0.09/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.12 % Command : run_Leo-III---1.5 %s %d 0.12/0.32 % Computer : n005.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 960 0.12/0.32 % WCLimit : 120 0.12/0.32 % DateTime : Thu Jul 2 07:39:06 EDT 2020 0.12/0.32 % CPUTime : 0.12/0.33 % Leo-III: Strategy 1 (for '60') 32.06/9.10 % [INFO] Running in sequential loop mode. 32.06/9.10 % [CONFIG] Using configuration: timeout(60) with strategy 32.06/9.10 % [INFO] eprover registered as external prover. 32.06/9.10 % [INFO] cvc4 registered as external prover. 32.06/9.10 % [INFO] Parsing finished. Scanning for conjecture ... 32.06/9.10 % [INFO] Found a conjecture and 703 axioms. Running axiom selection ... 32.06/9.10 % [INFO] Axiom selection finished. Selected 387 axioms (removed 316 axioms). 32.06/9.10 % [INFO] Type checking passed. Searching for refutation ... 32.06/9.10 % [INFO] Killing All external provers ... 32.06/9.10 % Time passed: 8322ms 32.06/9.10 % Effective reasoning time: 5583ms 32.06/9.10 % Solved by strategy 32.06/9.10 % Axioms used in derivation (387): fact_523_in__below, fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_, fact_509_subsetI, fact_566_add__le__mono1, fact_673_Suc__neq__Zero, fact_679_less__eq__Suc__le__raw, fact_184_inv__f__eq, fact_395_add__less__le__mono, fact_667_one__is__add, fact_556_le__eq__less__or__eq, fact_74__096Lba_A_058_ALin_096, fact_180_pred__equals__eq2, fact_493_pred__subset__eq, fact_572_termination__basic__simps_I2_J, fact_684_inc__induct, fact_84_n_I2_J, fact_67_less__top, fact_218_PiE, fact_663_less__eq__Suc__le, fact_199_PiE, fact_616_neq0__conv, fact_111_ord__less__eq__trans, fact_95_order__less__asym, fact_626_ex__least__nat__le, fact_689_Suc__le__D, fact_544_below__Lin, fact_622_le__0__eq, fact_646_less__Suc__eq, fact_422_add__le__imp__le__left, fact_471_set__rev__mp, fact_541_eq__imp__le, fact_323_order__less__le__trans, fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, fact_235_xt1_I5_J, fact_578_funcsetI, fact_643_add__Suc, fact_318_xt1_I11_J, fact_284_order__le__less, fact_540_nat__le__linear, fact_442_subsetD, fact_210_PiE, fact_160_order__less__irrefl, fact_156_linorder__neq__iff, fact_388_inv__into__f__eq, fact_214_PiE, fact_421_one__reorient, fact_304_linorder__antisym__conv2, fact_225_order__refl, fact_585_Pi__I_H, fact_6__C2_C, fact_405_pred__subset__eq2, fact_559_less__or__eq__imp__le, fact_528_nat__neq__iff, fact_22_Pair__eq, fact_648_not__less__less__Suc__eq, fact_624_add__gr__0, fact_664_less__iff__Suc__add, fact_551_add__less__mono1, fact_428_add__le__cancel__right, fact_0_assms_I3_J, fact_644_add__Suc__right, fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_209_PiE, fact_169_mem__def, fact_420_ab__semigroup__add__class_Oadd__ac_I1_J, fact_535_nat__add__left__commute, fact_653_less__SucE, fact_470_set__mp, fact_693_nat_Oexhaust, fact_41_iso__tuple__UNIV__I, fact_512_psubsetD, fact_558_le__neq__implies__less, fact_309_order__le__imp__less__or__eq, fact_670_less__Suc0, fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_3__096P_A_058_AProf_096, fact_191_PiE, fact_650_less__SucI, fact_529_linorder__neqE__nat, fact_415_add__right__imp__eq, fact_476_set__rev__mp, fact_504_subsetI, fact_666_less__add__Suc1, fact_676_Suc__not__Zero, fact_263_order__eq__iff, fact_613_gr0I, fact_416_add__imp__eq, fact_135_order__less__imp__not__eq2, fact_419_add__left__cancel, fact_189_PiE, fact_517_psubsetD, fact_40_iso__tuple__UNIV__I, help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_, fact_29_top1I, fact_534_nat__add__commute, fact_287_linorder__antisym__conv1, fact_659_Suc__leI, fact_637_Suc__leD, fact_524_add__leE, fact_617_not__less0, fact_561_le__add1, fact_623_less__eq__nat_Osimps_I1_J, fact_627_less__imp__add__positive, fact_553_less__add__eq__less, fact_386_inv__into__f__f, fact_75__096a_A_126_061_Ab_096, fact_28_top1I, fact_649_less__antisym, fact_21_Pair__inject, fact_668_add__is__1, fact_542_le__trans, fact_207_PiE, fact_333_order__le__less__trans, fact_20_injh, fact_43_iso__tuple__UNIV__I, fact_594_inj__on__cong, fact_487_in__mono, fact_174_mem__def, fact_660_le__imp__less__Suc, fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_, fact_168_mem__def, fact_193_PiE, fact_508_subsetI, fact_625_ex__least__nat__less, fact_573_termination__basic__simps_I1_J, fact_232_xt1_I6_J, fact_661_Suc__le__eq, fact_372_Pi__mem, fact_208_PiE, fact_373_Pi__mem, fact_374_Pi__mem, fact_88_mkbot__Lin, fact_292_order__neq__le__trans, fact_557_less__imp__le__nat, fact_654_Suc__lessD, fact_71_assms_I1_J, fact_615_less__nat__zero__code, fact_197_PiE, fact_90_const__Lin__Prof, fact_612_le0, fact_569_less__mono__imp__le__mono, fact_598_card__bij, fact_631_Suc__n__not__le__n, fact_204_PiE, fact_391_Pi__I, fact_539_le__refl, fact_274_order__less__le, fact_582_Pi__cong, fact_527_less__not__refl, fact_563_nat__add__left__cancel__le, fact_549_trans__less__add1, fact_463_set__mp, fact_671_less__Suc__eq__0__disj, fact_433_add__strict__right__mono, fact_696_surjh, fact_662_less__Suc__eq__le, fact_23_IIA__def, fact_638_Suc__inject, fact_642_add__Suc__shift, fact_614_gr__implies__not0, fact_213_PiE, fact_188_dictatorI, fact_669_gr0__conv__Suc, fact_435_add__less__cancel__right, fact_179_in__above, fact_635_le__SucI, fact_32_UNIV__I, fact_576_funcsetI, fact_581_Pi__cong, fact_468_set__mp, fact_298_leD, fact_552_add__less__mono, fact_543_le__antisym, fact_568_mono__nat__linear__lb, fact_565_trans__le__add2, fact_219_PiE, fact_59_not__top__less, fact_247_ord__le__eq__trans, fact_127_order__less__asym_H, fact_554_add__lessD1, fact_628_lessI, fact_619_Nat_Oadd__0__right, fact_564_trans__le__add1, fact_503_Pi__mono, fact_394_less__add__one, fact_181_n_I3_J, fact_87_mktop__Lin, fact_620_add__is__0, fact_123_xt1_I9_J, fact_579_linear__alt, fact_206_PiE, fact_170_mem__def, fact_367_inj__on__contraD, fact_687_Suc__eq__plus1__left, fact_86_Lin__irrefl, fact_107_xt1_I2_J, fact_497_pred__subset__eq, fact_532_less__not__refl3, fact_390_Pi__I, fact_478_set__rev__mp, fact_640_Suc__n__not__n, fact_425_add__left__mono, fact_297_xt1_I12_J, fact_338_xt1_I8_J, fact_192_PiE, fact_173_mem__def, fact_645_not__less__eq, fact_360_top__le, fact_501_Pi__mono, fact_538_nat__add__right__cancel, fact_555_nat__less__le, fact_241_order__antisym, fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J, fact_618_plus__nat_Oadd__0, fact_380_dictator__def, fact_500_pred__subset__eq, fact_548_nat__add__left__cancel__less, fact_652_less__trans__Suc, fact_265_linorder__linear, fact_267_linorder__not__less, fact_8__C4_C, fact_4_in__mkbot, fact_429_add__less__imp__less__left, fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I, fact_2__096c_A_126_061_Ad_096, fact_195_PiE, fact_398_injI, fact_103_order__less__trans, fact_656_One__nat__def, fact_533_nat__less__cases, fact_151_less__imp__neq, fact_371_inj__onD, fact_655_Suc__less__SucD, fact_35_UNIV__I, fact_352_top__unique, fact_171_mem__def, fact_443_subsetD, fact_139_order__less__imp__not__eq, fact_205_PiE, fact_250_xt1_I3_J, fact_665_less__add__Suc2, fact_641_n__not__Suc__n, fact_314_order__le__neq__trans, fact_518_psubsetD, fact_577_funcsetI, fact_418_add__right__cancel, fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk, fact_115_xt1_I1_J, fact_382_inj__eq, fact_516_psubsetD, fact_574_termination__basic__simps_I5_J, fact_99_xt1_I10_J, fact_375_Prof__def, fact_85_notin__Lin__iff, fact_194_PiE, fact_651_Suc__lessI, fact_639_nat_Oinject, fact_678_Zero__not__Suc, fact_547_not__add__less2, fact_546_not__add__less1, fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_402_Pi__anti__mono, fact_256_order__antisym__conv, fact_677_nat_Osimps_I2_J, fact_424_add__mono, fact_575_in__rel__def, fact_621_add__eq__self__zero, fact_379_funcset__mem, fact_24_unanimity__def, fact_229_linorder__le__cases, fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am, fact_426_add__right__mono, fact_33_UNIV__I, fact_1_u, fact_155_not__less__iff__gr__or__eq, fact_9_pairwise__neutrality, fact_152_linorder__neqE, fact_14_PW, fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123, fact_629_Suc__mono, fact_467_set__mp, fact_675_nat_Osimps_I3_J, fact_695_nat__induct, fact_269_linorder__le__less__linear, fact_550_trans__less__add2, fact_692_not0__implies__Suc, fact_143_order__less__imp__not__less, fact_691_Suc__lessE, fact_560_le__add2, fact_484_in__mono, fact_253_ord__eq__le__trans, fact_475_set__rev__mp, fact_328_xt1_I7_J, fact_588_card__inj, fact_15_split__paired__All, fact_584_Pi__I_H, fact_567_add__le__mono, fact_583_Pi__I_H, fact_432_add__strict__left__mono, fact_536_nat__add__assoc, fact_633_le__Suc__eq, fact_537_nat__add__left__cancel, fact_611_less__zeroE, fact_19_n_I1_J, fact_632_not__less__eq__eq, fact_186_inv__f__f, fact_580_Pi__cong, fact_389_Pi__I, fact_485_in__mono, fact_686_gr0__implies__Suc, fact_694_zero__induct, fact_592_inj__onI, fact_7__C1_C, fact_674_Zero__neq__Suc, fact_531_less__not__refl2, fact_438_subsetD, fact_5_in__mktop, fact_630_zero__less__Suc, fact_525_add__leD1, fact_647_Suc__less__eq, fact_172_mem__def, fact_634_Suc__le__mono, fact_198_PiE, fact_430_add__less__imp__less__right, fact_445_subsetD, fact_212_PiE, fact_688_Suc__eq__plus1, fact_595_finite__indi, fact_571_termination__basic__simps_I4_J, fact_657_Suc__le__lessD, fact_434_add__less__cancel__left, fact_344_top__greatest, fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_, fact_365_inj__on__def, fact_396_add__le__less__mono, fact_119_ord__eq__less__trans, fact_480_in__mono, fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am, fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk, fact_685_less__imp__Suc__add, fact_154_linorder__less__linear, fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai, fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_285_leI, fact_220_complete__Lin, fact_279_less__le__not__le, fact_73__096Lab_A_058_ALin_096, fact_526_add__leD2, fact_511_subsetI, fact_530_less__irrefl__nat, fact_196_PiE, fact_369_inj__on__iff, fact_417_add__left__imp__eq, fact_80_PiProf, fact_10__C3_C, fact_519_psubsetD, fact_200_PiE, fact_431_add__strict__mono, fact_238_order__trans, fact_91_linorder__cases, fact_427_add__le__cancel__left, fact_147_order__less__not__sym, fact_286_not__leE, fact_690_lessE, fact_303_order__less__imp__le, fact_244_xt1_I4_J, fact_190_PiE, fact_260_order__eq__refl, fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_423_add__le__imp__le__right, fact_562_le__iff__add, fact_636_le__SucE, fact_393_inj__imp__inv__eq, fact_268_linorder__not__le, fact_570_termination__basic__simps_I3_J, fact_378_funcset__mem, fact_658_le__less__Suc__eq, fact_498_pred__subset__eq, fact_153_linorder__antisym__conv3, fact_384_injD, fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_409_subset__UNIV, fact_131_order__less__imp__triv, fact_211_PiE, fact_89_above__Lin, fact_377_funcset__mem, fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0 32.06/9.10 % No. of inferences in proof: 778 32.06/9.10 % No. of processed clauses: 1 32.06/9.10 % No. of generated clauses: 0 32.06/9.10 % No. of forward subsumed clauses: 0 32.06/9.10 % No. of backward subsumed clauses: 0 32.06/9.10 % No. of ground rewrite rules in store: 1 32.06/9.10 % No. of non-ground rewrite rules in store: 0 32.06/9.10 % No. of positive (non-rewrite) units in store: 0 32.06/9.10 % No. of negative (non-rewrite) units in store: 0 32.06/9.10 % No. of choice functions detected: 0 32.06/9.10 % No. of choice instantiations: 0 32.06/9.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8322 ms resp. 5583 ms w/o parsing 32.06/9.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 32.06/9.10 thf(arrow_475358991le_alt_type, type, arrow_475358991le_alt: $tType). 32.06/9.10 thf(arrow_1429601828e_indi_type, type, arrow_1429601828e_indi: $tType). 32.06/9.10 thf(nat_type, type, nat: $tType). 32.06/9.10 thf(product_unit_type, type, product_unit: $tType). 32.06/9.10 thf(produc1501160679le_alt_type, type, produc1501160679le_alt: $tType). 32.06/9.10 thf(all_type, type, all: ((produc1501160679le_alt > $o) > $o)). 32.06/9.10 thf(arrow_797024463le_IIA_type, type, arrow_797024463le_IIA: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)). 32.06/9.10 thf(arrow_823908191le_Lin_type, type, arrow_823908191le_Lin: ((produc1501160679le_alt > $o) > $o)). 32.06/9.10 thf(arrow_734252939e_Prof_type, type, arrow_734252939e_Prof: ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)). 32.06/9.10 thf(arrow_789600939_above_type, type, arrow_789600939_above: ((produc1501160679le_alt > $o) > (arrow_475358991le_alt > (arrow_475358991le_alt > (produc1501160679le_alt > $o))))). 32.06/9.10 thf(arrow_2098199487_below_type, type, arrow_2098199487_below: ((produc1501160679le_alt > $o) > (arrow_475358991le_alt > (arrow_475358991le_alt > (produc1501160679le_alt > $o))))). 32.06/9.10 thf(arrow_1212662430ctator_type, type, arrow_1212662430ctator: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > (arrow_1429601828e_indi > $o))). 32.06/9.10 thf(arrow_2054445623_mkbot_type, type, arrow_2054445623_mkbot: ((produc1501160679le_alt > $o) > (arrow_475358991le_alt > (produc1501160679le_alt > $o)))). 32.06/9.10 thf(arrow_55669061_mktop_type, type, arrow_55669061_mktop: ((produc1501160679le_alt > $o) > (arrow_475358991le_alt > (produc1501160679le_alt > $o)))). 32.06/9.10 thf(arrow_1706409458nimity_type, type, arrow_1706409458nimity: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)). 32.06/9.10 thf(finite_card_o_type, type, finite_card_o: (($o > $o) > nat)). 32.06/9.10 thf(finite97476818e_indi_type, type, finite97476818e_indi: ((arrow_1429601828e_indi > $o) > nat)). 32.06/9.10 thf(finite537683861le_alt_type, type, finite537683861le_alt: ((produc1501160679le_alt > $o) > nat)). 32.06/9.10 thf(finite_finite_o_type, type, finite_finite_o: (($o > $o) > $o)). 32.06/9.10 thf(finite664979089e_indi_type, type, finite664979089e_indi: ((arrow_1429601828e_indi > $o) > $o)). 32.06/9.10 thf(finite449174868le_alt_type, type, finite449174868le_alt: ((produc1501160679le_alt > $o) > $o)). 32.06/9.10 thf(in_rel1252994498le_alt_type, type, in_rel1252994498le_alt: ((produc1501160679le_alt > $o) > (arrow_475358991le_alt > (arrow_475358991le_alt > $o)))). 32.06/9.10 thf(inj_on867909093le_alt_type, type, inj_on867909093le_alt: (($o > produc1501160679le_alt) > (($o > $o) > $o))). 32.06/9.10 thf(inj_on978774663di_nat_type, type, inj_on978774663di_nat: ((arrow_1429601828e_indi > nat) > ((arrow_1429601828e_indi > $o) > $o))). 32.06/9.10 thf(inj_on1911943593_alt_o_type, type, inj_on1911943593_alt_o: ((produc1501160679le_alt > $o) > ((produc1501160679le_alt > $o) > $o))). 32.06/9.10 thf(pi_Arr195212324lt_o_o_type, type, pi_Arr195212324lt_o_o: ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > ($o > $o)) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > $o)))). 32.06/9.10 thf(pi_Arr338314351e_indi_type, type, pi_Arr338314351e_indi: ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > (arrow_1429601828e_indi > $o)) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi) > $o)))). 32.06/9.10 thf(pi_Arr830584606t_unit_type, type, pi_Arr830584606t_unit: ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > (product_unit > $o)) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > product_unit) > $o)))). 32.06/9.10 thf(pi_Arr1304755663_alt_o_type, type, pi_Arr1304755663_alt_o: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)))). 32.06/9.10 thf(pi_Arr952516694lt_o_o_type, type, pi_Arr952516694lt_o_o: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ($o > $o)) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > $o)))). 32.06/9.10 thf(pi_Arr1232280765e_indi_type, type, pi_Arr1232280765e_indi: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (arrow_1429601828e_indi > $o)) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi) > $o)))). 32.06/9.10 thf(pi_Arr1963174508t_unit_type, type, pi_Arr1963174508t_unit: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (product_unit > $o)) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > product_unit) > $o)))). 32.06/9.10 thf(pi_Pro422690258lt_o_o_type, type, pi_Pro422690258lt_o_o: (((produc1501160679le_alt > $o) > $o) > (((produc1501160679le_alt > $o) > ($o > $o)) > (((produc1501160679le_alt > $o) > $o) > $o)))). 32.06/9.10 thf(pi_Pro468373057e_indi_type, type, pi_Pro468373057e_indi: (((produc1501160679le_alt > $o) > $o) > (((produc1501160679le_alt > $o) > (arrow_1429601828e_indi > $o)) > (((produc1501160679le_alt > $o) > arrow_1429601828e_indi) > $o)))). 32.06/9.10 thf(pi_Pro1306850800t_unit_type, type, pi_Pro1306850800t_unit: (((produc1501160679le_alt > $o) > $o) > (((produc1501160679le_alt > $o) > (product_unit > $o)) > (((produc1501160679le_alt > $o) > product_unit) > $o)))). 32.06/9.10 thf(pi_o_A1186128886_alt_o_type, type, pi_o_A1186128886_alt_o: (($o > $o) > (($o > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)) > (($o > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > $o)))). 32.06/9.10 thf(pi_o_A1182933120_alt_o_type, type, pi_o_A1182933120_alt_o: (($o > $o) > (($o > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)) > (($o > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > $o)))). 32.06/9.10 thf(pi_o_P553196292_alt_o_type, type, pi_o_P553196292_alt_o: (($o > $o) > (($o > ((produc1501160679le_alt > $o) > $o)) > (($o > (produc1501160679le_alt > $o)) > $o)))). 32.06/9.10 thf(pi_o_P657324555le_alt_type, type, pi_o_P657324555le_alt: (($o > $o) > (($o > (produc1501160679le_alt > $o)) > (($o > produc1501160679le_alt) > $o)))). 32.06/9.10 thf(pi_Arr1564509167_alt_o_type, type, pi_Arr1564509167_alt_o: ((arrow_1429601828e_indi > $o) > ((arrow_1429601828e_indi > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)) > ((arrow_1429601828e_indi > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > $o)))). 32.06/9.10 thf(pi_Arr1060328391_alt_o_type, type, pi_Arr1060328391_alt_o: ((arrow_1429601828e_indi > $o) > ((arrow_1429601828e_indi > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)) > ((arrow_1429601828e_indi > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > $o)))). 32.06/9.10 thf(pi_Arr1929480907_alt_o_type, type, pi_Arr1929480907_alt_o: ((arrow_1429601828e_indi > $o) > ((arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o)) > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)))). 32.06/9.10 thf(pi_Arr329216900le_alt_type, type, pi_Arr329216900le_alt: ((arrow_1429601828e_indi > $o) > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((arrow_1429601828e_indi > produc1501160679le_alt) > $o)))). 32.06/9.10 thf(pi_Pro1782982558_alt_o_type, type, pi_Pro1782982558_alt_o: ((product_unit > $o) > ((product_unit > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)) > ((product_unit > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > $o)))). 32.06/9.10 thf(pi_Pro1662176984_alt_o_type, type, pi_Pro1662176984_alt_o: ((product_unit > $o) > ((product_unit > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)) > ((product_unit > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > $o)))). 32.06/9.10 thf(pi_Pro1312660828_alt_o_type, type, pi_Pro1312660828_alt_o: ((product_unit > $o) > ((product_unit > ((produc1501160679le_alt > $o) > $o)) > ((product_unit > (produc1501160679le_alt > $o)) > $o)))). 32.06/9.10 thf(pi_Pro701847987le_alt_type, type, pi_Pro701847987le_alt: ((product_unit > $o) > ((product_unit > (produc1501160679le_alt > $o)) > ((product_unit > produc1501160679le_alt) > $o)))). 32.06/9.10 thf(pi_Pro1701359055_alt_o_type, type, pi_Pro1701359055_alt_o: ((produc1501160679le_alt > $o) > ((produc1501160679le_alt > ($o > $o)) > ((produc1501160679le_alt > $o) > $o)))). 32.06/9.10 thf(pi_Pro1767455108e_indi_type, type, pi_Pro1767455108e_indi: ((produc1501160679le_alt > $o) > ((produc1501160679le_alt > (arrow_1429601828e_indi > $o)) > ((produc1501160679le_alt > arrow_1429601828e_indi) > $o)))). 32.06/9.10 thf(pi_Pro1475896499t_unit_type, type, pi_Pro1475896499t_unit: ((produc1501160679le_alt > $o) > ((produc1501160679le_alt > (product_unit > $o)) > ((produc1501160679le_alt > product_unit) > $o)))). 32.06/9.10 thf(one_one_nat_type, type, one_one_nat: nat). 32.06/9.10 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 32.06/9.10 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 32.06/9.10 thf(hilber598459244di_nat_type, type, hilber598459244di_nat: ((arrow_1429601828e_indi > $o) > ((arrow_1429601828e_indi > nat) > (nat > arrow_1429601828e_indi)))). 32.06/9.10 thf(if_Pro1561232536_alt_o_type, type, if_Pro1561232536_alt_o: ($o > ((produc1501160679le_alt > $o) > ((produc1501160679le_alt > $o) > (produc1501160679le_alt > $o))))). 32.06/9.10 thf(suc_type, type, suc: (nat > nat)). 32.06/9.10 thf(ord_le1859604819lt_o_o_type, type, ord_le1859604819lt_o_o: ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > $o))). 32.06/9.10 thf(ord_le157835011lt_o_o_type, type, ord_le157835011lt_o_o: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > $o))). 32.06/9.10 thf(ord_le910298367lt_o_o_type, type, ord_le910298367lt_o_o: (((produc1501160679le_alt > $o) > $o) > (((produc1501160679le_alt > $o) > $o) > $o))). 32.06/9.10 thf(ord_less_o_o_type, type, ord_less_o_o: (($o > $o) > (($o > $o) > $o))). 32.06/9.10 thf(ord_le988258430_alt_o_type, type, ord_le988258430_alt_o: ((produc1501160679le_alt > $o) > ((produc1501160679le_alt > $o) > $o))). 32.06/9.10 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 32.06/9.10 thf(ord_le134800455lt_o_o_type, type, ord_le134800455lt_o_o: ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > $o))). 32.06/9.10 thf(ord_le1063113995lt_o_o_type, type, ord_le1063113995lt_o_o: (((produc1501160679le_alt > $o) > $o) > (((produc1501160679le_alt > $o) > $o) > $o))). 32.06/9.10 thf(ord_less_eq_o_o_type, type, ord_less_eq_o_o: (($o > $o) > (($o > $o) > $o))). 32.06/9.10 thf(ord_le2080035663_alt_o_type, type, ord_le2080035663_alt_o: ((arrow_475358991le_alt > (arrow_475358991le_alt > $o)) > ((arrow_475358991le_alt > (arrow_475358991le_alt > $o)) > $o))). 32.06/9.10 thf(ord_le97612146_alt_o_type, type, ord_le97612146_alt_o: ((produc1501160679le_alt > $o) > ((produc1501160679le_alt > $o) > $o))). 32.06/9.10 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 32.06/9.10 thf(top_top_o_o_type, type, top_top_o_o: ($o > $o)). 32.06/9.10 thf(top_to988227749indi_o_type, type, top_to988227749indi_o: (arrow_1429601828e_indi > $o)). 32.06/9.10 thf(top_to1841428258_alt_o_type, type, top_to1841428258_alt_o: (produc1501160679le_alt > $o)). 32.06/9.10 thf(produc1347929815le_alt_type, type, produc1347929815le_alt: (arrow_475358991le_alt > (arrow_475358991le_alt > produc1501160679le_alt))). 32.06/9.10 thf(ord_at4362885an_nat_type, type, ord_at4362885an_nat: (nat > (nat > (nat > $o)))). 32.06/9.10 thf(image_484224243di_nat_type, type, image_484224243di_nat: ((arrow_1429601828e_indi > nat) > ((arrow_1429601828e_indi > $o) > (nat > $o)))). 32.06/9.10 thf(member1823529808lt_o_o_type, type, member1823529808lt_o_o: ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > (((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > $o) > $o))). 32.06/9.10 thf(member1452482393e_indi_type, type, member1452482393e_indi: ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi) > (((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi) > $o) > $o))). 32.06/9.10 thf(member1924666376t_unit_type, type, member1924666376t_unit: ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > product_unit) > (((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > product_unit) > $o) > $o))). 32.06/9.10 thf(member616898751_alt_o_type, type, member616898751_alt_o: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o) > $o))). 32.06/9.10 thf(member939334982lt_o_o_type, type, member939334982lt_o_o: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > $o) > $o))). 32.06/9.10 thf(member44294883e_indi_type, type, member44294883e_indi: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi) > $o) > $o))). 32.06/9.10 thf(member843528338t_unit_type, type, member843528338t_unit: (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > product_unit) > ((((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > product_unit) > $o) > $o))). 32.06/9.10 thf(member1961363906lt_o_o_type, type, member1961363906lt_o_o: (((produc1501160679le_alt > $o) > $o) > ((((produc1501160679le_alt > $o) > $o) > $o) > $o))). 32.06/9.10 thf(member304866663e_indi_type, type, member304866663e_indi: (((produc1501160679le_alt > $o) > arrow_1429601828e_indi) > ((((produc1501160679le_alt > $o) > arrow_1429601828e_indi) > $o) > $o))). 32.06/9.10 thf(member221730070t_unit_type, type, member221730070t_unit: (((produc1501160679le_alt > $o) > product_unit) > ((((produc1501160679le_alt > $o) > product_unit) > $o) > $o))). 32.06/9.10 thf(member1957863580_alt_o_type, type, member1957863580_alt_o: (($o > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > ((($o > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > $o) > $o))). 32.06/9.10 thf(member1394214384_alt_o_type, type, member1394214384_alt_o: (($o > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > ((($o > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > $o) > $o))). 32.06/9.10 thf(member1862122484_alt_o_type, type, member1862122484_alt_o: (($o > (produc1501160679le_alt > $o)) > ((($o > (produc1501160679le_alt > $o)) > $o) > $o))). 32.06/9.10 thf(member492167345le_alt_type, type, member492167345le_alt: (($o > produc1501160679le_alt) > ((($o > produc1501160679le_alt) > $o) > $o))). 32.06/9.10 thf(member811956313_alt_o_type, type, member811956313_alt_o: ((arrow_1429601828e_indi > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > (((arrow_1429601828e_indi > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > $o) > $o))). 32.06/9.10 thf(member1234151027_alt_o_type, type, member1234151027_alt_o: ((arrow_1429601828e_indi > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > (((arrow_1429601828e_indi > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > $o) > $o))). 32.06/9.10 thf(member526088951_alt_o_type, type, member526088951_alt_o: ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o) > $o))). 32.06/9.10 thf(member351225838le_alt_type, type, member351225838le_alt: ((arrow_1429601828e_indi > produc1501160679le_alt) > (((arrow_1429601828e_indi > produc1501160679le_alt) > $o) > $o))). 32.06/9.10 thf(member1536989448_alt_o_type, type, member1536989448_alt_o: ((product_unit > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > (((product_unit > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))) > $o) > $o))). 32.06/9.10 thf(member283501700_alt_o_type, type, member283501700_alt_o: ((product_unit > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > (((product_unit > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))) > $o) > $o))). 32.06/9.10 thf(member1661784200_alt_o_type, type, member1661784200_alt_o: ((product_unit > (produc1501160679le_alt > $o)) > (((product_unit > (produc1501160679le_alt > $o)) > $o) > $o))). 32.06/9.10 thf(member495332125le_alt_type, type, member495332125le_alt: ((product_unit > produc1501160679le_alt) > (((product_unit > produc1501160679le_alt) > $o) > $o))). 32.06/9.10 thf(member377231867_alt_o_type, type, member377231867_alt_o: ((produc1501160679le_alt > $o) > (((produc1501160679le_alt > $o) > $o) > $o))). 32.06/9.10 thf(member1640632174e_indi_type, type, member1640632174e_indi: ((produc1501160679le_alt > arrow_1429601828e_indi) > (((produc1501160679le_alt > arrow_1429601828e_indi) > $o) > $o))). 32.06/9.10 thf(member593902749t_unit_type, type, member593902749t_unit: ((produc1501160679le_alt > product_unit) > (((produc1501160679le_alt > product_unit) > $o) > $o))). 32.06/9.10 thf(member_o_type, type, member_o: ($o > (($o > $o) > $o))). 32.06/9.10 thf(member2052026769e_indi_type, type, member2052026769e_indi: (arrow_1429601828e_indi > ((arrow_1429601828e_indi > $o) > $o))). 32.06/9.10 thf(member_Product_unit_type, type, member_Product_unit: (product_unit > ((product_unit > $o) > $o))). 32.06/9.10 thf(member214075476le_alt_type, type, member214075476le_alt: (produc1501160679le_alt > ((produc1501160679le_alt > $o) > $o))). 32.06/9.10 thf(f_type, type, f: ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))). 32.06/9.10 thf(lab_type, type, lab: (produc1501160679le_alt > $o)). 32.06/9.10 thf(lba_type, type, lba: (produc1501160679le_alt > $o)). 32.06/9.10 thf(p_type, type, p: (arrow_1429601828e_indi > (produc1501160679le_alt > $o))). 32.06/9.10 thf(a_type, type, a: arrow_475358991le_alt). 32.06/9.10 thf(b_type, type, b: arrow_475358991le_alt). 32.06/9.10 thf(c_type, type, c: arrow_475358991le_alt). 32.06/9.10 thf(d_type, type, d: arrow_475358991le_alt). 32.06/9.10 thf(e_type, type, e: arrow_475358991le_alt). 32.06/9.10 thf(h_type, type, h: (arrow_1429601828e_indi > nat)). 32.06/9.10 thf(n_type, type, n: nat). 32.06/9.10 thf(319,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_le__add2)). 32.06/9.10 thf(1718,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 32.06/9.10 thf(74,axiom,((! [A:nat]: ((A != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_gr0I)). 32.06/9.10 thf(629,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 32.06/9.10 thf(176,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) <= (A != B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_order__le__neq__trans)). 32.06/9.10 thf(1190,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 32.06/9.10 thf(123,axiom,((! [A:$o,B:($o > $o),C:($o > $o)]: (((member_o @ A @ B) => (member_o @ A @ C)) <= (ord_less_eq_o_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_in__mono)). 32.06/9.10 thf(909,plain,((! [A:$o,B:($o > $o),C:($o > $o)]: (((member_o @ A @ (B)) => (member_o @ A @ (C))) | ~ (ord_less_eq_o_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 32.06/9.10 thf(373,axiom,((~ (! [A:nat]: (((! [B:nat]: ((ord_less_eq_nat @ B @ A) => (member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (f @ (^ [C:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ C) @ B) @ lab @ lba)))))) => (~ (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (f @ (^ [B:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ B) @ (plus_plus_nat @ A @ one_one_nat)) @ lab @ lba)))))) <= (ord_less_nat @ A @ (finite97476818e_indi @ top_to988227749indi_o)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_)). 32.06/9.10 thf(1850,plain,((~ (! [A:nat]: (((! [B:nat]: ((ord_less_eq_nat @ B @ A) => (member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (f @ (^ [C:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ C) @ B) @ lab @ lba)))))) => (~ (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (f @ (^ [B:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ B) @ (plus_plus_nat @ A @ one_one_nat)) @ lab @ lba)))))) | ~ (ord_less_nat @ A @ (finite97476818e_indi @ (top_to988227749indi_o))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])). 32.06/9.10 thf(360,axiom,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ B @ A) <= (! [C:produc1501160679le_alt]: ((member214075476le_alt @ C @ B) => (member214075476le_alt @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_subsetI)). 32.06/9.10 thf(1818,plain,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ (B) @ (A)) | ~ (! [C:produc1501160679le_alt]: ((member214075476le_alt @ C @ (B)) => (member214075476le_alt @ C @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 32.06/9.10 thf(279,axiom,((! [A:((produc1501160679le_alt > $o) > $o),B:((produc1501160679le_alt > $o) > $o)]: ((ord_le1063113995lt_o_o @ (^ [C:(produc1501160679le_alt > $o)]: (member377231867_alt_o @ C @ A)) @ (^ [C:(produc1501160679le_alt > $o)]: (member377231867_alt_o @ C @ B))) = (ord_le1063113995lt_o_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_pred__subset__eq)). 32.06/9.10 thf(1549,plain,((! [A:((produc1501160679le_alt > $o) > $o),B:((produc1501160679le_alt > $o) > $o)]: ((ord_le1063113995lt_o_o @ (^ [C:(produc1501160679le_alt > $o)]: (member377231867_alt_o @ C @ A)) @ (^ [C:(produc1501160679le_alt > $o)]: (member377231867_alt_o @ C @ B))) = (ord_le1063113995lt_o_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 32.06/9.10 thf(307,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ A) <= (ord_less_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_order__le__less__trans)). 32.06/9.10 thf(1686,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ A) | ~ (ord_less_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 32.06/9.10 thf(32,axiom,((! [A:nat,B:nat]: (((B != (suc @ A)) => (~ (! [C:nat]: ((B != (suc @ C)) <= (ord_less_nat @ A @ C))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_lessE)). 32.06/9.10 thf(479,plain,((! [A:nat,B:nat]: (((~ (B = (suc @ A))) => (~ (! [C:nat]: (~ (B = (suc @ C)) | ~ (ord_less_nat @ A @ C))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 32.06/9.10 thf(283,axiom,((! [A:arrow_475358991le_alt,B:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ B @ arrow_823908191le_Lin) => (member377231867_alt_o @ (arrow_2054445623_mkbot @ B @ A) @ arrow_823908191le_Lin)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mkbot__Lin)). 32.06/9.10 thf(1559,plain,((! [A:arrow_475358991le_alt,B:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ (B) @ (arrow_823908191le_Lin)) => (member377231867_alt_o @ (arrow_2054445623_mkbot @ B @ A) @ (arrow_823908191le_Lin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 32.06/9.10 thf(160,axiom,((! [A:$o]: (member_o @ A @ top_top_o_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I)). 32.06/9.10 thf(1083,plain,((! [A:$o]: (member_o @ A @ (top_top_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 32.06/9.10 thf(28,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_Suc__leD)). 32.06/9.10 thf(468,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 32.06/9.10 thf(297,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_trans__le__add1)). 32.06/9.10 thf(1596,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 32.06/9.10 thf(132,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_Suc__le__lessD)). 32.06/9.10 thf(994,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 32.06/9.10 thf(243,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) = (~ (ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_less__le__not__le)). 32.06/9.10 thf(1401,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) = (~ (ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 32.06/9.10 thf(93,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_le__add1)). 32.06/9.10 thf(741,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 32.06/9.10 thf(323,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > ($o > $o))]: ((member377231867_alt_o @ B @ (pi_Pro1701359055_alt_o @ C @ D)) => ((member_o @ (B @ A) @ (D @ A)) <= (member214075476le_alt @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_Pi__mem)). 32.06/9.10 thf(1728,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > ($o > $o))]: ((member377231867_alt_o @ (B) @ (pi_Pro1701359055_alt_o @ C @ D)) => ((member_o @ (B @ A) @ (D @ A)) | ~ (member214075476le_alt @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 32.06/9.10 thf(295,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_not__leE)). 32.06/9.10 thf(1591,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 32.06/9.10 thf(18,axiom,((! [A:nat]: ((A = zero_zero_nat) = (ord_less_nat @ A @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_less__Suc0)). 32.06/9.10 thf(440,plain,((! [A:nat]: ((A = zero_zero_nat) = (ord_less_nat @ A @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 32.06/9.10 thf(69,axiom,((! [A:nat,B:nat]: ((((suc @ A) != B) => (ord_less_nat @ (suc @ A) @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_Suc__lessI)). 32.06/9.10 thf(614,plain,((! [A:nat,B:nat]: (((~ ((suc @ A) = B)) => (ord_less_nat @ (suc @ A) @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 32.06/9.10 thf(110,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_nat__add__right__cancel)). 32.06/9.10 thf(861,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 32.06/9.10 thf(374,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt,E:arrow_475358991le_alt,F:arrow_475358991le_alt]: ((E != F) => ((C != D) => ((((member526088951_alt_o @ B @ arrow_734252939e_Prof) => ((((member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (f @ B)) => (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (f @ A))) <= (! [G:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A @ G)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (B @ G))))) <= (member526088951_alt_o @ A @ arrow_734252939e_Prof))) <= (F != C)) <= (E != D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__C1_C)). 32.06/9.10 thf(1855,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt,E:arrow_475358991le_alt,F:arrow_475358991le_alt]: ((~ (E = F)) => ((~ (C = D)) => (((member526088951_alt_o @ (B) @ (arrow_734252939e_Prof)) => (((member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (f @ B)) => (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (f @ A))) | ~ (! [G:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A @ G)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (B @ G)))) | ~ (member526088951_alt_o @ (A) @ (arrow_734252939e_Prof)))) | (F = C) | (E = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 32.06/9.10 thf(180,axiom,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o)]: (((member377231867_alt_o @ A @ B) => (member377231867_alt_o @ A @ C)) <= (ord_le910298367lt_o_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_psubsetD)). 32.06/9.10 thf(1200,plain,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o)]: (((member377231867_alt_o @ (A) @ (B)) => (member377231867_alt_o @ (A) @ (C))) | ~ (ord_le910298367lt_o_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 32.06/9.10 thf(256,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) = (ord_less_nat @ B @ (suc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_le__less__Suc__eq)). 32.06/9.10 thf(1443,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) = (ord_less_nat @ B @ (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 32.06/9.10 thf(356,axiom,((! [A:(produc1501160679le_alt > $o),B:($o > $o),C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ A @ (pi_Pro1701359055_alt_o @ C @ (^ [D:produc1501160679le_alt]: (B)))) <= (! [D:produc1501160679le_alt]: ((member214075476le_alt @ D @ C) => (member_o @ (A @ D) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_funcsetI)). 32.06/9.10 thf(1808,plain,((! [A:(produc1501160679le_alt > $o),B:($o > $o),C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ (A) @ (pi_Pro1701359055_alt_o @ C @ (^ [D:produc1501160679le_alt]: (B)))) | ~ (! [D:produc1501160679le_alt]: ((member214075476le_alt @ D @ (C)) => (member_o @ (A @ D) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 32.06/9.10 thf(260,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_less__not__refl)). 32.06/9.10 thf(1497,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 32.06/9.10 thf(36,axiom,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat)]: ((inj_on978774663di_nat @ C @ top_to988227749indi_o) => ((A = B) <= ((C @ A) = (C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_injD)). 32.06/9.10 thf(500,plain,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat)]: ((inj_on978774663di_nat @ (C) @ (top_to988227749indi_o)) => ((A = B) | ~ ((C @ A) = (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 32.06/9.10 thf(83,axiom,((! [A:arrow_1429601828e_indi,B:nat,C:(arrow_1429601828e_indi > nat)]: ((inj_on978774663di_nat @ C @ top_to988227749indi_o) => (((hilber598459244di_nat @ top_to988227749indi_o @ C @ B) = A) <= ((C @ A) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_inv__f__eq)). 32.06/9.10 thf(715,plain,((! [A:arrow_1429601828e_indi,B:nat,C:(arrow_1429601828e_indi > nat)]: ((inj_on978774663di_nat @ (C) @ (top_to988227749indi_o)) => (((hilber598459244di_nat @ (top_to988227749indi_o) @ (C) @ B) = A) | ~ ((C @ A) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 32.06/9.10 thf(380,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: ((arrow_797024463le_IIA @ A) = (! [B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((! [C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member526088951_alt_o @ C @ arrow_734252939e_Prof) => (! [D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((! [F:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (C @ F)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (B @ F)))) => ((member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (A @ C)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (A @ B))))))) <= (member526088951_alt_o @ B @ arrow_734252939e_Prof)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_IIA__def)). 32.06/9.10 thf(1872,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: ((arrow_797024463le_IIA @ (A)) = (! [B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (! [C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member526088951_alt_o @ (C) @ (arrow_734252939e_Prof)) => (! [D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((! [F:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (C @ F)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (B @ F)))) => ((member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (A @ C)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (A @ B)))))) | ~ (member526088951_alt_o @ (B) @ (arrow_734252939e_Prof))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 32.06/9.10 thf(216,axiom,((! [A:nat]: (member526088951_alt_o @ (^ [B:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ B) @ A) @ lab @ lba)) @ arrow_734252939e_Prof))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_PiProf)). 32.06/9.10 thf(1327,plain,((! [A:nat]: (member526088951_alt_o @ (^ [B:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ B) @ A) @ lab @ lba)) @ (arrow_734252939e_Prof)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 32.06/9.10 thf(192,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) => ((ord_less_eq_nat @ B @ A) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_ord__eq__le__trans)). 32.06/9.10 thf(1260,plain,((! [A:nat,B:nat,C:nat]: ((B = C) => ((ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 32.06/9.10 thf(337,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt,E:arrow_475358991le_alt,F:arrow_475358991le_alt]: ((((E != D) => ((F != C) => ((member526088951_alt_o @ B @ arrow_734252939e_Prof) => ((((member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (f @ B)) = (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (f @ A))) <= (! [G:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A @ G)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (B @ G))))) <= (member526088951_alt_o @ A @ arrow_734252939e_Prof))))) <= (C != D)) <= (E != F)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C2_C)). 32.06/9.10 thf(1761,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt,E:arrow_475358991le_alt,F:arrow_475358991le_alt]: (((~ (E = D)) => ((~ (F = C)) => ((member526088951_alt_o @ (B) @ (arrow_734252939e_Prof)) => (((member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (f @ B)) = (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (f @ A))) | ~ (! [G:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A @ G)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (B @ G)))) | ~ (member526088951_alt_o @ (A) @ (arrow_734252939e_Prof)))))) | (C = D) | (E = F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 32.06/9.10 thf(223,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_add__le__mono)). 32.06/9.10 thf(1342,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 32.06/9.10 thf(178,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_add__le__less__mono)). 32.06/9.10 thf(1196,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 32.06/9.10 thf(345,axiom,(((member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e)))))) = (member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ lab @ lba)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk)). 32.06/9.10 thf(1782,plain,(((member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e)))))) = (member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ lab @ lba)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 32.06/9.10 thf(290,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_add__le__mono1)). 32.06/9.10 thf(1576,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 32.06/9.10 thf(255,axiom,((! [A:product_unit,B:(product_unit > (produc1501160679le_alt > $o)),C:(product_unit > $o),D:(product_unit > ((produc1501160679le_alt > $o) > $o))]: (((~ (member_Product_unit @ A @ C)) <= (~ (member377231867_alt_o @ (B @ A) @ (D @ A)))) <= (member1661784200_alt_o @ B @ (pi_Pro1312660828_alt_o @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_PiE)). 32.06/9.10 thf(1441,plain,((! [A:product_unit,B:(product_unit > (produc1501160679le_alt > $o)),C:(product_unit > $o),D:(product_unit > ((produc1501160679le_alt > $o) > $o))]: (~ (member_Product_unit @ A @ (C)) | (member377231867_alt_o @ (B @ A) @ (D @ A)) | ~ (member1661784200_alt_o @ (B) @ (pi_Pro1312660828_alt_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 32.06/9.10 thf(150,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_linorder__less__linear)). 32.06/9.10 thf(1046,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 32.06/9.10 thf(230,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o))]: (((~ (member2052026769e_indi @ A @ C)) <= (~ (member616898751_alt_o @ (B @ A) @ (D @ A)))) <= (member811956313_alt_o @ B @ (pi_Arr1564509167_alt_o @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_PiE)). 32.06/9.10 thf(1359,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o))]: (~ (member2052026769e_indi @ A @ (C)) | (member616898751_alt_o @ (B @ A) @ (D @ A)) | ~ (member811956313_alt_o @ (B) @ (pi_Arr1564509167_alt_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 32.06/9.10 thf(322,axiom,((~ (! [A:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ A) => (~ (member377231867_alt_o @ A @ arrow_823908191le_Lin)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_)). 32.06/9.10 thf(1724,plain,((~ (! [A:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (A)) => (~ (member377231867_alt_o @ (A) @ (arrow_823908191le_Lin))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 32.06/9.10 thf(354,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o),D:arrow_475358991le_alt]: ((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (arrow_55669061_mktop @ C @ D)) = (((B = D) => (A != B)) & ((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ C) <= (B != D)) & (A != D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_in__mktop)). 32.06/9.10 thf(1803,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o),D:arrow_475358991le_alt]: ((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (arrow_55669061_mktop @ C @ D)) = (((B = D) => (~ (A = B))) & ((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (C)) | (B = D)) & ~ (A = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 32.06/9.10 thf(267,axiom,((a != b)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75__096a_A_126_061_Ab_096)). 32.06/9.10 thf(1518,plain,((~ (a = b))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 32.06/9.10 thf(86,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_add__less__imp__less__right)). 32.06/9.10 thf(724,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 32.06/9.10 thf(315,axiom,((! [A:(produc1501160679le_alt > $o)]: ~ (ord_le988258430_alt_o @ top_to1841428258_alt_o @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__top__less)). 32.06/9.10 thf(1709,plain,((! [A:(produc1501160679le_alt > $o)]: ~ (ord_le988258430_alt_o @ (top_to1841428258_alt_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 32.06/9.10 thf(56,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_nat_Osimps_I2_J)). 32.06/9.10 thf(570,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 32.06/9.10 thf(251,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_termination__basic__simps_I3_J)). 32.06/9.10 thf(1430,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 32.06/9.10 thf(84,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ A @ C) <= (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_xt1_I10_J)). 32.06/9.10 thf(719,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 32.06/9.10 thf(105,axiom,((! [A:nat,B:nat,C:nat]: (((C = A) => (ord_less_nat @ B @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ord__less__eq__trans)). 32.06/9.10 thf(785,plain,((! [A:nat,B:nat,C:nat]: (((C = A) => (ord_less_nat @ B @ A)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 32.06/9.10 thf(379,axiom,((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (p @ (hilber598459244di_nat @ top_to988227749indi_o @ h @ n)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0)). 32.06/9.10 thf(1871,plain,((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (p @ (hilber598459244di_nat @ top_to988227749indi_o @ h @ n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])). 32.06/9.10 thf(193,axiom,(((image_484224243di_nat @ h @ top_to988227749indi_o) = (ord_at4362885an_nat @ zero_zero_nat @ (finite97476818e_indi @ top_to988227749indi_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_surjh)). 32.06/9.10 thf(1264,plain,(((image_484224243di_nat @ h @ top_to988227749indi_o) = (ord_at4362885an_nat @ zero_zero_nat @ (finite97476818e_indi @ top_to988227749indi_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 32.06/9.10 thf(265,axiom,((! [A:nat,B:nat,C:nat]: (((B = A) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_xt1_I2_J)). 32.06/9.10 thf(1511,plain,((! [A:nat,B:nat,C:nat]: (((B = A) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 32.06/9.10 thf(365,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:arrow_475358991le_alt,D:arrow_475358991le_alt]: (((B = D) & (A = C)) = ((produc1347929815le_alt @ A @ B) = (produc1347929815le_alt @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Pair__eq)). 32.06/9.10 thf(1826,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:arrow_475358991le_alt,D:arrow_475358991le_alt]: (((B = D) & (A = C)) = ((produc1347929815le_alt @ A @ B) = (produc1347929815le_alt @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 32.06/9.10 thf(200,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_not__add__less2)). 32.06/9.10 thf(1279,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 32.06/9.10 thf(367,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt]: ((? [C:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ C) & (member377231867_alt_o @ C @ arrow_823908191le_Lin))) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_complete__Lin)). 32.06/9.10 thf(1832,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt]: (? [C:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (C)) & (member377231867_alt_o @ (C) @ (arrow_823908191le_Lin))) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])). 32.06/9.10 thf(155,axiom,((! [A:product_unit,B:(product_unit > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))),C:(product_unit > $o),D:(product_unit > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o))]: ((member1536989448_alt_o @ B @ (pi_Pro1782982558_alt_o @ C @ D)) => ((~ (member616898751_alt_o @ (B @ A) @ (D @ A))) => (~ (member_Product_unit @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_PiE)). 32.06/9.10 thf(1059,plain,((! [A:product_unit,B:(product_unit > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))),C:(product_unit > $o),D:(product_unit > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o))]: ((member1536989448_alt_o @ (B) @ (pi_Pro1782982558_alt_o @ C @ D)) => ((~ (member616898751_alt_o @ (B @ A) @ (D @ A))) => (~ (member_Product_unit @ A @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 32.06/9.10 thf(277,axiom,((! [A:((produc1501160679le_alt > $o) > $o),B:(produc1501160679le_alt > $o),C:((produc1501160679le_alt > $o) > $o)]: (((ord_le1063113995lt_o_o @ C @ A) => (member377231867_alt_o @ B @ A)) <= (member377231867_alt_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_set__rev__mp)). 32.06/9.10 thf(1545,plain,((! [A:((produc1501160679le_alt > $o) > $o),B:(produc1501160679le_alt > $o),C:((produc1501160679le_alt > $o) > $o)]: (((ord_le1063113995lt_o_o @ (C) @ (A)) => (member377231867_alt_o @ (B) @ (A))) | ~ (member377231867_alt_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 32.06/9.10 thf(352,axiom,((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ (plus_plus_nat @ n @ one_one_nat)) @ lab @ lba))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_n_I3_J)). 32.06/9.10 thf(1800,plain,((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ (plus_plus_nat @ n @ one_one_nat)) @ lab @ lba))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 32.06/9.10 thf(78,axiom,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat),D:(arrow_1429601828e_indi > $o)]: ((inj_on978774663di_nat @ C @ D) => ((A != B) => ((member2052026769e_indi @ A @ D) => (((C @ A) != (C @ B)) <= (member2052026769e_indi @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_inj__on__contraD)). 32.06/9.10 thf(638,plain,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat),D:(arrow_1429601828e_indi > $o)]: ((inj_on978774663di_nat @ (C) @ (D)) => ((~ (A = B)) => ((member2052026769e_indi @ A @ (D)) => (~ ((C @ A) = (C @ B)) | ~ (member2052026769e_indi @ B @ (D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 32.06/9.10 thf(289,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((C = A) => (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_ord__le__eq__trans)). 32.06/9.10 thf(1572,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((C = A) => (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 32.06/9.10 thf(287,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_trans__less__add1)). 32.06/9.10 thf(1568,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ C @ A)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 32.06/9.10 thf(341,axiom,((arrow_797024463le_IIA @ f)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I3_J)). 32.06/9.10 thf(1773,plain,((arrow_797024463le_IIA @ (f))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 32.06/9.10 thf(21,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_add__Suc__right)). 32.06/9.10 thf(448,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 32.06/9.10 thf(381,axiom,((! [A:arrow_1429601828e_indi,B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: (((arrow_1212662430ctator @ B @ A) <= (! [C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((! [D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((D != E) => ((member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (B @ C)) <= (member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (C @ A))))) <= (member526088951_alt_o @ C @ arrow_734252939e_Prof)))) <= (member616898751_alt_o @ B @ (pi_Arr1304755663_alt_o @ arrow_734252939e_Prof @ (^ [C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (arrow_823908191le_Lin))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_dictatorI)). 32.06/9.10 thf(1875,plain,((! [A:arrow_1429601828e_indi,B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: ((arrow_1212662430ctator @ (B) @ A) | ~ (! [C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (! [D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((~ (D = E)) => ((member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (B @ C)) | ~ (member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (C @ A)))) | ~ (member526088951_alt_o @ (C) @ (arrow_734252939e_Prof)))) | ~ (member616898751_alt_o @ (B) @ (pi_Arr1304755663_alt_o @ arrow_734252939e_Prof @ (^ [C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (arrow_823908191le_Lin))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])). 32.06/9.10 thf(166,axiom,((! [A:$o,B:nat,C:nat]: (((A) <= (ord_less_nat @ C @ B)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_order__less__imp__triv)). 32.06/9.10 thf(1100,plain,((! [A:$o,B:nat,C:nat]: ((A) | ~ (ord_less_nat @ C @ B) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 32.06/9.10 thf(11,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (A = B)) <= (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_less__SucE)). 32.06/9.10 thf(421,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (A = B)) | ~ (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 32.06/9.10 thf(384,axiom,((! [A:arrow_1429601828e_indi]: ((((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ lab) <= (ord_less_nat @ (h @ A) @ n)) & ((~ (ord_less_nat @ (h @ A) @ n)) => (member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ lba))) = (((ord_less_nat @ (h @ A) @ n) => (member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (arrow_55669061_mktop @ (p @ A) @ e))) & (((((h @ A) != n) => (member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (arrow_2054445623_mkbot @ (p @ A) @ e))) & ((member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (arrow_789600939_above @ (p @ A) @ c @ e)) <= ((h @ A) = n))) <= (~ (ord_less_nat @ (h @ A) @ n))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk)). 32.06/9.10 thf(1890,plain,((! [A:arrow_1429601828e_indi]: ((((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (lab)) | ~ (ord_less_nat @ (h @ A) @ n)) & ((~ (ord_less_nat @ (h @ A) @ n)) => (member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (lba)))) = (((ord_less_nat @ (h @ A) @ n) => (member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (arrow_55669061_mktop @ (p @ A) @ e))) & ((((~ ((h @ A) = n)) => (member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (arrow_2054445623_mkbot @ (p @ A) @ e))) & ((member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (arrow_789600939_above @ (p @ A) @ c @ e)) | ~ ((h @ A) = n))) | (ord_less_nat @ (h @ A) @ n)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])). 32.06/9.10 thf(138,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((produc1501160679le_alt > $o) > $o)]: (((member526088951_alt_o @ A @ C) => (member377231867_alt_o @ (B @ A) @ D)) <= (member616898751_alt_o @ B @ (pi_Arr1304755663_alt_o @ C @ (^ [E:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_funcset__mem)). 32.06/9.10 thf(1013,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((produc1501160679le_alt > $o) > $o)]: (((member526088951_alt_o @ (A) @ (C)) => (member377231867_alt_o @ (B @ A) @ (D))) | ~ (member616898751_alt_o @ (B) @ (pi_Arr1304755663_alt_o @ C @ (^ [E:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 32.06/9.10 thf(99,axiom,((! [A:nat,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat),D:(arrow_1429601828e_indi > $o)]: (((member2052026769e_indi @ B @ D) => (((C @ B) = A) => ((hilber598459244di_nat @ D @ C @ A) = B))) <= (inj_on978774663di_nat @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_inv__into__f__eq)). 32.06/9.10 thf(770,plain,((! [A:nat,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat),D:(arrow_1429601828e_indi > $o)]: (((member2052026769e_indi @ B @ (D)) => (((C @ B) = A) => ((hilber598459244di_nat @ (D) @ (C) @ A) = B))) | ~ (inj_on978774663di_nat @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 32.06/9.10 thf(242,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_order__less__irrefl)). 32.06/9.10 thf(1398,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 32.06/9.10 thf(117,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ B @ A) <= (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_linorder__cases)). 32.06/9.10 thf(881,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 32.06/9.10 thf(9,axiom,((! [A:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((! [C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: ((member616898751_alt_o @ C @ B) => (member616898751_alt_o @ C @ A))) => (ord_le134800455lt_o_o @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_subsetI)). 32.06/9.10 thf(416,plain,((! [A:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((! [C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: ((member616898751_alt_o @ (C) @ (B)) => (member616898751_alt_o @ (C) @ (A)))) => (ord_le134800455lt_o_o @ (B) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 32.06/9.10 thf(208,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_termination__basic__simps_I4_J)). 32.06/9.10 thf(1302,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 32.06/9.10 thf(317,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_add__leD1)). 32.06/9.10 thf(1714,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 32.06/9.10 thf(106,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_less__add__Suc1)). 32.06/9.10 thf(789,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 32.06/9.10 thf(357,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:($o > $o)]: (((member_o @ (B @ A) @ D) <= (member214075476le_alt @ A @ C)) <= (member377231867_alt_o @ B @ (pi_Pro1701359055_alt_o @ C @ (^ [E:produc1501160679le_alt]: (D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_funcset__mem)). 32.06/9.10 thf(1811,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:($o > $o)]: ((member_o @ (B @ A) @ (D)) | ~ (member214075476le_alt @ A @ (C)) | ~ (member377231867_alt_o @ (B) @ (pi_Pro1701359055_alt_o @ C @ (^ [E:produc1501160679le_alt]: (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 32.06/9.10 thf(375,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o)]: ((B @ A) = (member214075476le_alt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_mem__def)). 32.06/9.10 thf(1858,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o)]: ((B @ A) = (member214075476le_alt @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 32.06/9.10 thf(57,axiom,((~ (! [A:(arrow_1429601828e_indi > nat)]: ((inj_on978774663di_nat @ A @ top_to988227749indi_o) => ((image_484224243di_nat @ A @ top_to988227749indi_o) != (ord_at4362885an_nat @ zero_zero_nat @ (finite97476818e_indi @ top_to988227749indi_o))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123)). 32.06/9.10 thf(574,plain,((~ (! [A:(arrow_1429601828e_indi > nat)]: ((inj_on978774663di_nat @ (A) @ (top_to988227749indi_o)) => (~ ((image_484224243di_nat @ A @ top_to988227749indi_o) = (ord_at4362885an_nat @ zero_zero_nat @ (finite97476818e_indi @ top_to988227749indi_o)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 32.06/9.10 thf(173,axiom,((! [A:(produc1501160679le_alt > ($o > $o)),B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ B @ C) => (ord_le1063113995lt_o_o @ (pi_Pro1701359055_alt_o @ C @ A) @ (pi_Pro1701359055_alt_o @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Pi__anti__mono)). 32.06/9.10 thf(1183,plain,((! [A:(produc1501160679le_alt > ($o > $o)),B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ (B) @ (C)) => (ord_le1063113995lt_o_o @ (pi_Pro1701359055_alt_o @ C @ A) @ (pi_Pro1701359055_alt_o @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 32.06/9.10 thf(152,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((member616898751_alt_o @ A @ (pi_Arr1304755663_alt_o @ C @ B)) <= (! [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member526088951_alt_o @ D @ C) => (member377231867_alt_o @ (A @ D) @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_Pi__I_H)). 32.06/9.10 thf(1051,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((member616898751_alt_o @ (A) @ (pi_Arr1304755663_alt_o @ C @ B)) | ~ (! [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member526088951_alt_o @ (D) @ (C)) => (member377231867_alt_o @ (A @ D) @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 32.06/9.10 thf(235,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_leD)). 32.06/9.10 thf(1373,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 32.06/9.10 thf(19,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: (((member616898751_alt_o @ A @ B) => (member616898751_alt_o @ A @ C)) <= (ord_le134800455lt_o_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_in__mono)). 32.06/9.10 thf(443,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: (((member616898751_alt_o @ (A) @ (B)) => (member616898751_alt_o @ (A) @ (C))) | ~ (ord_le134800455lt_o_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 32.06/9.10 thf(147,axiom,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o)]: ((ord_le1063113995lt_o_o @ B @ C) => ((member377231867_alt_o @ A @ B) => (member377231867_alt_o @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_subsetD)). 32.06/9.10 thf(1040,plain,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o)]: ((ord_le1063113995lt_o_o @ (B) @ (C)) => ((member377231867_alt_o @ (A) @ (B)) => (member377231867_alt_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 32.06/9.10 thf(168,axiom,((! [A:$o,B:($o > $o),C:($o > $o)]: ((ord_less_o_o @ B @ C) => ((member_o @ A @ C) <= (member_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_psubsetD)). 32.06/9.10 thf(1109,plain,((! [A:$o,B:($o > $o),C:($o > $o)]: ((ord_less_o_o @ (B) @ (C)) => ((member_o @ A @ (C)) | ~ (member_o @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 32.06/9.10 thf(127,axiom,((! [A:nat,B:nat]: (((A = B) | (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_le__eq__less__or__eq)). 32.06/9.10 thf(981,plain,((! [A:nat,B:nat]: (((A = B) | (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 32.06/9.10 thf(237,axiom,((finite664979089e_indi @ top_to988227749indi_o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_finite__indi)). 32.06/9.10 thf(1377,plain,((finite664979089e_indi @ (top_to988227749indi_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 32.06/9.10 thf(100,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_add__leD2)). 32.06/9.10 thf(774,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 32.06/9.10 thf(240,axiom,((arrow_734252939e_Prof = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ (^ [A:arrow_1429601828e_indi]: (arrow_823908191le_Lin))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_Prof__def)). 32.06/9.10 thf(1394,plain,(((arrow_734252939e_Prof) = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ (^ [A:arrow_1429601828e_indi]: (arrow_823908191le_Lin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 32.06/9.10 thf(129,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o))]: ((member526088951_alt_o @ B @ (pi_Arr1929480907_alt_o @ C @ D)) => ((member2052026769e_indi @ A @ C) => (member377231867_alt_o @ (B @ A) @ (D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_Pi__mem)). 32.06/9.10 thf(988,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o))]: ((member526088951_alt_o @ (B) @ (pi_Arr1929480907_alt_o @ C @ D)) => ((member2052026769e_indi @ A @ (C)) => (member377231867_alt_o @ (B @ A) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 32.06/9.10 thf(311,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o))]: ((member1234151027_alt_o @ B @ (pi_Arr1060328391_alt_o @ C @ D)) => ((~ (member2052026769e_indi @ A @ C)) <= (~ (member526088951_alt_o @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_PiE)). 32.06/9.10 thf(1697,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o))]: ((member1234151027_alt_o @ (B) @ (pi_Arr1060328391_alt_o @ C @ D)) => (~ (member2052026769e_indi @ A @ (C)) | (member526088951_alt_o @ (B @ A) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 32.06/9.10 thf(268,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:(arrow_1429601828e_indi > $o),D:((produc1501160679le_alt > $o) > $o)]: (((member2052026769e_indi @ A @ C) => (member377231867_alt_o @ (B @ A) @ D)) <= (member526088951_alt_o @ B @ (pi_Arr1929480907_alt_o @ C @ (^ [E:arrow_1429601828e_indi]: (D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_funcset__mem)). 32.06/9.10 thf(1521,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:(arrow_1429601828e_indi > $o),D:((produc1501160679le_alt > $o) > $o)]: (((member2052026769e_indi @ A @ (C)) => (member377231867_alt_o @ (B @ A) @ (D))) | ~ (member526088951_alt_o @ (B) @ (pi_Arr1929480907_alt_o @ C @ (^ [E:arrow_1429601828e_indi]: (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 32.06/9.10 thf(38,axiom,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat),D:(arrow_1429601828e_indi > $o)]: (((((A = B) <= (member2052026769e_indi @ B @ D)) <= (member2052026769e_indi @ A @ D)) <= ((C @ A) = (C @ B))) <= (inj_on978774663di_nat @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_inj__onD)). 32.06/9.10 thf(507,plain,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat),D:(arrow_1429601828e_indi > $o)]: ((A = B) | ~ (member2052026769e_indi @ B @ (D)) | ~ (member2052026769e_indi @ A @ (D)) | ~ ((C @ A) = (C @ B)) | ~ (inj_on978774663di_nat @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 32.06/9.10 thf(43,axiom,((! [A:(arrow_1429601828e_indi > nat),B:(arrow_1429601828e_indi > nat),C:(arrow_1429601828e_indi > $o)]: ((! [D:arrow_1429601828e_indi]: ((member2052026769e_indi @ D @ C) => ((A @ D) = (B @ D)))) => ((inj_on978774663di_nat @ A @ C) = (inj_on978774663di_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_inj__on__cong)). 32.06/9.10 thf(527,plain,((! [A:(arrow_1429601828e_indi > nat),B:(arrow_1429601828e_indi > nat),C:(arrow_1429601828e_indi > $o)]: ((! [D:arrow_1429601828e_indi]: ((member2052026769e_indi @ D @ (C)) => ((A @ D) = (B @ D)))) => ((inj_on978774663di_nat @ (A) @ (C)) = (inj_on978774663di_nat @ (B) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 32.06/9.10 thf(187,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((ord_le134800455lt_o_o @ (pi_Arr1304755663_alt_o @ C @ A) @ (pi_Arr1304755663_alt_o @ C @ B)) <= (! [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((ord_le1063113995lt_o_o @ (A @ D) @ (B @ D)) <= (member526088951_alt_o @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_Pi__mono)). 32.06/9.10 thf(1215,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((ord_le134800455lt_o_o @ (pi_Arr1304755663_alt_o @ C @ A) @ (pi_Arr1304755663_alt_o @ C @ B)) | ~ (! [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((ord_le1063113995lt_o_o @ (A @ D) @ (B @ D)) | ~ (member526088951_alt_o @ (D) @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 32.06/9.10 thf(76,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_zero__less__Suc)). 32.06/9.10 thf(634,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 32.06/9.10 thf(387,axiom,((member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)). 32.06/9.10 thf(1896,plain,((member214075476le_alt @ (produc1347929815le_alt @ e @ d) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])). 32.06/9.10 thf(115,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_order__refl)). 32.06/9.10 thf(877,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 32.06/9.10 thf(4,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_add__eq__self__zero)). 32.06/9.10 thf(396,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 32.06/9.10 thf(270,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_order__less__imp__not__eq2)). 32.06/9.10 thf(1526,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 32.06/9.10 thf(377,axiom,((! [A:(produc1501160679le_alt > ($o > $o)),B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > $o)]: (((member377231867_alt_o @ B @ (pi_Pro1701359055_alt_o @ D @ A)) = (member377231867_alt_o @ C @ (pi_Pro1701359055_alt_o @ D @ A))) <= (! [E:produc1501160679le_alt]: ((member214075476le_alt @ E @ D) => ((C @ E) = (B @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_Pi__cong)). 32.06/9.10 thf(1863,plain,((! [A:(produc1501160679le_alt > ($o > $o)),B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > $o)]: (((member377231867_alt_o @ (B) @ (pi_Pro1701359055_alt_o @ D @ A)) = (member377231867_alt_o @ (C) @ (pi_Pro1701359055_alt_o @ D @ A))) | ~ (! [E:produc1501160679le_alt]: ((member214075476le_alt @ E @ (D)) => ((C @ E) = (B @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 32.06/9.10 thf(300,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((produc1501160679le_alt > $o) > $o),C:(arrow_1429601828e_indi > $o)]: ((member526088951_alt_o @ A @ (pi_Arr1929480907_alt_o @ C @ (^ [D:arrow_1429601828e_indi]: (B)))) <= (! [D:arrow_1429601828e_indi]: ((member377231867_alt_o @ (A @ D) @ B) <= (member2052026769e_indi @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_funcsetI)). 32.06/9.10 thf(1604,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((produc1501160679le_alt > $o) > $o),C:(arrow_1429601828e_indi > $o)]: ((member526088951_alt_o @ (A) @ (pi_Arr1929480907_alt_o @ C @ (^ [D:arrow_1429601828e_indi]: (B)))) | ~ (! [D:arrow_1429601828e_indi]: ((member377231867_alt_o @ (A @ D) @ (B)) | ~ (member2052026769e_indi @ D @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 32.06/9.10 thf(183,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > product_unit),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (product_unit > $o))]: (((~ (member526088951_alt_o @ A @ C)) <= (~ (member_Product_unit @ (B @ A) @ (D @ A)))) <= (member843528338t_unit @ B @ (pi_Arr1963174508t_unit @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_PiE)). 32.06/9.10 thf(1206,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > product_unit),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (product_unit > $o))]: (~ (member526088951_alt_o @ (A) @ (C)) | (member_Product_unit @ (B @ (A)) @ (D @ A)) | ~ (member843528338t_unit @ (B) @ (pi_Arr1963174508t_unit @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 32.06/9.10 thf(254,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) <= (A != B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_le__neq__implies__less)). 32.06/9.10 thf(1438,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 32.06/9.10 thf(108,axiom,((! [A:nat]: ((ord_less_nat @ A) = (ord_less_eq_nat @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_less__eq__Suc__le__raw)). 32.06/9.10 thf(793,plain,((! [A:nat]: ((ord_less_nat @ A) = (ord_less_eq_nat @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 32.06/9.10 thf(210,axiom,((! [A:(produc1501160679le_alt > $o)]: ((ord_le988258430_alt_o @ A @ top_to1841428258_alt_o) = (A != top_to1841428258_alt_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__top)). 32.06/9.10 thf(1306,plain,((! [A:(produc1501160679le_alt > $o)]: ((ord_le988258430_alt_o @ (A) @ (top_to1841428258_alt_o)) = (~ ((A) = (top_to1841428258_alt_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 32.06/9.10 thf(221,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ C)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_trans__less__add2)). 32.06/9.10 thf(1338,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ C)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 32.06/9.10 thf(158,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A)) = (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_nat__neq__iff)). 32.06/9.10 thf(1067,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A)) = (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 32.06/9.10 thf(378,axiom,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > ($o > $o)),C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ A @ (pi_Pro1701359055_alt_o @ C @ B)) <= (! [D:produc1501160679le_alt]: ((member_o @ (A @ D) @ (B @ D)) <= (member214075476le_alt @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_Pi__I_H)). 32.06/9.10 thf(1868,plain,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > ($o > $o)),C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ (A) @ (pi_Pro1701359055_alt_o @ C @ B)) | ~ (! [D:produc1501160679le_alt]: ((member_o @ (A @ D) @ (B @ D)) | ~ (member214075476le_alt @ D @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 32.06/9.10 thf(324,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > produc1501160679le_alt),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member351225838le_alt @ B @ (pi_Arr329216900le_alt @ C @ D)) => ((~ (member2052026769e_indi @ A @ C)) <= (~ (member214075476le_alt @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_PiE)). 32.06/9.10 thf(1730,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > produc1501160679le_alt),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member351225838le_alt @ (B) @ (pi_Arr329216900le_alt @ C @ D)) => (~ (member2052026769e_indi @ A @ (C)) | (member214075476le_alt @ (B @ A) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 32.06/9.10 thf(198,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) => ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)) <= (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_add__strict__mono)). 32.06/9.10 thf(1274,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) => ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)) | ~ (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 32.06/9.10 thf(190,axiom,((! [A:($o > $o),B:($o > $o)]: ((ord_less_eq_o_o @ (^ [C:$o]: (member_o @ C @ A)) @ (^ [C:$o]: (member_o @ C @ B))) = (ord_less_eq_o_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_pred__subset__eq)). 32.06/9.10 thf(1223,plain,((! [A:($o > $o),B:($o > $o)]: ((ord_less_eq_o_o @ (^ [C:$o]: (member_o @ C @ A)) @ (^ [C:$o]: (member_o @ C @ B))) = (ord_less_eq_o_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 32.06/9.10 thf(148,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_add__less__imp__less__left)). 32.06/9.10 thf(1042,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 32.06/9.10 thf(64,axiom,((! [A:nat,B:nat]: (((A = (suc @ B)) | (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_le__Suc__eq)). 32.06/9.10 thf(598,plain,((! [A:nat,B:nat]: (((A = (suc @ B)) | (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 32.06/9.10 thf(332,axiom,((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ lab)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096)). 32.06/9.10 thf(1751,plain,((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (lab))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 32.06/9.10 thf(12,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((ord_le134800455lt_o_o @ B @ C) => ((member616898751_alt_o @ A @ B) => (member616898751_alt_o @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_subsetD)). 32.06/9.10 thf(424,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((ord_le134800455lt_o_o @ (B) @ (C)) => ((member616898751_alt_o @ (A) @ (B)) => (member616898751_alt_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 32.06/9.10 thf(6,axiom,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat),D:(arrow_1429601828e_indi > $o)]: ((inj_on978774663di_nat @ C @ D) => (((member2052026769e_indi @ A @ D) => ((B = A) = ((C @ B) = (C @ A)))) <= (member2052026769e_indi @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_inj__on__iff)). 32.06/9.10 thf(407,plain,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat),D:(arrow_1429601828e_indi > $o)]: ((inj_on978774663di_nat @ (C) @ (D)) => (((member2052026769e_indi @ A @ (D)) => ((B = A) = ((C @ B) = (C @ A)))) | ~ (member2052026769e_indi @ B @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 32.06/9.10 thf(88,axiom,((! [A:($o > produc1501160679le_alt),B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:($o > $o)]: (((inj_on1911943593_alt_o @ B @ C) => ((member492167345le_alt @ A @ (pi_o_P657324555le_alt @ D @ (^ [E:$o]: (C)))) => (((finite449174868le_alt @ C) => (((finite537683861le_alt @ C) = (finite_card_o @ D)) <= (finite_finite_o @ D))) <= (inj_on867909093le_alt @ A @ D)))) <= (member377231867_alt_o @ B @ (pi_Pro1701359055_alt_o @ C @ (^ [E:produc1501160679le_alt]: (D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_card__bij)). 32.06/9.10 thf(729,plain,((! [A:($o > produc1501160679le_alt),B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:($o > $o)]: (((inj_on1911943593_alt_o @ (B) @ (C)) => ((member492167345le_alt @ (A) @ (pi_o_P657324555le_alt @ D @ (^ [E:$o]: (C)))) => (((finite449174868le_alt @ (C)) => (((finite537683861le_alt @ (C)) = (finite_card_o @ (D))) | ~ (finite_finite_o @ (D)))) | ~ (inj_on867909093le_alt @ (A) @ (D))))) | ~ (member377231867_alt_o @ (B) @ (pi_Pro1701359055_alt_o @ C @ (^ [E:produc1501160679le_alt]: (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 32.06/9.10 thf(383,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:arrow_475358991le_alt,D:arrow_475358991le_alt]: ((~ ((A = C) => (B != D))) <= ((produc1347929815le_alt @ A @ B) = (produc1347929815le_alt @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Pair__inject)). 32.06/9.10 thf(1883,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:arrow_475358991le_alt,D:arrow_475358991le_alt]: (~ ((A = C) => (~ (B = D))) | ~ ((produc1347929815le_alt @ A @ B) = (produc1347929815le_alt @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])). 32.06/9.10 thf(389,axiom,((! [A:(produc1501160679le_alt > $o)]: ((all @ A) = (! [B:arrow_475358991le_alt,C:arrow_475358991le_alt]: (A @ (produc1347929815le_alt @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_split__paired__All)). 32.06/9.10 thf(1900,plain,((! [A:(produc1501160679le_alt > $o)]: ((all @ (A)) = (! [B:arrow_475358991le_alt,C:arrow_475358991le_alt]: (A @ (produc1347929815le_alt @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 32.06/9.10 thf(321,axiom,((member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)). 32.06/9.10 thf(1723,plain,((member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 32.06/9.10 thf(95,axiom,((! [A:$o]: (member_o @ A @ top_top_o_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_UNIV__I)). 32.06/9.10 thf(746,plain,((! [A:$o]: (member_o @ A @ (top_top_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 32.06/9.10 thf(163,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ($o > $o))]: ((member939334982lt_o_o @ B @ (pi_Arr952516694lt_o_o @ C @ D)) => ((~ (member526088951_alt_o @ A @ C)) <= (~ (member_o @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_PiE)). 32.06/9.10 thf(1091,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ($o > $o))]: ((member939334982lt_o_o @ (B) @ (pi_Arr952516694lt_o_o @ C @ D)) => (~ (member526088951_alt_o @ (A) @ (C)) | (member_o @ (B @ (A)) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 32.06/9.10 thf(141,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_xt1_I9_J)). 32.06/9.10 thf(1021,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 32.06/9.10 thf(102,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_nat__le__linear)). 32.06/9.10 thf(778,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 32.06/9.10 thf(229,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) => ((ord_less_eq_nat @ A @ C) => (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_xt1_I3_J)). 32.06/9.10 thf(1355,plain,((! [A:nat,B:nat,C:nat]: ((B = C) => ((ord_less_eq_nat @ A @ C) => (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 32.06/9.10 thf(292,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_less__imp__neq)). 32.06/9.10 thf(1580,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 32.06/9.10 thf(288,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_add__left__mono)). 32.06/9.10 thf(1570,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 32.06/9.10 thf(169,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > nat)]: (((hilber598459244di_nat @ top_to988227749indi_o @ B @ (B @ A)) = A) <= (inj_on978774663di_nat @ B @ top_to988227749indi_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inv__f__f)). 32.06/9.10 thf(1174,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > nat)]: (((hilber598459244di_nat @ (top_to988227749indi_o) @ (B) @ (B @ A)) = A) | ~ (inj_on978774663di_nat @ (B) @ (top_to988227749indi_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 32.06/9.10 thf(363,axiom,((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)). 32.06/9.10 thf(1824,plain,((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])). 32.06/9.10 thf(305,axiom,((! [A:$o,B:($o > $o),C:($o > $o)]: ((ord_less_eq_o_o @ B @ C) => ((member_o @ A @ C) <= (member_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_set__mp)). 32.06/9.10 thf(1619,plain,((! [A:$o,B:($o > $o),C:($o > $o)]: ((ord_less_eq_o_o @ (B) @ (C)) => ((member_o @ A @ (C)) | ~ (member_o @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 32.06/9.10 thf(234,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_add__le__cancel__left)). 32.06/9.10 thf(1370,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 32.06/9.10 thf(248,axiom,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o)]: (((member377231867_alt_o @ A @ B) => (member377231867_alt_o @ A @ C)) <= (ord_le1063113995lt_o_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_set__mp)). 32.06/9.10 thf(1423,plain,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o)]: (((member377231867_alt_o @ (A) @ (B)) => (member377231867_alt_o @ (A) @ (C))) | ~ (ord_le1063113995lt_o_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 32.06/9.10 thf(116,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: (((member526088951_alt_o @ A @ B) => (member526088951_alt_o @ A @ C)) <= (ord_le157835011lt_o_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_psubsetD)). 32.06/9.10 thf(879,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: (((member526088951_alt_o @ (A) @ (B)) => (member526088951_alt_o @ (A) @ (C))) | ~ (ord_le157835011lt_o_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 32.06/9.10 thf(59,axiom,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat)]: (((A = B) = ((C @ A) = (C @ B))) <= (inj_on978774663di_nat @ C @ top_to988227749indi_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_inj__eq)). 32.06/9.10 thf(583,plain,((! [A:arrow_1429601828e_indi,B:arrow_1429601828e_indi,C:(arrow_1429601828e_indi > nat)]: (((A = B) = ((C @ A) = (C @ B))) | ~ (inj_on978774663di_nat @ (C) @ (top_to988227749indi_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 32.06/9.10 thf(348,axiom,((? [A:nat]: ((ord_less_nat @ A @ (finite97476818e_indi @ top_to988227749indi_o)) & ! [B:nat]: ((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (f @ (^ [C:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ C) @ B) @ lab @ lba)))) <= (ord_less_eq_nat @ B @ A)) & (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (f @ (^ [B:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ B) @ (plus_plus_nat @ A @ one_one_nat)) @ lab @ lba))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I)). 32.06/9.10 thf(1787,plain,((? [A:nat]: ((ord_less_nat @ A @ (finite97476818e_indi @ (top_to988227749indi_o))) & ! [B:nat]: ((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (f @ (^ [C:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ C) @ B) @ lab @ lba)))) | ~ (ord_less_eq_nat @ B @ A)) & (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (f @ (^ [B:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ B) @ (plus_plus_nat @ A @ one_one_nat)) @ lab @ lba))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 32.06/9.10 thf(185,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_termination__basic__simps_I1_J)). 32.06/9.10 thf(1210,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ C @ A)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 32.06/9.10 thf(143,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_linorder__le__cases)). 32.06/9.10 thf(1027,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 32.06/9.10 thf(245,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (ord_less_eq_nat @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_xt1_I12_J)). 32.06/9.10 thf(1407,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | ~ (ord_less_eq_nat @ B @ A) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 32.06/9.10 thf(50,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_le__SucI)). 32.06/9.10 thf(551,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 32.06/9.10 thf(205,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((B @ A) = (member616898751_alt_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_mem__def)). 32.06/9.10 thf(1291,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((B @ (A)) = (member616898751_alt_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 32.06/9.10 thf(124,axiom,((! [A:arrow_1429601828e_indi]: (top_to988227749indi_o @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_top1I)). 32.06/9.10 thf(974,plain,((! [A:arrow_1429601828e_indi]: (top_to988227749indi_o @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 32.06/9.10 thf(167,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) = (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_order__antisym__conv)). 32.06/9.10 thf(1106,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) = (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 32.06/9.10 thf(55,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_n__not__Suc__n)). 32.06/9.10 thf(566,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 32.06/9.10 thf(33,axiom,((! [A:(nat > $o),B:nat]: (((A @ zero_zero_nat) <= (! [C:nat]: ((A @ C) <= (A @ (suc @ C))))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_zero__induct)). 32.06/9.10 thf(484,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) | ~ (! [C:nat]: ((A @ C) | ~ (A @ (suc @ C)))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 32.06/9.10 thf(145,axiom,((! [A:product_unit,B:(product_unit > $o)]: ((B @ A) = (member_Product_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_mem__def)). 32.06/9.10 thf(1032,plain,((! [A:product_unit,B:(product_unit > $o)]: ((B @ A) = (member_Product_unit @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 32.06/9.10 thf(368,axiom,(((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ (plus_plus_nat @ n @ one_one_nat)) @ lab @ lba)))) = (member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am)). 32.06/9.10 thf(1837,plain,(((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ (plus_plus_nat @ n @ one_one_nat)) @ lab @ lba)))) = (member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 32.06/9.10 thf(299,axiom,((! [A:arrow_1429601828e_indi]: (member2052026769e_indi @ A @ top_to988227749indi_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_UNIV__I)). 32.06/9.10 thf(1602,plain,((! [A:arrow_1429601828e_indi]: (member2052026769e_indi @ A @ (top_to988227749indi_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 32.06/9.10 thf(281,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_less__irrefl__nat)). 32.06/9.10 thf(1555,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 32.06/9.10 thf(16,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_less__zeroE)). 32.06/9.10 thf(435,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 32.06/9.10 thf(227,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_add__le__imp__le__right)). 32.06/9.10 thf(1350,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 32.06/9.10 thf(114,axiom,((! [A:nat,B:nat]: ((A = B) = ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_order__eq__iff)). 32.06/9.10 thf(874,plain,((! [A:nat,B:nat]: ((A = B) = ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 32.06/9.10 thf(196,axiom,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o),D:((produc1501160679le_alt > $o) > ($o > $o))]: ((member1961363906lt_o_o @ B @ (pi_Pro422690258lt_o_o @ C @ D)) => ((~ (member377231867_alt_o @ A @ C)) <= (~ (member_o @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_PiE)). 32.06/9.10 thf(1270,plain,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o),D:((produc1501160679le_alt > $o) > ($o > $o))]: ((member1961363906lt_o_o @ (B) @ (pi_Pro422690258lt_o_o @ C @ D)) => (~ (member377231867_alt_o @ (A) @ (C)) | (member_o @ (B @ (A)) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 32.06/9.10 thf(236,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_xt1_I7_J)). 32.06/9.10 thf(1375,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 32.06/9.10 thf(157,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) = ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_add__left__cancel)). 32.06/9.10 thf(1064,plain,((! [A:nat,B:nat,C:nat]: ((B = C) = ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 32.06/9.10 thf(249,axiom,((! [A:(produc1501160679le_alt > $o)]: (ord_le97612146_alt_o @ A @ top_to1841428258_alt_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_top__greatest)). 32.06/9.10 thf(1425,plain,((! [A:(produc1501160679le_alt > $o)]: (ord_le97612146_alt_o @ (A) @ (top_to1841428258_alt_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 32.06/9.10 thf(136,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_add__left__imp__eq)). 32.06/9.10 thf(1006,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 32.06/9.10 thf(62,axiom,((one_one_nat = (suc @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_One__nat__def)). 32.06/9.10 thf(593,plain,((one_one_nat = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 32.06/9.10 thf(104,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_xt1_I6_J)). 32.06/9.10 thf(783,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 32.06/9.10 thf(162,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ A) <= (ord_less_eq_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_order__less__le__trans)). 32.06/9.10 thf(1089,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ A) | ~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 32.06/9.10 thf(275,axiom,((! [A:arrow_1429601828e_indi]: (member2052026769e_indi @ A @ top_to988227749indi_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I)). 32.06/9.10 thf(1541,plain,((! [A:arrow_1429601828e_indi]: (member2052026769e_indi @ A @ (top_to988227749indi_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 32.06/9.10 thf(272,axiom,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o)]: ((ord_le1063113995lt_o_o @ B @ C) => ((member377231867_alt_o @ A @ C) <= (member377231867_alt_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_in__mono)). 32.06/9.10 thf(1534,plain,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o),C:((produc1501160679le_alt > $o) > $o)]: ((ord_le1063113995lt_o_o @ (B) @ (C)) => ((member377231867_alt_o @ (A) @ (C)) | ~ (member377231867_alt_o @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 32.06/9.10 thf(350,axiom,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > ($o > $o)),C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ A @ (pi_Pro1701359055_alt_o @ C @ B)) <= (! [D:produc1501160679le_alt]: ((member214075476le_alt @ D @ C) => (member_o @ (A @ D) @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_Pi__I)). 32.06/9.10 thf(1794,plain,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > ($o > $o)),C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ (A) @ (pi_Pro1701359055_alt_o @ C @ B)) | ~ (! [D:produc1501160679le_alt]: ((member214075476le_alt @ D @ (C)) => (member_o @ (A @ D) @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 32.06/9.10 thf(259,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_less__not__refl3)). 32.06/9.10 thf(1493,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 32.06/9.10 thf(231,axiom,((! [A:nat,B:nat]: (((A = B) | (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_order__le__less)). 32.06/9.10 thf(1361,plain,((! [A:nat,B:nat]: (((A = B) | (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 32.06/9.10 thf(172,axiom,((member377231867_alt_o @ lab @ arrow_823908191le_Lin)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73__096Lab_A_058_ALin_096)). 32.06/9.10 thf(1182,plain,((member377231867_alt_o @ (lab) @ (arrow_823908191le_Lin))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 32.06/9.10 thf(31,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_not__less0)). 32.06/9.10 thf(476,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 32.06/9.10 thf(370,axiom,((c != d)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096)). 32.06/9.10 thf(1842,plain,((~ (c = d))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])). 32.06/9.10 thf(293,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_order__eq__refl)). 32.06/9.10 thf(1584,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 32.06/9.10 thf(349,axiom,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ A @ B) = (ord_le97612146_alt_o @ (^ [C:produc1501160679le_alt]: (member214075476le_alt @ C @ A)) @ (^ [C:produc1501160679le_alt]: (member214075476le_alt @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_pred__subset__eq)). 32.06/9.10 thf(1791,plain,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ (A) @ (B)) = (ord_le97612146_alt_o @ (^ [C:produc1501160679le_alt]: (member214075476le_alt @ C @ A)) @ (^ [C:produc1501160679le_alt]: (member214075476le_alt @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 32.06/9.10 thf(257,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_add__strict__left__mono)). 32.06/9.10 thf(1446,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 32.06/9.10 thf(61,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((A = B) = (ord_less_nat @ A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_not__less__less__Suc__eq)). 32.06/9.10 thf(590,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((A = B) = (ord_less_nat @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 32.06/9.10 thf(118,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_less__iff__Suc__add)). 32.06/9.10 thf(884,plain,((! [A:nat,B:nat]: ((? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 32.06/9.10 thf(217,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > product_unit),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),D:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > (product_unit > $o))]: ((member1924666376t_unit @ B @ (pi_Arr830584606t_unit @ C @ D)) => ((~ (member616898751_alt_o @ A @ C)) <= (~ (member_Product_unit @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_PiE)). 32.06/9.10 thf(1329,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > product_unit),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),D:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > (product_unit > $o))]: ((member1924666376t_unit @ (B) @ (pi_Arr830584606t_unit @ C @ D)) => (~ (member616898751_alt_o @ (A) @ (C)) | (member_Product_unit @ (B @ (A)) @ (D @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 32.06/9.10 thf(328,axiom,((~ (! [A:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ A) => (~ (member377231867_alt_o @ A @ arrow_823908191le_Lin)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_)). 32.06/9.10 thf(1739,plain,((~ (! [A:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (A)) => (~ (member377231867_alt_o @ (A) @ (arrow_823908191le_Lin))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 32.06/9.10 thf(46,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_gr__implies__not0)). 32.06/9.10 thf(537,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 32.06/9.10 thf(72,axiom,((! [A:nat]: ((suc @ A) != A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_Suc__n__not__n)). 32.06/9.10 thf(622,plain,((! [A:nat]: ~ ((suc @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 32.06/9.10 thf(81,axiom,((! [A:($o > $o),B:$o,C:($o > $o)]: (((ord_less_eq_o_o @ C @ A) => (member_o @ B @ A)) <= (member_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_set__rev__mp)). 32.06/9.10 thf(647,plain,((! [A:($o > $o),B:$o,C:($o > $o)]: (((ord_less_eq_o_o @ (C) @ (A)) => (member_o @ B @ (A))) | ~ (member_o @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 32.06/9.10 thf(294,axiom,((! [A:nat,B:nat]: ((A != B) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_linorder__neqE__nat)). 32.06/9.10 thf(1588,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 32.06/9.10 thf(92,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_le__antisym)). 32.06/9.10 thf(738,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 32.06/9.10 thf(194,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_linorder__le__less__linear)). 32.06/9.10 thf(1266,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 32.06/9.10 thf(280,axiom,((! [A:nat,B:nat]: (((B != A) => (ord_less_nat @ A @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_xt1_I11_J)). 32.06/9.10 thf(1552,plain,((! [A:nat,B:nat]: (((~ (B = A)) => (ord_less_nat @ A @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 32.06/9.10 thf(24,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_Suc__less__SucD)). 32.06/9.10 thf(457,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 32.06/9.10 thf(128,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) => ((ord_less_nat @ C @ A) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_ord__eq__less__trans)). 32.06/9.10 thf(984,plain,((! [A:nat,B:nat,C:nat]: ((B = C) => ((ord_less_nat @ C @ A) => (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 32.06/9.10 thf(85,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_less__Suc__eq__le)). 32.06/9.10 thf(721,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 32.06/9.10 thf(320,axiom,((! [A:arrow_1429601828e_indi]: ((((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ lba) <= (~ (ord_less_nat @ (h @ A) @ (plus_plus_nat @ n @ one_one_nat)))) & ((ord_less_nat @ (h @ A) @ (plus_plus_nat @ n @ one_one_nat)) => (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ lab))) = (((~ (ord_less_nat @ (h @ A) @ n)) => ((((h @ A) != n) => (member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e))) & ((member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (arrow_789600939_above @ (p @ A) @ c @ e)) <= ((h @ A) = n)))) & ((member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (arrow_55669061_mktop @ (p @ A) @ e)) <= (ord_less_nat @ (h @ A) @ n)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am)). 32.06/9.10 thf(1720,plain,((! [A:arrow_1429601828e_indi]: ((((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (lba)) | (ord_less_nat @ (h @ A) @ (plus_plus_nat @ n @ one_one_nat))) & ((ord_less_nat @ (h @ A) @ (plus_plus_nat @ n @ one_one_nat)) => (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (lab)))) = (((~ (ord_less_nat @ (h @ A) @ n)) => (((~ ((h @ A) = n)) => (member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e))) & ((member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (arrow_789600939_above @ (p @ A) @ c @ e)) | ~ ((h @ A) = n)))) & ((member214075476le_alt @ (produc1347929815le_alt @ c @ e) @ (arrow_55669061_mktop @ (p @ A) @ e)) | ~ (ord_less_nat @ (h @ A) @ n)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 32.06/9.10 thf(364,axiom,((member526088951_alt_o @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e)))) @ arrow_734252939e_Prof)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai)). 32.06/9.10 thf(1825,plain,((member526088951_alt_o @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e)))) @ (arrow_734252939e_Prof))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])). 32.06/9.10 thf(215,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_order__antisym)). 32.06/9.10 thf(1324,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 32.06/9.10 thf(271,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ A @ C) <= (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_xt1_I4_J)). 32.06/9.10 thf(1530,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ A @ C) | ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 32.06/9.10 thf(274,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_order__less__imp__le)). 32.06/9.10 thf(1539,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 32.06/9.10 thf(37,axiom,((! [A:nat,B:nat]: ((A = B) <= ((suc @ A) = (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_Suc__inject)). 32.06/9.10 thf(503,plain,((! [A:nat,B:nat]: ((A = B) | ~ ((suc @ A) = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 32.06/9.10 thf(66,axiom,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_le__SucE)). 32.06/9.10 thf(605,plain,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 32.06/9.10 thf(219,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ A @ C) <= (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_xt1_I8_J)). 32.06/9.10 thf(1333,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 32.06/9.10 thf(181,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ C)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_termination__basic__simps_I2_J)). 32.06/9.10 thf(1202,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ C)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 32.06/9.10 thf(161,axiom,((! [A:nat,B:nat,C:nat]: ((~ ((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C))) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_add__leE)). 32.06/9.10 thf(1086,plain,((! [A:nat,B:nat,C:nat]: (~ (~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 32.06/9.10 thf(310,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_order__less__asym_H)). 32.06/9.10 thf(1695,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 32.06/9.10 thf(47,axiom,((! [A:nat]: ((~ (! [B:nat]: (A != (suc @ B)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_nat_Oexhaust)). 32.06/9.10 thf(541,plain,((! [A:nat]: (~ (! [B:nat]: ~ (A = (suc @ B))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 32.06/9.10 thf(285,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_add__strict__right__mono)). 32.06/9.10 thf(1563,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 32.06/9.10 thf(266,axiom,((! [A:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ top_to1841428258_alt_o @ A) = (A = top_to1841428258_alt_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_top__unique)). 32.06/9.10 thf(1515,plain,((! [A:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ (top_to1841428258_alt_o) @ (A)) = ((A) = (top_to1841428258_alt_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 32.06/9.10 thf(386,axiom,((member526088951_alt_o @ p @ arrow_734252939e_Prof)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096)). 32.06/9.10 thf(1895,plain,((member526088951_alt_o @ (p) @ (arrow_734252939e_Prof))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])). 32.06/9.10 thf(304,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((! [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member526088951_alt_o @ D @ C) => (member377231867_alt_o @ (A @ D) @ (B @ D)))) => (member616898751_alt_o @ A @ (pi_Arr1304755663_alt_o @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_Pi__I)). 32.06/9.10 thf(1616,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((! [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member526088951_alt_o @ (D) @ (C)) => (member377231867_alt_o @ (A @ D) @ (B @ D)))) => (member616898751_alt_o @ (A) @ (pi_Arr1304755663_alt_o @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 32.06/9.10 thf(174,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_xt1_I5_J)). 32.06/9.10 thf(1185,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 32.06/9.10 thf(60,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_nat_Osimps_I3_J)). 32.06/9.10 thf(586,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 32.06/9.10 thf(325,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > ($o > $o))]: (((~ (member214075476le_alt @ A @ C)) <= (~ (member_o @ (B @ A) @ (D @ A)))) <= (member377231867_alt_o @ B @ (pi_Pro1701359055_alt_o @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_PiE)). 32.06/9.10 thf(1732,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > ($o > $o))]: (~ (member214075476le_alt @ A @ (C)) | (member_o @ (B @ A) @ (D @ A)) | ~ (member377231867_alt_o @ (B) @ (pi_Pro1701359055_alt_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 32.06/9.10 thf(316,axiom,((! [A:arrow_475358991le_alt,B:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ (arrow_55669061_mktop @ B @ A) @ arrow_823908191le_Lin) <= (member377231867_alt_o @ B @ arrow_823908191le_Lin)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_mktop__Lin)). 32.06/9.10 thf(1712,plain,((! [A:arrow_475358991le_alt,B:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ (arrow_55669061_mktop @ B @ A) @ (arrow_823908191le_Lin)) | ~ (member377231867_alt_o @ (B) @ (arrow_823908191le_Lin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 32.06/9.10 thf(153,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_add__less__le__mono)). 32.06/9.10 thf(1054,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 32.06/9.10 thf(203,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_add__mono)). 32.06/9.10 thf(1286,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 32.06/9.10 thf(146,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((! [E:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member526088951_alt_o @ E @ D) => ((B @ E) = (C @ E)))) => ((member616898751_alt_o @ C @ (pi_Arr1304755663_alt_o @ D @ A)) = (member616898751_alt_o @ B @ (pi_Arr1304755663_alt_o @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_Pi__cong)). 32.06/9.10 thf(1035,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((! [E:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member526088951_alt_o @ (E) @ (D)) => ((B @ E) = (C @ E)))) => ((member616898751_alt_o @ (C) @ (pi_Arr1304755663_alt_o @ D @ A)) = (member616898751_alt_o @ (B) @ (pi_Arr1304755663_alt_o @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 32.06/9.10 thf(122,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_nat @ A @ B) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_order__neq__le__trans)). 32.06/9.10 thf(906,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((ord_less_nat @ A @ B) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 32.06/9.10 thf(97,axiom,((! [A:$o,B:($o > $o)]: ((member_o @ A @ B) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_mem__def)). 32.06/9.10 thf(750,plain,((! [A:$o,B:($o > $o)]: ((member_o @ A @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 32.06/9.10 thf(338,axiom,((! [A:$o,B:($o > produc1501160679le_alt),C:($o > $o),D:($o > (produc1501160679le_alt > $o))]: ((member492167345le_alt @ B @ (pi_o_P657324555le_alt @ C @ D)) => ((~ (member_o @ A @ C)) <= (~ (member214075476le_alt @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_PiE)). 32.06/9.10 thf(1764,plain,((! [A:$o,B:($o > produc1501160679le_alt),C:($o > $o),D:($o > (produc1501160679le_alt > $o))]: ((member492167345le_alt @ (B) @ (pi_o_P657324555le_alt @ C @ D)) => (~ (member_o @ A @ (C)) | (member214075476le_alt @ (B @ A) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 32.06/9.10 thf(65,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_Zero__not__Suc)). 32.06/9.10 thf(601,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 32.06/9.10 thf(40,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (B = (suc @ C))) <= (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_Suc__le__D)). 32.06/9.10 thf(513,plain,((! [A:nat,B:nat]: (? [C:nat]: (B = (suc @ C)) | ~ (ord_less_eq_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 32.06/9.10 thf(334,axiom,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ A @ B) = (ord_le2080035663_alt_o @ (^ [C:arrow_475358991le_alt,D:arrow_475358991le_alt]: (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ A)) @ (^ [C:arrow_475358991le_alt,D:arrow_475358991le_alt]: (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_pred__subset__eq2)). 32.06/9.10 thf(1754,plain,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ (A) @ (B)) = (ord_le2080035663_alt_o @ (^ [C:arrow_475358991le_alt,D:arrow_475358991le_alt]: (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ A)) @ (^ [C:arrow_475358991le_alt,D:arrow_475358991le_alt]: (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 32.06/9.10 thf(14,axiom,((! [A:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((member616898751_alt_o @ B @ C) => ((member616898751_alt_o @ B @ A) <= (ord_le134800455lt_o_o @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_set__rev__mp)). 32.06/9.10 thf(430,plain,((! [A:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((member616898751_alt_o @ (B) @ (C)) => ((member616898751_alt_o @ (B) @ (A)) | ~ (ord_le134800455lt_o_o @ (C) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 32.06/9.10 thf(89,axiom,((! [A:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ top_to1841428258_alt_o @ A) => (A = top_to1841428258_alt_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_top__le)). 32.06/9.10 thf(732,plain,((! [A:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ (top_to1841428258_alt_o) @ (A)) => ((A) = (top_to1841428258_alt_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 32.06/9.10 thf(346,axiom,((! [A:(produc1501160679le_alt > $o),B:produc1501160679le_alt,C:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ B @ C) => ((member214075476le_alt @ B @ A) <= (ord_le97612146_alt_o @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_set__rev__mp)). 32.06/9.10 thf(1784,plain,((! [A:(produc1501160679le_alt > $o),B:produc1501160679le_alt,C:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ B @ (C)) => ((member214075476le_alt @ B @ (A)) | ~ (ord_le97612146_alt_o @ (C) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])). 32.06/9.10 thf(333,axiom,((! [A:produc1501160679le_alt]: (member214075476le_alt @ A @ top_to1841428258_alt_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_iso__tuple__UNIV__I)). 32.06/9.10 thf(1752,plain,((! [A:produc1501160679le_alt]: (member214075476le_alt @ A @ (top_to1841428258_alt_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 32.06/9.10 thf(94,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_nat__add__left__cancel__le)). 32.06/9.10 thf(743,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 32.06/9.10 thf(58,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_Suc__neq__Zero)). 32.06/9.10 thf(579,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 32.06/9.10 thf(8,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_not__less__eq)). 32.06/9.10 thf(413,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 32.06/9.10 thf(191,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (((plus_plus_nat @ A @ C) = B) & (ord_less_nat @ zero_zero_nat @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_less__imp__add__positive)). 32.06/9.10 thf(1256,plain,((! [A:nat,B:nat]: (? [C:nat]: (((plus_plus_nat @ A @ C) = B) & (ord_less_nat @ zero_zero_nat @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 32.06/9.10 thf(48,axiom,((! [A:nat,B:nat]: ((? [C:nat]: ((ord_less_nat @ C @ B) & (A = (suc @ C))) | (A = zero_zero_nat)) = (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_less__Suc__eq__0__disj)). 32.06/9.10 thf(545,plain,((! [A:nat,B:nat]: ((? [C:nat]: ((ord_less_nat @ C @ B) & (A = (suc @ C))) | (A = zero_zero_nat)) = (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 32.06/9.10 thf(79,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_Nat_Oadd__0__right)). 32.06/9.10 thf(641,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 32.06/9.10 thf(347,axiom,((arrow_1706409458nimity @ f)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_u)). 32.06/9.10 thf(1786,plain,((arrow_1706409458nimity @ (f))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 32.06/9.10 thf(20,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_add__Suc)). 32.06/9.10 thf(445,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 32.06/9.10 thf(314,axiom,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > arrow_1429601828e_indi),C:((produc1501160679le_alt > $o) > $o),D:((produc1501160679le_alt > $o) > (arrow_1429601828e_indi > $o))]: (((~ (member377231867_alt_o @ A @ C)) <= (~ (member2052026769e_indi @ (B @ A) @ (D @ A)))) <= (member304866663e_indi @ B @ (pi_Pro468373057e_indi @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_PiE)). 32.06/9.10 thf(1707,plain,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > arrow_1429601828e_indi),C:((produc1501160679le_alt > $o) > $o),D:((produc1501160679le_alt > $o) > (arrow_1429601828e_indi > $o))]: (~ (member377231867_alt_o @ (A) @ (C)) | (member2052026769e_indi @ (B @ (A)) @ (D @ A)) | ~ (member304866663e_indi @ (B) @ (pi_Pro468373057e_indi @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 32.06/9.10 thf(212,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_less__not__refl2)). 32.06/9.10 thf(1312,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 32.06/9.10 thf(68,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_plus__nat_Oadd__0)). 32.06/9.10 thf(611,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 32.06/9.10 thf(35,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_less__SucI)). 32.06/9.10 thf(498,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 32.06/9.10 thf(388,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o)]: (((A != B) => ((member214075476le_alt @ (produc1347929815le_alt @ B @ A) @ C) = (~ (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ C)))) <= (member377231867_alt_o @ C @ arrow_823908191le_Lin)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_notin__Lin__iff)). 32.06/9.10 thf(1897,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o)]: (((~ (A = B)) => ((member214075476le_alt @ (produc1347929815le_alt @ B @ A) @ (C)) = (~ (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (C))))) | ~ (member377231867_alt_o @ (C) @ (arrow_823908191le_Lin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 32.06/9.10 thf(3,axiom,((! [A:(arrow_1429601828e_indi > nat)]: ((! [B:arrow_1429601828e_indi,C:arrow_1429601828e_indi]: (((A @ B) = (A @ C)) => (B = C))) => (inj_on978774663di_nat @ A @ top_to988227749indi_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_injI)). 32.06/9.10 thf(391,plain,((! [A:(arrow_1429601828e_indi > nat)]: ((! [B:arrow_1429601828e_indi,C:arrow_1429601828e_indi]: (((A @ B) = (A @ C)) => (B = C))) => (inj_on978774663di_nat @ (A) @ (top_to988227749indi_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 32.06/9.10 thf(262,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_nat__add__left__cancel)). 32.06/9.10 thf(1503,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 32.06/9.10 thf(120,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) => (((plus_plus_nat @ A @ D) = (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_less__add__eq__less)). 32.06/9.10 thf(900,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) => (((plus_plus_nat @ A @ D) = (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 32.06/9.10 thf(201,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_add__le__imp__le__left)). 32.06/9.10 thf(1282,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 32.06/9.10 thf(91,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_add__right__mono)). 32.06/9.10 thf(736,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 32.06/9.10 thf(22,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_less__nat__zero__code)). 32.06/9.10 thf(451,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 32.06/9.10 thf(340,axiom,((~ (member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ lab))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096)). 32.06/9.10 thf(1771,plain,((~ (member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (lab)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 32.06/9.10 thf(353,axiom,((! [A:produc1501160679le_alt]: (member214075476le_alt @ A @ top_to1841428258_alt_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_UNIV__I)). 32.06/9.10 thf(1801,plain,((! [A:produc1501160679le_alt]: (member214075476le_alt @ A @ (top_to1841428258_alt_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 32.06/9.10 thf(309,axiom,((! [A:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),D:(arrow_1429601828e_indi > $o)]: (((member526088951_alt_o @ B @ (pi_Arr1929480907_alt_o @ D @ A)) = (member526088951_alt_o @ C @ (pi_Arr1929480907_alt_o @ D @ A))) <= (! [E:arrow_1429601828e_indi]: (((B @ E) = (C @ E)) <= (member2052026769e_indi @ E @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_Pi__cong)). 32.06/9.10 thf(1690,plain,((! [A:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),D:(arrow_1429601828e_indi > $o)]: (((member526088951_alt_o @ (B) @ (pi_Arr1929480907_alt_o @ D @ A)) = (member526088951_alt_o @ (C) @ (pi_Arr1929480907_alt_o @ D @ A))) | ~ (! [E:arrow_1429601828e_indi]: (((B @ E) = (C @ E)) | ~ (member2052026769e_indi @ E @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 32.06/9.10 thf(355,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ B @ C) => ((member214075476le_alt @ A @ B) => (member214075476le_alt @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_subsetD)). 32.06/9.10 thf(1806,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ (B) @ (C)) => ((member214075476le_alt @ A @ (B)) => (member214075476le_alt @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[355])). 32.06/9.10 thf(10,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_lessI)). 32.06/9.10 thf(419,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 32.06/9.10 thf(130,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_leI)). 32.06/9.10 thf(990,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 32.06/9.10 thf(133,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) = (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_linorder__not__le)). 32.06/9.10 thf(996,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) = (~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 32.06/9.10 thf(34,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_Suc__not__Zero)). 32.06/9.10 thf(494,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 32.06/9.10 thf(45,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_Suc__mono)). 32.06/9.10 thf(535,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 32.06/9.10 thf(361,axiom,((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ lba)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096)). 32.06/9.10 thf(1821,plain,((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (lba))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])). 32.06/9.10 thf(87,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ B) = (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_nat__add__commute)). 32.06/9.10 thf(726,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ B) = (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 32.06/9.10 thf(144,axiom,((! [A:(nat > arrow_1429601828e_indi),B:(arrow_1429601828e_indi > nat)]: ((((hilber598459244di_nat @ top_to988227749indi_o @ B) = A) <= (! [C:nat]: ((B @ (A @ C)) = C))) <= (inj_on978774663di_nat @ B @ top_to988227749indi_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_inj__imp__inv__eq)). 32.06/9.10 thf(1029,plain,((! [A:(nat > arrow_1429601828e_indi),B:(arrow_1429601828e_indi > nat)]: (((hilber598459244di_nat @ top_to988227749indi_o @ B) = (A)) | ~ (! [C:nat]: ((B @ (A @ C)) = C)) | ~ (inj_on978774663di_nat @ (B) @ (top_to988227749indi_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 32.06/9.10 thf(73,axiom,((! [A:nat]: ((A = zero_zero_nat) = (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_le__0__eq)). 32.06/9.10 thf(626,plain,((! [A:nat]: ((A = zero_zero_nat) = (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 32.06/9.10 thf(224,axiom,((! [A:product_unit,B:(product_unit > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))),C:(product_unit > $o),D:(product_unit > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o))]: (((~ (member_Product_unit @ A @ C)) <= (~ (member526088951_alt_o @ (B @ A) @ (D @ A)))) <= (member283501700_alt_o @ B @ (pi_Pro1662176984_alt_o @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_PiE)). 32.06/9.10 thf(1344,plain,((! [A:product_unit,B:(product_unit > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))),C:(product_unit > $o),D:(product_unit > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o))]: (~ (member_Product_unit @ A @ (C)) | (member526088951_alt_o @ (B @ A) @ (D @ A)) | ~ (member283501700_alt_o @ (B) @ (pi_Pro1662176984_alt_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 32.06/9.10 thf(308,axiom,((! [A:nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_less__add__one)). 32.06/9.10 thf(1688,plain,((! [A:nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 32.06/9.10 thf(170,axiom,((! [A:nat]: ((A = one_one_nat) = (one_one_nat = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_one__reorient)). 32.06/9.10 thf(1177,plain,((! [A:nat]: ((A = one_one_nat) = (one_one_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 32.06/9.10 thf(239,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((((! [D:nat]: (((A @ D) <= (A @ (suc @ D))) <= (ord_less_nat @ D @ C))) => (A @ B)) <= (A @ C)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_inc__induct)). 32.06/9.10 thf(1381,plain,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ D) | ~ (A @ (suc @ D)) | ~ (ord_less_nat @ D @ C))) => (A @ B)) | ~ (A @ C) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 32.06/9.10 thf(26,axiom,((! [A:(arrow_1429601828e_indi > nat),B:(arrow_1429601828e_indi > $o)]: ((! [C:arrow_1429601828e_indi]: ((! [D:arrow_1429601828e_indi]: ((((A @ C) = (A @ D)) => (C = D)) <= (member2052026769e_indi @ D @ B))) <= (member2052026769e_indi @ C @ B))) = (inj_on978774663di_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_inj__on__def)). 32.06/9.10 thf(462,plain,((! [A:(arrow_1429601828e_indi > nat),B:(arrow_1429601828e_indi > $o)]: ((! [C:arrow_1429601828e_indi]: (! [D:arrow_1429601828e_indi]: ((((A @ C) = (A @ D)) => (C = D)) | ~ (member2052026769e_indi @ D @ (B))) | ~ (member2052026769e_indi @ C @ (B)))) = (inj_on978774663di_nat @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 32.06/9.10 thf(156,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_less__eq__Suc__le)). 32.06/9.10 thf(1061,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 32.06/9.10 thf(5,axiom,((! [A:(arrow_1429601828e_indi > nat),B:(arrow_1429601828e_indi > $o)]: ((inj_on978774663di_nat @ A @ B) <= (! [C:arrow_1429601828e_indi,D:arrow_1429601828e_indi]: ((((C = D) <= ((A @ C) = (A @ D))) <= (member2052026769e_indi @ D @ B)) <= (member2052026769e_indi @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_inj__onI)). 32.06/9.10 thf(399,plain,((! [A:(arrow_1429601828e_indi > nat),B:(arrow_1429601828e_indi > $o)]: ((inj_on978774663di_nat @ (A) @ (B)) | ~ (! [C:arrow_1429601828e_indi,D:arrow_1429601828e_indi]: ((C = D) | ~ ((A @ C) = (A @ D)) | ~ (member2052026769e_indi @ D @ (B)) | ~ (member2052026769e_indi @ C @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 32.06/9.10 thf(312,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_nat__add__left__commute)). 32.06/9.10 thf(1699,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 32.06/9.10 thf(103,axiom,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((if_Pro1561232536_alt_o @ $false @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_)). 32.06/9.10 thf(780,plain,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((if_Pro1561232536_alt_o @ $false @ A @ B) = (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 32.06/9.10 thf(139,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_less__imp__Suc__add)). 32.06/9.10 thf(1015,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 32.06/9.10 thf(67,axiom,((! [A:nat]: ((A != zero_zero_nat) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_not0__implies__Suc)). 32.06/9.10 thf(608,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 32.06/9.10 thf(54,axiom,((! [A:nat,B:nat]: (((B = A) <= (ord_less_nat @ A @ (suc @ B))) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_less__antisym)). 32.06/9.10 thf(563,plain,((! [A:nat,B:nat]: ((B = A) | ~ (ord_less_nat @ A @ (suc @ B)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 32.06/9.10 thf(253,axiom,((! [A:(produc1501160679le_alt > $o),B:arrow_475358991le_alt,C:arrow_475358991le_alt]: (((member377231867_alt_o @ A @ arrow_823908191le_Lin) => (member377231867_alt_o @ (arrow_789600939_above @ A @ B @ C) @ arrow_823908191le_Lin)) <= (B != C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_above__Lin)). 32.06/9.10 thf(1435,plain,((! [A:(produc1501160679le_alt > $o),B:arrow_475358991le_alt,C:arrow_475358991le_alt]: (((member377231867_alt_o @ (A) @ (arrow_823908191le_Lin)) => (member377231867_alt_o @ (arrow_789600939_above @ A @ B @ C) @ (arrow_823908191le_Lin))) | (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 32.06/9.10 thf(232,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o)),C:(arrow_1429601828e_indi > $o)]: ((member526088951_alt_o @ A @ (pi_Arr1929480907_alt_o @ C @ B)) <= (! [D:arrow_1429601828e_indi]: ((member377231867_alt_o @ (A @ D) @ (B @ D)) <= (member2052026769e_indi @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_Pi__I)). 32.06/9.10 thf(1364,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o)),C:(arrow_1429601828e_indi > $o)]: ((member526088951_alt_o @ (A) @ (pi_Arr1929480907_alt_o @ C @ B)) | ~ (! [D:arrow_1429601828e_indi]: ((member377231867_alt_o @ (A @ D) @ (B @ D)) | ~ (member2052026769e_indi @ D @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 32.06/9.10 thf(17,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((ord_le134800455lt_o_o @ B @ C) => ((member616898751_alt_o @ A @ B) => (member616898751_alt_o @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_set__mp)). 32.06/9.10 thf(438,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((ord_le134800455lt_o_o @ (B) @ (C)) => ((member616898751_alt_o @ (A) @ (B)) => (member616898751_alt_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 32.06/9.10 thf(179,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_order__less__imp__not__less)). 32.06/9.10 thf(1198,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 32.06/9.10 thf(241,axiom,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o),C:($o > $o)]: ((member377231867_alt_o @ A @ (pi_Pro1701359055_alt_o @ B @ (^ [D:produc1501160679le_alt]: (C)))) => ((inj_on1911943593_alt_o @ A @ B) => ((ord_less_eq_nat @ (finite537683861le_alt @ B) @ (finite_card_o @ C)) <= (finite_finite_o @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_card__inj)). 32.06/9.10 thf(1396,plain,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o),C:($o > $o)]: ((member377231867_alt_o @ (A) @ (pi_Pro1701359055_alt_o @ B @ (^ [D:produc1501160679le_alt]: (C)))) => ((inj_on1911943593_alt_o @ (A) @ (B)) => ((ord_less_eq_nat @ (finite537683861le_alt @ (B)) @ (finite_card_o @ (C))) | ~ (finite_finite_o @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 32.06/9.10 thf(77,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_le0)). 32.06/9.10 thf(636,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 32.06/9.10 thf(149,axiom,((! [A:(produc1501160679le_alt > $o)]: ((member526088951_alt_o @ (^ [B:arrow_1429601828e_indi]: (A)) @ arrow_734252939e_Prof) <= (member377231867_alt_o @ A @ arrow_823908191le_Lin)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_const__Lin__Prof)). 32.06/9.10 thf(1044,plain,((! [A:(produc1501160679le_alt > $o)]: ((member526088951_alt_o @ (^ [B:arrow_1429601828e_indi]: (A)) @ (arrow_734252939e_Prof)) | ~ (member377231867_alt_o @ (A) @ (arrow_823908191le_Lin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 32.06/9.10 thf(30,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) = (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_Suc__less__eq)). 32.06/9.10 thf(473,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) = (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 32.06/9.10 thf(209,axiom,((! [A:produc1501160679le_alt]: (top_to1841428258_alt_o @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_top1I)). 32.06/9.10 thf(1304,plain,((! [A:produc1501160679le_alt]: (top_to1841428258_alt_o @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 32.06/9.10 thf(184,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ B @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order__less__trans)). 32.06/9.10 thf(1208,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ B @ A)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 32.06/9.10 thf(49,axiom,((! [A:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((ord_le134800455lt_o_o @ (^ [C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: (member616898751_alt_o @ C @ A)) @ (^ [C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: (member616898751_alt_o @ C @ B))) = (ord_le134800455lt_o_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_pred__subset__eq)). 32.06/9.10 thf(548,plain,((! [A:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((ord_le134800455lt_o_o @ (^ [C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: (member616898751_alt_o @ C @ A)) @ (^ [C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: (member616898751_alt_o @ C @ B))) = (ord_le134800455lt_o_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 32.06/9.10 thf(247,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_linorder__neqE)). 32.06/9.10 thf(1420,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 32.06/9.10 thf(306,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_less__add__Suc2)). 32.06/9.10 thf(1684,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 32.06/9.10 thf(264,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ A) <= (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_order__trans)). 32.06/9.10 thf(1509,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 32.06/9.10 thf(96,axiom,((inj_on978774663di_nat @ h @ top_to988227749indi_o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_injh)). 32.06/9.10 thf(749,plain,((inj_on978774663di_nat @ (h) @ (top_to988227749indi_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 32.06/9.10 thf(222,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),D:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > ($o > $o))]: ((member1823529808lt_o_o @ B @ (pi_Arr195212324lt_o_o @ C @ D)) => ((~ (member616898751_alt_o @ A @ C)) <= (~ (member_o @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_PiE)). 32.06/9.10 thf(1340,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),D:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > ($o > $o))]: ((member1823529808lt_o_o @ (B) @ (pi_Arr195212324lt_o_o @ C @ D)) => (~ (member616898751_alt_o @ (A) @ (C)) | (member_o @ (B @ (A)) @ (D @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 32.06/9.10 thf(140,axiom,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o)]: ((member377231867_alt_o @ A @ B) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_mem__def)). 32.06/9.10 thf(1018,plain,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > $o)]: ((member377231867_alt_o @ (A) @ (B)) = (B @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 32.06/9.10 thf(51,axiom,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_Suc__n__not__le__n)). 32.06/9.10 thf(553,plain,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 32.06/9.10 thf(151,axiom,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > product_unit),C:((produc1501160679le_alt > $o) > $o),D:((produc1501160679le_alt > $o) > (product_unit > $o))]: (((~ (member377231867_alt_o @ A @ C)) <= (~ (member_Product_unit @ (B @ A) @ (D @ A)))) <= (member221730070t_unit @ B @ (pi_Pro1306850800t_unit @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_PiE)). 32.06/9.10 thf(1049,plain,((! [A:(produc1501160679le_alt > $o),B:((produc1501160679le_alt > $o) > product_unit),C:((produc1501160679le_alt > $o) > $o),D:((produc1501160679le_alt > $o) > (product_unit > $o))]: (~ (member377231867_alt_o @ (A) @ (C)) | (member_Product_unit @ (B @ (A)) @ (D @ A)) | ~ (member221730070t_unit @ (B) @ (pi_Pro1306850800t_unit @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 32.06/9.10 thf(13,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C))))) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_Suc__lessE)). 32.06/9.10 thf(426,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (~ (B = (suc @ C))))) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 32.06/9.10 thf(336,axiom,((! [A:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (p @ A)) = (((~ (ord_less_nat @ (h @ A) @ n)) => ((((h @ A) != n) => (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (arrow_2054445623_mkbot @ (p @ A) @ e))) & ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (arrow_789600939_above @ (p @ A) @ c @ e)) <= ((h @ A) = n)))) & ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (arrow_55669061_mktop @ (p @ A) @ e)) <= (ord_less_nat @ (h @ A) @ n)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J)). 32.06/9.10 thf(1758,plain,((! [A:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (p @ A)) = (((~ (ord_less_nat @ (h @ A) @ n)) => (((~ ((h @ A) = n)) => (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (arrow_2054445623_mkbot @ (p @ A) @ e))) & ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (arrow_789600939_above @ (p @ A) @ c @ e)) | ~ ((h @ A) = n)))) & ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (arrow_55669061_mktop @ (p @ A) @ e)) | ~ (ord_less_nat @ (h @ A) @ n)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 32.06/9.10 thf(70,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_not__less__eq__eq)). 32.06/9.10 thf(617,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 32.06/9.10 thf(41,axiom,((! [A:nat,B:(nat > $o)]: (((B @ A) <= (! [C:nat]: ((B @ C) => (B @ (suc @ C))))) <= (B @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_nat__induct)). 32.06/9.10 thf(516,plain,((! [A:nat,B:(nat > $o)]: ((B @ A) | ~ (! [C:nat]: ((B @ C) => (B @ (suc @ C)))) | ~ (B @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 32.06/9.10 thf(371,axiom,((! [A:(produc1501160679le_alt > $o),B:arrow_475358991le_alt,C:arrow_475358991le_alt]: ((member214075476le_alt @ (produc1347929815le_alt @ B @ C) @ A) = (in_rel1252994498le_alt @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_in__rel__def)). 32.06/9.10 thf(1845,plain,((! [A:(produc1501160679le_alt > $o),B:arrow_475358991le_alt,C:arrow_475358991le_alt]: ((member214075476le_alt @ (produc1347929815le_alt @ B @ C) @ (A)) = (in_rel1252994498le_alt @ (A) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])). 32.06/9.10 thf(42,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_less__eq__nat_Osimps_I1_J)). 32.06/9.10 thf(525,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 32.06/9.10 thf(298,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order__less__imp__not__eq)). 32.06/9.10 thf(1598,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 32.06/9.10 thf(159,axiom,((! [A:nat,B:(nat > $o)]: (((? [C:nat]: ((B @ (plus_plus_nat @ C @ one_one_nat)) & ! [D:nat]: ((~ (B @ D)) <= (ord_less_eq_nat @ D @ C)) & (ord_less_nat @ C @ A))) <= (B @ A)) <= (~ (B @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_ex__least__nat__less)). 32.06/9.10 thf(1070,plain,((! [A:nat,B:(nat > $o)]: (? [C:nat]: ((B @ (plus_plus_nat @ C @ one_one_nat)) & ! [D:nat]: (~ (B @ D) | ~ (ord_less_eq_nat @ D @ C)) & (ord_less_nat @ C @ A)) | ~ (B @ A) | (B @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 32.06/9.10 thf(302,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:arrow_1429601828e_indi]: ((arrow_1212662430ctator @ A @ B) = (! [C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (((A @ C) = (C @ B)) <= (member526088951_alt_o @ C @ arrow_734252939e_Prof)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_dictator__def)). 32.06/9.10 thf(1611,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:arrow_1429601828e_indi]: ((arrow_1212662430ctator @ (A) @ B) = (! [C:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (((A @ C) = (C @ B)) | ~ (member526088951_alt_o @ (C) @ (arrow_734252939e_Prof))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 32.06/9.10 thf(329,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > arrow_1429601828e_indi),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > (arrow_1429601828e_indi > $o))]: (((~ (member2052026769e_indi @ (B @ A) @ (D @ A))) => (~ (member214075476le_alt @ A @ C))) <= (member1640632174e_indi @ B @ (pi_Pro1767455108e_indi @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_PiE)). 32.06/9.10 thf(1743,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > arrow_1429601828e_indi),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > (arrow_1429601828e_indi > $o))]: (((~ (member2052026769e_indi @ (B @ A) @ (D @ A))) => (~ (member214075476le_alt @ A @ (C)))) | ~ (member1640632174e_indi @ (B) @ (pi_Pro1767455108e_indi @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 32.06/9.10 thf(119,axiom,((! [A:nat,B:(nat > $o)]: ((~ (B @ zero_zero_nat)) => ((? [C:nat]: ((B @ C) & ! [D:nat]: ((ord_less_nat @ D @ C) => (~ (B @ D))) & (ord_less_eq_nat @ C @ A))) <= (B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_ex__least__nat__le)). 32.06/9.10 thf(887,plain,((! [A:nat,B:(nat > $o)]: ((~ (B @ zero_zero_nat)) => (? [C:nat]: ((B @ C) & ! [D:nat]: ((ord_less_nat @ D @ C) => (~ (B @ D))) & (ord_less_eq_nat @ C @ A)) | ~ (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 32.06/9.10 thf(344,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > product_unit),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > (product_unit > $o))]: ((member593902749t_unit @ B @ (pi_Pro1475896499t_unit @ C @ D)) => ((~ (member_Product_unit @ (B @ A) @ (D @ A))) => (~ (member214075476le_alt @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_PiE)). 32.06/9.10 thf(1780,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > product_unit),C:(produc1501160679le_alt > $o),D:(produc1501160679le_alt > (product_unit > $o))]: ((member593902749t_unit @ (B) @ (pi_Pro1475896499t_unit @ C @ D)) => ((~ (member_Product_unit @ (B @ A) @ (D @ A))) => (~ (member214075476le_alt @ A @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 32.06/9.10 thf(165,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_add__lessD1)). 32.06/9.10 thf(1098,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 32.06/9.10 thf(278,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o))]: ((member616898751_alt_o @ B @ (pi_Arr1304755663_alt_o @ C @ D)) => ((~ (member377231867_alt_o @ (B @ A) @ (D @ A))) => (~ (member526088951_alt_o @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_PiE)). 32.06/9.10 thf(1547,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o))]: ((member616898751_alt_o @ (B) @ (pi_Arr1304755663_alt_o @ C @ D)) => ((~ (member377231867_alt_o @ (B @ A) @ (D @ A))) => (~ (member526088951_alt_o @ (A) @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 32.06/9.10 thf(101,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o))]: ((member616898751_alt_o @ B @ (pi_Arr1304755663_alt_o @ C @ D)) => ((member526088951_alt_o @ A @ C) => (member377231867_alt_o @ (B @ A) @ (D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_Pi__mem)). 32.06/9.10 thf(776,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > ((produc1501160679le_alt > $o) > $o))]: ((member616898751_alt_o @ (B) @ (pi_Arr1304755663_alt_o @ C @ D)) => ((member526088951_alt_o @ (A) @ (C)) => (member377231867_alt_o @ (B @ A) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 32.06/9.10 thf(331,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: ((! [B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((! [C:arrow_475358991le_alt,D:arrow_475358991le_alt]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A @ B)) <= (! [E:arrow_1429601828e_indi]: (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (B @ E))))) <= (member526088951_alt_o @ B @ arrow_734252939e_Prof))) = (arrow_1706409458nimity @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_unanimity__def)). 32.06/9.10 thf(1748,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))]: ((! [B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (! [C:arrow_475358991le_alt,D:arrow_475358991le_alt]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A @ B)) | ~ (! [E:arrow_1429601828e_indi]: (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (B @ E)))) | ~ (member526088951_alt_o @ (B) @ (arrow_734252939e_Prof)))) = (arrow_1706409458nimity @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 32.06/9.10 thf(82,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_not__less__iff__gr__or__eq)). 32.06/9.10 thf(712,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 32.06/9.10 thf(135,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) = ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_nat__less__le)). 32.06/9.10 thf(1003,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) = ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 32.06/9.10 thf(318,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_less__imp__le__nat)). 32.06/9.10 thf(1716,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 32.06/9.10 thf(252,axiom,((! [A:(produc1501160679le_alt > $o),B:arrow_475358991le_alt,C:arrow_475358991le_alt]: (((member377231867_alt_o @ (arrow_2098199487_below @ A @ B @ C) @ arrow_823908191le_Lin) <= (member377231867_alt_o @ A @ arrow_823908191le_Lin)) <= (B != C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_below__Lin)). 32.06/9.10 thf(1432,plain,((! [A:(produc1501160679le_alt > $o),B:arrow_475358991le_alt,C:arrow_475358991le_alt]: ((member377231867_alt_o @ (arrow_2098199487_below @ A @ B @ C) @ (arrow_823908191le_Lin)) | ~ (member377231867_alt_o @ (A) @ (arrow_823908191le_Lin)) | (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 32.06/9.10 thf(358,axiom,((! [A:(produc1501160679le_alt > ($o > $o)),B:(produc1501160679le_alt > ($o > $o)),C:(produc1501160679le_alt > $o)]: ((! [D:produc1501160679le_alt]: ((member214075476le_alt @ D @ C) => (ord_less_eq_o_o @ (A @ D) @ (B @ D)))) => (ord_le1063113995lt_o_o @ (pi_Pro1701359055_alt_o @ C @ A) @ (pi_Pro1701359055_alt_o @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_Pi__mono)). 32.06/9.10 thf(1813,plain,((! [A:(produc1501160679le_alt > ($o > $o)),B:(produc1501160679le_alt > ($o > $o)),C:(produc1501160679le_alt > $o)]: ((! [D:produc1501160679le_alt]: ((member214075476le_alt @ D @ (C)) => (ord_less_eq_o_o @ (A @ D) @ (B @ D)))) => (ord_le1063113995lt_o_o @ (pi_Pro1701359055_alt_o @ C @ A) @ (pi_Pro1701359055_alt_o @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 32.06/9.10 thf(107,axiom,((! [A:(produc1501160679le_alt > $o)]: (ord_le97612146_alt_o @ A @ top_to1841428258_alt_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_subset__UNIV)). 32.06/9.10 thf(791,plain,((! [A:(produc1501160679le_alt > $o)]: (ord_le97612146_alt_o @ (A) @ (top_to1841428258_alt_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 32.06/9.10 thf(175,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_le__imp__less__Suc)). 32.06/9.10 thf(1188,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 32.06/9.10 thf(29,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_gr0__conv__Suc)). 32.06/9.10 thf(470,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 32.06/9.10 thf(188,axiom,((! [A:nat,B:nat,C:(nat > nat)]: ((! [D:nat,E:nat]: ((ord_less_nat @ (C @ D) @ (C @ E)) <= (ord_less_nat @ D @ E))) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (C @ A) @ (C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_less__mono__imp__le__mono)). 32.06/9.10 thf(1218,plain,((! [A:nat,B:nat,C:(nat > nat)]: ((! [D:nat,E:nat]: ((ord_less_nat @ (C @ D) @ (C @ E)) | ~ (ord_less_nat @ D @ E))) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (C @ A) @ (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 32.06/9.10 thf(244,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) = (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_linorder__not__less)). 32.06/9.10 thf(1404,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) = (~ (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 32.06/9.10 thf(276,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_trans__le__add2)). 32.06/9.10 thf(1543,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 32.06/9.10 thf(273,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_nat__add__left__cancel__less)). 32.06/9.10 thf(1536,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 32.06/9.10 thf(142,axiom,((! [A:nat,B:nat,C:nat]: ((A = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_add__right__imp__eq)). 32.06/9.10 thf(1023,plain,((! [A:nat,B:nat,C:nat]: ((A = C) | ~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 32.06/9.10 thf(313,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_less__or__eq__imp__le)). 32.06/9.10 thf(1702,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 32.06/9.10 thf(263,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_add__gr__0)). 32.06/9.10 thf(1506,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 32.06/9.10 thf(111,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_not__add__less1)). 32.06/9.10 thf(864,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 32.06/9.10 thf(250,axiom,((! [A:nat]: ((suc @ A) = (plus_plus_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_Suc__eq__plus1__left)). 32.06/9.10 thf(1427,plain,((! [A:nat]: ((suc @ A) = (plus_plus_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 32.06/9.10 thf(126,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > $o)]: ((member2052026769e_indi @ A @ B) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_mem__def)). 32.06/9.10 thf(978,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > $o)]: ((member2052026769e_indi @ A @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 32.06/9.10 thf(351,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o),D:arrow_475358991le_alt]: ((((A = D) => (A != B)) & ((A != D) => (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ C)) & (B != D)) = (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (arrow_2054445623_mkbot @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_in__mkbot)). 32.06/9.10 thf(1797,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o),D:arrow_475358991le_alt]: ((((A = D) => (~ (A = B))) & ((~ (A = D)) => (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (C))) & ~ (B = D)) = (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (arrow_2054445623_mkbot @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 32.06/9.10 thf(63,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_add__Suc__shift)). 32.06/9.10 thf(595,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 32.06/9.10 thf(189,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_termination__basic__simps_I5_J)). 32.06/9.10 thf(1221,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 32.06/9.10 thf(202,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_order__less__asym)). 32.06/9.10 thf(1284,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 32.06/9.10 thf(382,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ B @ C) => ((member214075476le_alt @ A @ C) <= (member214075476le_alt @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_set__mp)). 32.06/9.10 thf(1881,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: ((ord_le97612146_alt_o @ (B) @ (C)) => ((member214075476le_alt @ A @ (C)) | ~ (member214075476le_alt @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 32.06/9.10 thf(197,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: (((member616898751_alt_o @ A @ C) <= (member616898751_alt_o @ A @ B)) <= (ord_le1859604819lt_o_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_psubsetD)). 32.06/9.10 thf(1272,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o)]: ((member616898751_alt_o @ (A) @ (C)) | ~ (member616898751_alt_o @ (A) @ (B)) | ~ (ord_le1859604819lt_o_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 32.06/9.10 thf(27,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_neq0__conv)). 32.06/9.10 thf(465,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 32.06/9.10 thf(369,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((D != E) => ((((member526088951_alt_o @ B @ arrow_734252939e_Prof) => ((member526088951_alt_o @ A @ arrow_734252939e_Prof) => (((member214075476le_alt @ (produc1347929815le_alt @ E @ C) @ (f @ A)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (f @ B))) <= (! [F:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (B @ F)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ C) @ (A @ F))))))) <= (D != C)) <= (E != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C4_C)). 32.06/9.10 thf(1839,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((~ (D = E)) => (((member526088951_alt_o @ (B) @ (arrow_734252939e_Prof)) => ((member526088951_alt_o @ (A) @ (arrow_734252939e_Prof)) => (((member214075476le_alt @ (produc1347929815le_alt @ E @ C) @ (f @ A)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (f @ B))) | ~ (! [F:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ D @ E) @ (B @ F)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ C) @ (A @ F))))))) | (D = C) | (E = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 32.06/9.10 thf(213,axiom,((! [A:$o,B:($o > (produc1501160679le_alt > $o)),C:($o > $o),D:($o > ((produc1501160679le_alt > $o) > $o))]: ((member1862122484_alt_o @ B @ (pi_o_P553196292_alt_o @ C @ D)) => ((~ (member_o @ A @ C)) <= (~ (member377231867_alt_o @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_PiE)). 32.06/9.10 thf(1316,plain,((! [A:$o,B:($o > (produc1501160679le_alt > $o)),C:($o > $o),D:($o > ((produc1501160679le_alt > $o) > $o))]: ((member1862122484_alt_o @ (B) @ (pi_o_P553196292_alt_o @ C @ D)) => (~ (member_o @ A @ (C)) | (member377231867_alt_o @ (B @ A) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 32.06/9.10 thf(171,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),D:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > (arrow_1429601828e_indi > $o))]: ((member1452482393e_indi @ B @ (pi_Arr338314351e_indi @ C @ D)) => ((~ (member616898751_alt_o @ A @ C)) <= (~ (member2052026769e_indi @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_PiE)). 32.06/9.10 thf(1180,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi),C:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o),D:(((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > (arrow_1429601828e_indi > $o))]: ((member1452482393e_indi @ (B) @ (pi_Arr338314351e_indi @ C @ D)) => (~ (member616898751_alt_o @ (A) @ (C)) | (member2052026769e_indi @ (B @ (A)) @ (D @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 32.06/9.10 thf(52,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_Zero__neq__Suc)). 32.06/9.10 thf(556,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 32.06/9.10 thf(214,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > nat),C:(arrow_1429601828e_indi > $o)]: ((inj_on978774663di_nat @ B @ C) => ((member2052026769e_indi @ A @ C) => ((hilber598459244di_nat @ C @ B @ (B @ A)) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_inv__into__f__f)). 32.06/9.10 thf(1321,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > nat),C:(arrow_1429601828e_indi > $o)]: ((inj_on978774663di_nat @ (B) @ (C)) => ((member2052026769e_indi @ A @ (C)) => ((hilber598459244di_nat @ (C) @ (B) @ (B @ A)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 32.06/9.10 thf(258,axiom,((! [A:($o > $o),B:($o > $o)]: ((ord_less_eq_o_o @ B @ A) <= (! [C:$o]: ((member_o @ C @ A) <= (member_o @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_subsetI)). 32.06/9.10 thf(1448,plain,((! [A:($o > $o),B:($o > $o)]: ((ord_less_eq_o_o @ (B) @ (A)) | ~ (! [C:$o]: ((member_o @ C @ (A)) | ~ (member_o @ C @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 32.06/9.10 thf(137,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_add__less__cancel__right)). 32.06/9.10 thf(1010,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 32.06/9.10 thf(326,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt]: ((((member526088951_alt_o @ A @ arrow_734252939e_Prof) => (((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (f @ B)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ C) @ (f @ A))) <= (! [E:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (B @ E)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ C) @ (A @ E)))))) <= (member526088951_alt_o @ B @ arrow_734252939e_Prof)) <= (C != D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__C3_C)). 32.06/9.10 thf(1734,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt]: (((member526088951_alt_o @ (A) @ (arrow_734252939e_Prof)) => (((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (f @ B)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ C) @ (f @ A))) | ~ (! [E:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (B @ E)) = (member214075476le_alt @ (produc1347929815le_alt @ D @ C) @ (A @ E)))))) | ~ (member526088951_alt_o @ (B) @ (arrow_734252939e_Prof)) | (C = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 32.06/9.10 thf(125,axiom,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o))]: (((~ (member377231867_alt_o @ (B @ A) @ (D @ A))) => (~ (member2052026769e_indi @ A @ C))) <= (member526088951_alt_o @ B @ (pi_Arr1929480907_alt_o @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_PiE)). 32.06/9.10 thf(976,plain,((! [A:arrow_1429601828e_indi,B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:(arrow_1429601828e_indi > $o),D:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o))]: (((~ (member377231867_alt_o @ (B @ A) @ (D @ A))) => (~ (member2052026769e_indi @ A @ (C)))) | ~ (member526088951_alt_o @ (B) @ (pi_Arr1929480907_alt_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 32.06/9.10 thf(121,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) = (~ (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_linorder__antisym__conv2)). 32.06/9.10 thf(903,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) = (~ (ord_less_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 32.06/9.10 thf(199,axiom,((! [A:nat,B:nat]: (((A != B) & (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_order__less__le)). 32.06/9.10 thf(1276,plain,((! [A:nat,B:nat]: ((~ (A = B) & (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 32.06/9.10 thf(1,conjecture,((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 32.06/9.10 thf(2,negated_conjecture,((~ (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p)))),inference(neg_conjecture,[status(cth)],[1])). 32.06/9.10 thf(390,plain,((~ (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 32.06/9.10 thf(330,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt,E:arrow_475358991le_alt,F:arrow_475358991le_alt]: (((C != D) => (((member526088951_alt_o @ A @ arrow_734252939e_Prof) => ((! [G:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A @ G)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (B @ G)))) => ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (f @ A)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (f @ B))))) <= (member526088951_alt_o @ B @ arrow_734252939e_Prof))) <= (E != F)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pairwise__neutrality)). 32.06/9.10 thf(1745,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),C:arrow_475358991le_alt,D:arrow_475358991le_alt,E:arrow_475358991le_alt,F:arrow_475358991le_alt]: (((~ (C = D)) => (((member526088951_alt_o @ (A) @ (arrow_734252939e_Prof)) => ((! [G:arrow_1429601828e_indi]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A @ G)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (B @ G)))) => ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (f @ A)) = (member214075476le_alt @ (produc1347929815le_alt @ E @ F) @ (f @ B))))) | ~ (member526088951_alt_o @ (B) @ (arrow_734252939e_Prof)))) | (E = F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 32.06/9.10 thf(75,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ (suc @ B) @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_less__trans__Suc)). 32.06/9.10 thf(632,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ (suc @ B) @ A)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 32.06/9.10 thf(362,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ C @ arrow_823908191le_Lin) => ((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ C) => (~ (member214075476le_alt @ (produc1347929815le_alt @ B @ A) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Lin__irrefl)). 32.06/9.10 thf(1822,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ (C) @ (arrow_823908191le_Lin)) => ((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (C)) => (~ (member214075476le_alt @ (produc1347929815le_alt @ B @ A) @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])). 32.06/9.10 thf(269,axiom,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:((produc1501160679le_alt > $o) > $o),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((! [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member377231867_alt_o @ (A @ D) @ B) <= (member526088951_alt_o @ D @ C))) => (member616898751_alt_o @ A @ (pi_Arr1304755663_alt_o @ C @ (^ [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_funcsetI)). 32.06/9.10 thf(1523,plain,((! [A:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)),B:((produc1501160679le_alt > $o) > $o),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((! [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: ((member377231867_alt_o @ (A @ D) @ (B)) | ~ (member526088951_alt_o @ (D) @ (C)))) => (member616898751_alt_o @ (A) @ (pi_Arr1304755663_alt_o @ C @ (^ [D:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 32.06/9.10 thf(282,axiom,((ord_less_nat @ n @ (finite97476818e_indi @ top_to988227749indi_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n_I1_J)). 32.06/9.10 thf(1558,plain,((ord_less_nat @ n @ (finite97476818e_indi @ (top_to988227749indi_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 32.06/9.10 thf(376,axiom,(((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p)) = (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW)). 32.06/9.10 thf(1861,plain,(((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p)) = (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^ [A:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ A) @ n) @ (arrow_55669061_mktop @ (p @ A) @ e) @ (if_Pro1561232536_alt_o @ ((h @ A) = n) @ (arrow_789600939_above @ (p @ A) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ A) @ e)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])). 32.06/9.10 thf(39,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_add__is__1)). 32.06/9.10 thf(510,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 32.06/9.10 thf(343,axiom,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((! [C:arrow_475358991le_alt,D:arrow_475358991le_alt]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ B) = (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ A))) = (B = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_pred__equals__eq2)). 32.06/9.10 thf(1777,plain,((! [A:(produc1501160679le_alt > $o),B:(produc1501160679le_alt > $o)]: ((! [C:arrow_475358991le_alt,D:arrow_475358991le_alt]: ((member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (B)) = (member214075476le_alt @ (produc1347929815le_alt @ C @ D) @ (A)))) = ((B) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 32.06/9.10 thf(206,axiom,((! [A:$o,B:($o > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))),C:($o > $o),D:($o > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o))]: (((~ (member_o @ A @ C)) <= (~ (member526088951_alt_o @ (B @ A) @ (D @ A)))) <= (member1394214384_alt_o @ B @ (pi_o_A1182933120_alt_o @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_PiE)). 32.06/9.10 thf(1294,plain,((! [A:$o,B:($o > (arrow_1429601828e_indi > (produc1501160679le_alt > $o))),C:($o > $o),D:($o > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o))]: (~ (member_o @ A @ (C)) | (member526088951_alt_o @ (B @ A) @ (D @ A)) | ~ (member1394214384_alt_o @ (B) @ (pi_o_A1182933120_alt_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 32.06/9.10 thf(177,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o)),C:(arrow_1429601828e_indi > $o)]: ((member526088951_alt_o @ A @ (pi_Arr1929480907_alt_o @ C @ B)) <= (! [D:arrow_1429601828e_indi]: ((member377231867_alt_o @ (A @ D) @ (B @ D)) <= (member2052026769e_indi @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_Pi__I_H)). 32.06/9.10 thf(1193,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:(arrow_1429601828e_indi > ((produc1501160679le_alt > $o) > $o)),C:(arrow_1429601828e_indi > $o)]: ((member526088951_alt_o @ (A) @ (pi_Arr1929480907_alt_o @ C @ B)) | ~ (! [D:arrow_1429601828e_indi]: ((member377231867_alt_o @ (A @ D) @ (B @ D)) | ~ (member2052026769e_indi @ D @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 32.06/9.10 thf(186,axiom,((! [A:nat,B:nat]: (((A = B) = (ord_less_eq_nat @ A @ B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_linorder__antisym__conv1)). 32.06/9.10 thf(1212,plain,((! [A:nat,B:nat]: (((A = B) = (ord_less_eq_nat @ A @ B)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 32.06/9.10 thf(301,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_add__imp__eq)). 32.06/9.10 thf(1607,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 32.06/9.10 thf(303,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_Suc__leI)). 32.06/9.10 thf(1614,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 32.06/9.10 thf(385,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: (((member214075476le_alt @ A @ B) => (member214075476le_alt @ A @ C)) <= (ord_le97612146_alt_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_in__mono)). 32.06/9.10 thf(1893,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: (((member214075476le_alt @ A @ (B)) => (member214075476le_alt @ A @ (C))) | ~ (ord_le97612146_alt_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 32.06/9.10 thf(211,axiom,((! [A:nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ (plus_plus_nat @ (C @ A) @ B) @ (C @ (plus_plus_nat @ A @ B))) <= (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (C @ D) @ (C @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_mono__nat__linear__lb)). 32.06/9.10 thf(1309,plain,((! [A:nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ (plus_plus_nat @ (C @ A) @ B) @ (C @ (plus_plus_nat @ A @ B))) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (C @ D) @ (C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 32.06/9.10 thf(226,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_le__trans)). 32.06/9.10 thf(1348,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 32.06/9.10 thf(342,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o),D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((((((B != D) => (((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ C) <= (A != D)) & (((B = E) | (member214075476le_alt @ (produc1347929815le_alt @ E @ B) @ C)) <= (A = D)))) & ((B = D) => (member214075476le_alt @ (produc1347929815le_alt @ A @ E) @ C)) & (A != B)) = (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (arrow_2098199487_below @ C @ D @ E))) <= (member377231867_alt_o @ C @ arrow_823908191le_Lin)) <= (D != E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_in__below)). 32.06/9.10 thf(1774,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o),D:arrow_475358991le_alt,E:arrow_475358991le_alt]: (((((~ (B = D)) => (((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (C)) | (A = D)) & ((B = E) | (member214075476le_alt @ (produc1347929815le_alt @ E @ B) @ (C)) | ~ (A = D)))) & ((B = D) => (member214075476le_alt @ (produc1347929815le_alt @ A @ E) @ (C))) & ~ (A = B)) = (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (arrow_2098199487_below @ C @ D @ E))) | ~ (member377231867_alt_o @ (C) @ (arrow_823908191le_Lin)) | (D = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 32.06/9.10 thf(291,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_order__less__not__sym)). 32.06/9.10 thf(1578,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 32.06/9.10 thf(15,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Suc__le__mono)). 32.06/9.10 thf(432,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 32.06/9.10 thf(7,axiom,((! [A:nat,B:nat]: ((A = B) = ((suc @ A) = (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_nat_Oinject)). 32.06/9.10 thf(410,plain,((! [A:nat,B:nat]: ((A = B) = ((suc @ A) = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 32.06/9.10 thf(296,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((B @ A) = (member526088951_alt_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_mem__def)). 32.06/9.10 thf(1593,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o)]: ((B @ (A)) = (member526088951_alt_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 32.06/9.10 thf(90,axiom,((member377231867_alt_o @ lba @ arrow_823908191le_Lin)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74__096Lba_A_058_ALin_096)). 32.06/9.10 thf(735,plain,((member377231867_alt_o @ (lba) @ (arrow_823908191le_Lin))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 32.06/9.10 thf(134,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) => (ord_less_nat @ A @ B)) <= (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_xt1_I1_J)). 32.06/9.10 thf(999,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) => (ord_less_nat @ A @ B)) | ~ (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 32.06/9.10 thf(71,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_Suc__lessD)). 32.06/9.10 thf(620,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 32.06/9.10 thf(112,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_eq__imp__le)). 32.06/9.10 thf(867,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 32.06/9.10 thf(335,axiom,((member616898751_alt_o @ f @ (pi_Arr1304755663_alt_o @ arrow_734252939e_Prof @ (^ [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (arrow_823908191le_Lin))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_assms_I1_J)). 32.06/9.10 thf(1757,plain,((member616898751_alt_o @ (f) @ (pi_Arr1304755663_alt_o @ arrow_734252939e_Prof @ (^ [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o))]: (arrow_823908191le_Lin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 32.06/9.10 thf(359,axiom,((! [A:product_unit,B:(product_unit > produc1501160679le_alt),C:(product_unit > $o),D:(product_unit > (produc1501160679le_alt > $o))]: ((member495332125le_alt @ B @ (pi_Pro701847987le_alt @ C @ D)) => ((~ (member_Product_unit @ A @ C)) <= (~ (member214075476le_alt @ (B @ A) @ (D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_PiE)). 32.06/9.10 thf(1816,plain,((! [A:product_unit,B:(product_unit > produc1501160679le_alt),C:(product_unit > $o),D:(product_unit > (produc1501160679le_alt > $o))]: ((member495332125le_alt @ (B) @ (pi_Pro701847987le_alt @ C @ D)) => (~ (member_Product_unit @ A @ (C)) | (member214075476le_alt @ (B @ A) @ (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])). 32.06/9.10 thf(220,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_linorder__neq__iff)). 32.06/9.10 thf(1335,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 32.06/9.10 thf(284,axiom,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (arrow_1429601828e_indi > $o))]: (((~ (member526088951_alt_o @ A @ C)) <= (~ (member2052026769e_indi @ (B @ A) @ (D @ A)))) <= (member44294883e_indi @ B @ (pi_Arr1232280765e_indi @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_PiE)). 32.06/9.10 thf(1561,plain,((! [A:(arrow_1429601828e_indi > (produc1501160679le_alt > $o)),B:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > arrow_1429601828e_indi),C:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > $o),D:((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (arrow_1429601828e_indi > $o))]: (~ (member526088951_alt_o @ (A) @ (C)) | (member2052026769e_indi @ (B @ (A)) @ (D @ A)) | ~ (member44294883e_indi @ (B) @ (pi_Arr1232280765e_indi @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 32.06/9.10 thf(154,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) | (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_order__le__imp__less__or__eq)). 32.06/9.10 thf(1056,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 32.06/9.10 thf(204,axiom,((! [A:nat]: ((suc @ A) = (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_Suc__eq__plus1)). 32.06/9.10 thf(1288,plain,((! [A:nat]: ((suc @ A) = (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 32.06/9.10 thf(44,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)) | ((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_one__is__add)). 32.06/9.10 thf(532,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)) | ((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 32.06/9.10 thf(225,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_le__refl)). 32.06/9.10 thf(1346,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 32.06/9.10 thf(109,axiom,((! [A:$o,B:($o > $o),C:($o > $o)]: ((ord_less_eq_o_o @ B @ C) => ((member_o @ A @ B) => (member_o @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_subsetD)). 32.06/9.10 thf(796,plain,((! [A:$o,B:($o > $o),C:($o > $o)]: ((ord_less_eq_o_o @ (B) @ (C)) => ((member_o @ A @ (B)) => (member_o @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 32.06/9.10 thf(246,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ C @ B) <= (B = C)) => (((A @ C @ B) <= (ord_less_nat @ C @ B)) => (A @ C @ B))) <= ((A @ C @ B) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_nat__less__cases)). 32.06/9.10 thf(1410,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ C @ B) | ~ (B = C)) => (((A @ C @ B) | ~ (ord_less_nat @ C @ B)) => (A @ C @ B))) | ~ ((A @ C @ B) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 32.06/9.10 thf(98,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_add__right__cancel)). 32.06/9.10 thf(767,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 32.06/9.10 thf(164,axiom,((! [A:$o,B:($o > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))),C:($o > $o),D:($o > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o))]: (((~ (member_o @ A @ C)) <= (~ (member616898751_alt_o @ (B @ A) @ (D @ A)))) <= (member1957863580_alt_o @ B @ (pi_o_A1186128886_alt_o @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_PiE)). 32.06/9.10 thf(1093,plain,((! [A:$o,B:($o > ((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o))),C:($o > $o),D:($o > (((arrow_1429601828e_indi > (produc1501160679le_alt > $o)) > (produc1501160679le_alt > $o)) > $o))]: (~ (member_o @ A @ (C)) | (member616898751_alt_o @ (B @ A) @ (D @ A)) | ~ (member1957863580_alt_o @ (B) @ (pi_o_A1186128886_alt_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 32.06/9.10 thf(228,axiom,((! [A:((produc1501160679le_alt > $o) > $o),B:((produc1501160679le_alt > $o) > $o)]: ((ord_le1063113995lt_o_o @ B @ A) <= (! [C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ C @ A) <= (member377231867_alt_o @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_subsetI)). 32.06/9.10 thf(1352,plain,((! [A:((produc1501160679le_alt > $o) > $o),B:((produc1501160679le_alt > $o) > $o)]: ((ord_le1063113995lt_o_o @ (B) @ (A)) | ~ (! [C:(produc1501160679le_alt > $o)]: ((member377231867_alt_o @ (C) @ (A)) | ~ (member377231867_alt_o @ (C) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 32.06/9.10 thf(366,axiom,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o),D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((D != E) => (((((A != E) => (((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ C) <= (B != E)) & (((A = D) | (member214075476le_alt @ (produc1347929815le_alt @ A @ D) @ C)) <= (B = E)))) & ((member214075476le_alt @ (produc1347929815le_alt @ D @ B) @ C) <= (A = E)) & (A != B)) = (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (arrow_789600939_above @ C @ D @ E))) <= (member377231867_alt_o @ C @ arrow_823908191le_Lin))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_in__above)). 32.06/9.10 thf(1829,plain,((! [A:arrow_475358991le_alt,B:arrow_475358991le_alt,C:(produc1501160679le_alt > $o),D:arrow_475358991le_alt,E:arrow_475358991le_alt]: ((~ (D = E)) => (((((~ (A = E)) => (((member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (C)) | (B = E)) & ((A = D) | (member214075476le_alt @ (produc1347929815le_alt @ A @ D) @ (C)) | ~ (B = E)))) & ((member214075476le_alt @ (produc1347929815le_alt @ D @ B) @ (C)) | ~ (A = E)) & ~ (A = B)) = (member214075476le_alt @ (produc1347929815le_alt @ A @ B) @ (arrow_789600939_above @ C @ D @ E))) | ~ (member377231867_alt_o @ (C) @ (arrow_823908191le_Lin)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])). 32.06/9.10 thf(195,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) => ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)) <= (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_add__less__mono)). 32.06/9.10 thf(1268,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) => ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B)) | ~ (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 32.06/9.10 thf(238,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_ab__semigroup__add__class_Oadd__ac_I1_J)). 32.06/9.10 thf(1378,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 32.06/9.10 thf(80,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_add__less__cancel__left)). 32.06/9.10 thf(644,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 32.06/9.10 thf(25,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_add__is__0)). 32.06/9.10 thf(459,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 32.06/9.10 thf(131,axiom,((? [A:(produc1501160679le_alt > $o)]: (member377231867_alt_o @ A @ arrow_823908191le_Lin))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_linear__alt)). 32.06/9.10 thf(992,plain,((? [A:(produc1501160679le_alt > $o)]: (member377231867_alt_o @ (A) @ (arrow_823908191le_Lin)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 32.06/9.10 thf(261,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) = (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_Suc__le__eq)). 32.06/9.10 thf(1500,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) = (ord_less_eq_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 32.06/9.10 thf(207,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) = (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_add__le__cancel__right)). 32.06/9.10 thf(1299,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) = (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 32.06/9.10 thf(113,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_nat__add__assoc)). 32.06/9.10 thf(871,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 32.06/9.10 thf(218,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_add__less__mono1)). 32.06/9.10 thf(1331,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 32.06/9.10 thf(233,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_linorder__antisym__conv3)). 32.06/9.10 thf(1367,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 32.06/9.10 thf(327,axiom,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: (((member214075476le_alt @ A @ C) <= (member214075476le_alt @ A @ B)) <= (ord_le988258430_alt_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_psubsetD)). 32.06/9.10 thf(1737,plain,((! [A:produc1501160679le_alt,B:(produc1501160679le_alt > $o),C:(produc1501160679le_alt > $o)]: ((member214075476le_alt @ A @ (C)) | ~ (member214075476le_alt @ A @ (B)) | ~ (ord_le988258430_alt_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 32.06/9.10 thf(286,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) = (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_le__iff__add)). 32.06/9.10 thf(1565,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) = (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 32.06/9.10 thf(372,axiom,((! [A:nat]: ((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (f @ (^ [B:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ B) @ A) @ lab @ lba)))) <= (ord_less_eq_nat @ A @ n)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_n_I2_J)). 32.06/9.10 thf(1848,plain,((! [A:nat]: ((member214075476le_alt @ (produc1347929815le_alt @ b @ a) @ (f @ (^ [B:arrow_1429601828e_indi]: (if_Pro1561232536_alt_o @ (ord_less_nat @ (h @ B) @ A) @ lab @ lba)))) | ~ (ord_less_eq_nat @ A @ n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])). 32.06/9.10 thf(53,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_less__Suc__eq)). 32.06/9.10 thf(560,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 32.06/9.10 thf(339,axiom,((~ (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ lba))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096)). 32.06/9.10 thf(1769,plain,((~ (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ (lba)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 32.06/9.10 thf(182,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_linorder__linear)). 32.06/9.10 thf(1204,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 32.06/9.10 thf(23,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_gr0__implies__Suc)). 32.06/9.10 thf(454,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 32.06/9.10 thf(1903,plain,($false),inference(e,[status(thm)],[1718,629,1190,909,1850,1818,1549,1686,479,1559,1083,468,1596,994,1401,741,1728,1591,440,614,861,1855,1200,1443,1808,1497,500,715,1872,1327,1260,1761,1342,1196,1782,1576,1441,1046,1359,1724,1803,1518,724,1709,570,1430,719,785,1871,1264,1511,1826,1279,1832,1059,1545,1800,638,1572,1568,1773,448,1875,1100,421,1890,1013,770,1398,881,416,1302,1714,789,1811,1858,574,1183,1051,1373,443,1040,1109,981,1377,774,1394,988,1697,1521,507,527,1215,634,1896,877,396,1526,1863,1604,1206,1438,793,1306,1338,1067,1868,1730,1274,1223,1042,598,1751,424,407,729,1883,1900,1723,746,1091,1021,778,1355,1580,1570,1174,1824,1619,1370,1423,879,583,1787,1210,1027,1407,551,1291,974,1106,566,484,1032,1837,1602,1555,435,1350,874,1270,1375,1064,1425,1006,593,783,1089,1541,1534,1794,1493,1361,1182,476,1842,1584,1791,1446,590,884,1329,1739,537,622,647,1588,738,1266,1552,457,984,721,1720,1825,1324,1530,1539,503,605,1333,1202,1086,1695,541,1563,1515,1895,1616,1185,586,1732,1712,1054,1286,1035,906,750,1764,601,513,1754,430,732,1784,1752,743,579,413,1256,545,641,1786,445,1707,1312,611,498,1897,391,1503,900,1282,736,451,1771,1801,1690,1806,419,990,996,494,535,1821,726,1029,626,1344,1688,1177,1381,462,1061,399,1699,780,1015,608,563,1435,1364,438,1198,1396,636,1044,473,1304,1208,548,1420,1684,1509,749,1340,1018,553,1049,426,1758,617,516,1845,525,1598,1070,1611,1743,887,1780,1098,1547,776,1748,712,1003,1716,1432,1813,791,1188,470,1218,1404,1543,1536,1023,1702,1506,864,1427,978,1797,595,1221,1284,1881,1272,465,1839,1316,1180,556,1321,1448,1010,1734,976,903,1276,390,1745,632,1822,1523,1558,1861,510,1777,1294,1193,1212,1607,1614,1893,1309,1348,1774,1578,432,410,1593,735,999,620,867,1757,1816,1335,1561,1056,1288,532,1346,796,1410,767,1093,1352,1829,1268,1378,644,459,992,1500,1299,871,1331,1367,1737,1565,1848,560,1769,1204,454])). 32.06/9.10 % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 32.06/9.10 % [INFO] Killing All external provers ... 32.06/9.10 FINAL WATCH: 32.0 CPU 8.7 WC 32.06/9.10 EOF