0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : run_Leo-III %s %d THM 0.11/0.33 % Computer : n001.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1920 0.11/0.33 % WCLimit : 240 0.11/0.33 % DateTime : Wed Jul 30 03:19:05 EDT 2025 0.11/0.33 % CPUTime : 0.89/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 1.89/1.10 % [INFO] Parsing done (241ms). 1.89/1.11 % [INFO] Running in sequential loop mode. 2.64/1.33 % [INFO] eprover registered as external prover. 2.70/1.33 % [INFO] Scanning for conjecture ... 2.89/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 244 axioms. Running axiom selection ... 3.12/1.54 % [INFO] Axiom selection finished. Selected 244 axioms (removed 0 axioms). 3.69/1.69 % [INFO] Problem is higher-order (TPTP THF). 3.69/1.70 % [INFO] Type checking passed. 3.69/1.70 % [CONFIG] Using configuration: timeout(240) with strategy. Searching for refutation ... 70.97/31.62 % External prover 'e' found a proof! 70.97/31.62 % [INFO] Killing All external provers ... 70.97/31.62 % Time passed: 31102ms (effective reasoning time: 30509ms) 70.97/31.62 % Solved by strategy 70.97/31.62 % Axioms used in derivation (244): fact_161_minus__add__distrib, fact_13_f42, fact_197_diff__add__eq__diff__diff__swap, fact_128_eq__obj__rng__of__frac_Oaxioms_I2_J, fact_234_empty__Diff, fact_168_add_Ocommute, fact_191_diff__mono, fact_99_m__closed, fact_156_add__diff__cancel__right, fact_4_m__assoc, fact_148_add__right__cancel, fact_229_Compl__subset__Compl__iff, fact_0_f18, fact_208_add__le__imp__le__diff, fact_206_minus__diff__commute, fact_159_diff__add__cancel, fact_78_r__neg2, fact_108_add_Oinv__eq__1__iff, fact_115_semiring_Osemiring__simprules_I6_J, fact_25_f11, fact_75_add_Oinv__comm, fact_31_f16, fact_36_f34, fact_65_f8, fact_192_le__imp__neg__le, fact_112_submonoid__axioms, fact_145_uminus__add__conv__diff, fact_55_f39, fact_106_add_Ol__cancel__one_H, fact_194_le__minus__iff, fact_110_mult__submonoid__of__crng__axioms, fact_29__092_060open_062t_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062, fact_136_semiring_Osemiring__simprules_I1_J, fact_185_add__mono__thms__linordered__semiring_I1_J, fact_214_add_Oone__in__subset, fact_59_minus__closed, fact_203_group__cancel_Osub1, fact_217_carrier__not__empty, fact_162_minus__add__cancel, fact_222_Diff__eq__empty__iff, fact_144_diff__minus__eq__add, fact_153_add__le__cancel__left, fact_167_add_Oleft__commute, fact_183_add__left__mono, fact_9_add_Om__lcomm, fact_66_local_Osemiring__axioms, fact_176_diff__right__commute, fact_218_a__l__coset__subset__G, fact_97_add_Oinv__closed, fact_68_prod__eqI, fact_88_sum__zero__eq__neg, fact_123_add_Oint__pow__closed, fact_63_f4, fact_72_add_Or__inv__ex, fact_237_equals0D, fact_53_f31, fact_142_subset, fact_171_add_Oassoc, fact_42_f32, fact_157_add__diff__cancel__left_H, fact_8_add_Om__comm, fact_243_subset__eq, fact_182_add__right__mono, fact_57_f5, fact_11_f19, fact_10_f20, fact_121_add_Oint__pow__distrib, fact_212_diff__conv__add__uminus, fact_98_local_Ominus__zero, fact_169_group__add__class_Oadd_Oright__cancel, fact_41_f25, fact_173_group__cancel_Oadd1, fact_179_equation__minus__iff, fact_158_add__diff__cancel__left, fact_205_group__cancel_Oneg1, fact_184_add__mono, fact_216_a__lcos__m__assoc, fact_238_equals0I, fact_143_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Osubset, fact_33_f9, fact_193_minus__le__iff, fact_122_add_Oint__pow__mult__distrib, fact_92_inv__add, fact_50__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_092_060close_062, fact_46_Collect__mem__eq, fact_16_four__elem__comm, fact_71_local_Ominus__unique, fact_119_add__pow__ldistr__int, fact_189_diff__right__mono, fact_125_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Ois__submonoid, fact_154_neg__le__iff__le, fact_2_right__add__eq, fact_138_semiring_Ol__distr, fact_18_f21, fact_114_semiring_Osemiring__simprules_I11_J, fact_105_add_Or__cancel__one, fact_141_add_Oint__pow__mult, fact_64_f6, fact_95_zero__closed, fact_198_diff__add__eq, fact_224_all__not__in__conv, fact_22_f15, fact_211_ab__group__add__class_Oab__diff__conv__add__uminus, fact_137_semiring_Osemiring__simprules_I2_J, fact_96_local_Ominus__minus, fact_77_l__minus, fact_113_add_Oint__pow__inv, fact_232_empty__subsetI, fact_102_r__zero, fact_6_m__lcomm, fact_69_exE__realizer_H, fact_70_prod_Oexpand, fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062, fact_103_l__zero, fact_202_diff__eq__eq, fact_172_group__cancel_Oadd2, fact_213_group__cancel_Osub2, fact_20_f22, fact_170_add_Oleft__cancel, fact_35_f23, fact_132_semiring_Osemiring__simprules_I3_J, fact_146_le__add__diff__inverse, fact_81_add_Oinv__solve__right_H, fact_236_emptyE, fact_199_diff__diff__eq2, fact_225_Collect__empty__eq, fact_12_f41, fact_45_mem__Collect__eq, fact_210_diff__le__eq, fact_74_add_Ol__inv__ex, fact_67_minus__eq, fact_150_neg__equal__iff__equal, fact_34__092_060open_062t_A_092_060otimes_062_As_A_092_060otimes_062_Asnd_Ax_H_A_092_060in_062_Acarrier_AR_092_060close_062, fact_135_semiring_Osemiring__simprules_I5_J, fact_204_add_Oinverse__distrib__swap, fact_241_subsetD, fact_131_semiring_Osemiring__simprules_I8_J, fact_54_f37, fact_134_semiring_Osemiring__simprules_I7_J, fact_80_local_Ominus__add, fact_91_l__neg, fact_140_add_Oint__pow__neg, fact_60_add_Om__closed, fact_130_a__minus__def, fact_226_empty__Collect__eq, fact_82_add_Oinv__solve__right, fact_133_semiring_Osemiring__simprules_I12_J, fact_240_in__mono, fact_5_m__comm, fact_3_local_Oright__minus__eq, fact_58_f7, fact_151_add_Oinverse__inverse, fact_7_add_Om__assoc, fact_164_minus__diff__eq, fact_227_subsetI, fact_17_right__inv__add, fact_94__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_H_O_A_092_060lbrakk_062t_H_A_092_060in_062_AS_059_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_221_add__additive__subgroups, fact_174_add__mono__thms__linordered__semiring_I4_J, fact_111_prod__eq__iff, fact_49_f33, fact_47_Collect__cong, fact_124_add_Oint__pow__one, fact_220_set__add__closed, fact_101_l__null, fact_149_add__left__cancel, fact_233_Diff__empty, fact_239_ex__in__conv, fact_155_add__diff__cancel__right_H, fact_30__092_060open_062t_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_At_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Afst_Ay_H_J_092_060close_062, fact_230_Compl__anti__mono, fact_61_local_Oadd_Oright__cancel, fact_1_f17, fact_27_f27, fact_223_empty__iff, fact_235_Diff__cancel, fact_39__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_061_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062, fact_19_f40, fact_175_ab__semigroup__add__class_Oadd__ac_I1_J, fact_73_add_Oone__unique, fact_32_f24, fact_23__092_060open_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060in_062_Acarrier_AR_092_060close_062, fact_14_l__distr, fact_152_add__le__cancel__right, fact_231_subset__empty, fact_209_le__diff__eq, fact_104_add_Or__cancel__one_H, fact_190_diff__left__mono, fact_166_add__left__imp__eq, fact_126_mult__submonoid__of__crng_Oaxioms_I2_J, fact_40_f12, fact_83_add_Oinv__solve__left_H, fact_86_a__transpose__inv, fact_79_r__neg1, fact_187_add__mono__thms__linordered__semiring_I3_J, fact_28_f35, fact_196_diff__diff__add, fact_15_r__distr, fact_76_r__minus, fact_100_r__null, fact_56_f38, fact_107_add_Ol__cancel__one, fact_160_add__diff__cancel, fact_38_f13, fact_181_add__le__imp__le__left, fact_24_f28, fact_62_semiring__simprules_I3_J, fact_48_f30, fact_52__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062, fact_242_equalityE, fact_177_diff__eq__diff__eq, fact_219_setadd__subset__G, fact_120_add__pow__rdistr__int, fact_163_add__minus__cancel, fact_207_add__le__add__imp__diff__le, fact_87_eq__obj__rng__of__frac__axioms, fact_228_subset__antisym, fact_195_add__implies__diff, fact_165_add__right__imp__eq, fact_186_add__mono__thms__linordered__semiring_I2_J, fact_118_semiring_Or__distr, fact_37_f36, fact_44_f29, fact_188_diff__eq__diff__less__eq, fact_116_semiring_Ol__null, fact_84_add_Oinv__solve__left, fact_129_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Om__closed, fact_147_le__add__diff__inverse2, fact_89_r__neg, fact_93__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_O_A_092_060lbrakk_062t_A_092_060in_062_AS_059_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_139_add_Oint__pow__diff, fact_117_semiring_Or__null, fact_43_f26, fact_90_minus__equality, fact_26_f10, fact_180_add__le__imp__le__right, fact_178_minus__equation__iff, fact_109_mult__submonoid__of__rng__axioms, fact_85_add_Oinv__mult__group, fact_215_a__lcos__mult__one, fact_200_add__diff__eq, fact_201_eq__diff__eq, fact_51_f14, fact_127_mult__submonoid__of__rng_Oaxioms_I2_J 70.97/31.62 % No. of inferences in proof: 623 70.97/31.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 31102 ms resp. 30509 ms w/o parsing 71.81/31.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 71.81/31.82 thf(partia1833973666xt_a_b_type, type, partia1833973666xt_a_b: $tType). 71.81/31.82 thf(product_prod_a_a_type, type, product_prod_a_a: $tType). 71.81/31.82 thf(set_a_type, type, set_a: $tType). 71.81/31.82 thf(int_type, type, int: $tType). 71.81/31.82 thf(a_type, type, a: $tType). 71.81/31.82 thf(a_l_coset_a_b_type, type, a_l_coset_a_b: (partia1833973666xt_a_b > (a > (set_a > set_a)))). 71.81/31.82 thf(additi2104487374up_a_b_type, type, additi2104487374up_a_b: (set_a > (partia1833973666xt_a_b > $o))). 71.81/31.82 thf(set_add_a_b_type, type, set_add_a_b: (partia1833973666xt_a_b > (set_a > (set_a > set_a)))). 71.81/31.82 thf(partia1066395285xt_a_b_type, type, partia1066395285xt_a_b: (partia1833973666xt_a_b > set_a)). 71.81/31.82 thf(mult_a_ring_ext_a_b_type, type, mult_a_ring_ext_a_b: (partia1833973666xt_a_b > (a > (a > a)))). 71.81/31.82 thf(minus_minus_int_type, type, minus_minus_int: (int > (int > int))). 71.81/31.82 thf(minus_minus_set_a_type, type, minus_minus_set_a: (set_a > (set_a > set_a))). 71.81/31.82 thf(plus_plus_int_type, type, plus_plus_int: (int > (int > int))). 71.81/31.82 thf(uminus_uminus_int_type, type, uminus_uminus_int: (int > int)). 71.81/31.82 thf(uminus_uminus_set_a_type, type, uminus_uminus_set_a: (set_a > set_a)). 71.81/31.82 thf(locali1648887798ac_a_b_type, type, locali1648887798ac_a_b: (partia1833973666xt_a_b > (set_a > $o))). 71.81/31.82 thf(locali807230110ng_a_b_type, type, locali807230110ng_a_b: (partia1833973666xt_a_b > (set_a > $o))). 71.81/31.82 thf(locali880295127ng_a_b_type, type, locali880295127ng_a_b: (partia1833973666xt_a_b > (set_a > $o))). 71.81/31.82 thf(locali425460998xt_a_b_type, type, locali425460998xt_a_b: (partia1833973666xt_a_b > (set_a > $o))). 71.81/31.82 thf(bot_bot_set_a_type, type, bot_bot_set_a: set_a). 71.81/31.82 thf(ord_less_eq_int_type, type, ord_less_eq_int: (int > (int > $o))). 71.81/31.82 thf(ord_less_eq_set_a_type, type, ord_less_eq_set_a: (set_a > (set_a > $o))). 71.81/31.82 thf(product_fst_a_a_type, type, product_fst_a_a: (product_prod_a_a > a)). 71.81/31.82 thf(product_snd_a_a_type, type, product_snd_a_a: (product_prod_a_a > a)). 71.81/31.82 thf(a_inv_a_b_type, type, a_inv_a_b: (partia1833973666xt_a_b > (a > a))). 71.81/31.82 thf(a_minus_a_b_type, type, a_minus_a_b: (partia1833973666xt_a_b > (a > (a > a)))). 71.81/31.82 thf(add_pow_a_b_int_type, type, add_pow_a_b_int: (partia1833973666xt_a_b > (int > (a > a)))). 71.81/31.82 thf(add_a_b_type, type, add_a_b: (partia1833973666xt_a_b > (a > (a > a)))). 71.81/31.82 thf(zero_a_b_type, type, zero_a_b: (partia1833973666xt_a_b > a)). 71.81/31.82 thf(semiring_a_b_type, type, semiring_a_b: (partia1833973666xt_a_b > $o)). 71.81/31.82 thf(collect_a_type, type, collect_a: ((a > $o) > set_a)). 71.81/31.82 thf(member_a_type, type, member_a: (a > (set_a > $o))). 71.81/31.82 thf(r_type, type, r: partia1833973666xt_a_b). 71.81/31.82 thf(s_type, type, s: set_a). 71.81/31.82 thf(r2_type, type, r2: a). 71.81/31.82 thf(r3_type, type, r3: a). 71.81/31.82 thf(s2_type, type, s2: a). 71.81/31.82 thf(s3_type, type, s3: a). 71.81/31.82 thf(t_type, type, t: a). 71.81/31.82 thf(t2_type, type, t2: a). 71.81/31.82 thf(x_type, type, x: product_prod_a_a). 71.81/31.82 thf(y_type, type, y: product_prod_a_a). 71.81/31.82 thf(sk14_type, type, sk14: a). 71.81/31.82 thf(sk15_type, type, sk15: a). 71.81/31.82 thf(204,axiom,((member_a @ s3 @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_f20)). 71.81/31.82 thf(855,plain,((member_a @ s3 @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 71.81/31.82 thf(214,axiom,((member_a @ t2 @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_f17)). 71.81/31.82 thf(883,plain,((member_a @ t2 @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 71.81/31.82 thf(140,axiom,((! [A:a,B:a,C:a]: ((((add_a_b @ r @ B @ C) = (zero_a_b @ r)) => (((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((A = C) <= (member_a @ C @ (partia1066395285xt_a_b @ r)))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))) <= ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_local_Ominus__unique)). 71.81/31.82 thf(658,plain,((! [A:a,B:a,C:a]: (((add_a_b @ r @ A @ B) = (zero_a_b @ r)) => (((add_a_b @ r @ B @ C) = (zero_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ C @ (partia1066395285xt_a_b @ r)) => (A = C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 71.81/31.82 thf(659,plain,((! [A:a,B:a]: (((add_a_b @ r @ A @ B) = (zero_a_b @ r)) => (! [C:a]: (((add_a_b @ r @ B @ C) = (zero_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ C @ (partia1066395285xt_a_b @ r)) => (A = C))))))))),inference(miniscope,[status(thm)],[658])). 71.81/31.82 thf(660,plain,(! [C:a,B:a,A:a] : ((~ ((add_a_b @ r @ A @ B) = (zero_a_b @ r))) | (~ ((add_a_b @ r @ B @ C) = (zero_a_b @ r))) | (~ (member_a @ B @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ C @ (partia1066395285xt_a_b @ r))) | (A = C))),inference(cnf,[status(esa)],[659])). 71.81/31.82 thf(661,plain,(! [C:a,B:a,A:a] : (((add_a_b @ r @ A @ B) != (zero_a_b @ r)) | ((add_a_b @ r @ B @ C) != (zero_a_b @ r)) | (A = C) | (~ (member_a @ B @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ C @ (partia1066395285xt_a_b @ r))))),inference(lifteq,[status(thm)],[660])). 71.81/31.82 thf(208,axiom,((member_a @ t @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_f18)). 71.81/31.82 thf(866,plain,((member_a @ t @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 71.81/31.82 thf(1,conjecture,(((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 71.81/31.82 thf(2,negated_conjecture,((~ ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))),inference(neg_conjecture,[status(cth)],[1])). 71.81/31.82 thf(247,plain,((~ ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 71.81/31.82 thf(248,plain,(((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))),inference(lifteq,[status(thm)],[247])). 71.81/31.82 thf(1157,plain,(! [C:a,B:a,A:a] : (((add_a_b @ r @ A @ B) != (zero_a_b @ r)) | ((add_a_b @ r @ B @ C) != (zero_a_b @ r)) | (~ (member_a @ B @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ C @ (partia1066395285xt_a_b @ r))) | ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ A) != (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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))) | (C != (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))),inference(paramod_ordered,[status(thm)],[661,248])). 71.81/31.82 thf(1158,plain,(! [B:a,A:a] : (((add_a_b @ r @ A @ B) != (zero_a_b @ r)) | ((add_a_b @ r @ B @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) != (zero_a_b @ r)) | (~ (member_a @ B @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ A) != (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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))))),inference(pattern_uni,[status(thm)],[1157:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))]])). 71.81/31.82 thf(1253,plain,(! [B:a,A:a] : (((add_a_b @ r @ A @ B) != (zero_a_b @ r)) | ((add_a_b @ r @ B @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) != (zero_a_b @ r)) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ A) != (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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))) | ((member_a @ t @ (partia1066395285xt_a_b @ r)) != (member_a @ B @ (partia1066395285xt_a_b @ r))))),inference(paramod_ordered,[status(thm)],[866,1158])). 71.81/31.82 thf(1254,plain,(! [A:a] : (((add_a_b @ r @ A @ t) != (zero_a_b @ r)) | ((add_a_b @ r @ t @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) != (zero_a_b @ r)) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ A) != (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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))))),inference(pattern_uni,[status(thm)],[1253:[bind(A, $thf(A)),bind(B, $thf(t))]])). 71.81/31.82 thf(1534,plain,(! [A:a] : (((add_a_b @ r @ A @ t) != (zero_a_b @ r)) | ((add_a_b @ r @ t @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ A) != (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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))) | ((member_a @ t @ (partia1066395285xt_a_b @ r)) != (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(paramod_ordered,[status(thm)],[866,1254])). 71.81/31.82 thf(1535,plain,(((add_a_b @ r @ t @ t) != (zero_a_b @ r)) | ((add_a_b @ r @ t @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t))),inference(pattern_uni,[status(thm)],[1534:[bind(A, $thf(t))]])). 71.81/31.82 thf(2012,plain,(((add_a_b @ r @ t @ t) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ t @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) != (add_a_b @ r @ t @ t)) | ((zero_a_b @ r) != (zero_a_b @ r))),inference(eqfactor_ordered,[status(thm)],[1535])). 71.81/31.82 thf(2018,plain,(((add_a_b @ r @ t @ t) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | (r != r) | (t != t) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t)),inference(simp,[status(thm)],[2012])). 71.81/31.82 thf(2024,plain,(((add_a_b @ r @ t @ t) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t)),inference(simp,[status(thm)],[2018])). 71.81/31.82 thf(2139,plain,(((add_a_b @ r @ t @ t) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) != (member_a @ t @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[866,2024])). 71.81/31.82 thf(2357,plain,(((add_a_b @ r @ t @ t) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[2139])). 71.81/31.82 thf(2371,plain,(((add_a_b @ r @ t @ t) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t)),inference(simp,[status(thm)],[2357])). 71.81/31.82 thf(2373,plain,(! [C:a,B:a,A:a] : (((add_a_b @ r @ A @ B) != (zero_a_b @ r)) | ((add_a_b @ r @ B @ C) != (zero_a_b @ r)) | (~ (member_a @ B @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ C @ (partia1066395285xt_a_b @ r))) | (C != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | (A != (add_a_b @ r @ t @ t)))),inference(paramod_ordered,[status(thm)],[661,2371])). 71.81/31.82 thf(2374,plain,(! [B:a,A:a] : (((add_a_b @ r @ (add_a_b @ r @ t @ t) @ A) != (zero_a_b @ r)) | ((add_a_b @ r @ A @ B) != (zero_a_b @ r)) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ B @ (partia1066395285xt_a_b @ r))) | (B != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t))),inference(pattern_uni,[status(thm)],[2373:[bind(A, $thf(add_a_b @ r @ t @ t)),bind(B, $thf(B)),bind(C, $thf(C))]])). 71.81/31.82 thf(2511,plain,(! [A:a] : (((add_a_b @ r @ (add_a_b @ r @ t @ t) @ A) != (zero_a_b @ r)) | ((add_a_b @ r @ A @ (zero_a_b @ r)) != (zero_a_b @ r)) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ (zero_a_b @ r) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t))),inference(simp,[status(thm)],[2374])). 71.81/31.82 thf(158,axiom,((member_a @ (zero_a_b @ r) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__closed)). 71.81/31.82 thf(718,plain,((member_a @ (zero_a_b @ r) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 71.81/31.82 thf(2544,plain,(! [A:a] : (((add_a_b @ r @ (add_a_b @ r @ t @ t) @ A) != (zero_a_b @ r)) | ((add_a_b @ r @ A @ (zero_a_b @ r)) != (zero_a_b @ r)) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r))) | ~ (($true)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t))),inference(rewrite,[status(thm)],[2511,718])). 71.81/31.82 thf(2545,plain,(! [A:a] : (((add_a_b @ r @ (add_a_b @ r @ t @ t) @ A) != (zero_a_b @ r)) | ((add_a_b @ r @ A @ (zero_a_b @ r)) != (zero_a_b @ r)) | (~ (member_a @ A @ (partia1066395285xt_a_b @ r))) | (~ (member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t))),inference(simp,[status(thm)],[2544])). 71.81/31.82 thf(2548,plain,(! [A:a] : (((add_a_b @ r @ (add_a_b @ r @ t @ t) @ A) != (zero_a_b @ r)) | ((add_a_b @ r @ A @ (zero_a_b @ r)) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ t2 @ (partia1066395285xt_a_b @ r)) != (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(paramod_ordered,[status(thm)],[883,2545])). 71.81/31.82 thf(2549,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t)),inference(pattern_uni,[status(thm)],[2548:[bind(A, $thf(t2))]])). 71.81/31.82 thf(2999,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r)) != (member_a @ s3 @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[855,2549])). 71.81/31.82 thf(3013,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s3) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[2999])). 71.81/31.82 thf(3021,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s3)),inference(simp,[status(thm)],[3013])). 71.81/31.82 thf(191,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_f10)). 71.81/31.82 thf(809,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 71.81/31.82 thf(43,axiom,((! [A:set_a]: ((minus_minus_set_a @ bot_bot_set_a @ A) = bot_bot_set_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_empty__Diff)). 71.81/31.82 thf(365,plain,((! [A:set_a]: ((minus_minus_set_a @ bot_bot_set_a @ A) = bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 71.81/31.82 thf(236,axiom,(((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_f31)). 71.81/31.82 thf(941,plain,(((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 71.81/31.82 thf(179,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (zero_a_b @ r) @ A) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_l__null)). 71.81/31.82 thf(777,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (zero_a_b @ r) @ A) = (zero_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 71.81/31.82 thf(3,axiom,((! [A:int,B:int,C:int,D:int]: (((A = B) & (ord_less_eq_int @ C @ D)) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_add__mono__thms__linordered__semiring_I2_J)). 71.81/31.82 thf(249,plain,((! [A:int,B:int,C:int,D:int]: (((A = B) & (ord_less_eq_int @ C @ D)) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 71.81/31.82 thf(33,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((plus_plus_int @ (minus_minus_int @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_le__add__diff__inverse2)). 71.81/31.82 thf(333,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((plus_plus_int @ (minus_minus_int @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 71.81/31.82 thf(130,axiom,((! [A:a,B:a,C:a]: ((((member_a @ C @ (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 @ B @ (partia1066395285xt_a_b @ r))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add_Oinv__solve__left_H)). 71.81/31.82 thf(628,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 @ (a_inv_a_b @ r @ B) @ C) = A) = (C = (add_a_b @ r @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 71.81/31.82 thf(81,axiom,((! [A:int,B:int,C:int]: ((A = (plus_plus_int @ B @ C)) => ((uminus_uminus_int @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_group__cancel_Oneg1)). 71.81/31.82 thf(481,plain,((! [A:int,B:int,C:int]: ((A = (plus_plus_int @ B @ C)) => ((uminus_uminus_int @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 71.81/31.82 thf(39,axiom,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) => (A = bot_bot_set_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_equals0I)). 71.81/31.82 thf(352,plain,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) => (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 71.81/31.82 thf(57,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) <= (member_a @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_subset__eq)). 71.81/31.82 thf(407,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 71.81/31.82 thf(408,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),inference(lifteq,[status(thm)],[407])). 71.81/31.82 thf(71,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_145_uminus__add__conv__diff)). 71.81/31.82 thf(449,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)],[71])). 71.81/31.82 thf(47,axiom,((! [A:(a > $o)]: (((collect_a @ A) = bot_bot_set_a) = (! [B:a]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Collect__empty__eq)). 71.81/31.82 thf(379,plain,((! [A:(a > $o)]: (((collect_a @ (A)) = bot_bot_set_a) = (! [B:a]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 71.81/31.82 thf(380,plain,(! [A:(a > $o)] : ((((collect_a @ (A)) = bot_bot_set_a) = (! [B:a]: ~ (A @ B))))),inference(cnf,[status(esa)],[379])). 71.81/31.82 thf(381,plain,(! [A:(a > $o)] : ((((collect_a @ (A)) = bot_bot_set_a) = (! [B:a]: ~ (A @ B))))),inference(lifteq,[status(thm)],[380])). 71.81/31.82 thf(6280,plain,(! [A:(a > $o)] : ((~ ((collect_a @ (A)) = bot_bot_set_a)) | (! [B:a]: ~ (A @ B)))),inference(bool_ext,[status(thm)],[381])). 71.81/31.82 thf(6292,plain,(! [A:(a > $o)] : (((collect_a @ (A)) != bot_bot_set_a) | (! [B:a]: ~ (A @ B)))),inference(lifteq,[status(thm)],[6280])). 71.81/31.82 thf(6295,plain,(! [B:a,A:(a > $o)] : ((~ (A @ B)) | ((collect_a @ (A)) != bot_bot_set_a))),inference(cnf,[status(esa)],[6292])). 71.81/31.82 thf(113,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((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)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_local_Ominus__add)). 71.81/31.82 thf(582,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)) = (add_a_b @ r @ (a_inv_a_b @ r @ A) @ (a_inv_a_b @ r @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 71.81/31.82 thf(173,axiom,((! [A:a,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ C @ (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 @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add_Om__lcomm)). 71.81/31.82 thf(762,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 @ A @ (add_a_b @ r @ B @ C)) = (add_a_b @ r @ B @ (add_a_b @ r @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 71.81/31.82 thf(68,axiom,((! [A:partia1833973666xt_a_b,B:set_a]: ((ord_less_eq_set_a @ B @ (partia1066395285xt_a_b @ A)) <= (locali425460998xt_a_b @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Osubset)). 71.81/31.82 thf(440,plain,((! [A:partia1833973666xt_a_b,B:set_a]: ((locali425460998xt_a_b @ A @ B) => (ord_less_eq_set_a @ B @ (partia1066395285xt_a_b @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 71.81/31.82 thf(139,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_124_add_Oint__pow__one)). 71.81/31.82 thf(655,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)],[139])). 71.81/31.82 thf(89,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_149_add__left__cancel)). 71.81/31.82 thf(511,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)],[89])). 71.81/31.82 thf(10,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) = (ord_less_eq_int @ (uminus_uminus_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_minus__le__iff)). 71.81/31.82 thf(269,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) = (ord_less_eq_int @ (uminus_uminus_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 71.81/31.82 thf(146,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 @ (add_a_b @ r @ A @ B) @ C) = (add_a_b @ r @ A @ (add_a_b @ r @ B @ C))) <= (member_a @ C @ (partia1066395285xt_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add_Om__assoc)). 71.81/31.82 thf(677,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 @ (add_a_b @ r @ A @ B) @ C) = (add_a_b @ r @ A @ (add_a_b @ r @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 71.81/31.82 thf(2837,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r)) != (member_a @ t @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[866,2549])). 71.81/31.82 thf(3008,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[2837])). 71.81/31.82 thf(3017,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t)),inference(simp,[status(thm)],[3008])). 71.81/31.82 thf(49,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ (minus_minus_int @ B @ A)) = B) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_le__add__diff__inverse)). 71.81/31.82 thf(385,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((plus_plus_int @ A @ (minus_minus_int @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 71.81/31.82 thf(96,axiom,((! [A:set_a]: ((minus_minus_set_a @ A @ A) = bot_bot_set_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_Diff__cancel)). 71.81/31.82 thf(533,plain,((! [A:set_a]: ((minus_minus_set_a @ A @ A) = bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 71.81/31.82 thf(152,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add_Or__inv__ex)). 71.81/31.82 thf(698,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 71.81/31.82 thf(233,axiom,((! [A:a,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ A @ (add_a_b @ r @ (a_inv_a_b @ r @ A) @ B)) = B)) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_r__neg2)). 71.81/31.82 thf(930,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ A @ (add_a_b @ r @ (a_inv_a_b @ r @ A) @ B)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 71.81/31.82 thf(223,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_f27)). 71.81/31.82 thf(898,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 71.81/31.82 thf(216,axiom,((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_f42)). 71.81/31.82 thf(885,plain,((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 71.81/31.82 thf(21,axiom,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq)). 71.81/31.82 thf(301,plain,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 71.81/31.82 thf(28,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_201_eq__diff__eq)). 71.81/31.82 thf(320,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)],[28])). 71.81/31.82 thf(5,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_add__right__mono)). 71.81/31.82 thf(255,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 71.81/31.82 thf(256,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (! [C:int]: (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C)))))),inference(miniscope,[status(thm)],[255])). 71.81/31.82 thf(257,plain,(! [C:int,B:int,A:int] : ((~ (ord_less_eq_int @ A @ B)) | (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C)))),inference(cnf,[status(esa)],[256])). 71.81/31.82 thf(108,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_f24)). 71.81/31.82 thf(570,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 71.81/31.82 thf(159,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_92_inv__add)). 71.81/31.82 thf(719,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)],[159])). 71.81/31.82 thf(182,axiom,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_a_b @ A) => (((add_a_b @ A @ B @ (zero_a_b @ A)) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_semiring_Osemiring__simprules_I11_J)). 71.81/31.82 thf(785,plain,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ B @ (zero_a_b @ A)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 71.81/31.82 thf(138,axiom,((member_a @ s2 @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f19)). 71.81/31.82 thf(654,plain,((member_a @ s2 @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 71.81/31.82 thf(2551,plain,(! [A:a] : (((add_a_b @ r @ (add_a_b @ r @ t @ t) @ A) != (zero_a_b @ r)) | ((add_a_b @ r @ A @ (zero_a_b @ r)) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ s3 @ (partia1066395285xt_a_b @ r)) != (member_a @ A @ (partia1066395285xt_a_b @ r))))),inference(paramod_ordered,[status(thm)],[855,2545])). 71.81/31.82 thf(2552,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (zero_a_b @ r)) | ((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | (~ (member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r))) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t)),inference(pattern_uni,[status(thm)],[2551:[bind(A, $thf(s3))]])). 71.81/31.82 thf(5499,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (zero_a_b @ r)) | ((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r)) != (member_a @ s2 @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[654,2552])). 71.81/31.82 thf(5520,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (zero_a_b @ r)) | ((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s2) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[5499])). 71.81/31.82 thf(5540,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (zero_a_b @ r)) | ((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s2)),inference(simp,[status(thm)],[5520])). 71.81/31.82 thf(6102,plain,(((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s2) | ((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (add_a_b @ r @ s3 @ (zero_a_b @ r))) | ((zero_a_b @ r) != (zero_a_b @ r))),inference(eqfactor_ordered,[status(thm)],[5540])). 71.81/31.82 thf(6104,plain,(((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s2) | (r != r) | ((add_a_b @ r @ t @ t) != s3) | ((zero_a_b @ r) != s3)),inference(simp,[status(thm)],[6102])). 71.81/31.82 thf(6113,plain,(((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s2) | ((add_a_b @ r @ t @ t) != s3) | ((zero_a_b @ r) != s3)),inference(simp,[status(thm)],[6104])). 71.81/31.82 thf(234,axiom,((! [A:a,B:a,C:a]: (((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ C @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ B @ A) = (add_a_b @ r @ C @ A)) = (B = C)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_local_Oadd_Oright__cancel)). 71.81/31.82 thf(934,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) = (add_a_b @ r @ C @ A)) = (B = C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 71.81/31.82 thf(239,axiom,((locali1648887798ac_a_b @ r @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_eq__obj__rng__of__frac__axioms)). 71.81/31.82 thf(949,plain,((locali1648887798ac_a_b @ r @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 71.81/31.82 thf(99,axiom,((! [A:(a > $o)]: ((bot_bot_set_a = (collect_a @ A)) = (! [B:a]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_empty__Collect__eq)). 71.81/31.82 thf(542,plain,((! [A:(a > $o)]: ((bot_bot_set_a = (collect_a @ (A))) = (! [B:a]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 71.81/31.82 thf(153,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((A = (zero_a_b @ r)) <= (! [B:a]: (((add_a_b @ r @ A @ B) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add_Oone__unique)). 71.81/31.82 thf(702,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((! [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ A @ B) = B))) => (A = (zero_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 71.81/31.82 thf(170,axiom,((! [A:a,B:a,C:a]: (((a_minus_a_b @ r @ C @ A) = (a_minus_a_b @ r @ C @ B)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_local_Oright__minus__eq)). 71.81/31.82 thf(751,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)],[170])). 71.81/31.82 thf(61,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_198_diff__add__eq)). 71.81/31.82 thf(421,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)],[61])). 71.81/31.82 thf(24,axiom,((minus_minus_int = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_ab__group__add__class_Oab__diff__conv__add__uminus)). 71.81/31.82 thf(310,plain,(((minus_minus_int) = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 71.81/31.82 thf(311,plain,(((^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))) = (minus_minus_int))),inference(lifteq,[status(thm)],[310])). 71.81/31.82 thf(969,plain,(! [A:int] : (((^ [B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))) = (minus_minus_int @ A)))),inference(func_ext,[status(esa)],[311])). 71.81/31.82 thf(29,axiom,((! [A:int]: ((uminus_uminus_int @ (uminus_uminus_int @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_add_Oinverse__inverse)). 71.81/31.82 thf(323,plain,((! [A:int]: ((uminus_uminus_int @ (uminus_uminus_int @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 71.81/31.82 thf(324,plain,(! [A:int] : (((uminus_uminus_int @ (uminus_uminus_int @ A)) = A))),inference(cnf,[status(esa)],[323])). 71.81/31.82 thf(325,plain,(! [A:int] : (((uminus_uminus_int @ (uminus_uminus_int @ A)) = A))),inference(lifteq,[status(thm)],[324])). 71.81/31.82 thf(17,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_le__minus__iff)). 71.81/31.82 thf(289,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 71.81/31.82 thf(7,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_neg__le__iff__le)). 71.81/31.82 thf(261,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 71.81/31.82 thf(15,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_add__le__imp__le__left)). 71.81/31.82 thf(284,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) => (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 71.81/31.82 thf(175,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_f37)). 71.81/31.82 thf(770,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 71.81/31.82 thf(171,axiom,(((mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))) = (zero_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_f7)). 71.81/31.82 thf(756,plain,(((mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))) = (zero_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 71.81/31.82 thf(183,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_f16)). 71.81/31.82 thf(789,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 71.81/31.82 thf(82,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_206_minus__diff__commute)). 71.81/31.82 thf(485,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)],[82])). 71.81/31.82 thf(90,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ B @ C)) = (ord_less_eq_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_le__diff__eq)). 71.81/31.82 thf(514,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ B @ C)) = (ord_less_eq_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 71.81/31.82 thf(246,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_f8)). 71.81/31.82 thf(966,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 71.81/31.82 thf(136,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((add_a_b @ r @ B @ A) = (zero_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add_Ol__inv__ex)). 71.81/31.82 thf(646,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (? [B:a]: ((member_a @ B @ (partia1066395285xt_a_b @ r)) & ((add_a_b @ r @ B @ A) = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 71.81/31.82 thf(4,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__imp__neg__le)). 71.81/31.82 thf(253,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 71.81/31.82 thf(174,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (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 @ C @ (partia1066395285xt_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add_Oinv__solve__left)). 71.81/31.82 thf(766,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)) => ((A = (add_a_b @ r @ (a_inv_a_b @ r @ B) @ C)) = (C = (add_a_b @ r @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 71.81/31.82 thf(132,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_108_add_Oinv__eq__1__iff)). 71.81/31.82 thf(634,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((a_inv_a_b @ r @ A) = (zero_a_b @ r)) = (A = (zero_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 71.81/31.82 thf(53,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_196_diff__diff__add)). 71.81/31.82 thf(396,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)],[53])). 71.81/31.82 thf(202,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_f34)). 71.81/31.82 thf(849,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 71.81/31.82 thf(88,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_166_add__left__imp__eq)). 71.81/31.82 thf(507,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)],[88])). 71.81/31.82 thf(25,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_161_minus__add__distrib)). 71.81/31.82 thf(312,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)],[25])). 71.81/31.82 thf(18,axiom,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq)). 71.81/31.82 thf(292,plain,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 71.81/31.82 thf(72,axiom,((! [A:int,B:int]: (((uminus_uminus_int @ A) = (uminus_uminus_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_neg__equal__iff__equal)). 71.81/31.82 thf(452,plain,((! [A:int,B:int]: (((uminus_uminus_int @ A) = (uminus_uminus_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 71.81/31.82 thf(192,axiom,((! [A:set_a]: ((((! [B:a]: ((member_a @ (a_inv_a_b @ r @ B) @ A) <= (member_a @ B @ A))) => ((! [B:a]: ((member_a @ B @ A) => (! [C:a]: ((member_a @ (add_a_b @ r @ B @ C) @ A) <= (member_a @ C @ A))))) => (member_a @ (zero_a_b @ r) @ A))) <= (A != bot_bot_set_a)) <= (ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add_Oone__in__subset)). 71.81/31.82 thf(810,plain,((! [A:set_a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((~ (A = bot_bot_set_a)) => ((! [B:a]: ((member_a @ B @ A) => (member_a @ (a_inv_a_b @ r @ B) @ A))) => ((! [B:a]: ((member_a @ B @ A) => (! [C:a]: ((member_a @ C @ A) => (member_a @ (add_a_b @ r @ B @ C) @ A))))) => (member_a @ (zero_a_b @ r) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 71.81/31.82 thf(156,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_f25)). 71.81/31.82 thf(714,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 71.81/31.82 thf(221,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3)) @ (mult_a_ring_ext_a_b @ r @ t @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_f29)). 71.81/31.82 thf(894,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3)) @ (mult_a_ring_ext_a_b @ r @ t @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 71.81/31.82 thf(168,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((semiring_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))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_semiring_Osemiring__simprules_I3_J)). 71.81/31.82 thf(746,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)],[168])). 71.81/31.82 thf(105,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_89_r__neg)). 71.81/31.82 thf(561,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)],[105])). 71.81/31.82 thf(51,axiom,((! [A:set_a]: (ord_less_eq_set_a @ bot_bot_set_a @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_empty__subsetI)). 71.81/31.82 thf(391,plain,((! [A:set_a]: (ord_less_eq_set_a @ bot_bot_set_a @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 71.81/31.82 thf(392,plain,(! [A:set_a] : ((ord_less_eq_set_a @ bot_bot_set_a @ A))),inference(cnf,[status(esa)],[391])). 71.81/31.82 thf(62,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_170_add_Oleft__cancel)). 71.81/31.82 thf(424,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)],[62])). 71.81/31.82 thf(12,axiom,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_diff__eq__diff__less__eq)). 71.81/31.82 thf(275,plain,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 71.81/31.82 thf(163,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((A = (a_inv_a_b @ r @ B)) <= ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_sum__zero__eq__neg)). 71.81/31.82 thf(729,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) = (zero_a_b @ r)) => (A = (a_inv_a_b @ r @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 71.81/31.82 thf(6,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_eq_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_add__le__cancel__left)). 71.81/31.82 thf(258,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 71.81/31.82 thf(259,plain,(! [C:int,B:int,A:int] : (((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_eq_int @ B @ C)))),inference(cnf,[status(esa)],[258])). 71.81/31.82 thf(260,plain,(! [C:int,B:int,A:int] : (((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_eq_int @ B @ C)))),inference(lifteq,[status(thm)],[259])). 71.81/31.82 thf(207,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_79_r__neg1)). 71.81/31.82 thf(862,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (a_inv_a_b @ r @ A) @ (add_a_b @ r @ A @ B)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 71.81/31.82 thf(38,axiom,((! [A:set_a,B:set_a,C:a]: (((member_a @ C @ B) <= (member_a @ C @ A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_subsetD)). 71.81/31.82 thf(349,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 71.81/31.82 thf(129,axiom,((! [A:a,B:a]: (((member_a @ (mult_a_ring_ext_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_62_semiring__simprules_I3_J)). 71.81/31.82 thf(625,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)],[129])). 71.81/31.82 thf(213,axiom,((! [A:a,B:a,C:a]: (((((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))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add_Oinv__solve__right)). 71.81/31.82 thf(879,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)) => ((A = (add_a_b @ r @ B @ (a_inv_a_b @ r @ C))) = (B = (add_a_b @ r @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 71.81/31.82 thf(31,axiom,((! [A:partia1833973666xt_a_b,B:set_a]: ((locali425460998xt_a_b @ A @ B) => (locali425460998xt_a_b @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Ois__submonoid)). 71.81/31.82 thf(329,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 71.81/31.82 thf(142,axiom,(((mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))) = (zero_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_f5)). 71.81/31.82 thf(665,plain,(((mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))) = (zero_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 71.81/31.82 thf(84,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_202_diff__eq__eq)). 71.81/31.82 thf(493,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)],[84])). 71.81/31.82 thf(102,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_200_add__diff__eq)). 71.81/31.82 thf(551,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)],[102])). 71.81/31.82 thf(199,axiom,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_f33)). 71.81/31.82 thf(842,plain,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 71.81/31.82 thf(66,axiom,((minus_minus_int = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_diff__conv__add__uminus)). 71.81/31.82 thf(435,plain,(((minus_minus_int) = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 71.81/31.82 thf(6358,plain,(~ (($true)) | ((collect_a @ (^ [A:a]: (($true)))) != bot_bot_set_a)),inference(prim_subst,[status(thm)],[6295:[bind(A, $thf(^ [C:a]: (($true))))]])). 71.81/31.82 thf(6445,plain,(((collect_a @ (^ [A:a]: (($true)))) != bot_bot_set_a)),inference(simp,[status(thm)],[6358])). 71.81/31.82 thf(93,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_195_add__implies__diff)). 71.81/31.82 thf(522,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)],[93])). 71.81/31.82 thf(194,axiom,((~ (! [A:a]: (((mult_a_ring_ext_a_b @ r @ A @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))) != (zero_a_b @ r)) <= (member_a @ A @ s))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_H_O_A_092_060lbrakk_062t_H_A_092_060in_062_AS_059_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 71.81/31.82 thf(827,plain,((~ (! [A:a]: ((member_a @ A @ s) => (~ ((mult_a_ring_ext_a_b @ r @ A @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))) = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 71.81/31.82 thf(828,plain,((~ (! [A:a]: ((member_a @ A @ s) => (~ ((mult_a_ring_ext_a_b @ r @ A @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))) = (zero_a_b @ r))))))),inference(polarity_switch,[status(thm)],[827])). 71.81/31.82 thf(830,plain,((member_a @ sk14 @ s)),inference(cnf,[status(esa)],[828])). 71.81/31.82 thf(167,axiom,((! [A:partia1833973666xt_a_b,B:a]: ((((add_a_b @ A @ (zero_a_b @ A) @ B) = B) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_semiring_Osemiring__simprules_I6_J)). 71.81/31.82 thf(742,plain,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_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)],[167])). 71.81/31.82 thf(27,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_167_add_Oleft__commute)). 71.81/31.82 thf(317,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)],[27])). 71.81/31.82 thf(137,axiom,((! [A:a,B:int,C:int]: (((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))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_add_Oint__pow__mult)). 71.81/31.82 thf(650,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)],[137])). 71.81/31.82 thf(161,axiom,((! [A:set_a,B:a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((ord_less_eq_set_a @ (a_l_coset_a_b @ r @ B @ A) @ (partia1066395285xt_a_b @ r)) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_a__l__coset__subset__G)). 71.81/31.82 thf(725,plain,((! [A:set_a,B:a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (ord_less_eq_set_a @ (a_l_coset_a_b @ r @ B @ A) @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 71.81/31.82 thf(50,axiom,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_emptyE)). 71.81/31.82 thf(388,plain,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 71.81/31.82 thf(40,axiom,((! [A:int,B:int,C:int,D:int]: (((A = B) = (C = D)) <= ((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_diff__eq__diff__eq)). 71.81/31.82 thf(356,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)],[40])). 71.81/31.82 thf(86,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_162_minus__add__cancel)). 71.81/31.82 thf(499,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)],[86])). 71.81/31.82 thf(2996,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r)) != (member_a @ s2 @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[654,2549])). 71.81/31.82 thf(3009,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s2) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[2996])). 71.81/31.82 thf(3018,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != s2)),inference(simp,[status(thm)],[3009])). 71.81/31.82 thf(78,axiom,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ B @ A) => (A = B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_subset__antisym)). 71.81/31.82 thf(471,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 71.81/31.82 thf(215,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_f28)). 71.81/31.82 thf(884,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 71.81/31.82 thf(83,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_203_group__cancel_Osub1)). 71.81/31.82 thf(488,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)],[83])). 71.81/31.82 thf(35,axiom,((! [A:set_a]: ((minus_minus_set_a @ A @ bot_bot_set_a) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Diff__empty)). 71.81/31.82 thf(339,plain,((! [A:set_a]: ((minus_minus_set_a @ A @ bot_bot_set_a) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 71.81/31.82 thf(103,axiom,((! [A:set_a]: ((ord_less_eq_set_a @ A @ bot_bot_set_a) = (A = bot_bot_set_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_subset__empty)). 71.81/31.82 thf(554,plain,((! [A:set_a]: ((ord_less_eq_set_a @ A @ bot_bot_set_a) = (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 71.81/31.82 thf(144,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)) => ((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)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_m__assoc)). 71.81/31.82 thf(669,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)) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 71.81/31.82 thf(135,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (zero_a_b @ A) @ B) = (zero_a_b @ A))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_semiring_Ol__null)). 71.81/31.82 thf(642,plain,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ (zero_a_b @ A) @ B) = (zero_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 71.81/31.82 thf(94,axiom,((! [A:set_a,B:a]: ((~ (member_a @ B @ A)) <= (A = bot_bot_set_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_equals0D)). 71.81/31.82 thf(526,plain,((! [A:set_a,B:a]: ((A = bot_bot_set_a) => (~ (member_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 71.81/31.82 thf(133,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((a_inv_a_b @ r @ (a_inv_a_b @ r @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_local_Ominus__minus)). 71.81/31.82 thf(637,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((a_inv_a_b @ r @ (a_inv_a_b @ r @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 71.81/31.82 thf(162,axiom,((member_a @ (product_snd_a_a @ y) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_f21)). 71.81/31.82 thf(728,plain,((member_a @ (product_snd_a_a @ y) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 71.81/31.82 thf(3001,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r)) != (member_a @ (product_snd_a_a @ y) @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[728,2549])). 71.81/31.82 thf(3003,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != (product_snd_a_a @ y)) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[3001])). 71.81/31.82 thf(3032,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != (product_snd_a_a @ y))),inference(simp,[status(thm)],[3003])). 71.81/31.82 thf(293,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(cnf,[status(esa)],[292])). 71.81/31.82 thf(294,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(lifteq,[status(thm)],[293])). 71.81/31.82 thf(366,plain,(! [A:set_a] : (((minus_minus_set_a @ bot_bot_set_a @ A) = bot_bot_set_a))),inference(cnf,[status(esa)],[365])). 71.81/31.82 thf(367,plain,(! [A:set_a] : (((minus_minus_set_a @ bot_bot_set_a @ A) = bot_bot_set_a))),inference(lifteq,[status(thm)],[366])). 71.81/31.82 thf(4512,plain,(! [B:set_a,A:set_a] : (((collect_a @ (^ [C:a]: (member_a @ C @ A))) = bot_bot_set_a) | (A != (minus_minus_set_a @ bot_bot_set_a @ B)))),inference(paramod_ordered,[status(thm)],[294,367])). 71.81/31.82 thf(4513,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (minus_minus_set_a @ bot_bot_set_a @ A)))) = bot_bot_set_a))),inference(pattern_uni,[status(thm)],[4512:[bind(A, $thf(minus_minus_set_a @ bot_bot_set_a @ D)),bind(B, $thf(D))]])). 71.81/31.82 thf(4529,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (minus_minus_set_a @ bot_bot_set_a @ A)))) = bot_bot_set_a))),inference(simp,[status(thm)],[4513])). 71.81/31.82 thf(4530,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ bot_bot_set_a))) = bot_bot_set_a)),inference(rewrite,[status(thm)],[4529,367])). 71.81/31.82 thf(197,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((ord_less_eq_set_a @ B @ (partia1066395285xt_a_b @ r)) => (ord_less_eq_set_a @ (set_add_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_set__add__closed)). 71.81/31.82 thf(837,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((ord_less_eq_set_a @ B @ (partia1066395285xt_a_b @ r)) => (ord_less_eq_set_a @ (set_add_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 71.81/31.82 thf(52,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_176_diff__right__commute)). 71.81/31.82 thf(393,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)],[52])). 71.81/31.82 thf(117,axiom,((member_a @ t @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_f6)). 71.81/31.82 thf(595,plain,((member_a @ t @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 71.81/31.82 thf(389,plain,((~ (? [A:a]: (member_a @ A @ bot_bot_set_a)))),inference(miniscope,[status(thm)],[388])). 71.81/31.82 thf(390,plain,(! [A:a] : ((~ (member_a @ A @ bot_bot_set_a)))),inference(cnf,[status(esa)],[389])). 71.81/31.82 thf(983,plain,(! [A:a] : (((member_a @ t @ s) != (member_a @ A @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[595,390])). 71.81/31.82 thf(984,plain,(! [A:a] : ((t != A) | (s != bot_bot_set_a))),inference(simp,[status(thm)],[983])). 71.81/31.82 thf(985,plain,((s != bot_bot_set_a)),inference(simp,[status(thm)],[984])). 71.81/31.82 thf(166,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_6_m__lcomm)). 71.81/31.82 thf(738,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)) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 71.81/31.82 thf(228,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: (((((member_a @ D @ (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 @ C @ (partia1066395285xt_a_b @ A))) <= (member_a @ B @ (partia1066395285xt_a_b @ A))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_semiring_Osemiring__simprules_I12_J)). 71.81/31.82 thf(911,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)) => ((member_a @ D @ (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))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 71.81/31.82 thf(45,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_171_add_Oassoc)). 71.81/31.82 thf(371,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)],[45])). 71.81/31.82 thf(235,axiom,((((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) => (((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) <= (member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)))) <= (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062)). 71.81/31.82 thf(938,plain,(((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 71.81/31.82 thf(8,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_diff__right__mono)). 71.81/31.82 thf(264,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 71.81/31.82 thf(265,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (! [C:int]: (ord_less_eq_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)))))),inference(miniscope,[status(thm)],[264])). 71.81/31.82 thf(266,plain,(! [C:int,B:int,A:int] : ((~ (ord_less_eq_int @ A @ B)) | (ord_less_eq_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)))),inference(cnf,[status(esa)],[265])). 71.81/31.82 thf(131,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_130_a__minus__def)). 71.81/31.82 thf(632,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)],[131])). 71.81/31.82 thf(633,plain,(((^ [A:partia1833973666xt_a_b,B:a,C:a]: (add_a_b @ A @ B @ (a_inv_a_b @ A @ C))) = (a_minus_a_b))),inference(lifteq,[status(thm)],[632])). 71.81/31.82 thf(656,plain,(! [A:int] : (((add_pow_a_b_int @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r)))),inference(cnf,[status(esa)],[655])). 71.81/31.82 thf(657,plain,(! [A:int] : (((add_pow_a_b_int @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r)))),inference(lifteq,[status(thm)],[656])). 71.81/31.82 thf(177,axiom,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) = (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 @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ t) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ t) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_f26)). 71.81/31.82 thf(773,plain,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) = (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 @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ t) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ t) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 71.81/31.82 thf(185,axiom,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_f32)). 71.81/31.82 thf(794,plain,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 71.81/31.82 thf(114,axiom,((! [A:a]: (((add_a_b @ r @ (zero_a_b @ r) @ A) = A) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_l__zero)). 71.81/31.82 thf(586,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)],[114])). 71.81/31.82 thf(141,axiom,((! [A:a,B:a]: (((add_a_b @ r @ A @ B) = (zero_a_b @ r)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ B @ A) = (zero_a_b @ r)) <= (member_a @ B @ (partia1066395285xt_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add_Oinv__comm)). 71.81/31.82 thf(662,plain,((! [A:a,B:a]: (((add_a_b @ r @ A @ B) = (zero_a_b @ r)) => ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ B @ A) = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 71.81/31.82 thf(20,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= (ord_less_eq_int @ C @ D)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_add__mono)). 71.81/31.82 thf(298,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 71.81/31.82 thf(59,axiom,((plus_plus_int = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_add_Ocommute)). 71.81/31.82 thf(412,plain,(((plus_plus_int) = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 71.81/31.82 thf(126,axiom,(((mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29__092_060open_062t_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062)). 71.81/31.82 thf(618,plain,(((mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 71.81/31.82 thf(64,axiom,((! [A:partia1833973666xt_a_b,B:set_a]: ((locali880295127ng_a_b @ A @ B) <= (locali807230110ng_a_b @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mult__submonoid__of__crng_Oaxioms_I2_J)). 71.81/31.82 thf(430,plain,((! [A:partia1833973666xt_a_b,B:set_a]: ((locali807230110ng_a_b @ A @ B) => (locali880295127ng_a_b @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 71.81/31.82 thf(205,axiom,((! [A:a,B:a,C:a,D:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ C @ (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 @ D @ (partia1066395285xt_a_b @ r)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_four__elem__comm)). 71.81/31.82 thf(856,plain,((! [A:a,B:a,C:a,D:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 71.81/31.82 thf(149,axiom,((((=) @ product_prod_a_a) = (^ [A:product_prod_a_a,B:product_prod_a_a]: (((product_snd_a_a @ A) = (product_snd_a_a @ B)) & ((product_fst_a_a @ A) = (product_fst_a_a @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_prod__eq__iff)). 71.81/31.82 thf(689,plain,((((=) @ product_prod_a_a) = (^ [A:product_prod_a_a,B:product_prod_a_a]: (((product_snd_a_a @ A) = (product_snd_a_a @ B)) & ((product_fst_a_a @ A) = (product_fst_a_a @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 71.81/31.82 thf(164,axiom,((! [A:(a > (a > $o)),B:product_prod_a_a]: ((A @ (product_snd_a_a @ B) @ (product_fst_a_a @ B)) => (~ (! [C:a,D:a]: ~ (A @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_exE__realizer_H)). 71.81/31.82 thf(733,plain,((! [A:(a > (a > $o)),B:product_prod_a_a]: ((A @ (product_snd_a_a @ B) @ (product_fst_a_a @ B)) => (~ (! [C:a,D:a]: ~ (A @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 71.81/31.82 thf(151,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_8_add_Om__comm)). 71.81/31.82 thf(694,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) = (add_a_b @ r @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 71.81/31.82 thf(55,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_156_add__diff__cancel__right)). 71.81/31.82 thf(402,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)],[55])). 71.81/31.82 thf(16,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (ord_less_eq_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_add__le__cancel__right)). 71.81/31.82 thf(286,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (ord_less_eq_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 71.81/31.82 thf(111,axiom,(((partia1066395285xt_a_b @ r) != bot_bot_set_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_carrier__not__empty)). 71.81/31.82 thf(577,plain,((~ ((partia1066395285xt_a_b @ r) = bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 71.81/31.82 thf(578,plain,((~ ((partia1066395285xt_a_b @ r) = bot_bot_set_a))),inference(polarity_switch,[status(thm)],[577])). 71.81/31.82 thf(579,plain,(((partia1066395285xt_a_b @ r) != bot_bot_set_a)),inference(lifteq,[status(thm)],[578])). 71.81/31.82 thf(14,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (minus_minus_int @ C @ B) @ (minus_minus_int @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_diff__left__mono)). 71.81/31.82 thf(281,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (minus_minus_int @ C @ B) @ (minus_minus_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 71.81/31.82 thf(100,axiom,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_empty__iff)). 71.81/31.82 thf(545,plain,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 71.81/31.82 thf(413,plain,(((plus_plus_int) = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),inference(lifteq,[status(thm)],[412])). 71.81/31.82 thf(155,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_102_r__zero)). 71.81/31.82 thf(711,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)],[155])). 71.81/31.82 thf(70,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_165_add__right__imp__eq)). 71.81/31.82 thf(445,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)],[70])). 71.81/31.82 thf(48,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ (uminus_uminus_set_a @ A) @ (uminus_uminus_set_a @ B)) = (ord_less_eq_set_a @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Compl__subset__Compl__iff)). 71.81/31.82 thf(382,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ (uminus_uminus_set_a @ A) @ (uminus_uminus_set_a @ B)) = (ord_less_eq_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 71.81/31.82 thf(109,axiom,((! [A:a,B:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ (uminus_uminus_int @ B) @ A) = (a_inv_a_b @ r @ (add_pow_a_b_int @ r @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_add_Oint__pow__neg)). 71.81/31.82 thf(572,plain,((! [A:a,B:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_pow_a_b_int @ r @ (uminus_uminus_int @ B) @ A) = (a_inv_a_b @ r @ (add_pow_a_b_int @ r @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 71.81/31.82 thf(122,axiom,((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_f41)). 71.81/31.82 thf(611,plain,((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 71.81/31.82 thf(76,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (minus_minus_int @ A @ B) @ C) = (ord_less_eq_int @ A @ (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_diff__le__eq)). 71.81/31.82 thf(466,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (minus_minus_int @ A @ B) @ C) = (ord_less_eq_int @ A @ (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 71.81/31.82 thf(230,axiom,((! [A:a,B:a,C:int]: ((member_a @ A @ (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 @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_add__pow__ldistr__int)). 71.81/31.82 thf(919,plain,((! [A:a,B:a,C:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 71.81/31.82 thf(238,axiom,((~ (! [A:a]: (((mult_a_ring_ext_a_b @ r @ A @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))) != (zero_a_b @ r)) <= (member_a @ A @ s))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_O_A_092_060lbrakk_062t_A_092_060in_062_AS_059_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 71.81/31.82 thf(944,plain,((~ (! [A:a]: ((member_a @ A @ s) => (~ ((mult_a_ring_ext_a_b @ r @ A @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))) = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 71.81/31.82 thf(945,plain,((~ (! [A:a]: ((member_a @ A @ s) => (~ ((mult_a_ring_ext_a_b @ r @ A @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))) = (zero_a_b @ r))))))),inference(polarity_switch,[status(thm)],[944])). 71.81/31.82 thf(947,plain,((member_a @ sk15 @ s)),inference(cnf,[status(esa)],[945])). 71.81/31.82 thf(120,axiom,((! [A:set_a,B:set_a]: (((additi2104487374up_a_b @ (set_add_a_b @ r @ A @ B) @ r) <= (additi2104487374up_a_b @ B @ r)) <= (additi2104487374up_a_b @ A @ r)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_add__additive__subgroups)). 71.81/31.82 thf(604,plain,((! [A:set_a,B:set_a]: ((additi2104487374up_a_b @ A @ r) => ((additi2104487374up_a_b @ B @ r) => (additi2104487374up_a_b @ (set_add_a_b @ r @ A @ B) @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 71.81/31.82 thf(147,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a]: ((semiring_a_b @ A) => (((member_a @ C @ (partia1066395285xt_a_b @ A)) => ((add_a_b @ A @ B @ C) = (add_a_b @ A @ C @ B))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_semiring_Osemiring__simprules_I7_J)). 71.81/31.82 thf(681,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)) => ((add_a_b @ A @ B @ C) = (add_a_b @ A @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 71.81/31.82 thf(11,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C))) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_diff__mono)). 71.81/31.82 thf(272,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 71.81/31.82 thf(273,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (! [C:int,D:int]: ((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C))))))),inference(miniscope,[status(thm)],[272])). 71.81/31.82 thf(274,plain,(! [D:int,C:int,B:int,A:int] : ((~ (ord_less_eq_int @ A @ B)) | (~ (ord_less_eq_int @ C @ D)) | (ord_less_eq_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C)))),inference(cnf,[status(esa)],[273])). 71.81/31.82 thf(181,axiom,((locali880295127ng_a_b @ r @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_mult__submonoid__of__rng__axioms)). 71.81/31.82 thf(784,plain,((locali880295127ng_a_b @ r @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 71.81/31.82 thf(165,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_97_add_Oinv__closed)). 71.81/31.82 thf(736,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (member_a @ (a_inv_a_b @ r @ A) @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 71.81/31.82 thf(65,axiom,((! [A:set_a]: ((? [B:a]: (member_a @ B @ A)) = (A != bot_bot_set_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_ex__in__conv)). 71.81/31.82 thf(432,plain,((! [A:set_a]: ((? [B:a]: (member_a @ B @ A)) = (~ (A = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 71.81/31.82 thf(433,plain,(! [A:set_a] : (((? [B:a]: (member_a @ B @ A)) = (~ (A = bot_bot_set_a))))),inference(cnf,[status(esa)],[432])). 71.81/31.82 thf(434,plain,(! [A:set_a] : (((? [B:a]: (member_a @ B @ A)) = (~ (A = bot_bot_set_a))))),inference(lifteq,[status(thm)],[433])). 71.81/31.82 thf(270,plain,(! [B:int,A:int] : (((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) = (ord_less_eq_int @ (uminus_uminus_int @ B) @ A)))),inference(cnf,[status(esa)],[269])). 71.81/31.82 thf(271,plain,(! [B:int,A:int] : (((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) = (ord_less_eq_int @ (uminus_uminus_int @ B) @ A)))),inference(lifteq,[status(thm)],[270])). 71.81/31.82 thf(119,axiom,((! [A:a,B:a,C:a]: (((add_a_b @ r @ C @ A) = (add_a_b @ r @ C @ B)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_right__add__eq)). 71.81/31.82 thf(599,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)],[119])). 71.81/31.82 thf(42,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_197_diff__add__eq__diff__diff__swap)). 71.81/31.82 thf(362,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)],[42])). 71.81/31.82 thf(107,axiom,((! [A:partia1833973666xt_a_b,B:set_a,C:a,D:a]: ((locali425460998xt_a_b @ A @ B) => ((member_a @ C @ B) => ((member_a @ D @ B) => (member_a @ (mult_a_ring_ext_a_b @ A @ C @ D) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Om__closed)). 71.81/31.82 thf(567,plain,((! [A:partia1833973666xt_a_b,B:set_a,C:a,D:a]: ((locali425460998xt_a_b @ A @ B) => ((member_a @ C @ B) => ((member_a @ D @ B) => (member_a @ (mult_a_ring_ext_a_b @ A @ C @ D) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 71.81/31.82 thf(219,axiom,((member_a @ t2 @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_f4)). 71.81/31.82 thf(890,plain,((member_a @ t2 @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 71.81/31.82 thf(2835,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r)) != (member_a @ t2 @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[883,2549])). 71.81/31.82 thf(3012,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[2835])). 71.81/31.82 thf(3020,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2)),inference(simp,[status(thm)],[3012])). 71.81/31.82 thf(4198,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2) | ((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (add_a_b @ r @ t2 @ (zero_a_b @ r))) | ((zero_a_b @ r) != (zero_a_b @ r))),inference(eqfactor_ordered,[status(thm)],[3020])). 71.81/31.82 thf(4200,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2) | (r != r) | ((add_a_b @ r @ t @ t) != t2) | ((zero_a_b @ r) != t2)),inference(simp,[status(thm)],[4198])). 71.81/31.82 thf(4203,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2) | ((zero_a_b @ r) != t2)),inference(simp,[status(thm)],[4200])). 71.81/31.82 thf(172,axiom,((! [A:partia1833973666xt_a_b,B:a]: (((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ B @ (zero_a_b @ A)) = (zero_a_b @ A))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_semiring_Or__null)). 71.81/31.82 thf(758,plain,((! [A:partia1833973666xt_a_b,B:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => ((mult_a_ring_ext_a_b @ A @ B @ (zero_a_b @ A)) = (zero_a_b @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 71.81/31.82 thf(534,plain,(! [A:set_a] : (((minus_minus_set_a @ A @ A) = bot_bot_set_a))),inference(cnf,[status(esa)],[533])). 71.81/31.82 thf(535,plain,(! [A:set_a] : (((minus_minus_set_a @ A @ A) = bot_bot_set_a))),inference(lifteq,[status(thm)],[534])). 71.81/31.82 thf(187,axiom,((! [A:a,B:a]: ((member_a @ A @ (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 @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_l__minus)). 71.81/31.82 thf(799,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 71.81/31.82 thf(229,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_104_add_Or__cancel__one_H)). 71.81/31.82 thf(915,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((A = (add_a_b @ r @ B @ A)) = (B = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 71.81/31.82 thf(237,axiom,((semiring_a_b @ r)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_local_Osemiring__axioms)). 71.81/31.82 thf(943,plain,((semiring_a_b @ r)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 71.81/31.82 thf(32,axiom,((! [A:set_a,B:set_a]: (((minus_minus_set_a @ A @ B) = bot_bot_set_a) = (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Diff__eq__empty__iff)). 71.81/31.82 thf(330,plain,((! [A:set_a,B:set_a]: (((minus_minus_set_a @ A @ B) = bot_bot_set_a) = (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 71.81/31.82 thf(201,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34__092_060open_062t_A_092_060otimes_062_As_A_092_060otimes_062_Asnd_Ax_H_A_092_060in_062_Acarrier_AR_092_060close_062)). 71.81/31.82 thf(848,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 71.81/31.82 thf(92,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ (uminus_uminus_set_a @ B) @ (uminus_uminus_set_a @ A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Compl__anti__mono)). 71.81/31.82 thf(520,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ (uminus_uminus_set_a @ B) @ (uminus_uminus_set_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 71.81/31.82 thf(148,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((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)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_r__minus)). 71.81/31.82 thf(685,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 71.81/31.82 thf(54,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_add__diff__cancel)). 71.81/31.82 thf(399,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 71.81/31.82 thf(243,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_f15)). 71.81/31.82 thf(959,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 71.81/31.82 thf(13,axiom,((! [A:(a > $o),B:(a > $o)]: (((collect_a @ A) = (collect_a @ B)) <= (! [C:a]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong)). 71.81/31.82 thf(278,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)],[13])). 71.81/31.82 thf(180,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)) => ((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)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_add_Oint__pow__mult__distrib)). 71.81/31.82 thf(780,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)) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 71.81/31.82 thf(23,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((C = D) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_add__mono__thms__linordered__semiring_I3_J)). 71.81/31.82 thf(306,plain,((! [A:int,B:int,C:int,D:int]: (((C = D) & (ord_less_eq_int @ A @ B)) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 71.81/31.82 thf(5503,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (zero_a_b @ r)) | ((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r)) != (member_a @ t2 @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[883,2552])). 71.81/31.82 thf(5518,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (zero_a_b @ r)) | ((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[5503])). 71.81/31.82 thf(5538,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (zero_a_b @ r)) | ((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2)),inference(simp,[status(thm)],[5518])). 71.81/31.82 thf(5716,plain,(((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2) | ((add_a_b @ r @ (add_a_b @ r @ t @ t) @ s3) != (add_a_b @ r @ s3 @ (zero_a_b @ r))) | ((zero_a_b @ r) != (zero_a_b @ r))),inference(eqfactor_ordered,[status(thm)],[5538])). 71.81/31.82 thf(5718,plain,(((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2) | (r != r) | ((add_a_b @ r @ t @ t) != s3) | ((zero_a_b @ r) != s3)),inference(simp,[status(thm)],[5716])). 71.81/31.82 thf(5725,plain,(((add_a_b @ r @ s3 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t2) | ((add_a_b @ r @ t @ t) != s3) | ((zero_a_b @ r) != s3)),inference(simp,[status(thm)],[5718])). 71.81/31.82 thf(73,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_204_add_Oinverse__distrib__swap)). 71.81/31.82 thf(455,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)],[73])). 71.81/31.82 thf(9,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) => (ord_less_eq_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_add__le__imp__le__right)). 71.81/31.82 thf(267,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) => (ord_less_eq_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 71.81/31.82 thf(203,axiom,((! [A:a,B:a,C:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((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))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_add_Oint__pow__distrib)). 71.81/31.82 thf(851,plain,((! [A:a,B:a,C:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 71.81/31.82 thf(115,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((ord_less_eq_set_a @ (set_add_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)) <= (ord_less_eq_set_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_setadd__subset__G)). 71.81/31.82 thf(589,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((ord_less_eq_set_a @ B @ (partia1066395285xt_a_b @ r)) => (ord_less_eq_set_a @ (set_add_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 71.81/31.82 thf(101,axiom,((! [A:int,B:int]: (((uminus_uminus_int @ A) = B) = ((uminus_uminus_int @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_minus__equation__iff)). 71.81/31.82 thf(548,plain,((! [A:int,B:int]: (((uminus_uminus_int @ A) = B) = ((uminus_uminus_int @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 71.81/31.82 thf(169,axiom,(((mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3)) @ (mult_a_ring_ext_a_b @ r @ t @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30__092_060open_062t_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_At_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Afst_Ay_H_J_092_060close_062)). 71.81/31.82 thf(749,plain,(((mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3)) @ (mult_a_ring_ext_a_b @ r @ t @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 71.81/31.82 thf(125,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_f13)). 71.81/31.82 thf(617,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 71.81/31.82 thf(36,axiom,((! [A:int,B:int,C:int,D:int]: ((((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) => ((ord_less_eq_int @ (minus_minus_int @ C @ B) @ D) <= (ord_less_eq_int @ C @ (plus_plus_int @ D @ B)))) <= (ord_less_eq_int @ C @ (plus_plus_int @ D @ B))) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_add__le__add__imp__diff__le)). 71.81/31.82 thf(342,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) => ((ord_less_eq_int @ C @ (plus_plus_int @ D @ B)) => ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) => ((ord_less_eq_int @ C @ (plus_plus_int @ D @ B)) => (ord_less_eq_int @ (minus_minus_int @ C @ B) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 71.81/31.82 thf(196,axiom,((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_f39)). 71.81/31.82 thf(836,plain,((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 71.81/31.82 thf(95,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ C @ B)) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_add__le__imp__le__diff)). 71.81/31.82 thf(531,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) => (ord_less_eq_int @ A @ (minus_minus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 71.81/31.82 thf(232,axiom,((! [A:a,B:a]: (((member_a @ B @ s) => (member_a @ (mult_a_ring_ext_a_b @ r @ A @ B) @ s)) <= (member_a @ A @ s)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_m__closed)). 71.81/31.82 thf(927,plain,((! [A:a,B:a]: ((member_a @ A @ s) => ((member_a @ B @ s) => (member_a @ (mult_a_ring_ext_a_b @ r @ A @ B) @ s))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 71.81/31.82 thf(46,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_172_group__cancel_Oadd2)). 71.81/31.82 thf(374,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 71.81/31.82 thf(74,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_213_group__cancel_Osub2)). 71.81/31.82 thf(458,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((minus_minus_int @ D @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (minus_minus_int @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 71.81/31.82 thf(193,axiom,((! [A:set_a,B:a,C:a]: (((((a_l_coset_a_b @ r @ B @ (a_l_coset_a_b @ r @ C @ A)) = (a_l_coset_a_b @ r @ (add_a_b @ r @ B @ C) @ A)) <= (member_a @ C @ (partia1066395285xt_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= (ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_a__lcos__m__assoc)). 71.81/31.82 thf(823,plain,((! [A:set_a,B:a,C:a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((member_a @ C @ (partia1066395285xt_a_b @ r)) => ((a_l_coset_a_b @ r @ B @ (a_l_coset_a_b @ r @ C @ A)) = (a_l_coset_a_b @ r @ (add_a_b @ r @ B @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 71.81/31.82 thf(178,axiom,(((a_inv_a_b @ r @ (zero_a_b @ r)) = (zero_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_local_Ominus__zero)). 71.81/31.82 thf(775,plain,(((a_inv_a_b @ r @ (zero_a_b @ r)) = (zero_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 71.81/31.82 thf(776,plain,(((a_inv_a_b @ r @ (zero_a_b @ r)) = (zero_a_b @ r))),inference(lifteq,[status(thm)],[775])). 71.81/31.82 thf(104,axiom,((! [A:a,B:a,C:a]: (((member_a @ B @ (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 @ C @ (partia1066395285xt_a_b @ r)))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_l__distr)). 71.81/31.82 thf(557,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)) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 71.81/31.82 thf(690,plain,(((^ [A:product_prod_a_a,B:product_prod_a_a]: (((product_snd_a_a @ A) = (product_snd_a_a @ B)) & ((product_fst_a_a @ A) = (product_fst_a_a @ B)))) = ((=) @ product_prod_a_a))),inference(lifteq,[status(thm)],[689])). 71.81/31.82 thf(134,axiom,(((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (a_minus_a_b @ r @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062)). 71.81/31.82 thf(640,plain,(((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (a_minus_a_b @ r @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 71.81/31.82 thf(19,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_add__left__mono)). 71.81/31.82 thf(295,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 71.81/31.82 thf(211,axiom,((! [A:a,B:a,C:a]: (((add_a_b @ r @ A @ B) = C) => ((((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))) <= (member_a @ A @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_a__transpose__inv)). 71.81/31.82 thf(872,plain,((! [A:a,B:a,C:a]: (((add_a_b @ r @ A @ B) = C) => ((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 @ (a_inv_a_b @ r @ A) @ C) = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 71.81/31.82 thf(154,axiom,((! [A:a,B:int]: (((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))) <= (member_a @ A @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_add_Oint__pow__inv)). 71.81/31.82 thf(707,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)],[154])). 71.81/31.82 thf(218,axiom,((! [A:partia1833973666xt_a_b,B:a,C: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))) <= (semiring_a_b @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_semiring_Osemiring__simprules_I1_J)). 71.81/31.82 thf(887,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 @ (add_a_b @ A @ B @ C) @ (partia1066395285xt_a_b @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 71.81/31.82 thf(60,axiom,((! [A:set_a,B:set_a]: ((~ ((~ (ord_less_eq_set_a @ B @ A)) <= (ord_less_eq_set_a @ A @ B))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_equalityE)). 71.81/31.82 thf(414,plain,((! [A:set_a,B:set_a]: ((A = B) => (~ ((ord_less_eq_set_a @ A @ B) => (~ (ord_less_eq_set_a @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 71.81/31.82 thf(241,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_f11)). 71.81/31.82 thf(954,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 71.81/31.82 thf(4965,plain,(! [B:set_a,A:set_a] : (((collect_a @ (^ [C:a]: (member_a @ C @ A))) = bot_bot_set_a) | (A != (minus_minus_set_a @ B @ B)))),inference(paramod_ordered,[status(thm)],[294,535])). 71.81/31.82 thf(4966,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (minus_minus_set_a @ A @ A)))) = bot_bot_set_a))),inference(pattern_uni,[status(thm)],[4965:[bind(A, $thf(minus_minus_set_a @ D @ D)),bind(B, $thf(D))]])). 71.81/31.82 thf(4971,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (minus_minus_set_a @ A @ A)))) = bot_bot_set_a))),inference(simp,[status(thm)],[4966])). 71.81/31.82 thf(58,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) <= (! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_subsetI)). 71.81/31.82 thf(409,plain,((! [A:set_a,B:set_a]: ((! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 71.81/31.82 thf(112,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_f23)). 71.81/31.82 thf(580,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 71.81/31.82 thf(262,plain,(! [B:int,A:int] : (((ord_less_eq_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ A)))),inference(cnf,[status(esa)],[261])). 71.81/31.82 thf(263,plain,(! [B:int,A:int] : (((ord_less_eq_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_eq_int @ B @ A)))),inference(lifteq,[status(thm)],[262])). 71.81/31.82 thf(128,axiom,((member_a @ (product_fst_a_a @ x) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_f22)). 71.81/31.82 thf(624,plain,((member_a @ (product_fst_a_a @ x) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 71.81/31.82 thf(3000,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((member_a @ (add_a_b @ r @ t @ t) @ (partia1066395285xt_a_b @ r)) != (member_a @ (product_fst_a_a @ x) @ (partia1066395285xt_a_b @ r)))),inference(paramod_ordered,[status(thm)],[624,2549])). 71.81/31.82 thf(3011,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != (product_fst_a_a @ x)) | ((partia1066395285xt_a_b @ r) != (partia1066395285xt_a_b @ r))),inference(simp,[status(thm)],[3000])). 71.81/31.82 thf(3019,plain,(((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (zero_a_b @ r)) | ((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != (product_fst_a_a @ x))),inference(simp,[status(thm)],[3011])). 71.81/31.82 thf(145,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_107_add_Ol__cancel__one)). 71.81/31.82 thf(673,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)],[145])). 71.81/31.82 thf(87,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_group__cancel_Oadd1)). 71.81/31.82 thf(502,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)],[87])). 71.81/31.82 thf(198,axiom,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) = (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 @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_061_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062)). 71.81/31.82 thf(840,plain,(((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) = (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 @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 71.81/31.82 thf(75,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_148_add__right__cancel)). 71.81/31.82 thf(463,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)],[75])). 71.81/31.82 thf(110,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_f14)). 71.81/31.82 thf(576,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 71.81/31.82 thf(3194,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t) | ((add_a_b @ r @ (add_a_b @ r @ t @ t) @ t2) != (add_a_b @ r @ t2 @ (zero_a_b @ r))) | ((zero_a_b @ r) != (zero_a_b @ r))),inference(eqfactor_ordered,[status(thm)],[3017])). 71.81/31.82 thf(3196,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t) | (r != r) | ((add_a_b @ r @ t @ t) != t2) | ((zero_a_b @ r) != t2)),inference(simp,[status(thm)],[3194])). 71.81/31.82 thf(3206,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != t) | ((add_a_b @ r @ t @ t) != t) | ((add_a_b @ r @ t @ t) != t2) | ((zero_a_b @ r) != t2)),inference(simp,[status(thm)],[3196])). 71.81/31.82 thf(3404,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ t @ t) != t) | ((add_a_b @ r @ t @ t) != t2) | ((zero_a_b @ r) != t2) | ((add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) != (add_a_b @ r @ t @ t)) | (t != t)),inference(eqfactor_ordered,[status(thm)],[3206])). 71.81/31.82 thf(3406,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ t @ t) != t) | ((add_a_b @ r @ t @ t) != t2) | ((zero_a_b @ r) != t2) | (r != r) | ((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) != t) | ((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) != t)),inference(simp,[status(thm)],[3404])). 71.81/31.82 thf(3412,plain,(((add_a_b @ r @ t2 @ (zero_a_b @ r)) != (zero_a_b @ r)) | ((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) != (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ t)) | ((add_a_b @ r @ t @ t) != t) | ((add_a_b @ r @ t @ t) != t2) | ((zero_a_b @ r) != t2) | ((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) != t) | ((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) != t)),inference(simp,[status(thm)],[3406])). 71.81/31.82 thf(41,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_169_group__add__class_Oadd_Oright__cancel)). 71.81/31.82 thf(359,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)],[41])). 71.81/31.82 thf(226,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_f38)). 71.81/31.82 thf(907,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 71.81/31.82 thf(190,axiom,((locali425460998xt_a_b @ r @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_submonoid__axioms)). 71.81/31.82 thf(808,plain,((locali425460998xt_a_b @ r @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 71.81/31.82 thf(34,axiom,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ A) => (member_a @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_in__mono)). 71.81/31.82 thf(336,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 71.81/31.82 thf(124,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((semiring_a_b @ A) => ((member_a @ B @ (partia1066395285xt_a_b @ A)) => (((member_a @ D @ (partia1066395285xt_a_b @ 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 @ C @ (partia1066395285xt_a_b @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_semiring_Or__distr)). 71.81/31.82 thf(613,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)) => ((member_a @ D @ (partia1066395285xt_a_b @ 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))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 71.81/31.82 thf(123,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_f9)). 71.81/31.82 thf(612,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 71.81/31.82 thf(212,axiom,((! [A:product_prod_a_a,B:product_prod_a_a]: (((A = B) <= ((product_snd_a_a @ A) = (product_snd_a_a @ B))) <= ((product_fst_a_a @ A) = (product_fst_a_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_prod__eqI)). 71.81/31.82 thf(876,plain,((! [A:product_prod_a_a,B:product_prod_a_a]: (((product_fst_a_a @ A) = (product_fst_a_a @ B)) => (((product_snd_a_a @ A) = (product_snd_a_a @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 71.81/31.82 thf(555,plain,(! [A:set_a] : (((ord_less_eq_set_a @ A @ bot_bot_set_a) = (A = bot_bot_set_a)))),inference(cnf,[status(esa)],[554])). 71.81/31.82 thf(556,plain,(! [A:set_a] : (((ord_less_eq_set_a @ A @ bot_bot_set_a) = (A = bot_bot_set_a)))),inference(lifteq,[status(thm)],[555])). 71.81/31.82 thf(98,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_158_add__diff__cancel__left)). 71.81/31.82 thf(539,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)],[98])). 71.81/31.82 thf(225,axiom,((! [A:a,B:a,C:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((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))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_add__pow__rdistr__int)). 71.81/31.82 thf(903,plain,((! [A:a,B:a,C:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 71.81/31.82 thf(220,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_67_minus__eq)). 71.81/31.82 thf(891,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)],[220])). 71.81/31.82 thf(176,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) = (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 @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_f36)). 71.81/31.82 thf(771,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) = (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 @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ s2 @ s3)) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 71.81/31.82 thf(44,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_175_ab__semigroup__add__class_Oadd__ac_I1_J)). 71.81/31.82 thf(368,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)],[44])). 71.81/31.82 thf(200,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((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)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add_Oinv__mult__group)). 71.81/31.82 thf(844,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)) = (add_a_b @ r @ (a_inv_a_b @ r @ B) @ (a_inv_a_b @ r @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 71.81/31.82 thf(222,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) = (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 @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_f35)). 71.81/31.82 thf(896,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) = (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 @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 71.81/31.82 thf(22,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((ord_less_eq_int @ A @ B) & (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_add__mono__thms__linordered__semiring_I1_J)). 71.81/31.82 thf(304,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ A @ B) & (ord_less_eq_int @ C @ D)) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 71.81/31.82 thf(415,plain,(! [B:set_a,A:set_a] : ((~ (A = B)) | (ord_less_eq_set_a @ A @ B))),inference(cnf,[status(esa)],[414])). 71.81/31.82 thf(417,plain,(! [B:set_a,A:set_a] : ((A != B) | (ord_less_eq_set_a @ A @ B))),inference(lifteq,[status(thm)],[415])). 71.81/31.82 thf(418,plain,(! [A:set_a] : ((ord_less_eq_set_a @ A @ A))),inference(simp,[status(thm)],[417])). 71.81/31.82 thf(245,axiom,((! [A:set_a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((a_l_coset_a_b @ r @ (zero_a_b @ r) @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_a__lcos__mult__one)). 71.81/31.82 thf(963,plain,((! [A:set_a]: ((ord_less_eq_set_a @ A @ (partia1066395285xt_a_b @ r)) => ((a_l_coset_a_b @ r @ (zero_a_b @ r) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 71.81/31.82 thf(91,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_144_diff__minus__eq__add)). 71.81/31.82 thf(517,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)],[91])). 71.81/31.82 thf(143,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) = (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 @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_f12)). 71.81/31.82 thf(667,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) = (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 @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ t2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 71.81/31.82 thf(80,axiom,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) = (A = bot_bot_set_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_all__not__in__conv)). 71.81/31.82 thf(478,plain,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) = (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 71.81/31.82 thf(224,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((semiring_a_b @ A) => ((member_a @ B @ (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 @ C @ (partia1066395285xt_a_b @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_semiring_Osemiring__simprules_I5_J)). 71.81/31.82 thf(899,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)) => ((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))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 71.81/31.82 thf(195,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_15_r__distr)). 71.81/31.82 thf(832,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)) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 71.81/31.82 thf(37,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_199_diff__diff__eq2)). 71.81/31.82 thf(346,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)],[37])). 71.81/31.82 thf(97,axiom,((! [A:int,B:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_diff__add__cancel)). 71.81/31.82 thf(536,plain,((! [A:int,B:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 71.81/31.82 thf(157,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)))) = (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 @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y))) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y))) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_092_060close_062)). 71.81/31.82 thf(716,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)))) = (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 @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y))) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y))) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 71.81/31.82 thf(127,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((A = (add_a_b @ r @ A @ B)) = (B = (zero_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_add_Ol__cancel__one_H)). 71.81/31.82 thf(620,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((A = (add_a_b @ r @ A @ B)) = (B = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 71.81/31.82 thf(26,axiom,((! [A:partia1833973666xt_a_b,B:set_a]: ((locali425460998xt_a_b @ A @ B) <= (locali880295127ng_a_b @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_mult__submonoid__of__rng_Oaxioms_I2_J)). 71.81/31.82 thf(315,plain,((! [A:partia1833973666xt_a_b,B:set_a]: ((locali880295127ng_a_b @ A @ B) => (locali425460998xt_a_b @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 71.81/31.82 thf(967,plain,(! [A:int] : (((plus_plus_int @ A) = (^ [B:int]: (plus_plus_int @ B @ A))))),inference(func_ext,[status(esa)],[413])). 71.81/31.82 thf(240,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((semiring_a_b @ A) => ((member_a @ B @ (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)))) <= (member_a @ C @ (partia1066395285xt_a_b @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_semiring_Ol__distr)). 71.81/31.82 thf(950,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)) => ((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))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 71.81/31.82 thf(56,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_137_semiring_Osemiring__simprules_I2_J)). 71.81/31.82 thf(405,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)],[56])). 71.81/31.82 thf(184,axiom,((! [A:a,B:a,C:a]: ((((((add_a_b @ r @ B @ (a_inv_a_b @ r @ C)) = A) = (B = (add_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_81_add_Oinv__solve__right_H)). 71.81/31.82 thf(790,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)],[184])). 71.81/31.82 thf(209,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (((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)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_m__comm)). 71.81/31.82 thf(867,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ A @ B) = (mult_a_ring_ext_a_b @ r @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 71.81/31.82 thf(106,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (a_inv_a_b @ r @ A) @ A) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_l__neg)). 71.81/31.82 thf(564,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (a_inv_a_b @ r @ A) @ A) = (zero_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 71.81/31.82 thf(30,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_163_add__minus__cancel)). 71.81/31.82 thf(326,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)],[30])). 71.81/31.82 thf(340,plain,(! [A:set_a] : (((minus_minus_set_a @ A @ bot_bot_set_a) = A))),inference(cnf,[status(esa)],[339])). 71.81/31.82 thf(341,plain,(! [A:set_a] : (((minus_minus_set_a @ A @ bot_bot_set_a) = A))),inference(lifteq,[status(thm)],[340])). 71.81/31.82 thf(268,plain,(! [C:int,B:int,A:int] : ((~ (ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B))) | (ord_less_eq_int @ A @ C))),inference(cnf,[status(esa)],[267])). 71.81/31.82 thf(189,axiom,((member_a @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23__092_060open_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060in_062_Acarrier_AR_092_060close_062)). 71.81/31.82 thf(807,plain,((member_a @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 71.81/31.82 thf(67,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_add__diff__cancel__right_H)). 71.81/31.82 thf(437,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 71.81/31.82 thf(79,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D)) <= ((C = D) & (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_add__mono__thms__linordered__semiring_I4_J)). 71.81/31.82 thf(474,plain,((! [A:int,B:int,C:int,D:int]: (((C = D) & (A = B)) => ((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 71.81/31.82 thf(244,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ (a_minus_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_minus__closed)). 71.81/31.82 thf(960,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (member_a @ (a_minus_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 71.81/31.82 thf(242,axiom,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ B @ A) = A) = (B = (zero_a_b @ r))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_add_Or__cancel__one)). 71.81/31.82 thf(955,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (((add_a_b @ r @ B @ A) = A) = (B = (zero_a_b @ r))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 71.81/31.82 thf(186,axiom,((! [A:a,B:a]: (((((a_inv_a_b @ r @ B) = A) <= (member_a @ A @ (partia1066395285xt_a_b @ r))) <= (member_a @ B @ (partia1066395285xt_a_b @ r))) <= ((add_a_b @ r @ A @ B) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_minus__equality)). 71.81/31.82 thf(796,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)) => ((a_inv_a_b @ r @ B) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 71.81/31.82 thf(217,axiom,((locali807230110ng_a_b @ r @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_mult__submonoid__of__crng__axioms)). 71.81/31.82 thf(886,plain,((locali807230110ng_a_b @ r @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 71.81/31.82 thf(63,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_164_minus__diff__eq)). 71.81/31.82 thf(427,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)],[63])). 71.81/31.82 thf(206,axiom,(((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_f40)). 71.81/31.82 thf(860,plain,(((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 @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 71.81/31.82 thf(118,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_60_add_Om__closed)). 71.81/31.82 thf(596,plain,((! [A:a,B:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((member_a @ B @ (partia1066395285xt_a_b @ r)) => (member_a @ (add_a_b @ r @ A @ B) @ (partia1066395285xt_a_b @ r)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 71.81/31.82 thf(227,axiom,((! [A:a,B:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (member_a @ (add_pow_a_b_int @ r @ B @ A) @ (partia1066395285xt_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add_Oint__pow__closed)). 71.81/31.82 thf(908,plain,((! [A:a,B:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => (member_a @ (add_pow_a_b_int @ r @ B @ A) @ (partia1066395285xt_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 71.81/31.82 thf(150,axiom,((! [A:product_prod_a_a,B:product_prod_a_a]: ((A = B) <= (((product_snd_a_a @ A) = (product_snd_a_a @ B)) & ((product_fst_a_a @ A) = (product_fst_a_a @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_prod_Oexpand)). 71.81/31.82 thf(691,plain,((! [A:product_prod_a_a,B:product_prod_a_a]: ((((product_snd_a_a @ A) = (product_snd_a_a @ B)) & ((product_fst_a_a @ A) = (product_fst_a_a @ B))) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 71.81/31.82 thf(69,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add__diff__cancel__left_H)). 71.81/31.82 thf(442,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 71.81/31.82 thf(210,axiom,((ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_subset)). 71.81/31.82 thf(871,plain,((ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 71.81/31.82 thf(121,axiom,((! [A:a,B:a,C:a]: ((member_a @ A @ (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))) <= (member_a @ B @ (partia1066395285xt_a_b @ r)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_right__inv__add)). 71.81/31.82 thf(607,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)) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 71.81/31.82 thf(160,axiom,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_f30)). 71.81/31.82 thf(723,plain,(((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 71.81/31.82 thf(254,plain,(! [B:int,A:int] : ((~ (ord_less_eq_int @ A @ B)) | (ord_less_eq_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)))),inference(cnf,[status(esa)],[253])). 71.81/31.82 thf(188,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_139_add_Oint__pow__diff)). 71.81/31.82 thf(803,plain,((! [A:a,B:int,C:int]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 71.81/31.82 thf(77,axiom,((! [A:partia1833973666xt_a_b,B:set_a]: ((locali1648887798ac_a_b @ A @ B) => (locali807230110ng_a_b @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_eq__obj__rng__of__frac_Oaxioms_I2_J)). 71.81/31.82 thf(469,plain,((! [A:partia1833973666xt_a_b,B:set_a]: ((locali1648887798ac_a_b @ A @ B) => (locali807230110ng_a_b @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 71.81/31.82 thf(231,axiom,((! [A:partia1833973666xt_a_b,B:a,C:a,D:a]: ((semiring_a_b @ A) => (((member_a @ C @ (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 @ D @ (partia1066395285xt_a_b @ A)))) <= (member_a @ B @ (partia1066395285xt_a_b @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_semiring_Osemiring__simprules_I8_J)). 71.81/31.82 thf(923,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)) => ((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)],[231])). 71.81/31.82 thf(116,axiom,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_r__null)). 71.81/31.82 thf(592,plain,((! [A:a]: ((member_a @ A @ (partia1066395285xt_a_b @ r)) => ((mult_a_ring_ext_a_b @ r @ A @ (zero_a_b @ r)) = (zero_a_b @ r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 71.81/31.82 thf(85,axiom,((! [A:int,B:int]: ((A = (uminus_uminus_int @ B)) = (B = (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_equation__minus__iff)). 71.81/31.82 thf(496,plain,((! [A:int,B:int]: ((A = (uminus_uminus_int @ B)) = (B = (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 71.81/31.82 thf(6818,plain,(($false)),inference(e,[status(thm)],[3021,809,365,941,777,249,333,628,481,352,408,449,247,379,6295,1158,582,762,440,655,511,269,677,3017,385,533,698,930,898,885,301,320,1254,257,570,719,785,6113,934,949,542,702,751,2552,421,969,325,289,261,284,770,756,789,485,514,966,646,253,766,634,866,2371,396,849,507,312,292,452,248,661,810,381,5540,714,894,746,561,392,424,407,275,729,260,862,349,625,879,329,665,493,551,842,435,6445,522,830,742,317,650,725,388,356,499,3018,471,884,488,339,554,669,642,526,637,3032,4530,837,393,985,738,654,911,371,938,266,633,657,773,794,586,662,718,298,412,618,430,264,856,689,733,694,402,286,579,1535,281,545,413,577,711,391,445,382,572,611,466,919,947,604,681,274,784,736,434,271,599,362,567,890,4203,758,367,535,323,799,915,943,330,848,520,685,399,959,827,278,780,306,5725,658,455,883,267,851,5538,589,548,255,749,617,342,836,531,944,927,374,458,823,776,557,690,640,295,872,707,887,414,954,4971,409,580,855,263,310,3019,673,502,840,463,576,3412,359,907,2545,808,336,613,595,612,876,556,539,903,891,771,368,844,896,304,258,390,632,418,963,517,667,478,272,899,832,346,536,716,620,315,432,967,950,405,790,867,564,326,294,341,268,807,437,474,960,955,796,886,2549,624,728,427,860,596,908,691,442,871,607,723,3020,254,803,469,923,775,592,496])). 71.81/31.82 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 71.81/31.82 % [INFO] Killing All external provers ... 71.81/31.87 EOF