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 85.07/18.35 thf(175,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno1623170614_Add_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_poly__deriv_Osimps_I4_J)). 85.07/18.35 thf(834,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno1623170614_Add_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 85.07/18.35 thf(111,axiom,((! [A:polyno727731844poly_a,B:(nat > nat)]: (((! [C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((B != (^ [F:nat]: (if_nat @ (D = F) @ (plus_plus_nat @ one_one_nat @ (polyno1674775833reen_a @ E @ D)) @ zero_zero_nat))) <= (A = (polyno1057396216e_CN_a @ C @ D @ E)))) => ((((((((? [C:polyno727731844poly_a]: (A = (polyno96675367_Neg_a @ C))) => (B != (^ [C:nat]: (zero_zero_nat)))) => (~ ((B != (^ [C:nat]: (zero_zero_nat))) <= (? [C:polyno727731844poly_a,D:nat]: (A = (polyno1538138524e_Pw_a @ C @ D)))))) <= ((B != (^ [C:nat]: (zero_zero_nat))) <= (? [C:polyno727731844poly_a,D:polyno727731844poly_a]: (A = (polyno1491482291_Mul_a @ C @ D))))) <= ((B != (^ [C:nat]: (zero_zero_nat))) <= (? [C:polyno727731844poly_a,D:polyno727731844poly_a]: (A = (polyno975704247_Sub_a @ C @ D))))) <= ((? [C:polyno727731844poly_a,D:polyno727731844poly_a]: (A = (polyno1623170614_Add_a @ C @ D))) => (B != (^ [C:nat]: (zero_zero_nat))))) <= ((? [C:nat]: (A = (polyno2024845497ound_a @ C))) => (B != (^ [C:nat]: (zero_zero_nat))))) <= ((? [C:a]: (A = (polyno439679028le_C_a @ C))) => (B != (^ [C:nat]: (zero_zero_nat)))))) <= ((polyno1674775833reen_a @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_degreen_Oelims)). 85.07/18.35 thf(574,plain,((! [A:polyno727731844poly_a,B:(nat > nat)]: (((polyno1674775833reen_a @ A) = (B)) => ((! [C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((A = (polyno1057396216e_CN_a @ C @ D @ E)) => (~ ((B) = (^ [F:nat]: (if_nat @ (D = F) @ (plus_plus_nat @ one_one_nat @ (polyno1674775833reen_a @ E @ D)) @ zero_zero_nat)))))) => (((? [C:a]: (A = (polyno439679028le_C_a @ C))) => (~ ((B) = (^ [C:nat]: (zero_zero_nat))))) => (((? [C:nat]: (A = (polyno2024845497ound_a @ C))) => (~ ((B) = (^ [C:nat]: (zero_zero_nat))))) => (((? [C:polyno727731844poly_a,D:polyno727731844poly_a]: (A = (polyno1623170614_Add_a @ C @ D))) => (~ ((B) = (^ [C:nat]: (zero_zero_nat))))) => (((? [C:polyno727731844poly_a,D:polyno727731844poly_a]: (A = (polyno975704247_Sub_a @ C @ D))) => (~ ((B) = (^ [C:nat]: (zero_zero_nat))))) => (((? [C:polyno727731844poly_a,D:polyno727731844poly_a]: (A = (polyno1491482291_Mul_a @ C @ D))) => (~ ((B) = (^ [C:nat]: (zero_zero_nat))))) => (((? [C:polyno727731844poly_a]: (A = (polyno96675367_Neg_a @ C))) => (~ ((B) = (^ [C:nat]: (zero_zero_nat))))) => (~ ((? [C:polyno727731844poly_a,D:nat]: (A = (polyno1538138524e_Pw_a @ C @ D))) => (~ ((B) = (^ [C:nat]: (zero_zero_nat)))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 85.07/18.35 thf(45,axiom,((! [A:a,B:a,C:a]: ((times_times_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_ring__class_Oring__distribs_I2_J)). 85.07/18.35 thf(353,plain,((! [A:a,B:a,C:a]: ((times_times_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 85.07/18.35 thf(171,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1372495879olyh_a @ (polyno784948432ift1_a @ A) @ zero_zero_nat) <= (A != (polyno439679028le_C_a @ zero_zero_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_shift1__isnpolyh)). 85.07/18.35 thf(821,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((~ (A = (polyno439679028le_C_a @ zero_zero_a))) => (polyno1372495879olyh_a @ (polyno784948432ift1_a @ A) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 85.07/18.35 thf(131,axiom,((! [A:(polyno727731844poly_a > polyno727731844poly_a),B:nat,C:polyno727731844poly_a]: ((A @ (compow1114216044poly_a @ B @ A @ C)) = (compow1114216044poly_a @ B @ A @ (A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_funpow__swap1)). 85.07/18.35 thf(692,plain,((! [A:(polyno727731844poly_a > polyno727731844poly_a),B:nat,C:polyno727731844poly_a]: ((A @ (compow1114216044poly_a @ B @ (A) @ C)) = (compow1114216044poly_a @ B @ (A) @ (A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 85.07/18.35 thf(4,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => (polyno1372495879olyh_a @ (polyno1884029055head_a @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_head__isnpolyh)). 85.07/18.35 thf(221,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => (polyno1372495879olyh_a @ (polyno1884029055head_a @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 85.07/18.35 thf(185,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1538138524e_Pw_a @ A @ B) @ C) = (polyno1491482291_Mul_a @ (polyno1538138524e_Pw_a @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_polymul_Osimps_I10_J)). 85.07/18.35 thf(866,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1538138524e_Pw_a @ A @ B) @ C) = (polyno1491482291_Mul_a @ (polyno1538138524e_Pw_a @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 85.07/18.35 thf(157,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((! [C:list_a]: ((polyno896877631f_bs_a @ C @ A) => ((polyno422358502poly_a @ C @ A) = zero_zero_a))) => (A = (polyno439679028le_C_a @ zero_zero_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_isnpolyh__zero__iff)). 85.07/18.35 thf(774,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((! [C:list_a]: ((polyno896877631f_bs_a @ C @ A) => ((polyno422358502poly_a @ C @ A) = zero_zero_a))) => (A = (polyno439679028le_C_a @ zero_zero_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 85.07/18.35 thf(121,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno567601229eadn_a @ (polyno1623170614_Add_a @ A @ B)) = (^ [C:nat]: (polyno1623170614_Add_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_headn_Osimps_I4_J)). 85.07/18.35 thf(660,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno567601229eadn_a @ (polyno1623170614_Add_a @ A @ B)) = (^ [C:nat]: (polyno1623170614_Add_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 85.07/18.35 thf(11,axiom,((! [A:a]: ((polyno567601229eadn_a @ (polyno439679028le_C_a @ A)) = (^ [B:nat]: (polyno439679028le_C_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_headn_Osimps_I2_J)). 85.07/18.35 thf(243,plain,((! [A:a]: ((polyno567601229eadn_a @ (polyno439679028le_C_a @ A)) = (^ [B:nat]: (polyno439679028le_C_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 85.07/18.35 thf(68,axiom,((! [A:nat]: ((polyno1465139388head_a @ (polyno2024845497ound_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_behead_Osimps_I3_J)). 85.07/18.35 thf(428,plain,((! [A:nat]: ((polyno1465139388head_a @ (polyno2024845497ound_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 85.07/18.35 thf(34,axiom,((! [A:nat,B:polyno727731844poly_a]: ((((polyno1397854436bst0_a @ B @ (polyno2024845497ound_a @ A)) = B) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => ((polyno1397854436bst0_a @ B @ (polyno2024845497ound_a @ A)) = (polyno2024845497ound_a @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_polysubst0_Osimps_I2_J)). 85.07/18.35 thf(312,plain,((! [A:nat,B:polyno727731844poly_a]: (((A = zero_zero_nat) => ((polyno1397854436bst0_a @ B @ (polyno2024845497ound_a @ A)) = B)) & ((~ (A = zero_zero_nat)) => ((polyno1397854436bst0_a @ B @ (polyno2024845497ound_a @ A)) = (polyno2024845497ound_a @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 85.07/18.35 thf(127,axiom,((! [A:nat,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno2024845497ound_a @ A) != (polyno1491482291_Mul_a @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_poly_Odistinct_I19_J)). 85.07/18.35 thf(678,plain,((! [A:nat,B:polyno727731844poly_a,C:polyno727731844poly_a]: ~ ((polyno2024845497ound_a @ A) = (polyno1491482291_Mul_a @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 85.07/18.35 thf(102,axiom,((! [A:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno96675367_Neg_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_poly__deriv_Osimps_I7_J)). 85.07/18.35 thf(546,plain,((! [A:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno96675367_Neg_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 85.07/18.35 thf(204,axiom,((! [A:nat,B:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno2024845497ound_a @ A) @ B) = (polyno1491482291_Mul_a @ (polyno2024845497ound_a @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_polymul_Osimps_I5_J)). 85.07/18.35 thf(925,plain,((! [A:nat,B:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno2024845497ound_a @ A) @ B) = (polyno1491482291_Mul_a @ (polyno2024845497ound_a @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 85.07/18.35 thf(153,axiom,((! [A:a]: ((times_times_a @ A @ one_one_a) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_mult_Oright__neutral)). 85.07/18.35 thf(761,plain,((! [A:a]: ((times_times_a @ A @ one_one_a) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 85.07/18.35 thf(167,axiom,((! [A:list_a,B:a,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno562434098cmul_a @ B @ C)) = (polyno422358502poly_a @ A @ (polyno1491482291_Mul_a @ (polyno439679028le_C_a @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_poly__cmul)). 85.07/18.35 thf(810,plain,((! [A:list_a,B:a,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno562434098cmul_a @ B @ C)) = (polyno422358502poly_a @ A @ (polyno1491482291_Mul_a @ (polyno439679028le_C_a @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 85.07/18.35 thf(54,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D)) <= ((C = D) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_add__mono__thms__linordered__semiring_I4_J)). 85.07/18.35 thf(381,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)],[54])). 85.07/18.35 thf(98,axiom,((! [A:nat,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno2024845497ound_a @ A) != (polyno1623170614_Add_a @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_poly_Odistinct_I15_J)). 85.07/18.35 thf(534,plain,((! [A:nat,B:polyno727731844poly_a,C:polyno727731844poly_a]: ~ ((polyno2024845497ound_a @ A) = (polyno1623170614_Add_a @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 85.07/18.35 thf(92,axiom,((! [A:list_a,B:nat,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (compow1114216044poly_a @ B @ polyno784948432ift1_a @ C)) = (polyno422358502poly_a @ A @ (polyno1491482291_Mul_a @ (polyno1538138524e_Pw_a @ (polyno2024845497ound_a @ zero_zero_nat) @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_funpow__shift1)). 85.07/18.35 thf(512,plain,((! [A:list_a,B:nat,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (compow1114216044poly_a @ B @ (polyno784948432ift1_a) @ C)) = (polyno422358502poly_a @ A @ (polyno1491482291_Mul_a @ (polyno1538138524e_Pw_a @ (polyno2024845497ound_a @ zero_zero_nat) @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 85.07/18.35 thf(208,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:polyno727731844poly_a,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1623170614_Add_a @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1623170614_Add_a @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_polymul_Osimps_I12_J)). 85.07/18.35 thf(942,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:polyno727731844poly_a,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1623170614_Add_a @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1623170614_Add_a @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 85.07/18.35 thf(71,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1465139388head_a @ (polyno975704247_Sub_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_behead_Osimps_I5_J)). 85.07/18.35 thf(439,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1465139388head_a @ (polyno975704247_Sub_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 85.07/18.35 thf(20,axiom,((! [A:a,B:a,C:a]: ((times_times_a @ A @ (plus_plus_a @ B @ C)) = (plus_plus_a @ (times_times_a @ A @ B) @ (times_times_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_ring__class_Oring__distribs_I1_J)). 85.07/18.35 thf(270,plain,((! [A:a,B:a,C:a]: ((times_times_a @ A @ (plus_plus_a @ B @ C)) = (plus_plus_a @ (times_times_a @ A @ B) @ (times_times_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 85.07/18.35 thf(97,axiom,((! [A:nat,B:(polyno727731844poly_a > polyno727731844poly_a),C:polyno727731844poly_a,D:nat]: (((polyno1372495879olyh_a @ (compow1114216044poly_a @ D @ B @ C) @ A) <= (polyno1372495879olyh_a @ C @ A)) <= (! [E:polyno727731844poly_a]: ((polyno1372495879olyh_a @ (B @ E) @ A) <= (polyno1372495879olyh_a @ E @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_funpow__isnpolyh)). 85.07/18.35 thf(529,plain,((! [A:nat,B:(polyno727731844poly_a > polyno727731844poly_a),C:polyno727731844poly_a,D:nat]: ((! [E:polyno727731844poly_a]: ((polyno1372495879olyh_a @ E @ A) => (polyno1372495879olyh_a @ (B @ E) @ A))) => ((polyno1372495879olyh_a @ C @ A) => (polyno1372495879olyh_a @ (compow1114216044poly_a @ D @ (B) @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 85.07/18.35 thf(195,axiom,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1491482291_Mul_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_poly__cmul_Osimps_I6_J)). 85.07/18.35 thf(894,plain,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1491482291_Mul_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 85.07/18.35 thf(172,axiom,((! [A:polyno727731844poly_a]: (polyno190918219poly_a @ (polyno955999183nate_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_polynate__norm)). 85.07/18.35 thf(825,plain,((! [A:polyno727731844poly_a]: (polyno190918219poly_a @ (polyno955999183nate_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 85.07/18.35 thf(211,axiom,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: (((polyno896877631f_bs_a @ A @ (polyno1934269411ymul_a @ B @ C)) <= (polyno896877631f_bs_a @ A @ C)) <= (polyno896877631f_bs_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_wf__bs__polyul)). 85.07/18.35 thf(952,plain,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno896877631f_bs_a @ A @ B) => ((polyno896877631f_bs_a @ A @ C) => (polyno896877631f_bs_a @ A @ (polyno1934269411ymul_a @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 85.07/18.35 thf(184,axiom,((! [A:polyno727731844poly_a,B:nat]: (((polyno1934269411ymul_a @ (polyno439679028le_C_a @ one_one_a) @ A) = A) <= (polyno1372495879olyh_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_polymul__1_I2_J)). 85.07/18.35 thf(862,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1934269411ymul_a @ (polyno439679028le_C_a @ one_one_a) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 85.07/18.35 thf(29,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/sandbox/benchmark/theBenchmark.p',fact_282_add_Oassoc)). 85.07/18.35 thf(297,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)],[29])). 85.07/18.35 thf(143,axiom,((! [A:a]: ((times_times_a @ A @ zero_zero_a) = zero_zero_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_mult__zero__right)). 85.07/18.35 thf(729,plain,((! [A:a]: ((times_times_a @ A @ zero_zero_a) = zero_zero_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 85.07/18.35 thf(62,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_verit__sum__simplify)). 85.07/18.35 thf(407,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 85.07/18.35 thf(114,axiom,((! [A:polyno727731844poly_a,B:a]: ((polyno1397854436bst0_a @ A @ (polyno439679028le_C_a @ B)) = (polyno439679028le_C_a @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_polysubst0_Osimps_I1_J)). 85.07/18.35 thf(630,plain,((! [A:polyno727731844poly_a,B:a]: ((polyno1397854436bst0_a @ A @ (polyno439679028le_C_a @ B)) = (polyno439679028le_C_a @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 85.07/18.35 thf(22,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: (((polyno578545843gree_a @ A) = zero_zero_nat) <= (polyno1372495879olyh_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_degree__npolyhCN)). 85.07/18.35 thf(275,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: ((polyno1372495879olyh_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ D) => ((polyno578545843gree_a @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 85.07/18.35 thf(160,axiom,((! [A:a]: ((polyno1465139388head_a @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_behead_Osimps_I2_J)). 85.07/18.35 thf(788,plain,((! [A:a]: ((polyno1465139388head_a @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 85.07/18.35 thf(14,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_add__cancel__right__right)). 85.07/18.35 thf(252,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 85.07/18.35 thf(190,axiom,((! [A:a,B:polyno727731844poly_a,C:nat]: ((polyno562434098cmul_a @ A @ (polyno1538138524e_Pw_a @ B @ C)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1538138524e_Pw_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_poly__cmul_Osimps_I8_J)). 85.07/18.35 thf(879,plain,((! [A:a,B:polyno727731844poly_a,C:nat]: ((polyno562434098cmul_a @ A @ (polyno1538138524e_Pw_a @ B @ C)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1538138524e_Pw_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 85.07/18.35 thf(128,axiom,((! [A:nat,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ((polyno2024845497ound_a @ A) != (polyno1057396216e_CN_a @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_poly_Odistinct_I25_J)). 85.07/18.35 thf(682,plain,((! [A:nat,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ~ ((polyno2024845497ound_a @ A) = (polyno1057396216e_CN_a @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 85.07/18.35 thf(36,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno578545843gree_a @ (polyno1491482291_Mul_a @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_degree_Osimps_I6_J)). 85.07/18.35 thf(324,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno578545843gree_a @ (polyno1491482291_Mul_a @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 85.07/18.35 thf(25,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_add__eq__self__zero)). 85.07/18.35 thf(285,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 85.07/18.35 thf(210,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: (((((polyno1934269411ymul_a @ A @ C) = (polyno439679028le_C_a @ zero_zero_a)) = ((A = (polyno439679028le_C_a @ zero_zero_a)) | (C = (polyno439679028le_C_a @ zero_zero_a)))) <= (polyno1372495879olyh_a @ C @ D)) <= (polyno1372495879olyh_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_polymul__eq0__iff)). 85.07/18.35 thf(948,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1372495879olyh_a @ C @ D) => (((polyno1934269411ymul_a @ A @ C) = (polyno439679028le_C_a @ zero_zero_a)) = ((A = (polyno439679028le_C_a @ zero_zero_a)) | (C = (polyno439679028le_C_a @ zero_zero_a)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 85.07/18.35 thf(56,axiom,((! [A:$o]: ((A = ($true)) | (A = ($false))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Nat__Onat_T)). 85.07/18.35 thf(388,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 85.07/18.35 thf(46,axiom,((! [A:nat]: ((polyno1884029055head_a @ (polyno2024845497ound_a @ A)) = (polyno2024845497ound_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_head_Osimps_I3_J)). 85.07/18.35 thf(356,plain,((! [A:nat]: ((polyno1884029055head_a @ (polyno2024845497ound_a @ A)) = (polyno2024845497ound_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 85.07/18.35 thf(186,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno975704247_Sub_a @ A @ B) @ C) = (polyno1491482291_Mul_a @ (polyno975704247_Sub_a @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_polymul_Osimps_I7_J)). 85.07/18.35 thf(869,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno975704247_Sub_a @ A @ B) @ C) = (polyno1491482291_Mul_a @ (polyno975704247_Sub_a @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 85.07/18.35 thf(182,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1538138524e_Pw_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1538138524e_Pw_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_polymul_Osimps_I28_J)). 85.07/18.35 thf(857,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1538138524e_Pw_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1538138524e_Pw_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 85.07/18.35 thf(94,axiom,((times_times_a = (^ [A:a,B:a]: (times_times_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_mult_Ocommute)). 85.07/18.35 thf(519,plain,(((times_times_a) = (^ [A:a,B:a]: (times_times_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 85.07/18.35 thf(147,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1465139388head_a @ (polyno1491482291_Mul_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_behead_Osimps_I6_J)). 85.07/18.35 thf(742,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1465139388head_a @ (polyno1491482291_Mul_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 85.07/18.35 thf(124,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1372495879olyh_a @ (polyno1491482291_Mul_a @ A @ B)) = (^ [C:nat]: (($false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_isnpolyh_Osimps_I6_J)). 85.07/18.35 thf(669,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1372495879olyh_a @ (polyno1491482291_Mul_a @ A @ B)) = (^ [C:nat]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 85.07/18.35 thf(85,axiom,((! [A:a,B:a]: (((times_times_a @ A @ B) = A) = ((A = zero_zero_a) | (B = one_one_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_mult__cancel__left2)). 85.07/18.35 thf(489,plain,((! [A:a,B:a]: (((times_times_a @ A @ B) = A) = ((A = zero_zero_a) | (B = one_one_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 85.07/18.35 thf(198,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:polyno727731844poly_a,E:nat]: ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1538138524e_Pw_a @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1538138524e_Pw_a @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_polymul_Osimps_I16_J)). 85.07/18.35 thf(901,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:polyno727731844poly_a,E:nat]: ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1538138524e_Pw_a @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1538138524e_Pw_a @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 85.07/18.35 thf(129,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno975704247_Sub_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_poly__deriv_Osimps_I5_J)). 85.07/18.35 thf(686,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno975704247_Sub_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 85.07/18.35 thf(81,axiom,((! [A:a]: ((times_times_a @ A @ one_one_a) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_mult_Ocomm__neutral)). 85.07/18.35 thf(476,plain,((! [A:a]: ((times_times_a @ A @ one_one_a) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 85.07/18.35 thf(176,axiom,((! [A:a]: ((times_times_a @ one_one_a @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_comm__monoid__mult__class_Omult__1)). 85.07/18.35 thf(837,plain,((! [A:a]: ((times_times_a @ one_one_a @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 85.07/18.35 thf(134,axiom,((! [A:a,B:a,C:a]: ((((times_times_a @ B @ A) = (times_times_a @ C @ A)) = (B = C)) <= (A != zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_mult__right__cancel)). 85.07/18.35 thf(701,plain,((! [A:a,B:a,C:a]: ((~ (A = zero_zero_a)) => (((times_times_a @ B @ A) = (times_times_a @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 85.07/18.35 thf(93,axiom,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno439679028le_C_a @ A) != (polyno1623170614_Add_a @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_poly_Odistinct_I3_J)). 85.07/18.35 thf(515,plain,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ~ ((polyno439679028le_C_a @ A) = (polyno1623170614_Add_a @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 85.07/18.35 thf(9,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1674775833reen_a @ (polyno1491482291_Mul_a @ A @ B)) = (^ [C:nat]: (zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_degreen_Osimps_I6_J)). 85.07/18.35 thf(237,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1674775833reen_a @ (polyno1491482291_Mul_a @ A @ B)) = (^ [C:nat]: (zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 85.07/18.35 thf(115,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a]: ((polyno2115742616onst_a @ (polyno1057396216e_CN_a @ A @ B @ C)) = (polyno2115742616onst_a @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_headconst_Osimps_I1_J)). 85.07/18.35 thf(633,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a]: ((polyno2115742616onst_a @ (polyno1057396216e_CN_a @ A @ B @ C)) = (polyno2115742616onst_a @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 85.07/18.35 thf(120,axiom,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1006823949_aux_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (polyno562434098cmul_a @ A @ (polyno1491482291_Mul_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_poly__deriv__aux_Osimps_I6_J)). 85.07/18.35 thf(657,plain,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1006823949_aux_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (polyno562434098cmul_a @ A @ (polyno1491482291_Mul_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 85.07/18.35 thf(59,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_zero__neq__one)). 85.07/18.35 thf(398,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 85.07/18.35 thf(162,axiom,((! [A:a]: ((one_one_a = A) = (A = one_one_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_one__reorient)). 85.07/18.35 thf(794,plain,((! [A:a]: ((one_one_a = A) = (A = one_one_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 85.07/18.35 thf(193,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1623170614_Add_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1623170614_Add_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_polymul_Osimps_I24_J)). 85.07/18.35 thf(888,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1623170614_Add_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1623170614_Add_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 85.07/18.35 thf(67,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_add__0__iff)). 85.07/18.35 thf(425,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 85.07/18.35 thf(18,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_zero__eq__add__iff__both__eq__0)). 85.07/18.35 thf(264,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 85.07/18.35 thf(148,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1397854436bst0_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (polyno1491482291_Mul_a @ (polyno1397854436bst0_a @ A @ B) @ (polyno1397854436bst0_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_polysubst0_Osimps_I6_J)). 85.07/18.35 thf(745,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1397854436bst0_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (polyno1491482291_Mul_a @ (polyno1397854436bst0_a @ A @ B) @ (polyno1397854436bst0_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 85.07/18.35 thf(23,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno1057396216e_CN_a @ A @ zero_zero_nat @ B)) = (polyno1006823949_aux_a @ one_one_a @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_poly__deriv_Osimps_I1_J)). 85.07/18.35 thf(279,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno1057396216e_CN_a @ A @ zero_zero_nat @ B)) = (polyno1006823949_aux_a @ one_one_a @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 85.07/18.35 thf(130,axiom,((! [A:list_a,B:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno784948432ift1_a @ B)) = (polyno422358502poly_a @ A @ (polyno1491482291_Mul_a @ (polyno2024845497ound_a @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_shift1)). 85.07/18.35 thf(689,plain,((! [A:list_a,B:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno784948432ift1_a @ B)) = (polyno422358502poly_a @ A @ (polyno1491482291_Mul_a @ (polyno2024845497ound_a @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 85.07/18.35 thf(170,axiom,((! [A:nat]: (polyno1372495879olyh_a @ (polyno439679028le_C_a @ one_one_a) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_one__normh)). 85.07/18.35 thf(819,plain,((! [A:nat]: (polyno1372495879olyh_a @ (polyno439679028le_C_a @ one_one_a) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 85.07/18.35 thf(144,axiom,((! [A:polyno727731844poly_a,B:nat,C:nat]: ((polyno1372495879olyh_a @ A @ B) => (((polyno567601229eadn_a @ A @ C) = (polyno439679028le_C_a @ zero_zero_a)) = (A = (polyno439679028le_C_a @ zero_zero_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_headn__nz)). 85.07/18.35 thf(732,plain,((! [A:polyno727731844poly_a,B:nat,C:nat]: ((polyno1372495879olyh_a @ A @ B) => (((polyno567601229eadn_a @ A @ C) = (polyno439679028le_C_a @ zero_zero_a)) = (A = (polyno439679028le_C_a @ zero_zero_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 85.07/18.35 thf(178,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1934269411ymul_a @ A @ (polyno2024845497ound_a @ B)) = (polyno1491482291_Mul_a @ A @ (polyno2024845497ound_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_polymul_Osimps_I17_J)). 85.07/18.35 thf(843,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1934269411ymul_a @ A @ (polyno2024845497ound_a @ B)) = (polyno1491482291_Mul_a @ A @ (polyno2024845497ound_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 85.07/18.35 thf(188,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ A @ (polyno1623170614_Add_a @ B @ C)) = (polyno1491482291_Mul_a @ A @ (polyno1623170614_Add_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_polymul_Osimps_I18_J)). 85.07/18.35 thf(875,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ A @ (polyno1623170614_Add_a @ B @ C)) = (polyno1491482291_Mul_a @ A @ (polyno1623170614_Add_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 85.07/18.35 thf(27,axiom,((! [A:a,B:a,C:a,D:a]: (((A != B) & (C != D)) = ((plus_plus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ D)) != (plus_plus_a @ (times_times_a @ A @ D) @ (times_times_a @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_crossproduct__noteq)). 85.07/18.35 thf(291,plain,((! [A:a,B:a,C:a,D:a]: ((~ (A = B) & ~ (C = D)) = (~ ((plus_plus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ D)) = (plus_plus_a @ (times_times_a @ A @ D) @ (times_times_a @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 85.07/18.35 thf(213,axiom,((! [A:nat,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno2024845497ound_a @ A) @ (polyno1057396216e_CN_a @ B @ C @ D)) = (polyno1491482291_Mul_a @ (polyno2024845497ound_a @ A) @ (polyno1057396216e_CN_a @ B @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_polymul_Osimps_I23_J)). 85.07/18.35 thf(958,plain,((! [A:nat,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno2024845497ound_a @ A) @ (polyno1057396216e_CN_a @ B @ C @ D)) = (polyno1491482291_Mul_a @ (polyno2024845497ound_a @ A) @ (polyno1057396216e_CN_a @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 85.07/18.35 thf(107,axiom,((! [A:nat,B:nat]: (((polyno2024845497ound_a @ A) = (polyno2024845497ound_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_poly_Oinject_I2_J)). 85.07/18.35 thf(562,plain,((! [A:nat,B:nat]: (((polyno2024845497ound_a @ A) = (polyno2024845497ound_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 85.07/18.35 thf(199,axiom,((! [A:a,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ((((polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1057396216e_CN_a @ B @ C @ D)) = (polyno1057396216e_CN_a @ (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ B) @ C @ (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ D))) <= (A != zero_zero_a)) & (((polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1057396216e_CN_a @ B @ C @ D)) = (polyno439679028le_C_a @ zero_zero_a)) <= (A = zero_zero_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_polymul_Osimps_I2_J)). 85.07/18.35 thf(904,plain,((! [A:a,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: (((~ (A = zero_zero_a)) => ((polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1057396216e_CN_a @ B @ C @ D)) = (polyno1057396216e_CN_a @ (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ B) @ C @ (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ D)))) & ((A = zero_zero_a) => ((polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1057396216e_CN_a @ B @ C @ D)) = (polyno439679028le_C_a @ zero_zero_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 85.07/18.35 thf(58,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ D @ zero_zero_nat)) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ D @ (plus_plus_nat @ D @ E)))) => (A @ B @ C))) <= (! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_Euclid__induct)). 85.07/18.35 thf(391,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ D @ (plus_plus_nat @ D @ E)))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 85.07/18.35 thf(73,axiom,((! [A:a,B:a]: (((polyno439679028le_C_a @ A) = (polyno439679028le_C_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_poly_Oinject_I1_J)). 85.07/18.35 thf(445,plain,((! [A:a,B:a]: (((polyno439679028le_C_a @ A) = (polyno439679028le_C_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 85.07/18.35 thf(88,axiom,((! [A:a,B:a]: (((B != zero_zero_a) => ((times_times_a @ A @ B) != zero_zero_a)) <= (A != zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_no__zero__divisors)). 85.07/18.35 thf(498,plain,((! [A:a,B:a]: ((~ (A = zero_zero_a)) => ((~ (B = zero_zero_a)) => (~ ((times_times_a @ A @ B) = zero_zero_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 85.07/18.35 thf(78,axiom,((! [A:a,B:a]: (((times_times_a @ A @ B) = zero_zero_a) = ((A = zero_zero_a) | (B = zero_zero_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_mult__eq__0__iff)). 85.07/18.35 thf(466,plain,((! [A:a,B:a]: (((times_times_a @ A @ B) = zero_zero_a) = ((A = zero_zero_a) | (B = zero_zero_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 85.07/18.35 thf(44,axiom,((! [A:a,B:a,C:a]: ((times_times_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_distrib__right)). 85.07/18.35 thf(350,plain,((! [A:a,B:a,C:a]: ((times_times_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 85.07/18.35 thf(100,axiom,((! [A:a]: ((times_times_a @ one_one_a @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_mult_Oleft__neutral)). 85.07/18.35 thf(540,plain,((! [A:a]: ((times_times_a @ one_one_a @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 85.07/18.35 thf(125,axiom,((! [A:nat]: ((polyno1372495879olyh_a @ (polyno2024845497ound_a @ A)) = (^ [B:nat]: (($false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_isnpolyh_Osimps_I3_J)). 85.07/18.35 thf(672,plain,((! [A:nat]: ((polyno1372495879olyh_a @ (polyno2024845497ound_a @ A)) = (^ [B:nat]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 85.07/18.35 thf(154,axiom,((! [A:nat]: ((polyno567601229eadn_a @ (polyno2024845497ound_a @ A)) = (^ [B:nat]: (polyno2024845497ound_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_headn_Osimps_I3_J)). 85.07/18.35 thf(764,plain,((! [A:nat]: ((polyno567601229eadn_a @ (polyno2024845497ound_a @ A)) = (^ [B:nat]: (polyno2024845497ound_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 85.07/18.35 thf(174,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: (((polyno190918219poly_a @ B) => (polyno190918219poly_a @ (polyno1418491367ysub_a @ A @ B))) <= (polyno190918219poly_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_polysub__norm)). 85.07/18.35 thf(831,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno190918219poly_a @ A) => ((polyno190918219poly_a @ B) => (polyno190918219poly_a @ (polyno1418491367ysub_a @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 85.07/18.35 thf(145,axiom,((! [A:a]: ((polyno212464073eriv_a @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_poly__deriv_Osimps_I2_J)). 85.07/18.35 thf(736,plain,((! [A:a]: ((polyno212464073eriv_a @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 85.07/18.35 thf(31,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno578545843gree_a @ (polyno1623170614_Add_a @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_degree_Osimps_I4_J)). 85.07/18.35 thf(303,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno578545843gree_a @ (polyno1623170614_Add_a @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 85.07/18.35 thf(48,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_add__left__imp__eq)). 85.07/18.35 thf(362,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)],[48])). 85.07/18.35 thf(75,axiom,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (times_times_a @ (polyno422358502poly_a @ A @ B) @ (polyno422358502poly_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Ipoly_Osimps_I6_J)). 85.07/18.35 thf(451,plain,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (times_times_a @ (polyno422358502poly_a @ A @ B) @ (polyno422358502poly_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 85.07/18.35 thf(91,axiom,((! [A:a,B:a,C:a]: ((times_times_a @ A @ (times_times_a @ B @ C)) = (times_times_a @ B @ (times_times_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_mult_Oleft__commute)). 85.07/18.35 thf(509,plain,((! [A:a,B:a,C:a]: ((times_times_a @ A @ (times_times_a @ B @ C)) = (times_times_a @ B @ (times_times_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 85.07/18.35 thf(70,axiom,((! [A:a,B:a,C:a,D:a,E:a]: ((A != zero_zero_a) => (((plus_plus_a @ B @ (times_times_a @ A @ D)) != (plus_plus_a @ C @ (times_times_a @ A @ E))) <= ((B = C) & (D != E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_add__scale__eq__noteq)). 85.07/18.35 thf(434,plain,((! [A:a,B:a,C:a,D:a,E:a]: ((~ (A = zero_zero_a)) => (((B = C) & ~ (D = E)) => (~ ((plus_plus_a @ B @ (times_times_a @ A @ D)) = (plus_plus_a @ C @ (times_times_a @ A @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 85.07/18.35 thf(152,axiom,((! [A:a,B:a]: ((A = (times_times_a @ B @ A)) = ((B = one_one_a) | (A = zero_zero_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_mult__cancel__right1)). 85.07/18.35 thf(758,plain,((! [A:a,B:a]: ((A = (times_times_a @ B @ A)) = ((B = one_one_a) | (A = zero_zero_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 85.07/18.35 thf(49,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_add__is__0)). 85.07/18.35 thf(367,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 85.07/18.35 thf(169,axiom,((! [A:a,B:a,C:a]: (((times_times_a @ A @ B) = (times_times_a @ C @ B)) = ((A = C) | (B = zero_zero_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_mult__cancel__right)). 85.07/18.35 thf(816,plain,((! [A:a,B:a,C:a]: (((times_times_a @ A @ B) = (times_times_a @ C @ B)) = ((A = C) | (B = zero_zero_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 85.07/18.35 thf(142,axiom,((zero_zero_a != one_one_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_zero__neq__one)). 85.07/18.35 thf(726,plain,((~ (zero_zero_a = one_one_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 85.07/18.35 thf(83,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a]: ((polyno955999183nate_a @ (polyno1057396216e_CN_a @ A @ B @ C)) = (polyno955999183nate_a @ (polyno1623170614_Add_a @ A @ (polyno1491482291_Mul_a @ (polyno2024845497ound_a @ B) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_polynate_Osimps_I7_J)). 85.07/18.35 thf(483,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a]: ((polyno955999183nate_a @ (polyno1057396216e_CN_a @ A @ B @ C)) = (polyno955999183nate_a @ (polyno1623170614_Add_a @ A @ (polyno1491482291_Mul_a @ (polyno2024845497ound_a @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 85.07/18.35 thf(10,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_Nat_Oadd__0__right)). 85.07/18.35 thf(240,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 85.07/18.35 thf(215,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1623170614_Add_a @ A @ B) @ C) = (polyno1491482291_Mul_a @ (polyno1623170614_Add_a @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_polymul_Osimps_I6_J)). 85.07/18.35 thf(964,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1623170614_Add_a @ A @ B) @ C) = (polyno1491482291_Mul_a @ (polyno1623170614_Add_a @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 85.07/18.35 thf(201,axiom,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno1623170614_Add_a @ B @ C)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1623170614_Add_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_poly__cmul_Osimps_I4_J)). 85.07/18.35 thf(915,plain,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno1623170614_Add_a @ B @ C)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno1623170614_Add_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 85.07/18.35 thf(38,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_comm__monoid__add__class_Oadd__0)). 85.07/18.35 thf(330,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 85.07/18.35 thf(77,axiom,((! [A:polyno727731844poly_a,B:nat,C:list_a]: (((polyno422358502poly_a @ C @ (polyno1623170614_Add_a @ (polyno1491482291_Mul_a @ (polyno1884029055head_a @ A) @ (polyno1538138524e_Pw_a @ (polyno2024845497ound_a @ zero_zero_nat) @ (polyno578545843gree_a @ A))) @ (polyno1465139388head_a @ A))) = (polyno422358502poly_a @ C @ A)) <= (polyno1372495879olyh_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_behead)). 85.07/18.35 thf(462,plain,((! [A:polyno727731844poly_a,B:nat,C:list_a]: ((polyno1372495879olyh_a @ A @ B) => ((polyno422358502poly_a @ C @ (polyno1623170614_Add_a @ (polyno1491482291_Mul_a @ (polyno1884029055head_a @ A) @ (polyno1538138524e_Pw_a @ (polyno2024845497ound_a @ zero_zero_nat) @ (polyno578545843gree_a @ A))) @ (polyno1465139388head_a @ A))) = (polyno422358502poly_a @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 85.07/18.35 thf(173,axiom,((! [A:a,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ((polyno439679028le_C_a @ A) != (polyno1057396216e_CN_a @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_poly_Odistinct_I13_J)). 85.07/18.35 thf(827,plain,((! [A:a,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ~ ((polyno439679028le_C_a @ A) = (polyno1057396216e_CN_a @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 85.07/18.35 thf(5,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_group__cancel_Oadd2)). 85.07/18.35 thf(223,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 85.07/18.35 thf(32,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_add__right__cancel)). 85.07/18.35 thf(306,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)],[32])). 85.07/18.35 thf(19,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1884029055head_a @ (polyno1623170614_Add_a @ A @ B)) = (polyno1623170614_Add_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_head_Osimps_I4_J)). 85.07/18.35 thf(267,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1884029055head_a @ (polyno1623170614_Add_a @ A @ B)) = (polyno1623170614_Add_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 85.07/18.35 thf(69,axiom,((! [A:a,B:a]: (((times_times_a @ A @ B) = B) = ((B = zero_zero_a) | (A = one_one_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_mult__cancel__right2)). 85.07/18.35 thf(431,plain,((! [A:a,B:a]: (((times_times_a @ A @ B) = B) = ((B = zero_zero_a) | (A = one_one_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 85.07/18.35 thf(119,axiom,((! [A:a,B:nat]: ((polyno439679028le_C_a @ A) != (polyno2024845497ound_a @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_poly_Odistinct_I1_J)). 85.07/18.35 thf(653,plain,((! [A:a,B:nat]: ~ ((polyno439679028le_C_a @ A) = (polyno2024845497ound_a @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 85.07/18.35 thf(203,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (polyno1491482291_Mul_a @ A @ (polyno1491482291_Mul_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_polymul_Osimps_I20_J)). 85.07/18.35 thf(922,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ A @ (polyno1491482291_Mul_a @ B @ C)) = (polyno1491482291_Mul_a @ A @ (polyno1491482291_Mul_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 85.07/18.35 thf(200,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: (((polyno190918219poly_a @ (polyno1934269411ymul_a @ A @ B)) <= (polyno190918219poly_a @ B)) <= (polyno190918219poly_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_polymul__norm)). 85.07/18.35 thf(912,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno190918219poly_a @ A) => ((polyno190918219poly_a @ B) => (polyno190918219poly_a @ (polyno1934269411ymul_a @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 85.07/18.35 thf(95,axiom,((! [A:polyno727731844poly_a,B:nat]: ((((polyno2115742616onst_a @ A) = zero_zero_a) = (A = (polyno439679028le_C_a @ zero_zero_a))) <= (polyno1372495879olyh_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_headconst__zero)). 85.07/18.35 thf(521,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => (((polyno2115742616onst_a @ A) = zero_zero_a) = (A = (polyno439679028le_C_a @ zero_zero_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 85.07/18.35 thf(116,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((polyno1623170614_Add_a @ A @ B) != (polyno1057396216e_CN_a @ C @ D @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_poly_Odistinct_I35_J)). 85.07/18.35 thf(636,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ~ ((polyno1623170614_Add_a @ A @ B) = (polyno1057396216e_CN_a @ C @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 85.07/18.35 thf(132,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1372495879olyh_a @ (polyno1623170614_Add_a @ A @ B)) = (^ [C:nat]: (($false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_isnpolyh_Osimps_I4_J)). 85.07/18.35 thf(695,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1372495879olyh_a @ (polyno1623170614_Add_a @ A @ B)) = (^ [C:nat]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 85.07/18.35 thf(80,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1465139388head_a @ (polyno1538138524e_Pw_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_behead_Osimps_I8_J)). 85.07/18.35 thf(473,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1465139388head_a @ (polyno1538138524e_Pw_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 85.07/18.35 thf(141,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((polyno1491482291_Mul_a @ A @ B) != (polyno1057396216e_CN_a @ C @ D @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_poly_Odistinct_I49_J)). 85.07/18.35 thf(722,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ~ ((polyno1491482291_Mul_a @ A @ B) = (polyno1057396216e_CN_a @ C @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 85.07/18.35 thf(126,axiom,((! [A:a,B:a,C:a]: (((times_times_a @ A @ B) = (times_times_a @ A @ C)) = ((A = zero_zero_a) | (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_mult__cancel__left)). 85.07/18.35 thf(675,plain,((! [A:a,B:a,C:a]: (((times_times_a @ A @ B) = (times_times_a @ A @ C)) = ((A = zero_zero_a) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 85.07/18.35 thf(122,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:polyno727731844poly_a,E:nat,F:polyno727731844poly_a]: (((polyno1057396216e_CN_a @ A @ B @ C) = (polyno1057396216e_CN_a @ D @ E @ F)) = ((C = F) & (B = E) & (A = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_poly_Oinject_I8_J)). 85.07/18.35 thf(663,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:polyno727731844poly_a,E:nat,F:polyno727731844poly_a]: (((polyno1057396216e_CN_a @ A @ B @ C) = (polyno1057396216e_CN_a @ D @ E @ F)) = ((C = F) & (B = E) & (A = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 85.07/18.35 thf(15,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1884029055head_a @ (polyno1057396216e_CN_a @ A @ zero_zero_nat @ B)) = (polyno1884029055head_a @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_head_Osimps_I1_J)). 85.07/18.35 thf(255,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1884029055head_a @ (polyno1057396216e_CN_a @ A @ zero_zero_nat @ B)) = (polyno1884029055head_a @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 85.07/18.35 thf(104,axiom,((! [A:a,B:a,C:a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ab__semigroup__mult__class_Omult__ac_I1_J)). 85.07/18.35 thf(553,plain,((! [A:a,B:a,C:a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 85.07/18.35 thf(96,axiom,((! [A:polyno727731844poly_a,B:nat,C:nat]: ((((polyno567601229eadn_a @ A @ C) != (polyno439679028le_C_a @ zero_zero_a)) <= (A != (polyno439679028le_C_a @ zero_zero_a))) <= (polyno1372495879olyh_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_headnz)). 85.07/18.35 thf(525,plain,((! [A:polyno727731844poly_a,B:nat,C:nat]: ((polyno1372495879olyh_a @ A @ B) => ((~ (A = (polyno439679028le_C_a @ zero_zero_a))) => (~ ((polyno567601229eadn_a @ A @ C) = (polyno439679028le_C_a @ zero_zero_a))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 85.07/18.35 thf(137,axiom,((! [A:a,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno1057396216e_CN_a @ B @ C @ D)) = (polyno1057396216e_CN_a @ (polyno562434098cmul_a @ A @ B) @ C @ (polyno562434098cmul_a @ A @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_poly__cmul_Osimps_I2_J)). 85.07/18.35 thf(712,plain,((! [A:a,B:polyno727731844poly_a,C:nat,D:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno1057396216e_CN_a @ B @ C @ D)) = (polyno1057396216e_CN_a @ (polyno562434098cmul_a @ A @ B) @ C @ (polyno562434098cmul_a @ A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 85.07/18.35 thf(117,axiom,((! [A:polyno727731844poly_a]: ((polyno784948432ift1_a @ A) != (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_shift1__nz)). 85.07/18.35 thf(640,plain,((! [A:polyno727731844poly_a]: ~ ((polyno784948432ift1_a @ A) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 85.07/18.35 thf(187,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1491482291_Mul_a @ A @ B) @ C) = (polyno1491482291_Mul_a @ (polyno1491482291_Mul_a @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_polymul_Osimps_I8_J)). 85.07/18.35 thf(872,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1491482291_Mul_a @ A @ B) @ C) = (polyno1491482291_Mul_a @ (polyno1491482291_Mul_a @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 85.07/18.35 thf(37,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_add_Oright__neutral)). 85.07/18.35 thf(327,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 85.07/18.35 thf(146,axiom,((! [A:polyno727731844poly_a]: ((polyno1465139388head_a @ (polyno96675367_Neg_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_behead_Osimps_I7_J)). 85.07/18.35 thf(739,plain,((! [A:polyno727731844poly_a]: ((polyno1465139388head_a @ (polyno96675367_Neg_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 85.07/18.35 thf(135,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: ((polyno1372495879olyh_a @ A @ B) => (((! [E:list_a]: ((polyno422358502poly_a @ E @ A) = (polyno422358502poly_a @ E @ C))) = (A = C)) <= (polyno1372495879olyh_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_isnpolyh__unique)). 85.07/18.35 thf(705,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1372495879olyh_a @ C @ D) => ((! [E:list_a]: ((polyno422358502poly_a @ E @ A) = (polyno422358502poly_a @ E @ C))) = (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 85.07/18.35 thf(24,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno567601229eadn_a @ (polyno1491482291_Mul_a @ A @ B)) = (^ [C:nat]: (polyno1491482291_Mul_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_headn_Osimps_I6_J)). 85.07/18.35 thf(282,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno567601229eadn_a @ (polyno1491482291_Mul_a @ A @ B)) = (^ [C:nat]: (polyno1491482291_Mul_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 85.07/18.35 thf(161,axiom,((! [A:a,B:a]: ((polyno1006823949_aux_a @ A @ (polyno439679028le_C_a @ B)) = (polyno562434098cmul_a @ A @ (polyno439679028le_C_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_poly__deriv__aux_Osimps_I2_J)). 85.07/18.35 thf(791,plain,((! [A:a,B:a]: ((polyno1006823949_aux_a @ A @ (polyno439679028le_C_a @ B)) = (polyno562434098cmul_a @ A @ (polyno439679028le_C_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 85.07/18.35 thf(50,axiom,((! [A:a]: ((polyno1884029055head_a @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_head_Osimps_I2_J)). 85.07/18.35 thf(370,plain,((! [A:a]: ((polyno1884029055head_a @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 85.07/18.35 thf(139,axiom,((! [A:nat]: (polyno1372495879olyh_a @ (polyno439679028le_C_a @ zero_zero_a) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_zero__normh)). 85.07/18.35 thf(717,plain,((! [A:nat]: (polyno1372495879olyh_a @ (polyno439679028le_C_a @ zero_zero_a) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 85.07/18.35 thf(89,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => (((polyno1884029055head_a @ A) = (polyno439679028le_C_a @ zero_zero_a)) = (A = (polyno439679028le_C_a @ zero_zero_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_head__nz)). 85.07/18.35 thf(502,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => (((polyno1884029055head_a @ A) = (polyno439679028le_C_a @ zero_zero_a)) = (A = (polyno439679028le_C_a @ zero_zero_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 85.07/18.35 thf(177,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno955999183nate_a @ (polyno1491482291_Mul_a @ A @ B)) = (polyno1934269411ymul_a @ (polyno955999183nate_a @ A) @ (polyno955999183nate_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_polynate_Osimps_I4_J)). 85.07/18.35 thf(840,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno955999183nate_a @ (polyno1491482291_Mul_a @ A @ B)) = (polyno1934269411ymul_a @ (polyno955999183nate_a @ A) @ (polyno955999183nate_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 85.07/18.35 thf(47,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1884029055head_a @ (polyno1491482291_Mul_a @ A @ B)) = (polyno1491482291_Mul_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_head_Osimps_I6_J)). 85.07/18.35 thf(359,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1884029055head_a @ (polyno1491482291_Mul_a @ A @ B)) = (polyno1491482291_Mul_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 85.07/18.35 thf(40,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/sandbox/benchmark/theBenchmark.p',fact_280_group__cancel_Oadd1)). 85.07/18.35 thf(336,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)],[40])). 85.07/18.35 thf(110,axiom,((! [A:list_a,B:a]: ((polyno422358502poly_a @ A @ (polyno439679028le_C_a @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Ipoly_Osimps_I1_J)). 85.07/18.35 thf(571,plain,((! [A:list_a,B:a]: ((polyno422358502poly_a @ A @ (polyno439679028le_C_a @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 85.07/18.35 thf(7,axiom,((! [A:a,B:a,C:a,D:a]: (((plus_plus_a @ (times_times_a @ A @ B) @ (times_times_a @ C @ D)) = (plus_plus_a @ (times_times_a @ A @ D) @ (times_times_a @ C @ B))) = ((A = C) | (B = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_crossproduct__eq)). 85.07/18.35 thf(231,plain,((! [A:a,B:a,C:a,D:a]: (((plus_plus_a @ (times_times_a @ A @ B) @ (times_times_a @ C @ D)) = (plus_plus_a @ (times_times_a @ A @ D) @ (times_times_a @ C @ B))) = ((A = C) | (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 85.07/18.35 thf(105,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ (polyno1538138524e_Pw_a @ A @ B)) = (^ [C:nat]: (($false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_isnpolyh_Osimps_I8_J)). 85.07/18.35 thf(556,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ (polyno1538138524e_Pw_a @ A @ B)) = (^ [C:nat]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 85.07/18.35 thf(206,axiom,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno1934269411ymul_a @ B @ C)) = (times_times_a @ (polyno422358502poly_a @ A @ B) @ (polyno422358502poly_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_polymul)). 85.07/18.35 thf(931,plain,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno1934269411ymul_a @ B @ C)) = (times_times_a @ (polyno422358502poly_a @ A @ B) @ (polyno422358502poly_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 85.07/18.35 thf(87,axiom,((! [A:list_a,B:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno955999183nate_a @ B)) = (polyno422358502poly_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_polynate)). 85.07/18.35 thf(495,plain,((! [A:list_a,B:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (polyno955999183nate_a @ B)) = (polyno422358502poly_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 85.07/18.35 thf(194,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno2024845497ound_a @ D)) = (polyno1491482291_Mul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno2024845497ound_a @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_polymul_Osimps_I11_J)). 85.07/18.35 thf(891,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno2024845497ound_a @ D)) = (polyno1491482291_Mul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno2024845497ound_a @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 85.07/18.35 thf(3,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_add__left__cancel)). 85.07/18.35 thf(218,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)],[3])). 85.07/18.35 thf(149,axiom,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno439679028le_C_a @ A) != (polyno1491482291_Mul_a @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_poly_Odistinct_I7_J)). 85.07/18.35 thf(748,plain,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ~ ((polyno439679028le_C_a @ A) = (polyno1491482291_Mul_a @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 85.07/18.35 thf(16,axiom,((! [A:a,B:a,C:a]: ((times_times_a @ A @ (plus_plus_a @ B @ C)) = (plus_plus_a @ (times_times_a @ A @ B) @ (times_times_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_distrib__left)). 85.07/18.35 thf(258,plain,((! [A:a,B:a,C:a]: ((times_times_a @ A @ (plus_plus_a @ B @ C)) = (plus_plus_a @ (times_times_a @ A @ B) @ (times_times_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 85.07/18.35 thf(60,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_add__cancel__left__right)). 85.07/18.35 thf(401,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 85.07/18.35 thf(65,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: (((polyno1674775833reen_a @ A @ B) = zero_zero_nat) <= (polyno1372495879olyh_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_degreen__npolyhCN)). 85.07/18.35 thf(418,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: ((polyno1372495879olyh_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ D) => ((polyno1674775833reen_a @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 85.07/18.35 thf(158,axiom,((! [A:a,B:a,C:a]: ((A != zero_zero_a) => (((times_times_a @ A @ B) = (times_times_a @ A @ C)) = (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_mult__left__cancel)). 85.07/18.35 thf(781,plain,((! [A:a,B:a,C:a]: ((~ (A = zero_zero_a)) => (((times_times_a @ A @ B) = (times_times_a @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 85.07/18.35 thf(214,axiom,((! [A:list_a,B:nat,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (compow1114216044poly_a @ B @ polyno784948432ift1_a @ C)) = (polyno422358502poly_a @ A @ (polyno1934269411ymul_a @ (compow1114216044poly_a @ B @ polyno784948432ift1_a @ (polyno439679028le_C_a @ one_one_a)) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_funpow__shift1__1)). 85.07/18.35 thf(961,plain,((! [A:list_a,B:nat,C:polyno727731844poly_a]: ((polyno422358502poly_a @ A @ (compow1114216044poly_a @ B @ (polyno784948432ift1_a) @ C)) = (polyno422358502poly_a @ A @ (polyno1934269411ymul_a @ (compow1114216044poly_a @ B @ (polyno784948432ift1_a) @ (polyno439679028le_C_a @ one_one_a)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 85.07/18.35 thf(168,axiom,((! [A:nat]: ((polyno212464073eriv_a @ (polyno2024845497ound_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_poly__deriv_Osimps_I3_J)). 85.07/18.35 thf(813,plain,((! [A:nat]: ((polyno212464073eriv_a @ (polyno2024845497ound_a @ A)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 85.07/18.35 thf(109,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1397854436bst0_a @ A @ (polyno1623170614_Add_a @ B @ C)) = (polyno1623170614_Add_a @ (polyno1397854436bst0_a @ A @ B) @ (polyno1397854436bst0_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_polysubst0_Osimps_I4_J)). 85.07/18.35 thf(568,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno1397854436bst0_a @ A @ (polyno1623170614_Add_a @ B @ C)) = (polyno1623170614_Add_a @ (polyno1397854436bst0_a @ A @ B) @ (polyno1397854436bst0_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 85.07/18.35 thf(53,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/sandbox/benchmark/theBenchmark.p',fact_278_ab__semigroup__add__class_Oadd__ac_I1_J)). 85.07/18.35 thf(378,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)],[53])). 85.07/18.35 thf(12,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_add_Oleft__neutral)). 85.07/18.35 thf(246,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 85.07/18.35 thf(103,axiom,((! [A:a,B:polyno727731844poly_a,C:nat]: ((polyno439679028le_C_a @ A) != (polyno1538138524e_Pw_a @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_poly_Odistinct_I11_J)). 85.07/18.35 thf(549,plain,((! [A:a,B:polyno727731844poly_a,C:nat]: ~ ((polyno439679028le_C_a @ A) = (polyno1538138524e_Pw_a @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 85.07/18.35 thf(164,axiom,((! [A:a]: ((polyno955999183nate_a @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_polynate_Osimps_I8_J)). 85.07/18.35 thf(800,plain,((! [A:a]: ((polyno955999183nate_a @ (polyno439679028le_C_a @ A)) = (polyno439679028le_C_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 85.07/18.35 thf(30,axiom,((! [A:a]: ((polyno578545843gree_a @ (polyno439679028le_C_a @ A)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_degree_Osimps_I2_J)). 85.07/18.35 thf(300,plain,((! [A:a]: ((polyno578545843gree_a @ (polyno439679028le_C_a @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 85.07/18.35 thf(150,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno1491482291_Mul_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_poly__deriv_Osimps_I6_J)). 85.07/18.35 thf(752,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno212464073eriv_a @ (polyno1491482291_Mul_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 85.07/18.35 thf(63,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_add__right__imp__eq)). 85.07/18.35 thf(410,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)],[63])). 85.07/18.35 thf(66,axiom,((! [A:(polyno727731844poly_a > polyno727731844poly_a),B:polyno727731844poly_a]: ((compow1114216044poly_a @ zero_zero_nat @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_funpow__0)). 85.07/18.35 thf(422,plain,((! [A:(polyno727731844poly_a > polyno727731844poly_a),B:polyno727731844poly_a]: ((compow1114216044poly_a @ zero_zero_nat @ (A) @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 85.07/18.35 thf(21,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ (polyno1465139388head_a @ A) @ B) <= (polyno1372495879olyh_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_behead__isnpolyh)). 85.07/18.35 thf(273,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => (polyno1372495879olyh_a @ (polyno1465139388head_a @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 85.07/18.35 thf(51,axiom,((! [A:nat]: ((polyno1674775833reen_a @ (polyno2024845497ound_a @ A)) = (^ [B:nat]: (zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_degreen_Osimps_I3_J)). 85.07/18.35 thf(373,plain,((! [A:nat]: ((polyno1674775833reen_a @ (polyno2024845497ound_a @ A)) = (^ [B:nat]: (zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 85.07/18.35 thf(41,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_one__reorient)). 85.07/18.35 thf(341,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 85.07/18.35 thf(90,axiom,((! [A:a]: ((polyno1372495879olyh_a @ (polyno439679028le_C_a @ A)) = (^ [B:nat]: (($true)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_isnpolyh_Osimps_I1_J)). 85.07/18.35 thf(506,plain,((! [A:a]: ((polyno1372495879olyh_a @ (polyno439679028le_C_a @ A)) = (^ [B:nat]: (($true)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 85.07/18.35 thf(166,axiom,((! [A:a,B:a]: (((B = zero_zero_a) | (A = zero_zero_a)) <= ((times_times_a @ A @ B) = zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_divisors__zero)). 85.07/18.35 thf(807,plain,((! [A:a,B:a]: (((times_times_a @ A @ B) = zero_zero_a) => ((B = zero_zero_a) | (A = zero_zero_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 85.07/18.35 thf(212,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1491482291_Mul_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1491482291_Mul_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_polymul_Osimps_I26_J)). 85.07/18.35 thf(955,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:nat,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1491482291_Mul_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1491482291_Mul_a @ A @ B) @ (polyno1057396216e_CN_a @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 85.07/18.35 thf(28,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_add__cancel__right__left)). 85.07/18.35 thf(294,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 85.07/18.35 thf(202,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1934269411ymul_a @ A @ (polyno439679028le_C_a @ zero_zero_a)) = (polyno439679028le_C_a @ zero_zero_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_polymul__0_I1_J)). 85.07/18.35 thf(918,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1934269411ymul_a @ A @ (polyno439679028le_C_a @ zero_zero_a)) = (polyno439679028le_C_a @ zero_zero_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 85.07/18.35 thf(196,axiom,((polyno1372495879olyh_a @ q @ n1)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_nq)). 85.07/18.35 thf(897,plain,((polyno1372495879olyh_a @ q @ n1)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 85.07/18.35 thf(155,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:polyno727731844poly_a]: (((polyno1623170614_Add_a @ A @ B) = (polyno1623170614_Add_a @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_poly_Oinject_I3_J)). 85.07/18.35 thf(767,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a,C:polyno727731844poly_a,D:polyno727731844poly_a]: (((polyno1623170614_Add_a @ A @ B) = (polyno1623170614_Add_a @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 85.07/18.35 thf(205,axiom,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno975704247_Sub_a @ B @ C)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno975704247_Sub_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_poly__cmul_Osimps_I5_J)). 85.07/18.35 thf(928,plain,((! [A:a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno562434098cmul_a @ A @ (polyno975704247_Sub_a @ B @ C)) = (polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno975704247_Sub_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 85.07/18.35 thf(64,axiom,((! [A:nat,B:nat]: ((if_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Nat__Onat_T)). 85.07/18.35 thf(415,plain,((! [A:nat,B:nat]: ((if_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 85.07/18.35 thf(112,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: (((polyno1372495879olyh_a @ C @ D) => (((polyno1418491367ysub_a @ A @ C) = (polyno439679028le_C_a @ zero_zero_a)) = (A = C))) <= (polyno1372495879olyh_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_polysub__0)). 85.07/18.35 thf(624,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1372495879olyh_a @ C @ D) => (((polyno1418491367ysub_a @ A @ C) = (polyno439679028le_C_a @ zero_zero_a)) = (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 85.07/18.35 thf(183,axiom,(((! [A:list_a]: ((polyno422358502poly_a @ A @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ A @ (polyno1934269411ymul_a @ q @ p)))) = ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062)). 85.07/18.35 thf(860,plain,(((! [A:list_a]: ((polyno422358502poly_a @ A @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ A @ (polyno1934269411ymul_a @ q @ p)))) = ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 85.07/18.35 thf(118,axiom,((! [A:nat,B:polyno727731844poly_a,C:polyno727731844poly_a,D:polyno727731844poly_a]: ((((polyno1397854436bst0_a @ B @ (polyno1057396216e_CN_a @ C @ A @ D)) = (polyno1623170614_Add_a @ (polyno1397854436bst0_a @ B @ C) @ (polyno1491482291_Mul_a @ B @ (polyno1397854436bst0_a @ B @ D)))) <= (A = zero_zero_nat)) & (((polyno1397854436bst0_a @ B @ (polyno1057396216e_CN_a @ C @ A @ D)) = (polyno1057396216e_CN_a @ (polyno1397854436bst0_a @ B @ C) @ A @ (polyno1397854436bst0_a @ B @ D))) <= (A != zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_polysubst0_Osimps_I8_J)). 85.07/18.35 thf(644,plain,((! [A:nat,B:polyno727731844poly_a,C:polyno727731844poly_a,D:polyno727731844poly_a]: (((A = zero_zero_nat) => ((polyno1397854436bst0_a @ B @ (polyno1057396216e_CN_a @ C @ A @ D)) = (polyno1623170614_Add_a @ (polyno1397854436bst0_a @ B @ C) @ (polyno1491482291_Mul_a @ B @ (polyno1397854436bst0_a @ B @ D))))) & ((~ (A = zero_zero_nat)) => ((polyno1397854436bst0_a @ B @ (polyno1057396216e_CN_a @ C @ A @ D)) = (polyno1057396216e_CN_a @ (polyno1397854436bst0_a @ B @ C) @ A @ (polyno1397854436bst0_a @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 85.07/18.35 thf(180,axiom,((! [A:a,B:a]: ((polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno439679028le_C_a @ B)) = (polyno439679028le_C_a @ (times_times_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_polymul_Osimps_I1_J)). 85.07/18.35 thf(850,plain,((! [A:a,B:a]: ((polyno1934269411ymul_a @ (polyno439679028le_C_a @ A) @ (polyno439679028le_C_a @ B)) = (polyno439679028le_C_a @ (times_times_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 85.07/18.35 thf(72,axiom,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno896877631f_bs_a @ A @ B) => ((polyno896877631f_bs_a @ A @ C) => (polyno896877631f_bs_a @ A @ (polyno1418491367ysub_a @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_wf__bs__polysub)). 85.07/18.35 thf(442,plain,((! [A:list_a,B:polyno727731844poly_a,C:polyno727731844poly_a]: ((polyno896877631f_bs_a @ A @ B) => ((polyno896877631f_bs_a @ A @ C) => (polyno896877631f_bs_a @ A @ (polyno1418491367ysub_a @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 85.07/18.35 thf(84,axiom,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1465139388head_a @ (polyno1623170614_Add_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_behead_Osimps_I4_J)). 85.07/18.35 thf(486,plain,((! [A:polyno727731844poly_a,B:polyno727731844poly_a]: ((polyno1465139388head_a @ (polyno1623170614_Add_a @ A @ B)) = (polyno439679028le_C_a @ zero_zero_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 85.07/18.35 thf(165,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno190918219poly_a @ A) => ((polyno190918219poly_a @ (compow1114216044poly_a @ B @ polyno784948432ift1_a @ A)) <= (A != (polyno439679028le_C_a @ zero_zero_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_funpow__shift1__isnpoly)). 85.07/18.35 thf(803,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno190918219poly_a @ A) => ((~ (A = (polyno439679028le_C_a @ zero_zero_a))) => (polyno190918219poly_a @ (compow1114216044poly_a @ B @ (polyno784948432ift1_a) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 85.07/18.35 thf(79,axiom,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1418491367ysub_a @ A @ A) = (polyno439679028le_C_a @ zero_zero_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_polysub__same__0)). 85.07/18.35 thf(469,plain,((! [A:polyno727731844poly_a,B:nat]: ((polyno1372495879olyh_a @ A @ B) => ((polyno1418491367ysub_a @ A @ A) = (polyno439679028le_C_a @ zero_zero_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 85.07/18.35 thf(33,axiom,((! [A:nat,B:nat]: ((if_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Nat__Onat_T)). 85.07/18.35 thf(309,plain,((! [A:nat,B:nat]: ((if_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 85.07/18.35 thf(101,axiom,((! [A:polyno727731844poly_a]: ((polyno190918219poly_a @ A) => ((A != (polyno439679028le_C_a @ zero_zero_a)) => (polyno190918219poly_a @ (polyno784948432ift1_a @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_shift1__isnpoly)). 85.07/18.35 thf(543,plain,((! [A:polyno727731844poly_a]: ((polyno190918219poly_a @ A) => ((~ (A = (polyno439679028le_C_a @ zero_zero_a))) => (polyno190918219poly_a @ (polyno784948432ift1_a @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 85.07/18.35 thf(151,axiom,((! [A:a]: ((polyno2115742616onst_a @ (polyno439679028le_C_a @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_headconst_Osimps_I2_J)). 85.07/18.35 thf(755,plain,((! [A:a]: ((polyno2115742616onst_a @ (polyno439679028le_C_a @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 85.07/18.35 thf(76,axiom,((! [A:a,B:a]: (((B != zero_zero_a) & (A != zero_zero_a)) <= ((times_times_a @ A @ B) != zero_zero_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_mult__not__zero)). 85.07/18.35 thf(454,plain,((! [A:a,B:a]: ((~ ((times_times_a @ A @ B) = zero_zero_a)) => (~ (B = zero_zero_a) & ~ (A = zero_zero_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 85.07/18.35 thf(191,axiom,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:polyno727731844poly_a,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1491482291_Mul_a @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1491482291_Mul_a @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_polymul_Osimps_I14_J)). 85.07/18.35 thf(882,plain,((! [A:polyno727731844poly_a,B:nat,C:polyno727731844poly_a,D:polyno727731844poly_a,E:polyno727731844poly_a]: ((polyno1934269411ymul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1491482291_Mul_a @ D @ E)) = (polyno1491482291_Mul_a @ (polyno1057396216e_CN_a @ A @ B @ C) @ (polyno1491482291_Mul_a @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 85.07/18.35 thf(16613,plain,(($false)),inference(e,[status(thm)],[878,479,347,846,234,666,249,333,628,385,797,715,698,945,538,404,898,709,885,288,565,389,719,785,344,934,559,853,770,228,448,261,216,492,321,376,834,574,353,821,692,221,866,774,660,243,428,312,678,546,925,761,810,381,534,512,942,439,270,529,894,825,952,862,297,729,407,630,275,788,252,879,682,324,285,948,388,356,869,857,519,742,669,489,901,686,476,837,701,515,237,633,657,398,794,888,425,264,745,279,689,819,732,843,875,291,958,562,904,391,445,498,466,350,540,672,764,831,736,303,362,451,509,434,758,367,816,726,483,240,964,915,330,462,827,223,306,267,431,653,922,912,521,636,695,473,722,675,663,255,553,525,712,640,872,327,739,705,282,791,370,717,502,840,359,336,571,231,556,931,495,891,218,748,258,401,418,781,961,813,568,378,246,549,800,300,752,410,422,273,373,341,506,807,955,294,918,897,767,928,415,624,860,644,850,442,486,803,469,309,543,755,454,882])). 85.07/18.35 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 85.07/18.35 % [INFO] Killing All external provers ... 0.16/18.48 EOF