0.00/0.02 % Leo-III: Strategy 1 (for '60') 20.72/12.55 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 20.72/12.55 % [INFO] Parsing done (799ms). 20.72/12.55 % [INFO] Running in sequential loop mode. 20.72/12.55 % [CONFIG] Using configuration: timeout(60) with strategy 20.72/12.55 % [INFO] eprover registered as external prover. 20.72/12.55 % [INFO] cvc4 registered as external prover. 20.72/12.55 % [INFO] Parsing finished. Scanning for conjecture ... 20.72/12.55 % [INFO] Found a conjecture and 282 axioms. Running axiom selection ... 20.72/12.55 % [INFO] Axiom selection finished. Selected 282 axioms (removed 0 axioms). 20.72/12.55 % [INFO] Problem is higher-order (TPTP THF). 20.72/12.55 % [INFO] Type checking passed. Searching for refutation ... 20.72/12.55 % External prover 'cvc4' found a proof! 20.72/12.55 % [INFO] Killing All external provers ... 20.72/12.55 % Time passed: 9616ms (effective reasoning time: 8011ms) 20.72/12.55 % Solved by strategy 20.72/12.55 % Axioms used in derivation (282): fact_257_minus__add__cancel, fact_249_abelian__group_Ominus__eq, fact_68_add__pow__rdistr__int, fact_223_a__transpose__inv, fact_261_uminus__add__conv__diff, fact_259_minus__diff__eq, fact_59_prod__cases, fact_159_group__add__class_Oadd_Oright__cancel, fact_176_eq__diff__eq, fact_133_diff__add__inverse2, fact_48_Collect__mem__eq, fact_130_nat__arith_Osuc1, fact_146_add__right__cancel, fact_35_right__inv__add, fact_56_old_Oprod_Oinducts, fact_279_comm__groupE_I1_J, fact_149_add__diff__cancel, fact_272_of__nat__add, fact_255_add_Oint__pow__neg, fact_165_group__cancel_Oadd1, fact_21_old_Oprod_Oinject, fact_156_add_Oleft__commute, fact_63_semiring_Osemiring__simprules_I6_J, fact_124_nat_Oinject, fact_275_comm__groupE_I4_J, fact_27_add_Om__comm, fact_214_inv__add, fact_264_ab__group__add__class_Oab__diff__conv__add__uminus, fact_198_group_Ol__inv__ex, fact_92_add_Ogroup__commutes__pow, fact_169_ab__semigroup__add__class_Oadd__ac_I1_J, fact_64_semiring_Ol__null, fact_6_f9, fact_188_Units__closed, fact_20_prod_Oinject, fact_127_n__not__Suc__n, fact_278_comm__groupE_I1_J, fact_148_add__left__cancel, fact_191_Units__one__closed, fact_190_Units__m__closed, fact_224_r__minus, fact_136_Nat_Odiff__cancel, fact_242_abelian__group_Ominus__minus, fact_233_add_Oint__pow__diff, fact_168_add__mono__thms__linordered__semiring_I4_J, fact_215_r__neg2, fact_258_minus__add__distrib, fact_28_add_Om__lcomm, fact_54_r__null, fact_201_group_OUnits__eq, fact_182_diff__diff__add, fact_250_abelian__group_Ol__neg, fact_86_semiring_Osemiring__simprules_I12_J, fact_263_diff__conv__add__uminus, fact_85_semiring_Osemiring__simprules_I7_J, fact_222_add_Oinv__mult__group, fact_238_Units__minus__one__closed, fact_144_add__diff__cancel__left, fact_49_Collect__cong, fact_134_diff__add__inverse, fact_218_add_Oinv__solve__right_H, fact_177_add__diff__eq, fact_75_add_Oint__pow__closed, fact_33_add_Ol__inv__ex, fact_252_abelian__group_Ominus__equality, fact_65_semiring_Or__null, fact_112_abelian__groupE_I2_J, fact_268_add_Oint__pow__neg__int, fact_50_Collect__cong, fact_30_local_Ominus__unique, fact_277_comm__groupE_I3_J, fact_83_semiring_Osemiring__simprules_I1_J, fact_139_add__diff__cancel__right, fact_202_group_OUnits__eq, fact_194_groupI, fact_180_diff__add__eq__diff__diff__swap, fact_91_add__pow__rdistr, fact_153_add__left__imp__eq, fact_226_add_Onat__pow__inv, fact_66_semiring_Or__distr, fact_274_comm__groupE_I4_J, fact_118_abelian__group_Oright__inv__add, fact_232_l__neg, fact_18_r__distr, fact_163_group__cancel_Oadd2, fact_89_add_Oint__pow__mult, fact_82_semiring_Osemiring__simprules_I8_J, fact_161_add_Oassoc, fact_178_diff__diff__eq2, fact_138_add__diff__cancel__right_H, fact_96_add_Onat__pow__closed, fact_7__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_H_H_A_092_060otimes_062_As_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062, fact_147_add__left__cancel, fact_8__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_092_060close_062, fact_111_abelian__groupE_I4_J, fact_245_units__of__one, fact_97_add_Onat__pow__one, fact_22_local_Osemiring__axioms, fact_151_add__right__imp__eq, fact_132_zero__induct__lemma, fact_125_old_Onat_Oinject, fact_128_diff__commute, fact_13__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_A_092_060otimes_062_Ar_H_H_J_A_092_060oplus_062_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_092_060close_062, fact_229_sum__zero__eq__neg, fact_166_group__cancel_Oadd1, fact_70_inv__unique, fact_204_group_Or__cancel__one_H, fact_126_Suc__inject, fact_114_abelian__groupI, fact_72_add_Oint__pow__distrib, fact_103_add_Onat__pow__Suc2, fact_100_semiring_Oadd__pow__ldistr, fact_186_Units__r__inv__ex, fact_212_group_Or__inv__ex, fact_32_add_Oone__unique, fact_117_abelian__group_Ofour__elem__comm, fact_10_f5, fact_51_add_Or__cancel__one, fact_42_r__zero, fact_25_m__lcomm, fact_256_add__minus__cancel, fact_24_m__comm, fact_31_add_Or__inv__ex, fact_95_add_Onat__pow__comm, fact_246_abelian__group_Ominus__add, fact_44_add_Or__cancel__one_H, fact_81_semiring_Osemiring__simprules_I3_J, fact_73_add_Oint__pow__mult__distrib, fact_154_add__left__imp__eq, fact_38_add_Om__closed, fact_69_add__pow__ldistr__int, fact_192_Units__l__cancel, fact_37_local_Oadd_Oright__cancel, fact_17_l__distr, fact_197_group_Ol__inv__ex, fact_267_minus__diff__commute, fact_46_mem__Collect__eq, fact_172_diff__right__commute, fact_152_add__right__imp__eq, fact_143_add__diff__cancel__left, fact_220_add_Oinv__solve__left_H, fact_122_diff__Suc__Suc, fact_58_Pair__inject, fact_45_mem__Collect__eq, fact_40_semiring__simprules_I3_J, fact_203_group_Or__cancel__one_H, fact_231_minus__equality, fact_164_group__cancel_Oadd2, fact_175_diff__eq__eq, fact_88_cring__fieldI2, fact_79_semiring_Osemiring__simprules_I4_J, fact_41_minus__closed, fact_211_group_Or__inv__ex, fact_189_Units__inv__comm, fact_11_f4, fact_237_add_Oinv__eq__1__iff, fact_171_diff__right__commute, fact_247_abelian__group_Or__neg2, fact_62_semiring_Osemiring__simprules_I11_J, fact_78_r__one, fact_173_diff__eq__diff__eq, fact_181_diff__diff__add, fact_115_abelian__groupE_I5_J, fact_184_add__implies__diff, fact_265_group__cancel_Oneg1, fact_123_add__Suc__right, fact_145_add__right__cancel, fact_131_add__Suc__shift, fact_266_add_Oinverse__distrib__swap, fact_104_add_Opow__eq__div2, fact_53_add_Ol__cancel__one, fact_221_add_Oinv__solve__left, fact_227_add_Oint__pow__inv, fact_67_semiring_Ol__distr, fact_193_groupI, fact_270_of__nat__eq__iff, fact_120_diff__diff__left, fact_43_l__zero, fact_243_a__minus__def, fact_12__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060otimes_062_Ar_H_H_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062, fact_34_add_Oinv__comm, fact_2_assms_I2_J, fact_240_units__of__mult, fact_260_diff__minus__eq__add, fact_108_add_Onat__pow__Suc, fact_1_assms_I3_J, fact_101_semiring_Oadd__pow__rdistr, fact_23_m__assoc, fact_216_r__neg1, fact_135_diff__cancel2, fact_74_semiring__simprules_I4_J, fact_105_minus__to__eq, fact_16_f12, fact_157_add_Ocommute, fact_235_add_Oinv__closed, fact_9_f10, fact_199_Group_Ogroup_Oright__cancel, fact_208_group_Or__cancel__one, fact_113_abelian__group_Ominus__closed, fact_15_f8, fact_3_assms_I1_J, fact_57_old_Oprod_Oexhaust, fact_217_local_Ominus__add, fact_196_group_Oinv__comm, fact_262_group__cancel_Osub2, fact_200_Group_Ogroup_Oright__cancel, fact_36_four__elem__comm, fact_280_comm__groupE_I2_J, fact_210_group_Ol__cancel__one, fact_236_local_Ominus__zero, fact_47_Collect__mem__eq, fact_179_diff__add__eq, fact_234_local_Ominus__minus, fact_228_minus__eq, fact_225_l__minus, fact_253_abelian__group_Oinv__add, fact_160_add_Oleft__cancel, fact_230_r__neg, fact_219_add_Oinv__solve__right, fact_87_semiring_Osemiring__simprules_I2_J, fact_55_l__null, fact_187_group__l__invI, fact_119_abelian__group_Ominus__to__eq, fact_109_abelian__groupE_I1_J, fact_107_is__abelian__group, fact_140_add__diff__cancel__right, fact_273_of__nat__add, fact_195_group_Oinv__comm, fact_60_surj__pair, fact_213_units__group, fact_93_add_Opow__mult__distrib, fact_137_add__diff__cancel__right_H, fact_206_group_Ol__cancel__one_H, fact_269_units__comm__group, fact_0_right__add__eq, fact_121_Suc__diff__diff, fact_129_add__Suc, fact_248_abelian__group_Or__neg1, fact_110_abelian__groupE_I3_J, fact_185_Units__l__inv__ex, fact_239_units__of__mult, fact_106_ring_Oequality, fact_14_f7, fact_271_of__nat__eq__iff, fact_244_units__of__one, fact_167_add__mono__thms__linordered__semiring_I4_J, fact_174_group__cancel_Osub1, fact_5__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_061_As_A_092_060otimes_062_A_Is_H_H_A_092_060otimes_062_As_H_J_A_092_060otimes_062_As_H_H_092_060close_062, fact_205_group_Ol__cancel__one_H, fact_61_f11, fact_80_semiring_Osemiring__simprules_I9_J, fact_209_group_Ol__cancel__one, fact_155_add_Oleft__commute, fact_158_add_Ocommute, fact_116_abelian__groupE_I6_J, fact_141_add__diff__cancel__left_H, fact_39_zero__closed, fact_254_abelian__group_Oa__transpose__inv, fact_71_one__unique, fact_170_ab__semigroup__add__class_Oadd__ac_I1_J, fact_76_add_Oint__pow__one, fact_26_add_Om__assoc, fact_98_one__not__zero, fact_29_local_Oright__minus__eq, fact_281_comm__groupE_I2_J, fact_90_add__pow__ldistr, fact_251_abelian__group_Or__neg, fact_183_add__implies__diff, fact_77_l__one, fact_99_integral, fact_142_add__diff__cancel__left_H, fact_276_comm__groupE_I3_J, fact_4_closed__rel__add, fact_162_add_Oassoc, fact_94_add_Onat__pow__distrib, fact_241_abelian__group_Oa__inv__closed, fact_52_add_Ol__cancel__one_H, fact_19__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_A_092_060otimes_062_Ar_H_H_J_A_092_060oplus_062_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_A_061_A_092_060zero_062_092_060close_062, fact_102_add_Onat__pow__mult, fact_150_diff__add__cancel, fact_207_group_Or__cancel__one, fact_84_semiring_Osemiring__simprules_I5_J 20.72/12.55 % No. of inferences in proof: 568 20.72/12.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9616 ms resp. 8011 ms w/o parsing 20.72/12.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 20.72/12.55 thf(partia1993116613t_unit_type, type, partia1993116613t_unit: $tType). 20.72/12.55 thf(partia1833973666xt_a_b_type, type, partia1833973666xt_a_b: $tType). 20.72/12.55 thf(partia96731725t_unit_type, type, partia96731725t_unit: $tType). 20.72/12.55 thf(set_Product_prod_a_a_type, type, set_Product_prod_a_a: $tType). 20.72/12.55 thf(product_prod_a_a_type, type, product_prod_a_a: $tType). 20.72/12.55 thf(set_a_type, type, set_a: $tType). 20.72/12.55 thf(nat_type, type, nat: $tType). 20.72/12.55 thf(int_type, type, int: $tType). 20.72/12.55 thf(b_type, type, b: $tType). 20.72/12.55 thf(a_type, type, a: $tType). 20.72/12.55 thf(partia206007992t_unit_type, type, partia206007992t_unit: (partia1993116613t_unit > set_Product_prod_a_a)). 20.72/12.55 thf(partia1955795460t_unit_type, type, partia1955795460t_unit: (partia96731725t_unit > set_a)). 20.72/12.55 thf(partia1066395285xt_a_b_type, type, partia1066395285xt_a_b: (partia1833973666xt_a_b > set_a)). 20.72/12.55 thf(units_a_Product_unit_type, type, units_a_Product_unit: (partia96731725t_unit > set_a)). 20.72/12.55 thf(units_a_ring_ext_a_b_type, type, units_a_ring_ext_a_b: (partia1833973666xt_a_b > set_a)). 20.72/12.55 thf(comm_g1684316527t_unit_type, type, comm_g1684316527t_unit: (partia96731725t_unit > $o)). 20.72/12.55 thf(comm_g791708116xt_a_b_type, type, comm_g791708116xt_a_b: (partia1833973666xt_a_b > $o)). 20.72/12.55 thf(group_a_Product_unit_type, type, group_a_Product_unit: (partia96731725t_unit > $o)). 20.72/12.55 thf(group_a_ring_ext_a_b_type, type, group_a_ring_ext_a_b: (partia1833973666xt_a_b > $o)). 20.72/12.55 thf(mult_a_Product_unit_type, type, mult_a_Product_unit: (partia96731725t_unit > (a > (a > a)))). 20.72/12.55 thf(mult_a_ring_ext_a_b_type, type, mult_a_ring_ext_a_b: (partia1833973666xt_a_b > (a > (a > a)))). 20.72/12.55 thf(one_a_Product_unit_type, type, one_a_Product_unit: (partia96731725t_unit > a)). 20.72/12.55 thf(one_a_ring_ext_a_b_type, type, one_a_ring_ext_a_b: (partia1833973666xt_a_b > a)). 20.72/12.55 thf(units_873712258t_unit_type, type, units_873712258t_unit: (partia96731725t_unit > partia96731725t_unit)). 20.72/12.55 thf(units_1411277569xt_a_b_type, type, units_1411277569xt_a_b: (partia1833973666xt_a_b > partia96731725t_unit)). 20.72/12.55 thf(minus_minus_int_type, type, minus_minus_int: (int > (int > int))). 20.72/12.55 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 20.72/12.55 thf(plus_plus_int_type, type, plus_plus_int: (int > (int > int))). 20.72/12.55 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 20.72/12.55 thf(uminus_uminus_int_type, type, uminus_uminus_int: (int > int)). 20.72/12.55 thf(suc_type, type, suc: (nat > nat)). 20.72/12.55 thf(semiri2019852685at_int_type, type, semiri2019852685at_int: (nat > int)). 20.72/12.55 thf(semiri1382578993at_nat_type, type, semiri1382578993at_nat: (nat > nat)). 20.72/12.55 thf(product_Pair_a_a_type, type, product_Pair_a_a: (a > (a > product_prod_a_a))). 20.72/12.55 thf(a_inv_a_b_type, type, a_inv_a_b: (partia1833973666xt_a_b > (a > a))). 20.72/12.55 thf(a_minus_a_b_type, type, a_minus_a_b: (partia1833973666xt_a_b > (a > (a > a)))). 20.72/12.55 thf(abelian_group_a_b_type, type, abelian_group_a_b: (partia1833973666xt_a_b > $o)). 20.72/12.55 thf(add_pow_a_b_int_type, type, add_pow_a_b_int: (partia1833973666xt_a_b > (int > (a > a)))). 20.72/12.55 thf(add_pow_a_b_nat_type, type, add_pow_a_b_nat: (partia1833973666xt_a_b > (nat > (a > a)))). 20.72/12.55 thf(field_a_b_type, type, field_a_b: (partia1833973666xt_a_b > $o)). 20.72/12.55 thf(add_a_b_type, type, add_a_b: (partia1833973666xt_a_b > (a > (a > a)))). 20.72/12.55 thf(more_a_b_type, type, more_a_b: (partia1833973666xt_a_b > b)). 20.72/12.55 thf(zero_a_b_type, type, zero_a_b: (partia1833973666xt_a_b > a)). 20.72/12.55 thf(semiring_a_b_type, type, semiring_a_b: (partia1833973666xt_a_b > $o)). 20.72/12.55 thf(collec645855634od_a_a_type, type, collec645855634od_a_a: ((product_prod_a_a > $o) > set_Product_prod_a_a)). 20.72/12.55 thf(collect_a_type, type, collect_a: ((a > $o) > set_a)). 20.72/12.55 thf(member449909584od_a_a_type, type, member449909584od_a_a: (product_prod_a_a > (set_Product_prod_a_a > $o))). 20.72/12.55 thf(member_a_type, type, member_a: (a > (set_a > $o))). 20.72/12.55 thf(r_type, type, r: partia1833973666xt_a_b). 20.72/12.55 thf(r2_type, type, r2: a). 20.72/12.55 thf(r3_type, type, r3: a). 20.72/12.55 thf(r4_type, type, r4: a). 20.72/12.55 thf(rel_type, type, rel: partia1993116613t_unit). 20.72/12.55 thf(s_type, type, s: a). 20.72/12.55 thf(s2_type, type, s2: a). 20.72/12.55 thf(s3_type, type, s3: a). 20.72/12.55 thf(107,axiom,((minus_minus_int = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_ab__group__add__class_Oab__diff__conv__add__uminus)). 20.72/12.55 thf(645,plain,(((minus_minus_int) = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 20.72/12.55 thf(154,axiom,((! [A:a,B:a,C:a,D:a]: (((product_Pair_a_a @ A @ B) = (product_Pair_a_a @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_prod_Oinject)). 20.72/12.55 thf(809,plain,((! [A:a,B:a,C:a,D:a]: (((product_Pair_a_a @ A @ B) = (product_Pair_a_a @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 20.72/12.55 thf(165,axiom,((! [A:a,B:a]: ((((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((A = B) <= ((a_minus_a_b @ r @ A @ B) = (zero_a_b @ r)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))) <= (abelian_group_a_b @ r)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_minus__to__eq)). 20.72/12.55 thf(846,plain,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((A = B) | ~ ((a_minus_a_b @ r @ A @ B) = (zero_a_b @ r)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r)) | ~ (abelian_group_a_b @ r)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 20.72/12.55 thf(179,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((abelian_group_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((a_minus_a_b @ A @ (a_minus_a_b @ A @ D @ B) @ C) = (a_minus_a_b @ A @ D @ (add_a_b @ A @ B @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_abelian__group_Oright__inv__add)). 20.72/12.55 thf(893,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((abelian_group_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((a_minus_a_b @ A @ (a_minus_a_b @ A @ D @ B) @ C) = (a_minus_a_b @ A @ D @ (add_a_b @ A @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 20.72/12.55 thf(146,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (add_a_b @ A @ B @ C) @ D) = (add_a_b @ A @ (mult_a_ring_ext_a_b @ A @ B @ D) @ (mult_a_ring_ext_a_b @ A @ C @ D)))))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_semiring_Ol__distr)). 20.72/12.55 thf(777,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (add_a_b @ A @ B @ C) @ D) = (add_a_b @ A @ (mult_a_ring_ext_a_b @ A @ B @ D) @ (mult_a_ring_ext_a_b @ A @ C @ D)))))) | ~ (semiring_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 20.72/12.55 thf(58,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_group__cancel_Oadd1)). 20.72/12.55 thf(481,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)],[58])). 20.72/12.55 thf(230,axiom,((! [A:set_Product_prod_a_a]: ((collec645855634od_a_a @ (^ [B:product_prod_a_a]: (member449909584od_a_a @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__mem__eq)). 20.72/12.55 thf(1083,plain,((! [A:set_Product_prod_a_a]: ((collec645855634od_a_a @ (^ [B:product_prod_a_a]: (member449909584od_a_a @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 20.72/12.55 thf(196,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((((member_a @ C @ (partia1066395285xt_a_b @ A)) => (member_a @ (add_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_semiring_Osemiring__simprules_I1_J)). 20.72/12.55 thf(962,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ C @ (partia1066395285xt_a_b @ A)) => (member_a @ (add_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (semiring_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 20.72/12.55 thf(54,axiom,((! [A:partia96731725t_unit]: (((units_a_Product_unit @ A) = (partia1955795460t_unit @ A)) <= (group_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_group_OUnits__eq)). 20.72/12.55 thf(468,plain,((! [A:partia96731725t_unit]: (((units_a_Product_unit @ A) = (partia1955795460t_unit @ A)) | ~ (group_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 20.72/12.55 thf(255,axiom,((semiring_a_b @ r)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Osemiring__axioms)). 20.72/12.55 thf(1158,plain,((semiring_a_b @ r)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 20.72/12.55 thf(227,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ (mult_a_ring_ext_a_b @ r @ s3 @ s3)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_f9)). 20.72/12.55 thf(1073,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ (mult_a_ring_ext_a_b @ r @ s3 @ s3)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 20.72/12.55 thf(48,axiom,((! [A:partia1833973666xt_a_b]: ((semiring_a_b @ A) => (member_a @ (zero_a_b @ A) @ (partia1066395285xt_a_b @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_semiring_Osemiring__simprules_I2_J)). 20.72/12.55 thf(449,plain,((! [A:partia1833973666xt_a_b]: ((semiring_a_b @ A) => (member_a @ (zero_a_b @ A) @ (partia1066395285xt_a_b @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 20.72/12.55 thf(250,axiom,((! [A:a]: ((((a_inv_a_b @ r @ A) = (zero_a_b @ r)) = (A = (zero_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add_Oinv__eq__1__iff)). 20.72/12.55 thf(1142,plain,((! [A:a]: ((((a_inv_a_b @ r @ A) = (zero_a_b @ r)) = (A = (zero_a_b @ r))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 20.72/12.55 thf(174,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ s) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_H_H_A_092_060otimes_062_As_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062)). 20.72/12.55 thf(878,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ s) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 20.72/12.55 thf(97,axiom,((! [A:partia96731725t_unit]: ((mult_a_Product_unit @ (units_873712258t_unit @ A)) = (mult_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_units__of__mult)). 20.72/12.55 thf(614,plain,((! [A:partia96731725t_unit]: ((mult_a_Product_unit @ (units_873712258t_unit @ A)) = (mult_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 20.72/12.55 thf(218,axiom,((comm_g1684316527t_unit @ (units_1411277569xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_units__comm__group)). 20.72/12.55 thf(1041,plain,((comm_g1684316527t_unit @ (units_1411277569xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 20.72/12.55 thf(260,axiom,((! [A:partia1833973666xt_a_b]: ((! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (! [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (member_a @ (add_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A)))))) => ((member_a @ (zero_a_b @ A) @ (partia1066395285xt_a_b @ A)) => ((! [B:a]: ((! [C:a]: ((! [D:a]: ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (add_a_b @ A @ B @ C) @ D) = (add_a_b @ A @ B @ (add_a_b @ A @ C @ D))))) <= (member_a @ C @ (partia1066395285xt_a_b @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))) => ((((abelian_group_a_b @ A) <= (! [B:a]: ((? [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) & ((add_a_b @ A @ C @ B) = (zero_a_b @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))))) <= (! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (zero_a_b @ A) @ B) = B)))) <= (! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (! [C:a]: (((add_a_b @ A @ B @ C) = (add_a_b @ A @ C @ B)) <= (member_a @ C @ (partia1066395285xt_a_b @ A)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_abelian__groupI)). 20.72/12.55 thf(1173,plain,((! [A:partia1833973666xt_a_b]: ((! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (! [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (member_a @ (add_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A)))))) => ((member_a @ (zero_a_b @ A) @ (partia1066395285xt_a_b @ A)) => ((! [B:a]: (! [C:a]: (! [D:a]: ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (add_a_b @ A @ B @ C) @ D) = (add_a_b @ A @ B @ (add_a_b @ A @ C @ D)))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))) => ((abelian_group_a_b @ A) | ~ (! [B:a]: (? [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) & ((add_a_b @ A @ C @ B) = (zero_a_b @ A))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))) | ~ (! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (zero_a_b @ A) @ B) = B))) | ~ (! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (! [C:a]: (((add_a_b @ A @ B @ C) = (add_a_b @ A @ C @ B)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 20.72/12.55 thf(33,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (minus_minus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_diff__right__commute)). 20.72/12.55 thf(384,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (minus_minus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 20.72/12.55 thf(63,axiom,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_of__nat__add)). 20.72/12.55 thf(500,plain,((! [A:nat,B:nat]: ((semiri1382578993at_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (semiri1382578993at_nat @ A) @ (semiri1382578993at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 20.72/12.55 thf(282,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ B @ (a_inv_a_b @ A @ B)) = (zero_a_b @ A))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_abelian__group_Or__neg)). 20.72/12.55 thf(1275,plain,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ B @ (a_inv_a_b @ A @ B)) = (zero_a_b @ A))) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 20.72/12.55 thf(124,axiom,((! [A:a,B:int]: (((add_pow_a_b_int @ r @ (uminus_uminus_int @ B) @ A) = (a_inv_a_b @ r @ (add_pow_a_b_int @ r @ B @ A))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add_Oint__pow__neg)). 20.72/12.55 thf(698,plain,((! [A:a,B:int]: (((add_pow_a_b_int @ r @ (uminus_uminus_int @ B) @ A) = (a_inv_a_b @ r @ (add_pow_a_b_int @ r @ B @ A))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 20.72/12.55 thf(21,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ A @ (plus_plus_int @ B @ C)) = (minus_minus_int @ (minus_minus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_diff__add__eq__diff__diff__swap)). 20.72/12.55 thf(340,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ A @ (plus_plus_int @ B @ C)) = (minus_minus_int @ (minus_minus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 20.72/12.55 thf(74,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => ((abelian_group_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((B = C) <= ((a_minus_a_b @ A @ B @ C) = (zero_a_b @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_abelian__group_Ominus__to__eq)). 20.72/12.55 thf(538,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => ((abelian_group_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((B = C) | ~ ((a_minus_a_b @ A @ B @ C) = (zero_a_b @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 20.72/12.55 thf(234,axiom,((member_a @ (zero_a_b @ r) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__closed)). 20.72/12.55 thf(1095,plain,((member_a @ (zero_a_b @ r) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 20.72/12.55 thf(207,axiom,((! [A:(product_prod_a_a > $o),B:product_prod_a_a]: ((! [C:a,D:a]: (A @ (product_Pair_a_a @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_old_Oprod_Oinducts)). 20.72/12.55 thf(1001,plain,((! [A:(product_prod_a_a > $o),B:product_prod_a_a]: ((! [C:a,D:a]: (A @ (product_Pair_a_a @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 20.72/12.55 thf(245,axiom,((! [A:a]: (((add_a_b @ r @ (a_inv_a_b @ r @ A) @ A) = (zero_a_b @ r)) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_l__neg)). 20.72/12.55 thf(1127,plain,((! [A:a]: (((add_a_b @ r @ (a_inv_a_b @ r @ A) @ A) = (zero_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 20.72/12.55 thf(199,axiom,((! [A:a,B:a,C:a]: ((A = B) => ((a_minus_a_b @ r @ C @ A) = (a_minus_a_b @ r @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_local_Oright__minus__eq)). 20.72/12.55 thf(973,plain,((! [A:a,B:a,C:a]: ((A = B) => ((a_minus_a_b @ r @ C @ A) = (a_minus_a_b @ r @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 20.72/12.55 thf(177,axiom,((! [A:a]: (((mult_a_ring_ext_a_b @ r @ (one_a_ring_ext_a_b @ r) @ A) = A) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_l__one)). 20.72/12.55 thf(885,plain,((! [A:a]: (((mult_a_ring_ext_a_b @ r @ (one_a_ring_ext_a_b @ r) @ A) = A) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 20.72/12.55 thf(220,axiom,((! [A:a,B:a]: ((((mult_a_ring_ext_a_b @ r @ A @ (a_inv_a_b @ r @ B)) = (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ A @ B))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_r__minus)). 20.72/12.55 thf(1046,plain,((! [A:a,B:a]: (((mult_a_ring_ext_a_b @ r @ A @ (a_inv_a_b @ r @ B)) = (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ A @ B))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 20.72/12.55 thf(148,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((a_inv_a_b @ A @ C) = B)) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= ((add_a_b @ A @ B @ C) = (zero_a_b @ A))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_abelian__group_Ominus__equality)). 20.72/12.55 thf(785,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((a_inv_a_b @ A @ C) = B)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ ((add_a_b @ A @ B @ C) = (zero_a_b @ A)) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 20.72/12.55 thf(163,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((((mult_a_ring_ext_a_b @ A @ B @ C) = B) = (C = (one_a_ring_ext_a_b @ A))) <= (member_a @ C @ (partia1066395285xt_a_b @ A)))) <= (group_a_ring_ext_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_group_Ol__cancel__one)). 20.72/12.55 thf(838,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((((mult_a_ring_ext_a_b @ A @ B @ C) = B) = (C = (one_a_ring_ext_a_b @ A))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)))) | ~ (group_a_ring_ext_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 20.72/12.55 thf(283,axiom,((member449909584od_a_a @ (product_Pair_a_a @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3)) @ (partia206007992t_unit @ rel))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_f12)). 20.72/12.55 thf(1279,plain,((member449909584od_a_a @ (product_Pair_a_a @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3)) @ (partia206007992t_unit @ rel))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 20.72/12.55 thf(52,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_add_Oassoc)). 20.72/12.55 thf(460,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 20.72/12.55 thf(186,axiom,((! [A:a,B:a]: ((((add_a_b @ r @ (a_inv_a_b @ r @ A) @ (add_a_b @ r @ A @ B)) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_r__neg1)). 20.72/12.55 thf(917,plain,((! [A:a,B:a]: (((add_a_b @ r @ (a_inv_a_b @ r @ A) @ (add_a_b @ r @ A @ B)) = B) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 20.72/12.55 thf(125,axiom,((! [A:a,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ A @ B) @ C) = (mult_a_ring_ext_a_b @ r @ A @ (mult_a_ring_ext_a_b @ r @ B @ C))) <= (member_a @ C @ (partia1066395285xt_a_b @ r)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_m__assoc)). 20.72/12.55 thf(702,plain,((! [A:a,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ A @ B) @ C) = (mult_a_ring_ext_a_b @ r @ A @ (mult_a_ring_ext_a_b @ r @ B @ C))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 20.72/12.55 thf(182,axiom,((! [A:a,B:a,C:int]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (add_pow_a_b_int @ r @ C @ A) @ (add_pow_a_b_int @ r @ C @ B)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add_Oint__pow__distrib)). 20.72/12.55 thf(902,plain,((! [A:a,B:a,C:int]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (add_pow_a_b_int @ r @ C @ A) @ (add_pow_a_b_int @ r @ C @ B)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 20.72/12.55 thf(232,axiom,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_a_b @ A) => (((mult_a_ring_ext_a_b @ A @ (zero_a_b @ A) @ B) = (zero_a_b @ A)) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_semiring_Ol__null)). 20.72/12.55 thf(1087,plain,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_a_b @ A) => (((mult_a_ring_ext_a_b @ A @ (zero_a_b @ A) @ B) = (zero_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 20.72/12.55 thf(172,axiom,((! [A:a,B:a,C:a]: ((((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ A @ B) @ C) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ A @ C) @ (mult_a_ring_ext_a_b @ r @ B @ C)))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_l__distr)). 20.72/12.55 thf(870,plain,((! [A:a,B:a,C:a]: (((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ A @ B) @ C) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ A @ C) @ (mult_a_ring_ext_a_b @ r @ B @ C)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 20.72/12.55 thf(198,axiom,((! [A:a,B:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ (uminus_uminus_int @ (semiri2019852685at_int @ B)) @ A) = (a_inv_a_b @ r @ (add_pow_a_b_nat @ r @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_add_Oint__pow__neg__int)). 20.72/12.55 thf(969,plain,((! [A:a,B:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ (uminus_uminus_int @ (semiri2019852685at_int @ B)) @ A) = (a_inv_a_b @ r @ (add_pow_a_b_nat @ r @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 20.72/12.55 thf(144,axiom,((! [A:a,B:a]: (((((add_a_b @ r @ B @ A) = (zero_a_b @ r)) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))) <= ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add_Oinv__comm)). 20.72/12.55 thf(770,plain,((! [A:a,B:a]: (((add_a_b @ r @ B @ A) = (zero_a_b @ r)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r)) | ~ ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 20.72/12.55 thf(42,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ (a_minus_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A)) <= (member_a @ C @ (partia1066395285xt_a_b @ A)))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_abelian__group_Ominus__closed)). 20.72/12.55 thf(416,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ (a_minus_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)))) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 20.72/12.55 thf(4,axiom,((! [A:nat,B:nat]: (((semiri1382578993at_nat @ A) = (semiri1382578993at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_of__nat__eq__iff)). 20.72/12.55 thf(289,plain,((! [A:nat,B:nat]: (((semiri1382578993at_nat @ A) = (semiri1382578993at_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 20.72/12.55 thf(237,axiom,((! [A:(product_prod_a_a > $o),B:product_prod_a_a]: ((! [C:a,D:a]: (A @ (product_Pair_a_a @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_prod__cases)). 20.72/12.55 thf(1100,plain,((! [A:(product_prod_a_a > $o),B:product_prod_a_a]: ((! [C:a,D:a]: (A @ (product_Pair_a_a @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 20.72/12.55 thf(242,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((((A = (add_a_b @ r @ B @ (a_inv_a_b @ r @ C))) = (B = (add_a_b @ r @ A @ C))) <= (member_a @ C @ (partia1066395285xt_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_add_Oinv__solve__right)). 20.72/12.55 thf(1115,plain,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((A = (add_a_b @ r @ B @ (a_inv_a_b @ r @ C))) = (B = (add_a_b @ r @ A @ C))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 20.72/12.55 thf(16,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_add__diff__cancel__left_H)). 20.72/12.55 thf(325,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 20.72/12.55 thf(188,axiom,((! [A:a,B:a,C:a,D:a]: (((member449909584od_a_a @ (product_Pair_a_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ D @ A) @ (mult_a_ring_ext_a_b @ r @ B @ C)) @ (mult_a_ring_ext_a_b @ r @ B @ D)) @ (partia206007992t_unit @ rel)) <= (member449909584od_a_a @ (product_Pair_a_a @ C @ D) @ (partia206007992t_unit @ rel))) <= (member449909584od_a_a @ (product_Pair_a_a @ A @ B) @ (partia206007992t_unit @ rel))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_closed__rel__add)). 20.72/12.55 thf(924,plain,((! [A:a,B:a,C:a,D:a]: ((member449909584od_a_a @ (product_Pair_a_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ D @ A) @ (mult_a_ring_ext_a_b @ r @ B @ C)) @ (mult_a_ring_ext_a_b @ r @ B @ D)) @ (partia206007992t_unit @ rel)) | ~ (member449909584od_a_a @ (product_Pair_a_a @ C @ D) @ (partia206007992t_unit @ rel)) | ~ (member449909584od_a_a @ (product_Pair_a_a @ A @ B) @ (partia206007992t_unit @ rel))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 20.72/12.55 thf(140,axiom,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((a_inv_a_b @ r @ B) = A) <= (member_a @ A @ (partia1066395285xt_a_b @ r)))) <= ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_minus__equality)). 20.72/12.55 thf(756,plain,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((a_inv_a_b @ r @ B) = A) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r)))) | ~ ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 20.72/12.55 thf(149,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ A @ (add_a_b @ r @ (a_inv_a_b @ r @ A) @ B)) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_r__neg2)). 20.72/12.55 thf(789,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ A @ (add_a_b @ r @ (a_inv_a_b @ r @ A) @ B)) = B) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 20.72/12.55 thf(162,axiom,((! [A:a,B:a,C:a]: ((((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((A = (add_a_b @ r @ (a_inv_a_b @ r @ B) @ C)) = (C = (add_a_b @ r @ B @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_add_Oinv__solve__left)). 20.72/12.55 thf(834,plain,((! [A:a,B:a,C:a]: (((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((A = (add_a_b @ r @ (a_inv_a_b @ r @ B) @ C)) = (C = (add_a_b @ r @ B @ A)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 20.72/12.55 thf(86,axiom,((! [A:partia96731725t_unit,B:a,C:a]: ((((member_a @ C @ (partia1955795460t_unit @ A)) => ((B = (mult_a_Product_unit @ A @ B @ C)) = (C = (one_a_Product_unit @ A)))) <= (member_a @ B @ (partia1955795460t_unit @ A))) <= (group_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_group_Ol__cancel__one_H)). 20.72/12.55 thf(574,plain,((! [A:partia96731725t_unit,B:a,C:a]: (((member_a @ C @ (partia1955795460t_unit @ A)) => ((B = (mult_a_Product_unit @ A @ B @ C)) = (C = (one_a_Product_unit @ A)))) | ~ (member_a @ B @ (partia1955795460t_unit @ A)) | ~ (group_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 20.72/12.55 thf(259,axiom,((! [A:a,B:a,C:nat]: (((add_a_b @ r @ A @ B) = (add_a_b @ r @ B @ A)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ B) = (add_a_b @ r @ B @ (add_pow_a_b_nat @ r @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add_Ogroup__commutes__pow)). 20.72/12.55 thf(1169,plain,((! [A:a,B:a,C:nat]: (((add_a_b @ r @ A @ B) = (add_a_b @ r @ B @ A)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ B) = (add_a_b @ r @ B @ (add_pow_a_b_nat @ r @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 20.72/12.55 thf(194,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_f10)). 20.72/12.55 thf(956,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 20.72/12.55 thf(171,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (((mult_a_ring_ext_a_b @ A @ B @ C) = (mult_a_ring_ext_a_b @ A @ C @ B)) <= (member_a @ C @ (partia1066395285xt_a_b @ A)))) <= (comm_g791708116xt_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_comm__groupE_I4_J)). 20.72/12.55 thf(866,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (((mult_a_ring_ext_a_b @ A @ B @ C) = (mult_a_ring_ext_a_b @ A @ C @ B)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)))) | ~ (comm_g791708116xt_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 20.72/12.55 thf(243,axiom,((! [A:a]: ((? [B:a]: (((add_a_b @ r @ A @ B) = (zero_a_b @ r)) & (member_a @ B @ (partia1066395285xt_a_b @ r)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add_Or__inv__ex)). 20.72/12.55 thf(1119,plain,((! [A:a]: (? [B:a]: (((add_a_b @ r @ A @ B) = (zero_a_b @ r)) & (member_a @ B @ (partia1066395285xt_a_b @ r))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 20.72/12.55 thf(239,axiom,((! [A:a,B:int,C:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ (plus_plus_int @ B @ C) @ A) = (add_a_b @ r @ (add_pow_a_b_int @ r @ B @ A) @ (add_pow_a_b_int @ r @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add_Oint__pow__mult)). 20.72/12.55 thf(1104,plain,((! [A:a,B:int,C:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ (plus_plus_int @ B @ C) @ A) = (add_a_b @ r @ (add_pow_a_b_int @ r @ B @ A) @ (add_pow_a_b_int @ r @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 20.72/12.55 thf(274,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a,E:a]: ((abelian_group_a_b @ A) => ((((member_a @ D @ (partia1066395285xt_a_b @ A)) => (((a_minus_a_b @ A @ (add_a_b @ A @ (a_minus_a_b @ A @ B @ D) @ C) @ E) = (a_minus_a_b @ A @ (a_minus_a_b @ A @ (add_a_b @ A @ B @ C) @ D) @ E)) <= (member_a @ E @ (partia1066395285xt_a_b @ A)))) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_abelian__group_Ofour__elem__comm)). 20.72/12.55 thf(1242,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a,E:a]: ((abelian_group_a_b @ A) => (((member_a @ D @ (partia1066395285xt_a_b @ A)) => (((a_minus_a_b @ A @ (add_a_b @ A @ (a_minus_a_b @ A @ B @ D) @ C) @ E) = (a_minus_a_b @ A @ (a_minus_a_b @ A @ (add_a_b @ A @ B @ C) @ D) @ E)) | ~ (member_a @ E @ (partia1066395285xt_a_b @ A)))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 20.72/12.55 thf(5,axiom,((! [A:partia96731725t_unit]: ((member_a @ (one_a_Product_unit @ A) @ (partia1955795460t_unit @ A)) <= (comm_g1684316527t_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_comm__groupE_I2_J)). 20.72/12.55 thf(292,plain,((! [A:partia96731725t_unit]: ((member_a @ (one_a_Product_unit @ A) @ (partia1955795460t_unit @ A)) | ~ (comm_g1684316527t_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 20.72/12.55 thf(32,axiom,((! [A:nat,B:nat,C:nat]: ((A = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_add__right__imp__eq)). 20.72/12.55 thf(380,plain,((! [A:nat,B:nat,C:nat]: ((A = C) | ~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 20.72/12.55 thf(67,axiom,((! [A:partia96731725t_unit,B:a]: ((group_a_Product_unit @ A) => ((? [C:a]: (((mult_a_Product_unit @ A @ C @ B) = (one_a_Product_unit @ A)) & (member_a @ C @ (partia1955795460t_unit @ A)))) <= (member_a @ B @ (partia1955795460t_unit @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_group_Ol__inv__ex)). 20.72/12.55 thf(512,plain,((! [A:partia96731725t_unit,B:a]: ((group_a_Product_unit @ A) => (? [C:a]: (((mult_a_Product_unit @ A @ C @ B) = (one_a_Product_unit @ A)) & (member_a @ C @ (partia1955795460t_unit @ A))) | ~ (member_a @ B @ (partia1955795460t_unit @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 20.72/12.55 thf(71,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_ab__semigroup__add__class_Oadd__ac_I1_J)). 20.72/12.55 thf(529,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 20.72/12.55 thf(150,axiom,((! [A:a,B:a,C:a,D:a]: (((product_Pair_a_a @ A @ B) = (product_Pair_a_a @ C @ D)) => (~ ((B != D) <= (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Pair__inject)). 20.72/12.55 thf(793,plain,((! [A:a,B:a,C:a,D:a]: (((product_Pair_a_a @ A @ B) = (product_Pair_a_a @ C @ D)) => (~ (~ (B = D) | ~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 20.72/12.55 thf(263,axiom,((! [A:a,B:a,C:a]: (((mult_a_ring_ext_a_b @ r @ A @ B) = (one_a_ring_ext_a_b @ r)) => (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((A = C) <= (member_a @ C @ (partia1066395285xt_a_b @ r))))) <= ((mult_a_ring_ext_a_b @ r @ B @ C) = (one_a_ring_ext_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_inv__unique)). 20.72/12.55 thf(1199,plain,((! [A:a,B:a,C:a]: (((mult_a_ring_ext_a_b @ r @ A @ B) = (one_a_ring_ext_a_b @ r)) => (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((A = C) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r))))) | ~ ((mult_a_ring_ext_a_b @ r @ B @ C) = (one_a_ring_ext_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 20.72/12.55 thf(128,axiom,((! [A:a,B:a,C:a]: ((((((member_a @ C @ (partia1066395285xt_a_b @ r)) => (A = C)) <= (member_a @ A @ (partia1066395285xt_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= ((add_a_b @ r @ B @ C) = (zero_a_b @ r))) <= ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_local_Ominus__unique)). 20.72/12.55 thf(714,plain,((! [A:a,B:a,C:a]: (((member_a @ C @ (partia1066395285xt_a_b @ r)) => (A = C)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ ((add_a_b @ r @ B @ C) = (zero_a_b @ r)) | ~ ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 20.72/12.55 thf(223,axiom,((! [A:a,B:a,C:a]: (((add_a_b @ r @ A @ B) = C) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (a_inv_a_b @ r @ A) @ C) = B)) <= (member_a @ B @ (partia1066395285xt_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_a__transpose__inv)). 20.72/12.55 thf(1057,plain,((! [A:a,B:a,C:a]: (((add_a_b @ r @ A @ B) = C) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (a_inv_a_b @ r @ A) @ C) = B)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 20.72/12.55 thf(19,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_add__Suc__shift)). 20.72/12.55 thf(334,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 20.72/12.55 thf(184,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ B @ (zero_a_b @ A)) = B)) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_semiring_Osemiring__simprules_I11_J)). 20.72/12.55 thf(910,plain,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ B @ (zero_a_b @ A)) = B)) | ~ (semiring_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 20.72/12.55 thf(269,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((comm_g791708116xt_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ (mult_a_ring_ext_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A)) <= (member_a @ C @ (partia1066395285xt_a_b @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_comm__groupE_I1_J)). 20.72/12.55 thf(1223,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((comm_g791708116xt_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ (mult_a_ring_ext_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 20.72/12.55 thf(233,axiom,((! [A:a,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((mult_a_ring_ext_a_b @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ C @ A) @ (mult_a_ring_ext_a_b @ r @ C @ B))) <= (member_a @ C @ (partia1066395285xt_a_b @ r)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_r__distr)). 20.72/12.55 thf(1091,plain,((! [A:a,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((mult_a_ring_ext_a_b @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ C @ A) @ (mult_a_ring_ext_a_b @ r @ C @ B))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 20.72/12.55 thf(159,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ (mult_a_ring_ext_a_b @ r @ s3 @ s2)) @ s3))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_061_As_A_092_060otimes_062_A_Is_H_H_A_092_060otimes_062_As_H_J_A_092_060otimes_062_As_H_H_092_060close_062)). 20.72/12.55 thf(825,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ (mult_a_ring_ext_a_b @ r @ s3 @ s2)) @ s3))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 20.72/12.55 thf(219,axiom,((! [A:a,B:a,C:int]: (((add_a_b @ r @ A @ B) = (add_a_b @ r @ B @ A)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((add_pow_a_b_int @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (add_pow_a_b_int @ r @ C @ A) @ (add_pow_a_b_int @ r @ C @ B))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add_Oint__pow__mult__distrib)). 20.72/12.55 thf(1042,plain,((! [A:a,B:a,C:int]: (((add_a_b @ r @ A @ B) = (add_a_b @ r @ B @ A)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((add_pow_a_b_int @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (add_pow_a_b_int @ r @ C @ A) @ (add_pow_a_b_int @ r @ C @ B))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 20.72/12.55 thf(277,axiom,((! [A:a,B:a,C:a]: (((((mult_a_ring_ext_a_b @ r @ A @ (mult_a_ring_ext_a_b @ r @ B @ C)) = (mult_a_ring_ext_a_b @ r @ B @ (mult_a_ring_ext_a_b @ r @ A @ C))) <= (member_a @ C @ (partia1066395285xt_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_m__lcomm)). 20.72/12.55 thf(1255,plain,((! [A:a,B:a,C:a]: (((mult_a_ring_ext_a_b @ r @ A @ (mult_a_ring_ext_a_b @ r @ B @ C)) = (mult_a_ring_ext_a_b @ r @ B @ (mult_a_ring_ext_a_b @ r @ A @ C))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 20.72/12.55 thf(91,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_diff__add__inverse)). 20.72/12.55 thf(598,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 20.72/12.55 thf(7,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_old_Onat_Oinject)). 20.72/12.55 thf(297,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 20.72/12.55 thf(156,axiom,((! [A:product_prod_a_a]: ? [B:a,C:a]: (A = (product_Pair_a_a @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_surj__pair)). 20.72/12.55 thf(815,plain,((! [A:product_prod_a_a]: ? [B:a,C:a]: (A = (product_Pair_a_a @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 20.72/12.55 thf(273,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (add_a_b @ r @ A @ B) @ C) = (add_a_b @ r @ A @ (add_a_b @ r @ B @ C)))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_add_Om__assoc)). 20.72/12.55 thf(1238,plain,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (add_a_b @ r @ A @ B) @ C) = (add_a_b @ r @ A @ (add_a_b @ r @ B @ C)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 20.72/12.55 thf(244,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (mult_a_ring_ext_a_b @ A @ B @ C) @ D) = (mult_a_ring_ext_a_b @ A @ B @ (mult_a_ring_ext_a_b @ A @ C @ D)))) <= (member_a @ C @ (partia1066395285xt_a_b @ A)))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_semiring_Osemiring__simprules_I8_J)). 20.72/12.55 thf(1123,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (mult_a_ring_ext_a_b @ A @ B @ C) @ D) = (mult_a_ring_ext_a_b @ A @ B @ (mult_a_ring_ext_a_b @ A @ C @ D)))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)))) | ~ (semiring_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 20.72/12.55 thf(170,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((((add_a_b @ A @ B @ C) = (add_a_b @ A @ C @ B)) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_abelian__groupE_I4_J)). 20.72/12.55 thf(862,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((add_a_b @ A @ B @ C) = (add_a_b @ A @ C @ B)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 20.72/12.55 thf(24,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/sandbox2/benchmark/theBenchmark.p',fact_164_group__cancel_Oadd2)). 20.72/12.55 thf(349,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)],[24])). 20.72/12.55 thf(39,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_add__diff__cancel__right_H)). 20.72/12.55 thf(407,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 20.72/12.55 thf(102,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (minus_minus_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_add__diff__cancel__left)). 20.72/12.55 thf(630,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (minus_minus_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 20.72/12.55 thf(83,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (plus_plus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_add__diff__eq)). 20.72/12.55 thf(566,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (plus_plus_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 20.72/12.55 thf(167,axiom,((! [A:a,B:int]: ((member_a @ (add_pow_a_b_int @ r @ B @ A) @ (partia1066395285xt_a_b @ r)) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add_Oint__pow__closed)). 20.72/12.55 thf(852,plain,((! [A:a,B:int]: ((member_a @ (add_pow_a_b_int @ r @ B @ A) @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 20.72/12.55 thf(113,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_diff__cancel2)). 20.72/12.55 thf(665,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 20.72/12.55 thf(256,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ r4) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ r3) @ r4))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060otimes_062_Ar_H_H_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062)). 20.72/12.55 thf(1159,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ r4) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ r3) @ r4))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 20.72/12.55 thf(229,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((a_inv_a_b @ A @ (add_a_b @ A @ B @ C)) = (a_minus_a_b @ A @ (a_inv_a_b @ A @ B) @ C))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_abelian__group_Oinv__add)). 20.72/12.55 thf(1079,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((a_inv_a_b @ A @ (add_a_b @ A @ B @ C)) = (a_minus_a_b @ A @ (a_inv_a_b @ A @ B) @ C))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 20.72/12.55 thf(78,axiom,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_add_Oinverse__distrib__swap)). 20.72/12.55 thf(551,plain,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 20.72/12.55 thf(127,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((a_inv_a_b @ r @ (add_a_b @ r @ A @ B)) = (a_minus_a_b @ r @ (a_inv_a_b @ r @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_inv__add)). 20.72/12.55 thf(710,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((a_inv_a_b @ r @ (add_a_b @ r @ A @ B)) = (a_minus_a_b @ r @ (a_inv_a_b @ r @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 20.72/12.55 thf(164,axiom,((! [A:a,B:nat,C:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((add_pow_a_b_nat @ r @ B @ A) = (add_pow_a_b_nat @ r @ C @ A)) => ((add_pow_a_b_nat @ r @ (minus_minus_nat @ B @ C) @ A) = (zero_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_add_Opow__eq__div2)). 20.72/12.55 thf(842,plain,((! [A:a,B:nat,C:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((add_pow_a_b_nat @ r @ B @ A) = (add_pow_a_b_nat @ r @ C @ A)) => ((add_pow_a_b_nat @ r @ (minus_minus_nat @ B @ C) @ A) = (zero_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 20.72/12.55 thf(1,conjecture,((member449909584od_a_a @ (product_Pair_a_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3))) @ (partia206007992t_unit @ rel))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 20.72/12.55 thf(2,negated_conjecture,((~ (member449909584od_a_a @ (product_Pair_a_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3))) @ (partia206007992t_unit @ rel)))),inference(neg_conjecture,[status(cth)],[1])). 20.72/12.55 thf(285,plain,((~ (member449909584od_a_a @ (product_Pair_a_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3))) @ (partia206007992t_unit @ rel)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 20.72/12.55 thf(118,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (((add_a_b @ A @ B @ C) = (add_a_b @ A @ C @ B)) <= (member_a @ C @ (partia1066395285xt_a_b @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_semiring_Osemiring__simprules_I7_J)). 20.72/12.55 thf(682,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (((add_a_b @ A @ B @ C) = (add_a_b @ A @ C @ B)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 20.72/12.55 thf(262,axiom,((! [A:a]: ((? [B:a]: (((mult_a_ring_ext_a_b @ r @ B @ A) = (one_a_ring_ext_a_b @ r)) & (member_a @ B @ (partia1066395285xt_a_b @ r)))) <= (member_a @ A @ (units_a_ring_ext_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_Units__l__inv__ex)). 20.72/12.55 thf(1195,plain,((! [A:a]: (? [B:a]: (((mult_a_ring_ext_a_b @ r @ B @ A) = (one_a_ring_ext_a_b @ r)) & (member_a @ B @ (partia1066395285xt_a_b @ r))) | ~ (member_a @ A @ (units_a_ring_ext_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 20.72/12.55 thf(87,axiom,((! [A:int,B:int]: ((minus_minus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ (uminus_uminus_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_minus__diff__commute)). 20.72/12.55 thf(578,plain,((! [A:int,B:int]: ((minus_minus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ (uminus_uminus_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 20.72/12.55 thf(173,axiom,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (a_inv_a_b @ r @ A) @ B) = (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ A @ B)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_l__minus)). 20.72/12.55 thf(874,plain,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (a_inv_a_b @ r @ A) @ B) = (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ A @ B)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 20.72/12.55 thf(278,axiom,((! [A:a,B:a]: ((((mult_a_ring_ext_a_b @ r @ A @ B) = (mult_a_ring_ext_a_b @ r @ B @ A)) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_m__comm)). 20.72/12.55 thf(1259,plain,((! [A:a,B:a]: (((mult_a_ring_ext_a_b @ r @ A @ B) = (mult_a_ring_ext_a_b @ r @ B @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 20.72/12.55 thf(109,axiom,((! [A:int,B:int,C:int,D:int]: (((A = B) & (C = D)) => ((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_add__mono__thms__linordered__semiring_I4_J)). 20.72/12.55 thf(650,plain,((! [A:int,B:int,C:int,D:int]: (((A = B) & (C = D)) => ((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 20.72/12.55 thf(225,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((! [B:a]: (((add_a_b @ r @ A @ B) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))) => (A = (zero_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add_Oone__unique)). 20.72/12.55 thf(1064,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((! [B:a]: (((add_a_b @ r @ A @ B) = B) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))) => (A = (zero_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 20.72/12.55 thf(241,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ A @ B) = A) = (B = (zero_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add_Ol__cancel__one)). 20.72/12.55 thf(1111,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ A @ B) = A) = (B = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 20.72/12.55 thf(38,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_n__not__Suc__n)). 20.72/12.55 thf(403,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 20.72/12.55 thf(235,axiom,((! [A:a]: (((mult_a_ring_ext_a_b @ r @ A @ (one_a_ring_ext_a_b @ r)) = A) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_r__one)). 20.72/12.55 thf(1096,plain,((! [A:a]: (((mult_a_ring_ext_a_b @ r @ A @ (one_a_ring_ext_a_b @ r)) = A) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 20.72/12.55 thf(248,axiom,((group_a_Product_unit @ (units_1411277569xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_units__group)). 20.72/12.55 thf(1138,plain,((group_a_Product_unit @ (units_1411277569xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 20.72/12.55 thf(95,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_add_Ocommute)). 20.72/12.55 thf(610,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 20.72/12.55 thf(203,axiom,(((mult_a_ring_ext_a_b @ r @ (one_a_ring_ext_a_b @ r) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))))) = (zero_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_f11)). 20.72/12.55 thf(989,plain,(((mult_a_ring_ext_a_b @ r @ (one_a_ring_ext_a_b @ r) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))))) = (zero_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 20.72/12.55 thf(123,axiom,((member_a @ (one_a_ring_ext_a_b @ r) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_semiring__simprules_I4_J)). 20.72/12.55 thf(697,plain,((member_a @ (one_a_ring_ext_a_b @ r) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 20.72/12.55 thf(272,axiom,((! [A:a,B:a,C:nat]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ A @ (add_pow_a_b_nat @ r @ C @ B)) = (add_pow_a_b_nat @ r @ C @ (mult_a_ring_ext_a_b @ r @ A @ B)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__pow__rdistr)). 20.72/12.55 thf(1234,plain,((! [A:a,B:a,C:nat]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ A @ (add_pow_a_b_nat @ r @ C @ B)) = (add_pow_a_b_nat @ r @ C @ (mult_a_ring_ext_a_b @ r @ A @ B)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 20.72/12.55 thf(176,axiom,((member449909584od_a_a @ (product_Pair_a_a @ r3 @ s2) @ (partia206007992t_unit @ rel))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I2_J)). 20.72/12.55 thf(884,plain,((member449909584od_a_a @ (product_Pair_a_a @ r3 @ s2) @ (partia206007992t_unit @ rel))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 20.72/12.55 thf(79,axiom,((! [A:int,B:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_diff__add__cancel)). 20.72/12.55 thf(554,plain,((! [A:int,B:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 20.72/12.55 thf(106,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_add_Oassoc)). 20.72/12.55 thf(642,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)],[106])). 20.72/12.55 thf(70,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_add__right__cancel)). 20.72/12.55 thf(526,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)],[70])). 20.72/12.55 thf(211,axiom,((! [A:a,B:a,C:a,D:a]: (((product_Pair_a_a @ A @ B) = (product_Pair_a_a @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_old_Oprod_Oinject)). 20.72/12.55 thf(1016,plain,((! [A:a,B:a,C:a,D:a]: (((product_Pair_a_a @ A @ B) = (product_Pair_a_a @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 20.72/12.55 thf(126,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (((add_a_b @ A @ B @ (add_a_b @ A @ C @ D)) = (add_a_b @ A @ C @ (add_a_b @ A @ B @ D))) <= (member_a @ D @ (partia1066395285xt_a_b @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_semiring_Osemiring__simprules_I12_J)). 20.72/12.55 thf(706,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (((add_a_b @ A @ B @ (add_a_b @ A @ C @ D)) = (add_a_b @ A @ C @ (add_a_b @ A @ B @ D))) | ~ (member_a @ D @ (partia1066395285xt_a_b @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 20.72/12.55 thf(17,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_diff__diff__add)). 20.72/12.55 thf(328,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 20.72/12.55 thf(55,axiom,((minus_minus_int = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_diff__conv__add__uminus)). 20.72/12.55 thf(471,plain,(((minus_minus_int) = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 20.72/12.55 thf(181,axiom,((member449909584od_a_a @ (product_Pair_a_a @ (mult_a_ring_ext_a_b @ r @ r3 @ r4) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (partia206007992t_unit @ rel))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_f5)). 20.72/12.55 thf(901,plain,((member449909584od_a_a @ (product_Pair_a_a @ (mult_a_ring_ext_a_b @ r @ r3 @ r4) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (partia206007992t_unit @ rel))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 20.72/12.55 thf(119,axiom,((! [A:a,B:a,C:nat]: (((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_nat @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ (add_pow_a_b_nat @ r @ C @ B))))) <= ((add_a_b @ r @ A @ B) = (add_a_b @ r @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_add_Opow__mult__distrib)). 20.72/12.55 thf(686,plain,((! [A:a,B:a,C:nat]: (((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_nat @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ (add_pow_a_b_nat @ r @ C @ B))))) | ~ ((add_a_b @ r @ A @ B) = (add_a_b @ r @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 20.72/12.55 thf(228,axiom,((! [A:product_prod_a_a]: ~ (! [B:a,C:a]: (A != (product_Pair_a_a @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_old_Oprod_Oexhaust)). 20.72/12.55 thf(1075,plain,((! [A:product_prod_a_a]: ~ (! [B:a,C:a]: ~ (A = (product_Pair_a_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 20.72/12.55 thf(236,axiom,((member449909584od_a_a @ (product_Pair_a_a @ (mult_a_ring_ext_a_b @ r @ r2 @ r4) @ (mult_a_ring_ext_a_b @ r @ s @ s3)) @ (partia206007992t_unit @ rel))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f4)). 20.72/12.55 thf(1099,plain,((member449909584od_a_a @ (product_Pair_a_a @ (mult_a_ring_ext_a_b @ r @ r2 @ r4) @ (mult_a_ring_ext_a_b @ r @ s @ s3)) @ (partia206007992t_unit @ rel))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 20.72/12.55 thf(110,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((minus_minus_int @ A @ D) = (plus_plus_int @ B @ (minus_minus_int @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_group__cancel_Osub1)). 20.72/12.55 thf(654,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((minus_minus_int @ A @ D) = (plus_plus_int @ B @ (minus_minus_int @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 20.72/12.55 thf(130,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_f8)). 20.72/12.55 thf(721,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 20.72/12.55 thf(84,axiom,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_of__nat__add)). 20.72/12.55 thf(569,plain,((! [A:nat,B:nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 20.72/12.55 thf(275,axiom,((! [A:a,B:nat]: (((add_pow_a_b_nat @ r @ B @ (a_inv_a_b @ r @ A)) = (a_inv_a_b @ r @ (add_pow_a_b_nat @ r @ B @ A))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add_Onat__pow__inv)). 20.72/12.55 thf(1246,plain,((! [A:a,B:nat]: (((add_pow_a_b_nat @ r @ B @ (a_inv_a_b @ r @ A)) = (a_inv_a_b @ r @ (add_pow_a_b_nat @ r @ B @ A))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 20.72/12.55 thf(64,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Nat_Odiff__cancel)). 20.72/12.55 thf(503,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 20.72/12.55 thf(108,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_add__diff__cancel__left_H)). 20.72/12.55 thf(647,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 20.72/12.55 thf(279,axiom,((! [A:a,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((((mult_a_ring_ext_a_b @ r @ A @ B) = (mult_a_ring_ext_a_b @ r @ A @ C)) = (B = C)) <= (member_a @ C @ (partia1066395285xt_a_b @ r)))) <= (member_a @ A @ (units_a_ring_ext_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Units__l__cancel)). 20.72/12.55 thf(1263,plain,((! [A:a,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((((mult_a_ring_ext_a_b @ r @ A @ B) = (mult_a_ring_ext_a_b @ r @ A @ C)) = (B = C)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r)))) | ~ (member_a @ A @ (units_a_ring_ext_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 20.72/12.55 thf(206,axiom,((! [A:a,B:a]: ((((add_a_b @ r @ A @ B) = (add_a_b @ r @ B @ A)) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add_Om__comm)). 20.72/12.55 thf(997,plain,((! [A:a,B:a]: (((add_a_b @ r @ A @ B) = (add_a_b @ r @ B @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 20.72/12.55 thf(221,axiom,((! [A:a,B:a,C:nat]: ((((mult_a_ring_ext_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ B) = (add_pow_a_b_nat @ r @ C @ (mult_a_ring_ext_a_b @ r @ A @ B))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__pow__ldistr)). 20.72/12.55 thf(1050,plain,((! [A:a,B:a,C:nat]: (((mult_a_ring_ext_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ B) = (add_pow_a_b_nat @ r @ C @ (mult_a_ring_ext_a_b @ r @ A @ B))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 20.72/12.55 thf(51,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_add__Suc)). 20.72/12.55 thf(457,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 20.72/12.55 thf(22,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ (a_inv_a_b @ A @ B) @ (partia1066395285xt_a_b @ A)) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_abelian__group_Oa__inv__closed)). 20.72/12.55 thf(343,plain,((! [A:partia1833973666xt_a_b,B:a]: ((member_a @ (a_inv_a_b @ A @ B) @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 20.72/12.55 thf(231,axiom,((member449909584od_a_a @ (product_Pair_a_a @ r4 @ s3) @ (partia206007992t_unit @ rel))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I3_J)). 20.72/12.55 thf(1086,plain,((member449909584od_a_a @ (product_Pair_a_a @ r4 @ s3) @ (partia206007992t_unit @ rel))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 20.72/12.55 thf(103,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_add__diff__cancel__right)). 20.72/12.55 thf(633,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 20.72/12.55 thf(153,axiom,((! [A:partia1833973666xt_a_b,B:a]: ((abelian_group_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (zero_a_b @ A) @ B) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_abelian__groupE_I5_J)). 20.72/12.55 thf(805,plain,((! [A:partia1833973666xt_a_b,B:a]: ((abelian_group_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (zero_a_b @ A) @ B) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 20.72/12.55 thf(187,axiom,((! [A:product_prod_a_a,B:(product_prod_a_a > $o)]: ((member449909584od_a_a @ A @ (collec645855634od_a_a @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq)). 20.72/12.55 thf(921,plain,((! [A:product_prod_a_a,B:(product_prod_a_a > $o)]: ((member449909584od_a_a @ A @ (collec645855634od_a_a @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 20.72/12.55 thf(222,axiom,((! [A:a,B:a]: (((member_a @ A @ (units_a_ring_ext_a_b @ r)) => ((member_a @ B @ (units_a_ring_ext_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ B @ A) = (one_a_ring_ext_a_b @ r)))) <= ((mult_a_ring_ext_a_b @ r @ A @ B) = (one_a_ring_ext_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Units__inv__comm)). 20.72/12.55 thf(1054,plain,((! [A:a,B:a]: (((member_a @ A @ (units_a_ring_ext_a_b @ r)) => ((member_a @ B @ (units_a_ring_ext_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ B @ A) = (one_a_ring_ext_a_b @ r)))) | ~ ((mult_a_ring_ext_a_b @ r @ A @ B) = (one_a_ring_ext_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 20.72/12.55 thf(214,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((((member_a @ C @ (partia1066395285xt_a_b @ A)) => (((add_a_b @ A @ (add_a_b @ A @ B @ C) @ D) = (add_a_b @ A @ B @ (add_a_b @ A @ C @ D))) <= (member_a @ D @ (partia1066395285xt_a_b @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_abelian__groupE_I3_J)). 20.72/12.55 thf(1026,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: (((member_a @ C @ (partia1066395285xt_a_b @ A)) => (((add_a_b @ A @ (add_a_b @ A @ B @ C) @ D) = (add_a_b @ A @ B @ (add_a_b @ A @ C @ D))) | ~ (member_a @ D @ (partia1066395285xt_a_b @ A)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 20.72/12.55 thf(145,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((((add_a_b @ r @ B @ A) = (add_a_b @ r @ C @ A)) = (B = C)) <= (member_a @ C @ (partia1066395285xt_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_local_Oadd_Oright__cancel)). 20.72/12.55 thf(773,plain,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((((add_a_b @ r @ B @ A) = (add_a_b @ r @ C @ A)) = (B = C)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 20.72/12.55 thf(112,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add__Suc__right)). 20.72/12.55 thf(662,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 20.72/12.55 thf(129,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (member_a @ (mult_a_ring_ext_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_semiring_Osemiring__simprules_I3_J)). 20.72/12.55 thf(718,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (member_a @ (mult_a_ring_ext_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 20.72/12.55 thf(178,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (? [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) & ((mult_a_ring_ext_a_b @ A @ B @ C) = (one_a_ring_ext_a_b @ A))))) <= (group_a_ring_ext_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_group_Or__inv__ex)). 20.72/12.55 thf(888,plain,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (? [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) & ((mult_a_ring_ext_a_b @ A @ B @ C) = (one_a_ring_ext_a_b @ A))))) | ~ (group_a_ring_ext_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 20.72/12.55 thf(183,axiom,((! [A:a,B:a]: ((((A = (add_a_b @ r @ A @ B)) = (B = (zero_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add_Ol__cancel__one_H)). 20.72/12.55 thf(906,plain,((! [A:a,B:a]: (((A = (add_a_b @ r @ A @ B)) = (B = (zero_a_b @ r))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 20.72/12.55 thf(197,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (zero_a_b @ A) @ B) = B)) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_semiring_Osemiring__simprules_I6_J)). 20.72/12.55 thf(965,plain,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (zero_a_b @ A) @ B) = B)) | ~ (semiring_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 20.72/12.55 thf(238,axiom,((member449909584od_a_a @ (product_Pair_a_a @ r2 @ s) @ (partia206007992t_unit @ rel))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I1_J)). 20.72/12.55 thf(1103,plain,((member449909584od_a_a @ (product_Pair_a_a @ r2 @ s) @ (partia206007992t_unit @ rel))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 20.72/12.55 thf(268,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => ((((add_a_b @ A @ (a_inv_a_b @ A @ B) @ (add_a_b @ A @ B @ C)) = C) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_abelian__group_Or__neg1)). 20.72/12.55 thf(1219,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => (((add_a_b @ A @ (a_inv_a_b @ A @ B) @ (add_a_b @ A @ B @ C)) = C) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 20.72/12.55 thf(92,axiom,((! [A:(product_prod_a_a > $o),B:(product_prod_a_a > $o)]: ((! [C:product_prod_a_a]: ((A @ C) = (B @ C))) => ((collec645855634od_a_a @ A) = (collec645855634od_a_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Collect__cong)). 20.72/12.55 thf(601,plain,((! [A:(product_prod_a_a > $o),B:(product_prod_a_a > $o)]: ((! [C:product_prod_a_a]: ((A @ C) = (B @ C))) => ((collec645855634od_a_a @ (A)) = (collec645855634od_a_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 20.72/12.55 thf(254,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((((add_a_b @ A @ B @ (add_a_b @ A @ (a_inv_a_b @ A @ B) @ C)) = C) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_abelian__group_Or__neg2)). 20.72/12.55 thf(1154,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((add_a_b @ A @ B @ (add_a_b @ A @ (a_inv_a_b @ A @ B) @ C)) = C) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 20.72/12.55 thf(44,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_diff__Suc__Suc)). 20.72/12.55 thf(423,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 20.72/12.55 thf(133,axiom,((! [A:partia1833973666xt_a_b]: ((mult_a_Product_unit @ (units_1411277569xt_a_b @ A)) = (mult_a_ring_ext_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_units__of__mult)). 20.72/12.55 thf(732,plain,((! [A:partia1833973666xt_a_b]: ((mult_a_Product_unit @ (units_1411277569xt_a_b @ A)) = (mult_a_ring_ext_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 20.72/12.55 thf(3,axiom,((! [A:partia96731725t_unit]: ((one_a_Product_unit @ (units_873712258t_unit @ A)) = (one_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_units__of__one)). 20.72/12.55 thf(286,plain,((! [A:partia96731725t_unit]: ((one_a_Product_unit @ (units_873712258t_unit @ A)) = (one_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 20.72/12.55 thf(195,axiom,((! [A:partia1833973666xt_a_b,B:a]: ((((add_a_b @ A @ (a_inv_a_b @ A @ B) @ B) = (zero_a_b @ A)) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_abelian__group_Ol__neg)). 20.72/12.55 thf(958,plain,((! [A:partia1833973666xt_a_b,B:a]: (((add_a_b @ A @ (a_inv_a_b @ A @ B) @ B) = (zero_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 20.72/12.55 thf(41,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_diff__diff__add)). 20.72/12.55 thf(413,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 20.72/12.55 thf(209,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_A_092_060otimes_062_Ar_H_H_J_A_092_060oplus_062_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_092_060close_062)). 20.72/12.55 thf(1007,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 20.72/12.55 thf(121,axiom,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4))))) = (zero_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_A_092_060otimes_062_Ar_H_H_J_A_092_060oplus_062_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_A_061_A_092_060zero_062_092_060close_062)). 20.72/12.55 thf(694,plain,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ r2 @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4))))) = (zero_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 20.72/12.55 thf(270,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((B = (mult_a_ring_ext_a_b @ A @ B @ C)) = (C = (one_a_ring_ext_a_b @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (group_a_ring_ext_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_group_Ol__cancel__one_H)). 20.72/12.55 thf(1226,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((B = (mult_a_ring_ext_a_b @ A @ B @ C)) = (C = (one_a_ring_ext_a_b @ A)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (group_a_ring_ext_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 20.72/12.55 thf(76,axiom,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_of__nat__eq__iff)). 20.72/12.55 thf(545,plain,((! [A:nat,B:nat]: (((semiri2019852685at_int @ A) = (semiri2019852685at_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 20.72/12.55 thf(85,axiom,((plus_plus_int = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add_Ocommute)). 20.72/12.55 thf(572,plain,(((plus_plus_int) = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 20.72/12.55 thf(12,axiom,((! [A:partia1833973666xt_a_b]: ((member_a @ (one_a_ring_ext_a_b @ A) @ (partia1066395285xt_a_b @ A)) <= (comm_g791708116xt_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_comm__groupE_I2_J)). 20.72/12.55 thf(313,plain,((! [A:partia1833973666xt_a_b]: ((member_a @ (one_a_ring_ext_a_b @ A) @ (partia1066395285xt_a_b @ A)) | ~ (comm_g791708116xt_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 20.72/12.55 thf(281,axiom,((! [A:a]: ((? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((add_a_b @ r @ B @ A) = (zero_a_b @ r)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add_Ol__inv__ex)). 20.72/12.55 thf(1271,plain,((! [A:a]: (? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((add_a_b @ r @ B @ A) = (zero_a_b @ r))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 20.72/12.55 thf(35,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_nat_Oinject)). 20.72/12.55 thf(391,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 20.72/12.55 thf(249,axiom,((! [A:a]: (((a_inv_a_b @ r @ (a_inv_a_b @ r @ A)) = A) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_local_Ominus__minus)). 20.72/12.55 thf(1139,plain,((! [A:a]: (((a_inv_a_b @ r @ (a_inv_a_b @ r @ A)) = A) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 20.72/12.55 thf(47,axiom,((! [A:partia96731725t_unit,B:a,C:a]: ((((member_a @ C @ (partia1955795460t_unit @ A)) => ((B = (mult_a_Product_unit @ A @ C @ B)) = (C = (one_a_Product_unit @ A)))) <= (member_a @ B @ (partia1955795460t_unit @ A))) <= (group_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_group_Or__cancel__one_H)). 20.72/12.55 thf(445,plain,((! [A:partia96731725t_unit,B:a,C:a]: (((member_a @ C @ (partia1955795460t_unit @ A)) => ((B = (mult_a_Product_unit @ A @ C @ B)) = (C = (one_a_Product_unit @ A)))) | ~ (member_a @ B @ (partia1955795460t_unit @ A)) | ~ (group_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 20.72/12.55 thf(192,axiom,(((! [A:a]: ((? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((mult_a_ring_ext_a_b @ r @ B @ A) = (one_a_ring_ext_a_b @ r)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r)))) => (group_a_ring_ext_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_group__l__invI)). 20.72/12.55 thf(936,plain,(((! [A:a]: (? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((mult_a_ring_ext_a_b @ r @ B @ A) = (one_a_ring_ext_a_b @ r))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r)))) => (group_a_ring_ext_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 20.72/12.55 thf(161,axiom,((! [A:a,B:a]: ((member_a @ A @ (units_a_ring_ext_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ A @ B) @ (units_a_ring_ext_a_b @ r)) <= (member_a @ B @ (units_a_ring_ext_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Units__m__closed)). 20.72/12.55 thf(831,plain,((! [A:a,B:a]: ((member_a @ A @ (units_a_ring_ext_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ A @ B) @ (units_a_ring_ext_a_b @ r)) | ~ (member_a @ B @ (units_a_ring_ext_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 20.72/12.55 thf(43,axiom,((! [A:partia96731725t_unit,B:a,C:a,D:a]: (((member_a @ B @ (partia1955795460t_unit @ A)) => (((member_a @ D @ (partia1955795460t_unit @ A)) => ((mult_a_Product_unit @ A @ (mult_a_Product_unit @ A @ B @ C) @ D) = (mult_a_Product_unit @ A @ B @ (mult_a_Product_unit @ A @ C @ D)))) <= (member_a @ C @ (partia1955795460t_unit @ A)))) <= (comm_g1684316527t_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_comm__groupE_I3_J)). 20.72/12.55 thf(419,plain,((! [A:partia96731725t_unit,B:a,C:a,D:a]: (((member_a @ B @ (partia1955795460t_unit @ A)) => (((member_a @ D @ (partia1955795460t_unit @ A)) => ((mult_a_Product_unit @ A @ (mult_a_Product_unit @ A @ B @ C) @ D) = (mult_a_Product_unit @ A @ B @ (mult_a_Product_unit @ A @ C @ D)))) | ~ (member_a @ C @ (partia1955795460t_unit @ A)))) | ~ (comm_g1684316527t_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 20.72/12.55 thf(31,axiom,((! [A:int,B:int,C:int]: ((A = (minus_minus_int @ B @ C)) = ((plus_plus_int @ A @ C) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_eq__diff__eq)). 20.72/12.55 thf(377,plain,((! [A:int,B:int,C:int]: ((A = (minus_minus_int @ B @ C)) = ((plus_plus_int @ A @ C) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 20.72/12.55 thf(49,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_ab__semigroup__add__class_Oadd__ac_I1_J)). 20.72/12.55 thf(451,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)],[49])). 20.72/12.55 thf(14,axiom,((! [A:partia96731725t_unit,B:a,C:a,D:a]: (((member_a @ B @ (partia1955795460t_unit @ A)) => ((member_a @ C @ (partia1955795460t_unit @ A)) => ((((mult_a_Product_unit @ A @ C @ B) = (mult_a_Product_unit @ A @ D @ B)) = (C = D)) <= (member_a @ D @ (partia1955795460t_unit @ A))))) <= (group_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Group_Ogroup_Oright__cancel)). 20.72/12.55 thf(318,plain,((! [A:partia96731725t_unit,B:a,C:a,D:a]: (((member_a @ B @ (partia1955795460t_unit @ A)) => ((member_a @ C @ (partia1955795460t_unit @ A)) => ((((mult_a_Product_unit @ A @ C @ B) = (mult_a_Product_unit @ A @ D @ B)) = (C = D)) | ~ (member_a @ D @ (partia1955795460t_unit @ A))))) | ~ (group_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 20.72/12.55 thf(9,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_diff__commute)). 20.72/12.55 thf(303,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 20.72/12.55 thf(142,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => (((member_a @ (add_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A)) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_abelian__groupE_I1_J)). 20.72/12.55 thf(764,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => ((member_a @ (add_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 20.72/12.55 thf(93,axiom,((! [A:partia96731725t_unit,B:a,C:a]: ((((member_a @ (mult_a_Product_unit @ A @ B @ C) @ (partia1955795460t_unit @ A)) <= (member_a @ C @ (partia1955795460t_unit @ A))) <= (member_a @ B @ (partia1955795460t_unit @ A))) <= (comm_g1684316527t_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_comm__groupE_I1_J)). 20.72/12.55 thf(604,plain,((! [A:partia96731725t_unit,B:a,C:a]: ((member_a @ (mult_a_Product_unit @ A @ B @ C) @ (partia1955795460t_unit @ A)) | ~ (member_a @ C @ (partia1955795460t_unit @ A)) | ~ (member_a @ B @ (partia1955795460t_unit @ A)) | ~ (comm_g1684316527t_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 20.72/12.55 thf(66,axiom,((! [A:partia1833973666xt_a_b]: (((one_a_ring_ext_a_b @ A) != (zero_a_b @ A)) <= (field_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_one__not__zero)). 20.72/12.55 thf(509,plain,((! [A:partia1833973666xt_a_b]: (~ ((one_a_ring_ext_a_b @ A) = (zero_a_b @ A)) | ~ (field_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 20.72/12.55 thf(175,axiom,((! [A:a,B:a,C:a,D:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((member_a @ D @ (partia1066395285xt_a_b @ r)) => ((a_minus_a_b @ r @ (add_a_b @ r @ (a_minus_a_b @ r @ A @ C) @ B) @ D) = (a_minus_a_b @ r @ (a_minus_a_b @ r @ (add_a_b @ r @ A @ B) @ C) @ D)))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_four__elem__comm)). 20.72/12.55 thf(880,plain,((! [A:a,B:a,C:a,D:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((member_a @ D @ (partia1066395285xt_a_b @ r)) => ((a_minus_a_b @ r @ (add_a_b @ r @ (a_minus_a_b @ r @ A @ C) @ B) @ D) = (a_minus_a_b @ r @ (a_minus_a_b @ r @ (add_a_b @ r @ A @ B) @ C) @ D)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 20.72/12.55 thf(57,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_add__left__imp__eq)). 20.72/12.55 thf(477,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)],[57])). 20.72/12.55 thf(34,axiom,((! [A:partia96731725t_unit,B:a,C:a]: ((group_a_Product_unit @ A) => (((((mult_a_Product_unit @ A @ B @ C) = B) = (C = (one_a_Product_unit @ A))) <= (member_a @ C @ (partia1955795460t_unit @ A))) <= (member_a @ B @ (partia1955795460t_unit @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_group_Ol__cancel__one)). 20.72/12.55 thf(387,plain,((! [A:partia96731725t_unit,B:a,C:a]: ((group_a_Product_unit @ A) => ((((mult_a_Product_unit @ A @ B @ C) = B) = (C = (one_a_Product_unit @ A))) | ~ (member_a @ C @ (partia1955795460t_unit @ A)) | ~ (member_a @ B @ (partia1955795460t_unit @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 20.72/12.55 thf(61,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_add__diff__cancel__right_H)). 20.72/12.55 thf(494,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 20.72/12.55 thf(73,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_diff__diff__left)). 20.72/12.55 thf(535,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 20.72/12.55 thf(99,axiom,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Collect__mem__eq)). 20.72/12.55 thf(621,plain,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 20.72/12.55 thf(252,axiom,((! [A:nat,B:a]: ((add_pow_a_b_nat @ r @ (suc @ A) @ B) = (add_a_b @ r @ (add_pow_a_b_nat @ r @ A @ B) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_add_Onat__pow__Suc)). 20.72/12.55 thf(1149,plain,((! [A:nat,B:a]: ((add_pow_a_b_nat @ r @ (suc @ A) @ B) = (add_a_b @ r @ (add_pow_a_b_nat @ r @ A @ B) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 20.72/12.55 thf(114,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_add__diff__cancel__left)). 20.72/12.55 thf(668,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 20.72/12.55 thf(224,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (member_a @ (mult_a_ring_ext_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_semiring__simprules_I3_J)). 20.72/12.55 thf(1061,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (member_a @ (mult_a_ring_ext_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 20.72/12.55 thf(169,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((((((mult_a_ring_ext_a_b @ A @ D @ (add_a_b @ A @ B @ C)) = (add_a_b @ A @ (mult_a_ring_ext_a_b @ A @ D @ B) @ (mult_a_ring_ext_a_b @ A @ D @ C))) <= (member_a @ D @ (partia1066395285xt_a_b @ A))) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_semiring_Or__distr)). 20.72/12.55 thf(858,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: (((mult_a_ring_ext_a_b @ A @ D @ (add_a_b @ A @ B @ C)) = (add_a_b @ A @ (mult_a_ring_ext_a_b @ A @ D @ B) @ (mult_a_ring_ext_a_b @ A @ D @ C))) | ~ (member_a @ D @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (semiring_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 20.72/12.55 thf(28,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_group__add__class_Oadd_Oright__cancel)). 20.72/12.55 thf(367,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 20.72/12.55 thf(69,axiom,((! [A:partia96731725t_unit,B:a]: (((? [C:a]: ((member_a @ C @ (partia1955795460t_unit @ A)) & ((mult_a_Product_unit @ A @ B @ C) = (one_a_Product_unit @ A)))) <= (member_a @ B @ (partia1955795460t_unit @ A))) <= (group_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_group_Or__inv__ex)). 20.72/12.55 thf(521,plain,((! [A:partia96731725t_unit,B:a]: (? [C:a]: ((member_a @ C @ (partia1955795460t_unit @ A)) & ((mult_a_Product_unit @ A @ B @ C) = (one_a_Product_unit @ A))) | ~ (member_a @ B @ (partia1955795460t_unit @ A)) | ~ (group_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 20.72/12.55 thf(37,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (A = B)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_add__mono__thms__linordered__semiring_I4_J)). 20.72/12.55 thf(399,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)],[37])). 20.72/12.55 thf(160,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((group_a_ring_ext_a_b @ A) => (((mult_a_ring_ext_a_b @ A @ B @ C) = (one_a_ring_ext_a_b @ A)) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ C @ B) = (one_a_ring_ext_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_group_Oinv__comm)). 20.72/12.55 thf(827,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((group_a_ring_ext_a_b @ A) => (((mult_a_ring_ext_a_b @ A @ B @ C) = (one_a_ring_ext_a_b @ A)) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ C @ B) = (one_a_ring_ext_a_b @ A))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 20.72/12.55 thf(104,axiom,((! [A:int,B:int]: ((minus_minus_int @ A @ (uminus_uminus_int @ B)) = (plus_plus_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_diff__minus__eq__add)). 20.72/12.55 thf(636,plain,((! [A:int,B:int]: ((minus_minus_int @ A @ (uminus_uminus_int @ B)) = (plus_plus_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 20.72/12.55 thf(82,axiom,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_uminus__add__conv__diff)). 20.72/12.55 thf(563,plain,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 20.72/12.55 thf(276,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((A = (one_a_ring_ext_a_b @ r)) <= (! [B:a]: (((mult_a_ring_ext_a_b @ r @ A @ B) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_one__unique)). 20.72/12.55 thf(1250,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((A = (one_a_ring_ext_a_b @ r)) | ~ (! [B:a]: (((mult_a_ring_ext_a_b @ r @ A @ B) = B) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 20.72/12.55 thf(36,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_group__cancel_Oadd1)). 20.72/12.55 thf(394,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 20.72/12.55 thf(202,axiom,((! [A:partia1833973666xt_a_b,B:partia1833973666xt_a_b]: (((((((A = B) <= ((more_a_b @ A) = (more_a_b @ B))) <= ((add_a_b @ A) = (add_a_b @ B))) <= ((zero_a_b @ A) = (zero_a_b @ B))) <= ((one_a_ring_ext_a_b @ A) = (one_a_ring_ext_a_b @ B))) <= ((mult_a_ring_ext_a_b @ A) = (mult_a_ring_ext_a_b @ B))) <= ((partia1066395285xt_a_b @ A) = (partia1066395285xt_a_b @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ring_Oequality)). 20.72/12.55 thf(986,plain,((! [A:partia1833973666xt_a_b,B:partia1833973666xt_a_b]: ((A = B) | ~ ((more_a_b @ A) = (more_a_b @ B)) | ~ ((add_a_b @ A) = (add_a_b @ B)) | ~ ((zero_a_b @ A) = (zero_a_b @ B)) | ~ ((one_a_ring_ext_a_b @ A) = (one_a_ring_ext_a_b @ B)) | ~ ((mult_a_ring_ext_a_b @ A) = (mult_a_ring_ext_a_b @ B)) | ~ ((partia1066395285xt_a_b @ A) = (partia1066395285xt_a_b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 20.72/12.55 thf(10,axiom,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ (plus_plus_int @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_minus__add__cancel)). 20.72/12.55 thf(306,plain,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ (plus_plus_int @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 20.72/12.55 thf(56,axiom,((! [A:partia96731725t_unit,B:a,C:a]: ((comm_g1684316527t_unit @ A) => ((member_a @ B @ (partia1955795460t_unit @ A)) => (((mult_a_Product_unit @ A @ B @ C) = (mult_a_Product_unit @ A @ C @ B)) <= (member_a @ C @ (partia1955795460t_unit @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_comm__groupE_I4_J)). 20.72/12.55 thf(473,plain,((! [A:partia96731725t_unit,B:a,C:a]: ((comm_g1684316527t_unit @ A) => ((member_a @ B @ (partia1955795460t_unit @ A)) => (((mult_a_Product_unit @ A @ B @ C) = (mult_a_Product_unit @ A @ C @ B)) | ~ (member_a @ C @ (partia1955795460t_unit @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 20.72/12.55 thf(216,axiom,((! [A:partia1833973666xt_a_b,B:a]: ((((mult_a_ring_ext_a_b @ A @ B @ (zero_a_b @ A)) = (zero_a_b @ A)) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_semiring_Or__null)). 20.72/12.55 thf(1034,plain,((! [A:partia1833973666xt_a_b,B:a]: (((mult_a_ring_ext_a_b @ A @ B @ (zero_a_b @ A)) = (zero_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (semiring_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 20.72/12.55 thf(45,axiom,((! [A:partia96731725t_unit]: ((! [B:a]: ((member_a @ B @ (partia1955795460t_unit @ A)) => (! [C:a]: ((member_a @ C @ (partia1955795460t_unit @ A)) => (member_a @ (mult_a_Product_unit @ A @ B @ C) @ (partia1955795460t_unit @ A)))))) => ((member_a @ (one_a_Product_unit @ A) @ (partia1955795460t_unit @ A)) => ((((group_a_Product_unit @ A) <= (! [B:a]: ((member_a @ B @ (partia1955795460t_unit @ A)) => (? [C:a]: ((member_a @ C @ (partia1955795460t_unit @ A)) & ((mult_a_Product_unit @ A @ C @ B) = (one_a_Product_unit @ A))))))) <= (! [B:a]: ((member_a @ B @ (partia1955795460t_unit @ A)) => ((mult_a_Product_unit @ A @ (one_a_Product_unit @ A) @ B) = B)))) <= (! [B:a]: ((! [C:a]: ((member_a @ C @ (partia1955795460t_unit @ A)) => (! [D:a]: ((member_a @ D @ (partia1955795460t_unit @ A)) => ((mult_a_Product_unit @ A @ (mult_a_Product_unit @ A @ B @ C) @ D) = (mult_a_Product_unit @ A @ B @ (mult_a_Product_unit @ A @ C @ D))))))) <= (member_a @ B @ (partia1955795460t_unit @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_groupI)). 20.72/12.55 thf(426,plain,((! [A:partia96731725t_unit]: ((! [B:a]: ((member_a @ B @ (partia1955795460t_unit @ A)) => (! [C:a]: ((member_a @ C @ (partia1955795460t_unit @ A)) => (member_a @ (mult_a_Product_unit @ A @ B @ C) @ (partia1955795460t_unit @ A)))))) => ((member_a @ (one_a_Product_unit @ A) @ (partia1955795460t_unit @ A)) => ((group_a_Product_unit @ A) | ~ (! [B:a]: ((member_a @ B @ (partia1955795460t_unit @ A)) => (? [C:a]: ((member_a @ C @ (partia1955795460t_unit @ A)) & ((mult_a_Product_unit @ A @ C @ B) = (one_a_Product_unit @ A)))))) | ~ (! [B:a]: ((member_a @ B @ (partia1955795460t_unit @ A)) => ((mult_a_Product_unit @ A @ (one_a_Product_unit @ A) @ B) = B))) | ~ (! [B:a]: (! [C:a]: ((member_a @ C @ (partia1955795460t_unit @ A)) => (! [D:a]: ((member_a @ D @ (partia1955795460t_unit @ A)) => ((mult_a_Product_unit @ A @ (mult_a_Product_unit @ A @ B @ C) @ D) = (mult_a_Product_unit @ A @ B @ (mult_a_Product_unit @ A @ C @ D)))))) | ~ (member_a @ B @ (partia1955795460t_unit @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 20.72/12.55 thf(117,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ r3) @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_092_060close_062)). 20.72/12.55 thf(680,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ r3) @ r4)) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s2) @ s3) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ r3 @ r4))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 20.72/12.55 thf(77,axiom,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_minus__add__distrib)). 20.72/12.55 thf(548,plain,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 20.72/12.55 thf(189,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((a_minus_a_b @ r @ (a_minus_a_b @ r @ C @ A) @ B) = (a_minus_a_b @ r @ C @ (add_a_b @ r @ A @ B))) <= (member_a @ C @ (partia1066395285xt_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_right__inv__add)). 20.72/12.55 thf(927,plain,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((a_minus_a_b @ r @ (a_minus_a_b @ r @ C @ A) @ B) = (a_minus_a_b @ r @ C @ (add_a_b @ r @ A @ B))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 20.72/12.55 thf(247,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((((member_a @ B @ (partia1066395285xt_a_b @ A)) => (((B = (zero_a_b @ A)) | (C = (zero_a_b @ A))) <= (member_a @ C @ (partia1066395285xt_a_b @ A)))) <= ((mult_a_ring_ext_a_b @ A @ B @ C) = (zero_a_b @ A))) <= (field_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_integral)). 20.72/12.55 thf(1134,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((B = (zero_a_b @ A)) | (C = (zero_a_b @ A)) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)))) | ~ ((mult_a_ring_ext_a_b @ A @ B @ C) = (zero_a_b @ A)) | ~ (field_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 20.72/12.55 thf(155,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ A @ (a_inv_a_b @ r @ A)) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_r__neg)). 20.72/12.55 thf(812,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ A @ (a_inv_a_b @ r @ A)) = (zero_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 20.72/12.55 thf(98,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Suc__inject)). 20.72/12.55 thf(617,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 20.72/12.55 thf(251,axiom,((! [A:a,B:a]: ((((a_inv_a_b @ r @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (a_inv_a_b @ r @ A) @ (a_inv_a_b @ r @ B))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_local_Ominus__add)). 20.72/12.55 thf(1145,plain,((! [A:a,B:a]: (((a_inv_a_b @ r @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (a_inv_a_b @ r @ A) @ (a_inv_a_b @ r @ B))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 20.72/12.55 thf(60,axiom,((! [A:nat,B:nat,C:nat]: (((suc @ A) = (plus_plus_nat @ B @ (suc @ C))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_nat__arith_Osuc1)). 20.72/12.55 thf(490,plain,((! [A:nat,B:nat,C:nat]: (((suc @ A) = (plus_plus_nat @ B @ (suc @ C))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 20.72/12.55 thf(116,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((((add_a_b @ A @ B @ C) = D) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (((add_a_b @ A @ (a_inv_a_b @ A @ B) @ D) = C) <= (member_a @ D @ (partia1066395285xt_a_b @ A)))))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_abelian__group_Oa__transpose__inv)). 20.72/12.55 thf(675,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((((add_a_b @ A @ B @ C) = D) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (((add_a_b @ A @ (a_inv_a_b @ A @ B) @ D) = C) | ~ (member_a @ D @ (partia1066395285xt_a_b @ A)))))) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 20.72/12.55 thf(264,axiom,((! [A:a,B:a,C:a]: ((A = B) => ((add_a_b @ r @ C @ A) = (add_a_b @ r @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_right__add__eq)). 20.72/12.55 thf(1203,plain,((! [A:a,B:a,C:a]: ((A = B) => ((add_a_b @ r @ C @ A) = (add_a_b @ r @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 20.72/12.55 thf(265,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((A = (add_a_b @ r @ B @ A)) = (B = (zero_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add_Or__cancel__one_H)). 20.72/12.55 thf(1208,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((A = (add_a_b @ r @ B @ A)) = (B = (zero_a_b @ r))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 20.72/12.56 thf(80,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_add_Oleft__commute)). 20.72/12.56 thf(557,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 20.72/12.56 thf(168,axiom,((! [A:a]: (((mult_a_ring_ext_a_b @ r @ (zero_a_b @ r) @ A) = (zero_a_b @ r)) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_l__null)). 20.72/12.56 thf(855,plain,((! [A:a]: (((mult_a_ring_ext_a_b @ r @ (zero_a_b @ r) @ A) = (zero_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 20.72/12.56 thf(120,axiom,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ B @ A) = A) = (B = (zero_a_b @ r)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add_Or__cancel__one)). 20.72/12.56 thf(690,plain,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ B @ A) = A) = (B = (zero_a_b @ r)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 20.72/12.56 thf(135,axiom,((member_a @ (a_inv_a_b @ r @ (one_a_ring_ext_a_b @ r)) @ (units_a_ring_ext_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_Units__minus__one__closed)). 20.72/12.56 thf(739,plain,((member_a @ (a_inv_a_b @ r @ (one_a_ring_ext_a_b @ r)) @ (units_a_ring_ext_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 20.72/12.56 thf(280,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((a_minus_a_b @ A @ B @ C) = (add_a_b @ A @ B @ (a_inv_a_b @ A @ C))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_abelian__group_Ominus__eq)). 20.72/12.56 thf(1267,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: (((a_minus_a_b @ A @ B @ C) = (add_a_b @ A @ B @ (a_inv_a_b @ A @ C))) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 20.72/12.56 thf(271,axiom,((! [A:a,B:nat,C:nat]: (((add_a_b @ r @ (add_pow_a_b_nat @ r @ B @ A) @ (add_pow_a_b_nat @ r @ C @ A)) = (add_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ (add_pow_a_b_nat @ r @ B @ A))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add_Onat__pow__comm)). 20.72/12.56 thf(1230,plain,((! [A:a,B:nat,C:nat]: (((add_a_b @ r @ (add_pow_a_b_nat @ r @ B @ A) @ (add_pow_a_b_nat @ r @ C @ A)) = (add_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ (add_pow_a_b_nat @ r @ B @ A))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 20.72/12.56 thf(18,axiom,((! [A:int,B:int]: ((uminus_uminus_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_minus__diff__eq)). 20.72/12.56 thf(331,plain,((! [A:int,B:int]: ((uminus_uminus_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 20.72/12.56 thf(46,axiom,((! [A:int,B:int,C:int]: (((uminus_uminus_int @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ C))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_group__cancel_Oneg1)). 20.72/12.56 thf(441,plain,((! [A:int,B:int,C:int]: (((uminus_uminus_int @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ C))) | ~ (A = (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 20.72/12.56 thf(53,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_group__cancel_Oadd2)). 20.72/12.56 thf(463,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C))) | ~ (A = (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 20.72/12.56 thf(26,axiom,((! [A:partia96731725t_unit,B:a,C:a]: (((member_a @ B @ (partia1955795460t_unit @ A)) => ((member_a @ C @ (partia1955795460t_unit @ A)) => (((mult_a_Product_unit @ A @ C @ B) = B) = (C = (one_a_Product_unit @ A))))) <= (group_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_group_Or__cancel__one)). 20.72/12.56 thf(359,plain,((! [A:partia96731725t_unit,B:a,C:a]: (((member_a @ B @ (partia1955795460t_unit @ A)) => ((member_a @ C @ (partia1955795460t_unit @ A)) => (((mult_a_Product_unit @ A @ C @ B) = B) = (C = (one_a_Product_unit @ A))))) | ~ (group_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 20.72/12.56 thf(246,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:nat]: (((((mult_a_ring_ext_a_b @ A @ (add_pow_a_b_nat @ A @ D @ B) @ C) = (add_pow_a_b_nat @ A @ D @ (mult_a_ring_ext_a_b @ A @ B @ C))) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_semiring_Oadd__pow__ldistr)). 20.72/12.56 thf(1130,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:nat]: (((mult_a_ring_ext_a_b @ A @ (add_pow_a_b_nat @ A @ D @ B) @ C) = (add_pow_a_b_nat @ A @ D @ (mult_a_ring_ext_a_b @ A @ B @ C))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (semiring_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 20.72/12.56 thf(217,axiom,((! [A:int]: ((add_pow_a_b_int @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add_Oint__pow__one)). 20.72/12.56 thf(1038,plain,((! [A:int]: ((add_pow_a_b_int @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 20.72/12.56 thf(89,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ (suc @ D)) => (A @ D))) => (A @ (minus_minus_nat @ B @ C))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zero__induct__lemma)). 20.72/12.56 thf(585,plain,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ (suc @ D)) => (A @ D))) => (A @ (minus_minus_nat @ B @ C))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 20.72/12.56 thf(29,axiom,((! [A:int,B:int,C:int]: (((minus_minus_int @ A @ B) = C) = (A = (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_diff__eq__eq)). 20.72/12.56 thf(370,plain,((! [A:int,B:int,C:int]: (((minus_minus_int @ A @ B) = C) = (A = (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 20.72/12.56 thf(137,axiom,((! [A:a,B:a,C:int]: ((((mult_a_ring_ext_a_b @ r @ A @ (add_pow_a_b_int @ r @ C @ B)) = (add_pow_a_b_int @ r @ C @ (mult_a_ring_ext_a_b @ r @ A @ B))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__pow__rdistr__int)). 20.72/12.56 thf(744,plain,((! [A:a,B:a,C:int]: (((mult_a_ring_ext_a_b @ r @ A @ (add_pow_a_b_int @ r @ C @ B)) = (add_pow_a_b_int @ r @ C @ (mult_a_ring_ext_a_b @ r @ A @ B))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 20.72/12.56 thf(213,axiom,((! [A:a,B:a]: (((member_a @ (add_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add_Om__closed)). 20.72/12.56 thf(1023,plain,((! [A:a,B:a]: ((member_a @ (add_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 20.72/12.56 thf(132,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (? [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) & ((add_a_b @ A @ C @ B) = (zero_a_b @ A))))) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_abelian__groupE_I6_J)). 20.72/12.56 thf(727,plain,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (? [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) & ((add_a_b @ A @ C @ B) = (zero_a_b @ A))))) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 20.72/12.56 thf(200,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:nat]: ((semiring_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ B @ (add_pow_a_b_nat @ A @ D @ C)) = (add_pow_a_b_nat @ A @ D @ (mult_a_ring_ext_a_b @ A @ B @ C)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_semiring_Oadd__pow__rdistr)). 20.72/12.56 thf(978,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:nat]: ((semiring_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ B @ (add_pow_a_b_nat @ A @ D @ C)) = (add_pow_a_b_nat @ A @ D @ (mult_a_ring_ext_a_b @ A @ B @ C)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 20.72/12.56 thf(90,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_add__left__cancel)). 20.72/12.56 thf(595,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)],[90])). 20.72/12.56 thf(96,axiom,((! [A:partia1833973666xt_a_b]: ((member_a @ (zero_a_b @ A) @ (partia1066395285xt_a_b @ A)) <= (abelian_group_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_abelian__groupE_I2_J)). 20.72/12.56 thf(612,plain,((! [A:partia1833973666xt_a_b]: ((member_a @ (zero_a_b @ A) @ (partia1066395285xt_a_b @ A)) | ~ (abelian_group_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 20.72/12.56 thf(62,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Suc__diff__diff)). 20.72/12.56 thf(497,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 20.72/12.56 thf(204,axiom,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ A @ B) = (zero_a_b @ r)) => (A = (a_inv_a_b @ r @ B)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_sum__zero__eq__neg)). 20.72/12.56 thf(991,plain,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ A @ B) = (zero_a_b @ r)) => (A = (a_inv_a_b @ r @ B)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 20.72/12.56 thf(101,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (minus_minus_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_add__diff__cancel__right)). 20.72/12.56 thf(627,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (minus_minus_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 20.72/12.56 thf(27,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_add__implies__diff)). 20.72/12.56 thf(363,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 20.72/12.56 thf(190,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((group_a_ring_ext_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((B = (mult_a_ring_ext_a_b @ A @ C @ B)) = (C = (one_a_ring_ext_a_b @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_group_Or__cancel__one_H)). 20.72/12.56 thf(931,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((group_a_ring_ext_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((B = (mult_a_ring_ext_a_b @ A @ C @ B)) = (C = (one_a_ring_ext_a_b @ A)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 20.72/12.56 thf(115,axiom,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_a_b @ A) => (((mult_a_ring_ext_a_b @ A @ (one_a_ring_ext_a_b @ A) @ B) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_semiring_Osemiring__simprules_I9_J)). 20.72/12.56 thf(671,plain,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_a_b @ A) => (((mult_a_ring_ext_a_b @ A @ (one_a_ring_ext_a_b @ A) @ B) = B) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 20.72/12.56 thf(88,axiom,((! [A:int,B:int,C:int]: ((A = C) <= ((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_add__right__imp__eq)). 20.72/12.56 thf(581,plain,((! [A:int,B:int,C:int]: ((A = C) | ~ ((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 20.72/12.56 thf(141,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (? [C:a]: (((mult_a_ring_ext_a_b @ A @ C @ B) = (one_a_ring_ext_a_b @ A)) & (member_a @ C @ (partia1066395285xt_a_b @ A))))) <= (group_a_ring_ext_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_group_Ol__inv__ex)). 20.72/12.56 thf(759,plain,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => (? [C:a]: (((mult_a_ring_ext_a_b @ A @ C @ B) = (one_a_ring_ext_a_b @ A)) & (member_a @ C @ (partia1066395285xt_a_b @ A))))) | ~ (group_a_ring_ext_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 20.72/12.56 thf(267,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (zero_a_b @ r) @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_l__zero)). 20.72/12.56 thf(1216,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (zero_a_b @ r) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 20.72/12.56 thf(240,axiom,((! [A:a,B:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (member_a @ (add_pow_a_b_nat @ r @ B @ A) @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add_Onat__pow__closed)). 20.72/12.56 thf(1108,plain,((! [A:a,B:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (member_a @ (add_pow_a_b_nat @ r @ B @ A) @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 20.72/12.56 thf(68,axiom,((! [A:partia1833973666xt_a_b,B:a]: ((abelian_group_a_b @ A) => (((a_inv_a_b @ A @ (a_inv_a_b @ A @ B)) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_abelian__group_Ominus__minus)). 20.72/12.56 thf(517,plain,((! [A:partia1833973666xt_a_b,B:a]: ((abelian_group_a_b @ A) => (((a_inv_a_b @ A @ (a_inv_a_b @ A @ B)) = B) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 20.72/12.56 thf(138,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ A @ (add_a_b @ r @ B @ C)) = (add_a_b @ r @ B @ (add_a_b @ r @ A @ C))) <= (member_a @ C @ (partia1066395285xt_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add_Om__lcomm)). 20.72/12.56 thf(748,plain,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ A @ (add_a_b @ r @ B @ C)) = (add_a_b @ r @ B @ (add_a_b @ r @ A @ C))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 20.72/12.56 thf(147,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((((((mult_a_ring_ext_a_b @ A @ C @ B) = B) = (C = (one_a_ring_ext_a_b @ A))) <= (member_a @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (group_a_ring_ext_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_group_Or__cancel__one)). 20.72/12.56 thf(781,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((((mult_a_ring_ext_a_b @ A @ C @ B) = B) = (C = (one_a_ring_ext_a_b @ A))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)) | ~ (group_a_ring_ext_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 20.72/12.56 thf(205,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) <= (member_a @ A @ (units_a_ring_ext_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Units__closed)). 20.72/12.56 thf(995,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (units_a_ring_ext_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 20.72/12.56 thf(215,axiom,((! [A:a,B:a]: ((((a_inv_a_b @ r @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (a_inv_a_b @ r @ B) @ (a_inv_a_b @ r @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add_Oinv__mult__group)). 20.72/12.56 thf(1030,plain,((! [A:a,B:a]: (((a_inv_a_b @ r @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (a_inv_a_b @ r @ B) @ (a_inv_a_b @ r @ A))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 20.72/12.56 thf(185,axiom,((! [A:nat]: ((add_pow_a_b_nat @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add_Onat__pow__one)). 20.72/12.56 thf(914,plain,((! [A:nat]: ((add_pow_a_b_nat @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 20.72/12.56 thf(261,axiom,((! [A:a]: ((member_a @ (a_inv_a_b @ r @ A) @ (partia1066395285xt_a_b @ r)) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add_Oinv__closed)). 20.72/12.56 thf(1193,plain,((! [A:a]: ((member_a @ (a_inv_a_b @ r @ A) @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 20.72/12.56 thf(266,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((a_inv_a_b @ A @ (add_a_b @ A @ B @ C)) = (add_a_b @ A @ (a_inv_a_b @ A @ B) @ (a_inv_a_b @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_abelian__group_Ominus__add)). 20.72/12.56 thf(1212,plain,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((abelian_group_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((a_inv_a_b @ A @ (add_a_b @ A @ B @ C)) = (add_a_b @ A @ (a_inv_a_b @ A @ B) @ (a_inv_a_b @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 20.72/12.56 thf(23,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_add_Oleft__cancel)). 20.72/12.56 thf(346,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 20.72/12.56 thf(257,axiom,((! [A:a]: ((member_a @ A @ (units_a_ring_ext_a_b @ r)) => (? [B:a]: (((mult_a_ring_ext_a_b @ r @ A @ B) = (one_a_ring_ext_a_b @ r)) & (member_a @ B @ (partia1066395285xt_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_Units__r__inv__ex)). 20.72/12.56 thf(1161,plain,((! [A:a]: ((member_a @ A @ (units_a_ring_ext_a_b @ r)) => (? [B:a]: (((mult_a_ring_ext_a_b @ r @ A @ B) = (one_a_ring_ext_a_b @ r)) & (member_a @ B @ (partia1066395285xt_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 20.72/12.56 thf(151,axiom,((! [A:a,B:a]: ((a_minus_a_b @ r @ A @ B) = (add_a_b @ r @ A @ (a_inv_a_b @ r @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_minus__eq)). 20.72/12.56 thf(800,plain,((! [A:a,B:a]: ((a_minus_a_b @ r @ A @ B) = (add_a_b @ r @ A @ (a_inv_a_b @ r @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 20.72/12.56 thf(8,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_diff__right__commute)). 20.72/12.56 thf(300,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 20.72/12.56 thf(139,axiom,((! [A:a,B:a,C:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_nat @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ (add_pow_a_b_nat @ r @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add_Onat__pow__distrib)). 20.72/12.56 thf(752,plain,((! [A:a,B:a,C:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_nat @ r @ C @ (add_a_b @ r @ A @ B)) = (add_a_b @ r @ (add_pow_a_b_nat @ r @ C @ A) @ (add_pow_a_b_nat @ r @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 20.72/12.56 thf(40,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_add__left__cancel)). 20.72/12.56 thf(410,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 20.72/12.56 thf(157,axiom,((! [A:a,B:int,C:int]: (((add_pow_a_b_int @ r @ (minus_minus_int @ B @ C) @ A) = (add_a_b @ r @ (add_pow_a_b_int @ r @ B @ A) @ (a_inv_a_b @ r @ (add_pow_a_b_int @ r @ C @ A)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_add_Oint__pow__diff)). 20.72/12.56 thf(818,plain,((! [A:a,B:int,C:int]: (((add_pow_a_b_int @ r @ (minus_minus_int @ B @ C) @ A) = (add_a_b @ r @ (add_pow_a_b_int @ r @ B @ A) @ (a_inv_a_b @ r @ (add_pow_a_b_int @ r @ C @ A)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 20.72/12.56 thf(30,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = C) => (A = (minus_minus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_add__implies__diff)). 20.72/12.56 thf(373,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = C) => (A = (minus_minus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 20.72/12.56 thf(134,axiom,((! [A:a,B:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ B @ (a_inv_a_b @ r @ A)) = (a_inv_a_b @ r @ (add_pow_a_b_int @ r @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add_Oint__pow__inv)). 20.72/12.56 thf(735,plain,((! [A:a,B:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ B @ (a_inv_a_b @ r @ A)) = (a_inv_a_b @ r @ (add_pow_a_b_int @ r @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 20.72/12.56 thf(13,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_add__right__cancel)). 20.72/12.56 thf(315,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 20.72/12.56 thf(284,axiom,((! [A:a,B:nat]: (((add_pow_a_b_nat @ r @ (suc @ B) @ A) = (add_a_b @ r @ A @ (add_pow_a_b_nat @ r @ B @ A))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Onat__pow__Suc2)). 20.72/12.56 thf(1280,plain,((! [A:a,B:nat]: (((add_pow_a_b_nat @ r @ (suc @ B) @ A) = (add_a_b @ r @ A @ (add_pow_a_b_nat @ r @ B @ A))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 20.72/12.56 thf(6,axiom,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) = (B @ C))) => ((collect_a @ A) = (collect_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__cong)). 20.72/12.56 thf(294,plain,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) = (B @ C))) => ((collect_a @ (A)) = (collect_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 20.72/12.56 thf(65,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_add_Oleft__commute)). 20.72/12.56 thf(506,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)],[65])). 20.72/12.56 thf(72,axiom,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mem__Collect__eq)). 20.72/12.56 thf(532,plain,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 20.72/12.56 thf(122,axiom,((abelian_group_a_b @ r)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_is__abelian__group)). 20.72/12.56 thf(696,plain,((abelian_group_a_b @ r)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 20.72/12.56 thf(258,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ C @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ B @ (a_inv_a_b @ r @ C)) = A) = (B = (add_a_b @ r @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add_Oinv__solve__right_H)). 20.72/12.56 thf(1165,plain,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ C @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ B @ (a_inv_a_b @ r @ C)) = A) = (B = (add_a_b @ r @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 20.72/12.56 thf(180,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((semiring_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (add_a_b @ A @ B @ C) @ D) = (add_a_b @ A @ B @ (add_a_b @ A @ C @ D))))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_semiring_Osemiring__simprules_I5_J)). 20.72/12.56 thf(897,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((semiring_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ (add_a_b @ A @ B @ C) @ D) = (add_a_b @ A @ B @ (add_a_b @ A @ C @ D))))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 20.72/12.56 thf(143,axiom,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (member_a @ (a_minus_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_minus__closed)). 20.72/12.56 thf(767,plain,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => (member_a @ (a_minus_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 20.72/12.56 thf(100,axiom,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((A = B) = (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_diff__eq__diff__eq)). 20.72/12.56 thf(624,plain,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((A = B) = (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 20.72/12.56 thf(136,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((comm_g791708116xt_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (mult_a_ring_ext_a_b @ A @ B @ C) @ D) = (mult_a_ring_ext_a_b @ A @ B @ (mult_a_ring_ext_a_b @ A @ C @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_comm__groupE_I3_J)). 20.72/12.56 thf(740,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((comm_g791708116xt_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (mult_a_ring_ext_a_b @ A @ B @ C) @ D) = (mult_a_ring_ext_a_b @ A @ B @ (mult_a_ring_ext_a_b @ A @ C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 20.72/12.56 thf(253,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ r3) @ r4))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_f7)). 20.72/12.56 thf(1152,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ (mult_a_ring_ext_a_b @ r @ s @ r3)) @ r4)) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ r2) @ r4)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ s3) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s @ r3) @ r4))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 20.72/12.56 thf(212,axiom,((! [A:a,B:nat,C:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (add_pow_a_b_nat @ r @ B @ A) @ (add_pow_a_b_nat @ r @ C @ A)) = (add_pow_a_b_nat @ r @ (plus_plus_nat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_add_Onat__pow__mult)). 20.72/12.56 thf(1019,plain,((! [A:a,B:nat,C:nat]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (add_pow_a_b_nat @ r @ B @ A) @ (add_pow_a_b_nat @ r @ C @ A)) = (add_pow_a_b_nat @ r @ (plus_plus_nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 20.72/12.56 thf(131,axiom,((! [A:a,B:a,C:int]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (add_pow_a_b_int @ r @ C @ A) @ B) = (add_pow_a_b_int @ r @ C @ (mult_a_ring_ext_a_b @ r @ A @ B)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_add__pow__ldistr__int)). 20.72/12.56 thf(723,plain,((! [A:a,B:a,C:int]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (add_pow_a_b_int @ r @ C @ A) @ B) = (add_pow_a_b_int @ r @ C @ (mult_a_ring_ext_a_b @ r @ A @ B)))) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 20.72/12.56 thf(158,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ A @ (zero_a_b @ r)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_r__zero)). 20.72/12.56 thf(822,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ A @ (zero_a_b @ r)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 20.72/12.56 thf(166,axiom,((a_minus_a_b = (^ [A:partia1833973666xt_a_b,B:a,C:a]: (add_a_b @ A @ B @ (a_inv_a_b @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_a__minus__def)). 20.72/12.56 thf(850,plain,(((a_minus_a_b) = (^ [A:partia1833973666xt_a_b,B:a,C:a]: (add_a_b @ A @ B @ (a_inv_a_b @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 20.72/12.56 thf(94,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_diff__add__inverse2)). 20.72/12.56 thf(607,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 20.72/12.56 thf(201,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((group_a_ring_ext_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((((mult_a_ring_ext_a_b @ A @ C @ B) = (mult_a_ring_ext_a_b @ A @ D @ B)) = (C = D)) <= (member_a @ D @ (partia1066395285xt_a_b @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Group_Ogroup_Oright__cancel)). 20.72/12.56 thf(982,plain,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((group_a_ring_ext_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((((mult_a_ring_ext_a_b @ A @ C @ B) = (mult_a_ring_ext_a_b @ A @ D @ B)) = (C = D)) | ~ (member_a @ D @ (partia1066395285xt_a_b @ A)))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 20.72/12.56 thf(208,axiom,((! [A:a]: (((mult_a_ring_ext_a_b @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r)) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_r__null)). 20.72/12.56 thf(1004,plain,((! [A:a]: (((mult_a_ring_ext_a_b @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 20.72/12.56 thf(15,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_add__diff__cancel)). 20.72/12.56 thf(322,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 20.72/12.56 thf(59,axiom,((! [A:partia96731725t_unit,B:a,C:a]: ((((mult_a_Product_unit @ A @ B @ C) = (one_a_Product_unit @ A)) => ((member_a @ B @ (partia1955795460t_unit @ A)) => ((member_a @ C @ (partia1955795460t_unit @ A)) => ((mult_a_Product_unit @ A @ C @ B) = (one_a_Product_unit @ A))))) <= (group_a_Product_unit @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_group_Oinv__comm)). 20.72/12.56 thf(486,plain,((! [A:partia96731725t_unit,B:a,C:a]: ((((mult_a_Product_unit @ A @ B @ C) = (one_a_Product_unit @ A)) => ((member_a @ B @ (partia1955795460t_unit @ A)) => ((member_a @ C @ (partia1955795460t_unit @ A)) => ((mult_a_Product_unit @ A @ C @ B) = (one_a_Product_unit @ A))))) | ~ (group_a_Product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 20.72/12.56 thf(152,axiom,(((a_inv_a_b @ r @ (zero_a_b @ r)) = (zero_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_local_Ominus__zero)). 20.72/12.56 thf(803,plain,(((a_inv_a_b @ r @ (zero_a_b @ r)) = (zero_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 20.72/12.56 thf(20,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_diff__add__eq)). 20.72/12.56 thf(337,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 20.72/12.56 thf(193,axiom,((! [A:partia1833973666xt_a_b]: (((member_a @ (one_a_ring_ext_a_b @ A) @ (partia1066395285xt_a_b @ A)) => ((! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (! [C:a]: ((! [D:a]: ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (mult_a_ring_ext_a_b @ A @ B @ C) @ D) = (mult_a_ring_ext_a_b @ A @ B @ (mult_a_ring_ext_a_b @ A @ C @ D))))) <= (member_a @ C @ (partia1066395285xt_a_b @ A)))))) => (((group_a_ring_ext_a_b @ A) <= (! [B:a]: ((? [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) & ((mult_a_ring_ext_a_b @ A @ C @ B) = (one_a_ring_ext_a_b @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))))) <= (! [B:a]: (((mult_a_ring_ext_a_b @ A @ (one_a_ring_ext_a_b @ A) @ B) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ A))))))) <= (! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (! [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (member_a @ (mult_a_ring_ext_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_groupI)). 20.72/12.56 thf(940,plain,((! [A:partia1833973666xt_a_b]: (((member_a @ (one_a_ring_ext_a_b @ A) @ (partia1066395285xt_a_b @ A)) => ((! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (! [C:a]: (! [D:a]: ((member_a @ D @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (mult_a_ring_ext_a_b @ A @ B @ C) @ D) = (mult_a_ring_ext_a_b @ A @ B @ (mult_a_ring_ext_a_b @ A @ C @ D)))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ A)))))) => ((group_a_ring_ext_a_b @ A) | ~ (! [B:a]: (? [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) & ((mult_a_ring_ext_a_b @ A @ C @ B) = (one_a_ring_ext_a_b @ A))) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A)))) | ~ (! [B:a]: (((mult_a_ring_ext_a_b @ A @ (one_a_ring_ext_a_b @ A) @ B) = B) | ~ (member_a @ B @ (partia1066395285xt_a_b @ A))))))) | ~ (! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (! [C:a]: ((member_a @ C @ (partia1066395285xt_a_b @ A)) => (member_a @ (mult_a_ring_ext_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 20.72/12.56 thf(25,axiom,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ D @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (minus_minus_int @ D @ C))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_group__cancel_Osub2)). 20.72/12.56 thf(354,plain,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ D @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (minus_minus_int @ D @ C))) | ~ (A = (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 20.72/12.56 thf(75,axiom,((! [A:partia1833973666xt_a_b]: ((semiring_a_b @ A) => (member_a @ (one_a_ring_ext_a_b @ A) @ (partia1066395285xt_a_b @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_semiring_Osemiring__simprules_I4_J)). 20.72/12.56 thf(543,plain,((! [A:partia1833973666xt_a_b]: ((semiring_a_b @ A) => (member_a @ (one_a_ring_ext_a_b @ A) @ (partia1066395285xt_a_b @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 20.72/12.56 thf(81,axiom,((! [A:partia1833973666xt_a_b]: ((one_a_Product_unit @ (units_1411277569xt_a_b @ A)) = (one_a_ring_ext_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_units__of__one)). 20.72/12.56 thf(560,plain,((! [A:partia1833973666xt_a_b]: ((one_a_Product_unit @ (units_1411277569xt_a_b @ A)) = (one_a_ring_ext_a_b @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 20.72/12.56 thf(105,axiom,((! [A:partia1833973666xt_a_b]: ((group_a_ring_ext_a_b @ A) => ((units_a_ring_ext_a_b @ A) = (partia1066395285xt_a_b @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_group_OUnits__eq)). 20.72/12.56 thf(639,plain,((! [A:partia1833973666xt_a_b]: ((group_a_ring_ext_a_b @ A) => ((units_a_ring_ext_a_b @ A) = (partia1066395285xt_a_b @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 20.72/12.56 thf(191,axiom,((member_a @ (one_a_ring_ext_a_b @ r) @ (units_a_ring_ext_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Units__one__closed)). 20.72/12.56 thf(935,plain,((member_a @ (one_a_ring_ext_a_b @ r) @ (units_a_ring_ext_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 20.72/12.56 thf(210,axiom,((((zero_a_b @ r) != (one_a_ring_ext_a_b @ r)) => ((field_a_b @ r) <= (! [A:a]: (((? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((mult_a_ring_ext_a_b @ r @ A @ B) = (one_a_ring_ext_a_b @ r)))) <= (A != (zero_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_cring__fieldI2)). 20.72/12.56 thf(1009,plain,(((~ ((zero_a_b @ r) = (one_a_ring_ext_a_b @ r))) => ((field_a_b @ r) | ~ (! [A:a]: (? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((mult_a_ring_ext_a_b @ r @ A @ B) = (one_a_ring_ext_a_b @ r))) | (A = (zero_a_b @ r)) | ~ (member_a @ A @ (partia1066395285xt_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 20.72/12.56 thf(11,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_add__left__imp__eq)). 20.72/12.56 thf(309,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 20.72/12.56 thf(111,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_diff__diff__eq2)). 20.72/12.56 thf(659,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 20.72/12.56 thf(50,axiom,((! [A:int,B:int]: ((plus_plus_int @ A @ (plus_plus_int @ (uminus_uminus_int @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add__minus__cancel)). 20.72/12.56 thf(454,plain,((! [A:int,B:int]: ((plus_plus_int @ A @ (plus_plus_int @ (uminus_uminus_int @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 20.72/12.56 thf(226,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((((add_a_b @ r @ (a_inv_a_b @ r @ B) @ C) = A) = (C = (add_a_b @ r @ B @ A))) <= (member_a @ C @ (partia1066395285xt_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_add_Oinv__solve__left_H)). 20.72/12.56 thf(1069,plain,((! [A:a,B:a,C:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((((add_a_b @ r @ (a_inv_a_b @ r @ B) @ C) = A) = (C = (add_a_b @ r @ B @ A))) | ~ (member_a @ C @ (partia1066395285xt_a_b @ r)) | ~ (member_a @ B @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 20.72/12.56 thf(1325,plain,($false),inference(cvc4,[status(thm)],[645,809,846,893,777,481,1083,962,468,1158,1073,449,1142,878,614,1041,1173,384,500,1275,698,340,538,1095,1001,1127,973,885,1046,785,838,1279,460,917,702,902,1087,870,969,770,416,289,1100,1115,325,924,756,789,834,574,1169,956,866,1119,1104,1242,292,380,512,529,793,1199,714,1057,334,910,1223,1091,825,1042,1255,598,297,815,1238,1123,862,349,407,630,566,852,665,1159,1079,551,710,842,285,682,1195,578,874,1259,650,1064,1111,403,1096,1138,610,989,697,1234,884,554,642,526,1016,706,328,471,901,686,1075,1099,654,721,569,1246,503,647,1263,997,1050,457,343,1086,633,805,921,1054,1026,773,662,718,888,906,965,1103,1219,601,1154,423,732,286,958,413,1007,694,1226,545,572,313,1271,391,1139,445,936,831,419,377,451,318,303,764,604,509,880,477,387,494,535,621,1149,668,1061,858,367,521,399,827,636,563,1250,394,986,306,473,1034,426,680,548,927,1134,812,617,1145,490,675,1203,1208,557,855,690,739,1267,1230,331,441,463,359,1130,1038,585,370,744,1023,727,978,595,612,497,991,627,363,931,671,581,759,1216,1108,517,748,781,995,1030,914,1193,1212,346,1161,800,300,752,410,818,373,735,315,1280,294,506,532,696,1165,897,767,624,740,1152,1019,723,822,850,607,982,1004,322,486,803,337,940,354,543,560,639,935,1009,309,659,454,1069])). 20.72/12.56 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 20.72/12.56 % [INFO] Killing All external provers ... 20.72/12.56 FINAL WATCH: 19.9 CPU 10.5 WC 20.72/12.56 Killed 1 orphans 20.72/12.56 Killed 1 orphans 20.72/12.56 EOF